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21 pages, 7150 KiB  
Article
Development of Lettuce Growth Monitoring Model Based on Three-Dimensional Reconstruction Technology
by Jun Ju, Minggui Zhang, Yingjun Zhang, Qi Chen, Yiting Gao, Yangyue Yu, Zhiqiang Wu, Youzhi Hu, Xiaojuan Liu, Jiali Song and Houcheng Liu
Agronomy 2025, 15(1), 29; https://doi.org/10.3390/agronomy15010029 - 26 Dec 2024
Viewed by 283
Abstract
Crop monitoring can promptly reflect the growth status of crops. However, conventional methods of growth monitoring, although simple and direct, have limitations such as destructive sampling, reliance on human experience, and slow detection speed. This study estimated the fresh weight of lettuce ( [...] Read more.
Crop monitoring can promptly reflect the growth status of crops. However, conventional methods of growth monitoring, although simple and direct, have limitations such as destructive sampling, reliance on human experience, and slow detection speed. This study estimated the fresh weight of lettuce (Lactuca sativa L.) in a plant factory with artificial light based on three-dimensional (3D) reconstruction technology. Data from different growth stages of lettuce were collected as the training dataset, while data from different plant forms of lettuce were used as the validation dataset. The partial least squares regression (PLSR) method was utilized for modeling, and K-fold cross-validation was performed to evaluate the model. The testing dataset of this model achieved a coefficient of determination (R2) of 0.9693, with root mean square error (RMSE) and mean absolute error (MAE) values of 3.3599 and 2.5232, respectively. Based on the performance of the validation set, an adaptation was made to develop a fresh weight estimation model for lettuce under far-red light conditions. To simplify the estimation model, reduce estimation costs, enhance estimation efficiency, and improve the lettuce growth monitoring method in plant factories, the plant height and canopy width data of lettuce were extracted to estimate the fresh weight of lettuce in addition. The testing dataset of the new model achieved an R2 value of 0.8970, with RMSE and MAE values of 3.1206 and 2.4576. Full article
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<p>The process of (<b>a</b>) image acquisition and (<b>b</b>) 3D reconstruction.</p>
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<p>The schematic diagram of the specific setup of the experiment. D21, 21 days after sowing; D28, 28 days after sowing; D35, 35 days after sowing.</p>
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<p>(<b>a</b>) Spectral composition of the light-emitting diode (LED) treatments measured at the top of the plant canopy and (<b>b</b>) the process of cultivation.</p>
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<p>The schematic diagram of the 2D metric-based biomass estimation model.</p>
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<p>The lettuce plants at 3 different growth stages: D21, 21 days after sowing; D28, 28 days after sowing; D35, 35 days after sowing.</p>
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<p>The (<b>a</b>) dry weight, (<b>b</b>) fresh weight, (<b>c</b>) leaf area, and (<b>d</b>) number of leaves of lettuce at different growth stages. D21, 21 days after sowing; D28, 28 days after sowing; D35, 35 days after sowing. Different letters indicate significant differences among growth stages according to Duncan’s multiple-range test (<span class="html-italic">p</span> ≤ 0.05).</p>
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<p>(<b>a</b>) The linear relationship between overhead projected area and fresh weight of lettuce. (<b>b</b>) The linear relationship between actual volume and fresh weight of lettuce.</p>
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<p>(<b>a</b>) The linear relationship between 3D reconstruction volume and actual volume of lettuce. (<b>b</b>) The linear relationship between 3D reconstruction volume and fresh weight of lettuce.</p>
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<p>Performance of the model on (<b>a</b>) the training set, (<b>b</b>) test set, (<b>c</b>) D21 datasets, (<b>d</b>) D28 datasets, and (<b>e</b>) D35 datasets. D21, 21 days after sowing; D28, 28 days after sowing; D35, 35 days after sowing.</p>
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<p>The 360° viewing angle of lettuce under different light treatments. W, entire growth stage used white light; A, entire growth stage used basal light with supplemental red and far-red light; FRR, the first 10 days of white light with far-red light and another 10 days with red light; RFR, the first 10 days of white light with red light and another 10 days with far-red light.</p>
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<p>Performance of the model on (<b>a</b>) validation set, (<b>b</b>) treatment W datasets, (<b>c</b>) treatment A datasets, (<b>d</b>) treatment FRR datasets, and (<b>e</b>) treatment RFR datasets. W, entire growth stage used white light; A, entire growth stage used basal light with supplemental red and far-red light; FRR, the first 10 days of white light with far-red light and another 10 days with red light; RFR, the first 10 days of white light with red light and another 10 days with far-red light.</p>
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<p>Performance of Model 1 on (<b>a</b>) the training set and (<b>b</b>) the test set.</p>
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<p>Performance of Model 2 on (<b>a</b>) the training set and (<b>b</b>) the test set.</p>
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<p>Performance of the model based on 2D metrics on (<b>a</b>) the training set and (<b>b</b>) the test set.</p>
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24 pages, 14227 KiB  
Article
Polynomial Regression-Based Predictive Expert System for Enhancing Hydraulic Press Performance over a 5G Network
by Denis Jankovič, Miha Pipan, Marko Šimic and Niko Herakovič
Appl. Sci. 2024, 14(24), 12016; https://doi.org/10.3390/app142412016 - 22 Dec 2024
Viewed by 632
Abstract
In industrial applications, hydraulic presses maintain workloads by controlling the hydraulic cylinder to extend and retract, ensuring optimum tracking performance in terms of position and force. Dealing with nonlinear and multinode systems, such as hydraulic systems, often requires an advanced approach that frequently [...] Read more.
In industrial applications, hydraulic presses maintain workloads by controlling the hydraulic cylinder to extend and retract, ensuring optimum tracking performance in terms of position and force. Dealing with nonlinear and multinode systems, such as hydraulic systems, often requires an advanced approach that frequently includes machine learning and artificial intelligence methods. Introducing an adaptive control system to significantly improve the response of hydraulic presses is a challenge. Therefore, a polynomial regression model predictive control (PR-MPC) mechanism is proposed in this paper to compensate for external disturbances such as the forming processes and friction dynamics. Using polynomial regression modeling and least squares optimization, the approach produces highly accurate data-driven models with an R2 value of 0.948 to 0.999. The simplicity of polynomial regression facilitates the integration of smart algorithms into an expert system with additional decision-making rules. Remote adaptive control integrated within a 5G network is based on I 4.0 distributed system guidelines that provide insights into the behavior of the hydraulic press. The results of real-time experiments have shown that the PR-MPC mechanism integrated into the expert system reduces the absolute response error of the hydraulic press by up to 98.7% compared to the initial control system with a PID regulation. Full article
(This article belongs to the Special Issue Research Progress on Hydraulic Fluid and Hydraulic Systems)
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<p>Research methodology flowchart.</p>
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<p>Investigation of a hydraulic press under external disturbances.</p>
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<p>Energy conversion in a hydraulic cylinder.</p>
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<p>Hydraulic press working area.</p>
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<p>Diagram of the observational and validation area.</p>
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<p>Smart hydraulic press with a real-time PR-MPC mechanism within an expert system.</p>
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<p>Polynomial regression model predictive control mechanism.</p>
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<p>Prediction surface plots for the bending phase: (<b>a</b>) initial friction conditions; (<b>b</b>) changed friction conditions.</p>
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<p>Prediction surface plots of the leveling phase: (<b>a</b>) experimental result, initial friction conditions; (<b>b</b>) experimental result, changed friction conditions.</p>
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<p>Prediction surface of the movement phase: experimental result, initial and changed friction conditions.</p>
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<p>Improvement of adaptive control mechanisms in the observation area.</p>
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<p>Improvement of adaptive control mechanisms in the existing observation area.</p>
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23 pages, 7833 KiB  
Article
Research on the Inversion of Key Growth Parameters of Rice Based on Multisource Remote Sensing Data and Deep Learning
by Jian Li, Jian Lu, Hongkun Fu, Wenlong Zou, Weijian Zhang, Weilin Yu and Yuxuan Feng
Agriculture 2024, 14(12), 2326; https://doi.org/10.3390/agriculture14122326 - 19 Dec 2024
Viewed by 346
Abstract
This study accurately inverts key growth parameters of rice, including Leaf Area Index (LAI), chlorophyll content (SPAD) value, and height, by integrating multisource remote sensing data (including MODIS and ERA5 imagery) and deep learning models. Dehui City in Jilin Province, China, was selected [...] Read more.
This study accurately inverts key growth parameters of rice, including Leaf Area Index (LAI), chlorophyll content (SPAD) value, and height, by integrating multisource remote sensing data (including MODIS and ERA5 imagery) and deep learning models. Dehui City in Jilin Province, China, was selected as the case study area, where multidimensional data including vegetation indices, ecological function parameters, and environmental variables were collected, covering seven key growth stages of rice. Data analysis and parameter prediction were conducted using a variety of machine learning and deep learning models including Partial Least Squares (PLSs), Support Vector Machine (SVM), Random Forest (RF), and Long Short-Term Memory Networks (LSTM), among which the LSTM model demonstrated superior performance, particularly at multiple critical time points. The results show that the LSTM performed best in inverting the three parameters, with the LAI inversion accuracy on 21 August reaching a coefficient of determination (R2) of 0.72, root mean square error (RMSE) of 0.34, and mean absolute error (MAE) of 0.27. The SPAD inversion accuracy on the same date achieved an R2 of 0.69, RMSE of 1.45, and MAE of 1.16. The height inversion accuracy on 25 July reached an R2 of 0.74, RMSE of 2.30, and MAE of 2.08. This study not only verifies the effectiveness of combining multisource data and advanced algorithms but also provides a scientific basis for the precision management and decision-making of rice cultivation. Full article
(This article belongs to the Section Digital Agriculture)
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<p>Map of the study area of Dehui City, Jilin Province, showing rice distribution and sampling points.</p>
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<p>Integrated framework for inverting key growth parameters of rice using multisource data and machine learning/deep learning models.</p>
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<p>Correlation between selected key variables and field-measured LAI on 6 July. Note: one asterisk (*), double asterisk (**), and threefold asterisks (***) indicate a correlation coefficient (r) with statistically significance levels of <span class="html-italic">p</span>-value &lt; 0.05, 0.01, and 0.001, respectively.</p>
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<p>Standardized SHAP values for features influencing LAI, SPAD, and height predictions across different dates.</p>
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<p>Comparison of R<sup>2</sup>, RMSE, and MAE for LAI, SPAD, and height predictions using different variable combinations across three growth stages. (<b>a</b>–<b>c</b>) represent the R<sup>2</sup> values for different variable combinations on 6 July, 25 July, and 21 August, respectively. (<b>d</b>–<b>f</b>) represent the RMSE for different variable combinations on 6 July, 25 July, and 21 August, respectively. (<b>g</b>–<b>i</b>) represent the MAE for different variable combinations on 6 July, 25 July, and 21 August, respectively.</p>
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<p>Spatial inversion maps of LAI, SPAD, and height across three key growth stages (6 July, 25 July, and 21 August). (<b>a</b>–<b>c</b>) are the spatial inversion maps of LAI at the three key growth stages. (<b>d</b>–<b>f</b>) are the spatial inversion maps of SPAD at the three key growth stages. (<b>g</b>–<b>i</b>) are the spatial inversion maps of height at the three key growth stages.</p>
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<p>Accuracy evaluation of predicted and measured LAI, SPAD, and height using the LSTM model at three key growth stages. (<b>a</b>–<b>c</b>) are accuracy evaluation of LAI for three periods. (<b>d</b>–<b>f</b>) are accuracy evaluation of SPAD for three periods. (<b>g</b>–<b>i</b>) are accuracy evaluation of Height for three periods.</p>
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20 pages, 6263 KiB  
Article
Aging-Related Gene-Based Prognostic Model for Lung Adenocarcinoma: Insights into Tumor Microenvironment and Therapeutic Implications
by Jin Wang, Hailong Zhang, Yaohui Feng, Xian Gong, Xiangrong Song, Meidan Wei, Yaoyu Hu and Jianxiang Li
Int. J. Mol. Sci. 2024, 25(24), 13572; https://doi.org/10.3390/ijms252413572 - 18 Dec 2024
Viewed by 617
Abstract
Lung cancer remains the leading cause of cancer-related mortality globally, with a poor prognosis primarily due to late diagnosis and limited treatment options. This research highlights the critical demand for advanced prognostic tools by creating a model centered on aging-related genes (ARGs) to [...] Read more.
Lung cancer remains the leading cause of cancer-related mortality globally, with a poor prognosis primarily due to late diagnosis and limited treatment options. This research highlights the critical demand for advanced prognostic tools by creating a model centered on aging-related genes (ARGs) to improve prediction and treatment strategies for lung adenocarcinoma (LUAD). By leveraging datasets from The Cancer Genome Atlas (TCGA) and Gene Expression Omnibus (GEO), we developed a prognostic model that integrates 14 ARGs using the least absolute shrinkage and selection operator (LASSO) alongside Cox regression analyses. The model exhibited strong predictive performance, achieving area under the curve (AUC) values greater than 0.8 for one-year survival in both internal and external validation cohorts. The risk scores generated by our model were significantly correlated with critical features of the tumor microenvironment, including the presence of cancer-associated fibroblasts (CAFs) and markers of immune evasion, such as T-cell dysfunction and exclusion. Higher risk scores correlated with a more tumor-promoting microenvironment and increased immune suppression, highlighting the model’s relevance in understanding LUAD progression. Additionally, XRCC6, a protein involved in DNA repair and cellular senescence, was found to be upregulated in LUAD. Functional assays demonstrated that the knockdown of XRCC6 led to decreased cell proliferation, whereas its overexpression alleviated DNA damage, highlighting its significance in tumor biology and its potential therapeutic applications. This study provides a novel ARG-based prognostic model for LUAD, offering valuable insights into tumor dynamics and the tumor microenvironment, which may guide the development of targeted therapies and improve patient outcomes. Full article
(This article belongs to the Section Molecular Genetics and Genomics)
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<p>Construction and performance of the ARGs prognostic model. (<b>A</b>) Identification of prognostic ARGs via univariate COX analysis; (<b>B</b>) Development of the prognostic model through multivariate COX analysis; (<b>C</b>) Analysis of risk score distributions and survival outcomes across high-risk and low-risk groups in the training cohort; (<b>D</b>) Heatmap illustrating the expression levels of ARGs in high-risk and low-risk groups within the training cohort; (<b>E</b>) TimeROC curves displaying ROC curves and AUC values for 1–5 years in the training cohort; (<b>F</b>) Survival curves for high- and low-risk groups in the training cohort.</p>
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<p>Validation of the model’s robustness in TCGA_LUAD and GSE31210 datasets. (<b>A</b>) Distribution of risk scores and survival outcomes in high- and low-risk groups within the TCGA_LUAD dataset; (<b>B</b>) Heatmap showing the expression of ARGs in high- and low-risk groups within the TCGA_LUAD dataset; (<b>C</b>) TimeROC curves displaying ROC curves and AUC values for 1–5 years in the TCGA_LUAD dataset; (<b>D</b>) Survival curves for high- and low-risk groups in the TCGA_LUAD dataset; (<b>E</b>) Distribution of risk scores and survival outcomes in high- and low-risk groups within the GSE31210 dataset; (<b>F</b>) Heatmap showing the expression of ARGs in high- and low-risk groups within the GSE31210 dataset; (<b>G</b>) TimeROC curves displaying ROC curves and AUC values for 1–5 years in the GSE31210 dataset; (<b>H</b>) Survival curves for high- and low-risk groups in the GSE31210 dataset.</p>
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<p>Identification of risk score as an independent prognostic indicator for overall survival in lung adenocarcinoma. (<b>A</b>) Outcomes of multivariate COX analysis that integrated significant factors identified in the univariate COX analysis from the TCGA_LUAD dataset; (<b>B</b>,<b>C</b>) Survival curves for high-risk and low-risk groups classified by N stage within the TCGA_LUAD dataset; (<b>D</b>,<b>E</b>) Survival curves for high-risk and low-risk groups categorized by T stage in the TCGA_LUAD dataset; (<b>F</b>) Findings from multivariate COX analysis that included significant factors from the univariate COX analysis in the GSE31210 dataset; (<b>G</b>,<b>H</b>) Survival curves for high- and low-risk groups stratified by Stage in the GSE31210 dataset. VIF, variance inflation factor.</p>
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<p>Construction and validation of the clinical predictive nomogram based on the TCGA_LUAD dataset. (<b>A</b>) A clinical predictive nomogram that integrates independent prognostic factors identified via multivariate COX regression analysis, where the total points displayed on the lower scale indicate the probabilities of overall survival at 1, 3, and 5 years; (<b>B</b>) Calibration plots illustrating the 1-, 3-, and 5-year overall survival predictions derived from the nomogram, using the GSE31210 dataset; (<b>C</b>) Kaplan–Meier curves for overall survival based on nomogram scores in the GSE31210 dataset; (<b>D</b>) Decision curve analysis (DCA) curves for the nomogram and risk score, predicting overall survival at 1, 3, and 5 years in the GSE31210 dataset. ARGs refer to aging-related genes; OS denotes overall survival; DCA stands for decision curve analysis.</p>
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<p>Risk Score Correlates with Immune Cell Infiltration. (<b>A</b>) A heatmap illustrating the correlation between the risk score and immune cell infiltration scores derived from XCELL in the TCGA_LUAD and GSE31210 datasets; Scatter plots depicting correlations between the risk score and the microenvironment score (<b>B</b>), stromal score (<b>C</b>), mast cell infiltration (<b>D</b>), and cancer-associated fibroblasts (CAF) (<b>E</b>) in the TCGA_LUAD dataset; (<b>F</b>) A heatmap displaying the correlation between the risk score and infiltration scores calculated by TIMER in the TCGA_LUAD and GSE31210 datasets; Scatter plots illustrating correlations between the risk score and the MDSC infiltration score (<b>G</b>), T-cell exclusion (<b>H</b>), and T-cell dysfunction (<b>I</b>) in the TCGA_LUAD dataset. TCGA, LUAD, CAF, TAM, MDSC.</p>
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<p>Risk Score Correlates with Antitumor Drug Sensitivity and Cellular Senescence. Volcano plots illustrating the results of the correlation analysis between the risk score and antitumor drug sensitivity in the TCGA-LUAD (<b>A</b>) and GSE31210 (<b>B</b>) datasets; (<b>C</b>) Heatmap displaying the intersection of drugs with |r| &gt; 0.3 from both correlation results; Scatter plots depicting the relationship between the risk score and sensitivity to doramapimod in the TCGA-LUAD (<b>D</b>) and GSE31210 (<b>E</b>) datasets; (<b>F</b>) A heatmap illustrating the intersection of correlation results between the risk score and genes related to the MAPK pathway in the TCGA-LUAD and GSE31210 datasets; Volcano plots demonstrating the results of the correlation analysis between the risk score and the expression of senescence-related genes from the CellAge database in the TCGA-LUAD (<b>G</b>) and GSE31210 (<b>H</b>) datasets; (<b>I</b>) Heatmap displaying the intersection of genes with |r| &gt; 0.3 from both correlation results; Volcano plots showing correlation analysis results between the risk score and the expression of genes in the KEGG Senescence pathway in the TCGA-LUAD (<b>J</b>) and GSE31210 (<b>K</b>) datasets; (<b>L</b>) Heatmap displaying the intersection of genes with |r| &gt; 0.3 from both correlation results.</p>
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<p>Risk score correlates with tumor progression. Volcano plots show the correlation analysis results of risk scores with oncogene expression in TCGA-LUAD (<b>A</b>) and GSE31210 (<b>B</b>) datasets. (<b>C</b>) Heatmap displaying the intersection of drugs with |r| &gt; 0.3 from both correlation results; heatmap showing GSEA enrichment results of biological processes (<b>D</b>) and signaling pathways (<b>E</b>) in both datasets; (<b>F</b>–<b>G</b>) GSEA plots illustrating risk score associations with DNA replication, recombination repair, cellular respiration, and leukocyte mediated immunity. Bubble plots illustrate the results of enrichment analysis for biological processes (<b>H</b>) and KEGG (<b>I</b>) pathways associated with differentially expressed genes between high-risk and low-risk groups in the TCGA-LUAD dataset.</p>
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<p>XRCC6 is highly expressed in LUAD and is related to cancer progression. (<b>A</b>) A heatmap illustrating the correlation analysis results of risk scores with ARGs in the TCGA-LUAD and GSE31210 datasets; (<b>B</b>) Volcano plot displaying correlation of <span class="html-italic">XRCC6</span> with cell ARGs from the CellAge database; (<b>C</b>) Heatmap displaying expression differences in <span class="html-italic">XRCC6</span> in tumor versus normal tissues across six LUAD datasets; (<b>D</b>) Lollipop plot showing the correlation between <span class="html-italic">XRCC6</span> expression and immune cell infiltration scores in the TCGA-LUAD dataset based on the XCELL algorithm; scatter plots showing correlation of <span class="html-italic">XRCC6</span> expression with immune score (<b>E</b>) and microenvironment score (<b>F</b>); (<b>G</b>) Lollipop plot showing correlation of XRCC6 expression with anti-cancer drug sensitivity scores in TCGA-LUAD dataset; (<b>H</b>) A scatter plot illustrating the correlation between <span class="html-italic">XRCC6</span> expression and tumor stemness scores as determined by the RNAss algorithm; (<b>I</b>,<b>J</b>) GSEA plots illustrating <span class="html-italic">XRCC6</span> associations with multiple key biological functions and signaling pathways. TCGA, LUAD.</p>
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<p>XRCC6 regulates proliferation and senescence in lung cancer cells. CCK-8 assay analyzing changes in proliferation of lung cancer cells A549 (<b>A</b>) and H1299 (<b>B</b>) following <span class="html-italic">XRCC6</span> knockdown; representative images (<b>C</b>) and quantitative data (<b>D</b>) of EdU assay analyzing cell proliferation; changes in <span class="html-italic">CDKN1A</span> (<b>E</b>) and <span class="html-italic">CDKN2A</span> (<b>F</b>) mRNA expression following H2O2-induced senescence and <span class="html-italic">XRCC6</span> overexpression; representative images (<b>G</b>) and quantification (<b>H</b>) of β-galactosidase staining; and representative images (<b>I</b>) and quantification (<b>J</b>) of γ-H2AX immunofluorescence. The different letters (a, b, c and d) represent statistically significant group differences (<span class="html-italic">p</span> &lt; 0.05).</p>
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23 pages, 2520 KiB  
Article
Evaluating Predictive Accuracy of Regression Models with First-Order Autoregressive Disturbances: A Comparative Approach Using Artificial Neural Networks and Classical Estimators
by Rauf I. Rauf, Masad A. Alrasheedi, Rasheedah Sadiq and Abdulrahman M. A. Aldawsari
Mathematics 2024, 12(24), 3966; https://doi.org/10.3390/math12243966 - 17 Dec 2024
Viewed by 720
Abstract
In the last decade, the size and complexity of datasets have expanded significantly, necessitating more sophisticated predictive methods. Despite this growth, limited research has been conducted on the effects of autocorrelation within widely used regression methods. This study addresses this gap by investigating [...] Read more.
In the last decade, the size and complexity of datasets have expanded significantly, necessitating more sophisticated predictive methods. Despite this growth, limited research has been conducted on the effects of autocorrelation within widely used regression methods. This study addresses this gap by investigating how autocorrelation impacts the predictive accuracy and efficiency of six regression approaches: Artificial Neural Network (ANN), Ordinary Least Squares (OLS), Cochrane–Orcutt (CO), Prais–Winsten (PW), Maximum Likelihood Estimation (MLE), and Restricted Maximum Likelihood Estimation (RMLE). The study evaluates each method’s performance on three datasets characterized by autocorrelation, comparing their predictive accuracy and variability. The analysis is structured into three phases: the first phase examines predictive accuracy across methods using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE); the second phase evaluates the efficiency of parameter estimation based on standard errors across methods; and the final phase visually assesses the closeness of predicted values to actual values through scatter plots. The results indicate that the ANN consistently provides the most accurate predictions, particularly in large sample sizes with extensive training data. For GDP data, the ANN achieved an MSE of 1.05 × 109, an MAE of 23,344.64, and an MAPE of 81.66%, demonstrating up to a 90% reduction in the MSE compared to OLS. These findings underscore the advantages of the ANN for predictive tasks involving autocorrelated data, highlighting its robustness and suitability for complex, large-scale datasets. This study provides practical guidance for selecting optimal prediction techniques in the presence of autocorrelation, recommending the ANN as the preferred method due to its superior performance. Full article
(This article belongs to the Section Probability and Statistics)
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<p>Graph of error (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) against (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>) showing autocorrelation.</p>
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<p>Actual and predicted number of people employed (100% testing).</p>
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<p>Graph of error (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) against (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>) showing autocorrelation.</p>
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<p>Actual and predicted MPG (average miles per gallon) (100% testing), where ML and REML denote maximum likelihood estimator and restricted maximum likelihood estimator.</p>
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<p>Graph of error (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) against (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>e</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>) showing autocorrelation.</p>
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<p>Actual and predicted GDP data (100% testing), where ML and REML denote maximum likelihood estimator and restricted maximum likelihood estimator.</p>
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26 pages, 5138 KiB  
Article
On Traub–Steffensen-Type Iteration Schemes With and Without Memory: Fractal Analysis Using Basins of Attraction
by Moin-ud-Din Junjua, Shahid Abdullah, Munish Kansal and Shabbir Ahmad
Fractal Fract. 2024, 8(12), 698; https://doi.org/10.3390/fractalfract8120698 - 26 Nov 2024
Viewed by 901
Abstract
This paper investigates the design and stability of Traub–Steffensen-type iteration schemes with and without memory for solving nonlinear equations. Steffensen’s method overcomes the drawback of the derivative evaluation of Newton’s scheme, but it has, in general, smaller sets of initial guesses that converge [...] Read more.
This paper investigates the design and stability of Traub–Steffensen-type iteration schemes with and without memory for solving nonlinear equations. Steffensen’s method overcomes the drawback of the derivative evaluation of Newton’s scheme, but it has, in general, smaller sets of initial guesses that converge to the desired root. Despite this drawback of Steffensen’s method, several researchers have developed higher-order iterative methods based on Steffensen’s scheme. Traub introduced a free parameter in Steffensen’s scheme to obtain the first parametric iteration method, which provides larger basins of attraction for specific values of the parameter. In this paper, we introduce a two-step derivative free fourth-order optimal iteration scheme based on Traub’s method by employing three free parameters and a weight function. We further extend it into a two-step eighth-order iteration scheme by means of memory with the help of suitable approximations of the involved parameters using Newton’s interpolation. The convergence analysis demonstrates that the proposed iteration scheme without memory has an order of convergence of 4, while its memory-based extension achieves an order of convergence of at least 7.993, attaining the efficiency index 7.9931/32. Two special cases of the proposed iteration scheme are also presented. Notably, the proposed methods compete with any optimal j-point method without memory. We affirm the superiority of the proposed iteration schemes in terms of efficiency index, absolute error, computational order of convergence, basins of attraction, and CPU time using comparisons with several existing iterative methods of similar kinds across diverse nonlinear equations. In general, for the comparison of iterative schemes, the basins of iteration are investigated on simple polynomials of the form zn1 in the complex plane. However, we investigate the stability and regions of convergence of the proposed iteration methods in comparison with some existing methods on a variety of nonlinear equations in terms of fractals of basins of attraction. The proposed iteration schemes generate the basins of attraction in less time with simple fractals and wider regions of convergence, confirming their stability and superiority in comparison with the existing methods. Full article
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Figure 1

Figure 1
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>z</mi> <mn>3</mn> </msup> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math> using Newton’s method (<a href="#FD1-fractalfract-08-00698" class="html-disp-formula">1</a>) and Steffensen’ method (<a href="#FD2-fractalfract-08-00698" class="html-disp-formula">2</a>).</p>
Full article ">Figure 2
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>z</mi> <mn>3</mn> </msup> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math> using Traub’s method (<a href="#FD3-fractalfract-08-00698" class="html-disp-formula">3</a>).</p>
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<p>Comparisons of various iterative methods with-memory in terms of absolute error <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>ω</mi> <mi>j</mi> </msub> <mrow> <mo>−</mo> <mi>α</mi> <mo>|</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in first three iterations.</p>
Full article ">Figure 3 Cont.
<p>Comparisons of various iterative methods with-memory in terms of absolute error <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>ω</mi> <mi>j</mi> </msub> <mrow> <mo>−</mo> <mi>α</mi> <mo>|</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in first three iterations.</p>
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<p>Comparisons of various iterative methods with-memory in terms of COC, EI, and CPU time for <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> respectively.</p>
Full article ">Figure 4 Cont.
<p>Comparisons of various iterative methods with-memory in terms of COC, EI, and CPU time for <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> respectively.</p>
Full article ">Figure 5
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">Figure 6
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">Figure 7
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">Figure 8
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">Figure 9
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">Figure 10
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">Figure 11
<p>Basins of attraction of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> using several iteration methods without memory.</p>
Full article ">
14 pages, 2934 KiB  
Article
Detecting Honey Adulteration: Advanced Approach Using UF-GC Coupled with Machine Learning
by Irene Punta-Sánchez, Tomasz Dymerski, José Luis P. Calle, Ana Ruiz-Rodríguez, Marta Ferreiro-González and Miguel Palma
Sensors 2024, 24(23), 7481; https://doi.org/10.3390/s24237481 - 23 Nov 2024
Viewed by 583
Abstract
This article introduces a novel approach to detecting honey adulteration by combining ultra-fast gas chromatography (UF-GC) with advanced machine learning techniques. Machine learning models, particularly support vector regression (SVR) and least absolute shrinkage and selection operator (LASSO), were applied to predict adulteration in [...] Read more.
This article introduces a novel approach to detecting honey adulteration by combining ultra-fast gas chromatography (UF-GC) with advanced machine learning techniques. Machine learning models, particularly support vector regression (SVR) and least absolute shrinkage and selection operator (LASSO), were applied to predict adulteration in orange blossom (OB) and sunflower (SF) honeys. The SVR model achieved R2 values above 0.90 for combined honey types. Treating OB and SF honeys separately resulted in a significant accuracy improvement, with R2 values exceeding 0.99. LASSO proved especially effective when honey types were treated individually. The integration of UF-GC with machine learning not only provides a reliable method for detecting honey adulteration, but also sets a precedent for future research in the application of this technique to other food products, potentially enhancing food authenticity across the industry. Full article
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Figure 1

Figure 1
<p>Circular dendrogram resulting from the hierarchical cluster analysis (HCA) of the dataset (D<sub>44<span class="html-italic">x</span>20002</sub>) with UF-GC; The names of the honey samples are colored according to their botanical origin: sunflower (purple) and orange blossom (orange). The four main clusters have been colored and labeled with letters A, B, C, and D. The average method with Euclidean distances was used.</p>
Full article ">Figure 2
<p>Score plot of PCA for orange blossom and sunflower honey.</p>
Full article ">
23 pages, 17855 KiB  
Article
Constitutive Modelling Analysis and Hot Deformation Process of AISI 8822H Steel
by Khaled Elanany, Wojciech Borek and Saad Ebied
Materials 2024, 17(23), 5713; https://doi.org/10.3390/ma17235713 - 22 Nov 2024
Viewed by 569
Abstract
This study used the Gleeble 3800 thermomechanical simulator to examine the hot deformation characteristics of AISI 8822H steel. The main goal was to understand the alloy’s behaviour under various thermomechanical settings, emphasising temperature ranges between 1173 K and 1323 K and strain rates [...] Read more.
This study used the Gleeble 3800 thermomechanical simulator to examine the hot deformation characteristics of AISI 8822H steel. The main goal was to understand the alloy’s behaviour under various thermomechanical settings, emphasising temperature ranges between 1173 K and 1323 K and strain rates from 0.01 s−1 to 10 s−1. This study aimed to enhance the alloy’s manufacturing process by offering a thorough understanding of the material’s response to these conditions. Four various constitutive models—Arrhenius-type, Johnson–Cook, modified Johnson–Cook, and Trimble—were used in a comprehensive technique to forecast flow stress values in order to meet the study’s goals. The accuracy of each model in forecasting the behaviour of the material under the given circumstances was assessed. A thorough comparison investigation revealed that the Trimble model was the most accurate model allowing prediction of material behaviour, with the maximum correlation factor (R = 0.99) and at least average absolute relative error (1.7%). On the other hand, the Johnson–Cook model had the least correlation factor (R = 0.92) and the maximum average absolute relative error (32.2%), indicating that it was the least accurate because it could not account for all softening effects. Full article
(This article belongs to the Special Issue Progress in Plastic Deformation of Metals and Alloys (Second Volume))
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Figure 1

Figure 1
<p>Schematic illustration representing the hot deformation process of AISI 8822H steel using the Gleeble simulator.</p>
Full article ">Figure 2
<p>True strain–stress curves of AISI 8822H steel at strain rates (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, (<b>d</b>) 10 s<sup>−1</sup>.</p>
Full article ">Figure 3
<p>Plots of (<b>a</b>) <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mi>σ</mi> </mrow> </mfenced> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>σ</mi> </mrow> </mfenced> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mi>l</mi> <mi>n</mi> <mfenced open="[" close="]" separators="|"> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>h</mi> <mfenced separators="|"> <mrow> <mi>α</mi> <mi>σ</mi> </mrow> </mfenced> </mrow> </mfenced> <mo>)</mo> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>l</mi> <mi>n</mi> <mo>[</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>h</mi> <mo>(</mo> <mi>α</mi> <mi>σ</mi> <mo>)</mo> <mo>]</mo> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mn>10000</mn> <mo>/</mo> <mi>T</mi> </mrow> </mfenced> </mrow> </semantics></math> to evaluate <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math>, n, and s, respectively, at 0.4 <math display="inline"><semantics> <mrow> <mi>ε</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Plots of <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>l</mi> <mi>n</mi> <mi>Z</mi> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mo>[</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>h</mi> <mo>(</mo> <mi>α</mi> <mi>σ</mi> <mo>)</mo> <mo>]</mo> </mrow> </mfenced> </mrow> </semantics></math> to evaluate lnA at 0.4 <math display="inline"><semantics> <mrow> <mi>ε</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Polynomial fitting of (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mi>ε</mi> </mrow> </semantics></math>, (<b>b</b>)<math display="inline"><semantics> <mrow> <mi>n</mi> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>ε</mi> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Q</mi> </mrow> <mrow> <mi>d</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>ε</mi> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <mi>A</mi> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mi>ε</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Comparison of the Arrhenius-type model’s anticipated and experimental stress data.</p>
Full article ">Figure 7
<p>Comparison of the Arrhenius-type model’s true strain–true stress anticipated and experimental flow stress data at temperature range (1173–1323 K) at (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, and (<b>d</b>) 10 s<sup>−1</sup>, respectively.</p>
Full article ">Figure 8
<p>Plots of <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mi>σ</mi> <mo>−</mo> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>)</mo> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mi>ε</mi> </mrow> </semantics></math> to evaluate <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>n</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>Plots of (<b>a</b>) <math display="inline"><semantics> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>σ</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <msup> <mrow> <mi>ε</mi> </mrow> <mrow> <msub> <mrow> <mi>n</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </msup> </mrow> </mfenced> </mrow> </mfrac> </mstyle> <mo>−</mo> <mn>1</mn> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <msup> <mrow> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> <mrow> <mo>*</mo> </mrow> </msup> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <mfenced separators="|"> <mrow> <mn>1</mn> <mo>−</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>σ</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <msup> <mrow> <mi>ε</mi> </mrow> <mrow> <msub> <mrow> <mi>n</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </msup> </mrow> </mfenced> </mrow> </mfrac> </mstyle> </mrow> </mfenced> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <msup> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>*</mo> </mrow> </msup> </mrow> </semantics></math> at strain range (0.2–0.6) to evaluate <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, respectively.</p>
Full article ">Figure 10
<p>Comparison of the Johnson–Cook model’s anticipated and experimental stress data.</p>
Full article ">Figure 11
<p>Comparison of the Johnson–Cook model’s true strain–true stress anticipated and experimental flow stress data at temperature range (1173–1323 K) at (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, and (<b>d</b>) 10 s<sup>−1</sup>, respectively.</p>
Full article ">Figure 12
<p>Plots of <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mi>σ</mi> <mo>−</mo> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>)</mo> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mi>ε</mi> </mrow> </semantics></math> to evaluate <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>n</mi> </mrow> <mrow> <mi>j</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msubsup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <msub> <mrow> <mi>Q</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>Plots of (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <mfenced separators="|"> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>σ</mi> </mrow> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>Q</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <msup> <mrow> <mi>ε</mi> </mrow> <mrow> <msubsup> <mrow> <mi>n</mi> </mrow> <mrow> <mi>j</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msubsup> </mrow> </msup> </mrow> </mfrac> </mstyle> </mrow> </mfenced> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <msup> <mrow> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> <mrow> <mo>*</mo> </mrow> </msup> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <mfenced separators="|"> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>σ</mi> </mrow> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>Q</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <msup> <mrow> <mi>ε</mi> </mrow> <mrow> <msubsup> <mrow> <mi>n</mi> </mrow> <mrow> <mi>j</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msubsup> </mrow> </msup> </mrow> </mfrac> </mstyle> </mrow> </mfenced> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <msup> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>*</mo> <mo>′</mo> </mrow> </msup> </mrow> </semantics></math> at strain range (0.2–0.6) to evaluate <math display="inline"><semantics> <mrow> <mi>r</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, respectively.</p>
Full article ">Figure 14
<p>Comparison of the modified Johnson–Cook model’s anticipated and experimental stress data.</p>
Full article ">Figure 15
<p>Comparison of the modified Johnson–Cook model’s true strain–true stress anticipated and experimental flow stress data at temperature range (1173–1323 K) at (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, and (<b>d</b>) 10 s<sup>−1</sup>, respectively.</p>
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<p>Plots of <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>l</mi> <mi>n</mi> <mi>σ</mi> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <msup> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> <mrow> <mo>*</mo> </mrow> </msup> <mo>)</mo> </mrow> </semantics></math> at strain range (0.2–0.6) at (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, and (<b>d</b>) 10 s<sup>−1</sup> to evaluate <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>I</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, respectively.</p>
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<p>Plots of (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>ε</mi> <mo>)</mo> </mrow> </semantics></math> to evaluate <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mrow> <mi>I</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mi>ε</mi> <mo>)</mo> </mrow> </semantics></math> to evaluate <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>n</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> at strain rate range (0.01–10 s<sup>−1</sup>).</p>
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<p>Polynomial fitting of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>n</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo> </mo> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">s</mi> <mo>.</mo> <mo> </mo> <mi>l</mi> <mi>n</mi> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math>.</p>
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<p>Comparison of the Trimble model’s anticipated and experimental stress data.</p>
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<p>Comparison of the Trimble model’s true strain–true stress anticipated and experimental stress data at temperature range (1173–1323 K) at (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, and (<b>d</b>) 10 s<sup>−1</sup>, respectively.</p>
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<p>Comparison of the experimental and anticipated stress data for the original and modified Johnson–Cook models.</p>
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<p>Comparison of the experimental and anticipated stress data for the four models.</p>
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<p>Comparison between true strain–true stress experimental curves and predicted flow stress values for the Arrhenius-type, Johnson–Cook, modified Johnson–Cook, and Trimble models at 1 s<sup>−1</sup> at (<b>a</b>) 1173 K, (<b>b</b>) 1223 K, (<b>c</b>) 1273 K, and (<b>d</b>) 1323 K, respectively.</p>
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<p>Comparison between true strain–true stress experimental curves and modelled flow stress values for the Arrhenius-type, Johnson–Cook, modified Johnson–Cook, and Trimble models at 1173 K at (<b>a</b>) 0.01 s<sup>−1</sup>, (<b>b</b>) 0.1 s<sup>−1</sup>, (<b>c</b>) 1 s<sup>−1</sup>, and (<b>d</b>) 10 s<sup>−1</sup>, respectively.</p>
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22 pages, 5386 KiB  
Article
A Novel Multi-Sensor Nonlinear Tightly-Coupled Framework for Composite Robot Localization and Mapping
by Lu Chen, Amir Hussain, Yu Liu, Jie Tan, Yang Li, Yuhao Yang, Haoyuan Ma, Shenbing Fu and Gun Li
Sensors 2024, 24(22), 7381; https://doi.org/10.3390/s24227381 - 19 Nov 2024
Viewed by 660
Abstract
Composite robots often encounter difficulties due to changes in illumination, external disturbances, reflective surface effects, and cumulative errors. These challenges significantly hinder their capabilities in environmental perception and the accuracy and reliability of pose estimation. We propose a nonlinear optimization approach to overcome [...] Read more.
Composite robots often encounter difficulties due to changes in illumination, external disturbances, reflective surface effects, and cumulative errors. These challenges significantly hinder their capabilities in environmental perception and the accuracy and reliability of pose estimation. We propose a nonlinear optimization approach to overcome these issues to develop an integrated localization and navigation framework, IIVL-LM (IMU, Infrared, Vision, and LiDAR Fusion for Localization and Mapping). This framework achieves tightly coupled integration at the data level using inputs from an IMU (Inertial Measurement Unit), an infrared camera, an RGB (Red, Green and Blue) camera, and LiDAR. We propose a real-time luminance calculation model and verify its conversion accuracy. Additionally, we designed a fast approximation method for the nonlinear weighted fusion of features from infrared and RGB frames based on luminance values. Finally, we optimize the VIO (Visual-Inertial Odometry) module in the R3LIVE++ (Robust, Real-time, Radiance Reconstruction with LiDAR-Inertial-Visual state Estimation) framework based on the infrared camera’s capability to acquire depth information. In a controlled study, using a simulated indoor rescue scenario dataset, the IIVL-LM system demonstrated significant performance enhancements in challenging luminance conditions, particularly in low-light environments. Specifically, the average RMSE ATE (Root Mean Square Error of absolute trajectory Error) improved by 23% to 39%, with reductions from 0.006 to 0.013. At the same time, we conducted comparative experiments using the publicly available TUM-VI (Technical University of Munich Visual-Inertial Dataset) without the infrared image input. It was found that no leading results were achieved, which verifies the importance of infrared image fusion. By maintaining the active engagement of at least three sensors at all times, the IIVL-LM system significantly boosts its robustness in both unknown and expansive environments while ensuring high precision. This enhancement is particularly critical for applications in complex environments, such as indoor rescue operations. Full article
(This article belongs to the Special Issue New Trends in Optical Imaging and Sensing Technologies)
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<p>IIVL-LM system framework applied to the composite robot.</p>
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<p>Schematic diagram of each module of the IIVL-LM system.</p>
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<p>Feature extraction performance of RGB and infrared images under extreme illuminance value. (<b>a</b>) Feature extraction performance of RGB images at a normalized illuminance value of 0.148. (<b>b</b>) Feature extraction performance of infrared images at a normalized illuminance value of 0.853.</p>
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<p>Weight-based nonlinear interpolation frame method.</p>
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<p>VIO (Optimized Visual-Inertial Odometry).</p>
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<p>Schematic diagram of IIVL-LM system and sensors deployed on composite robots. (<b>a</b>) Multi-sensor. (<b>b</b>) Composite robots.</p>
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<p>Comparison of X/Y axis data and actual trajectory of review robots under the IIVL-LM system. (<b>a</b>) Comparison of <span class="html-italic">X</span>-axis data. (<b>b</b>) Comparison of <span class="html-italic">Y</span>-axis data. (<b>c</b>) Actual testing and running trajectory of composite robots.</p>
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<p>The feature extraction results in the VIO module using RGB, infrared, and depth images under different lighting conditions in a small-scale indoor simulated environment. (<b>a</b>) The extraction of environmental features from RGB frames during the day. (<b>b</b>) Feature extraction of environmental characteristics from infrared frames during the day. (<b>c</b>) Feature extraction of environmental characteristics from infrared frames during the night. (<b>d</b>) Feature coordinates with depth values in the depth image.</p>
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<p>Real-time reconstruction process and radiance map of the small-scale indoor environment. (<b>a</b>) Real-time reconstruction process of the map. (<b>b</b>) Reconstructed radiance map of the small-scale indoor environment.</p>
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<p>Test conclusion and comparison under different illuminances. (<b>a</b>) RMSE ATE of all methods under different illuminance values. (<b>b</b>) Comparison between various methods and overall average.</p>
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<p>Test conclusion and comparison under multiple sequences in the TUM-VI dataset. (<b>a</b>) RMSE ATE of all methods under multiple sequences in the TUM-VI dataset. (<b>b</b>) Comparison between various methods and overall average.</p>
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<p>The test scenario on ORB-SLAM3.</p>
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15 pages, 1283 KiB  
Article
Diameter Increment Estimations of Open-Grown Stone Pine (Pinus pinea L.) Trees in Urban Parks in Istanbul, Türkiye
by Hacı Abdullah Uçan, Emrah Özdemir, Serhun Sağlam, Gafura Aylak Özdemir and Ender Makineci
Sustainability 2024, 16(22), 9793; https://doi.org/10.3390/su16229793 - 10 Nov 2024
Viewed by 737
Abstract
Open-grown trees in cities can improve environmental conditions by providing sustainable ecosystem services. Reliable data are necessary for assessing the functions of urban trees. The diameter at breast height (DBH), diameter increment, and annual ring measurements are the main parameters in the development [...] Read more.
Open-grown trees in cities can improve environmental conditions by providing sustainable ecosystem services. Reliable data are necessary for assessing the functions of urban trees. The diameter at breast height (DBH), diameter increment, and annual ring measurements are the main parameters in the development of reliable models. To model periodic mean diameter increments calculated for different time periods (5, 10, 15, 20, and 25 years), a total of 43 open-grown stone pines (Pinus pinea L.) of different diameter classes were sampled in several urban parks in Istanbul, Türkiye. The DBH was measured, and increment cores were extracted from each tree at 1.30 m stem height using an increment borer. Tree age at breast height was determined by counting annual rings, and periodic mean diameter increments were calculated for different periods based on the measured tree-ring widths. The periodic mean increments of different periods were related to the inside-bark diameter at breast height and tree age. Since there was no significant relationship between tree age and periodic mean increments for each period’s length, as shown in the correlation analysis, models used to estimate the periodic mean increments of inside-bark DBH were developed using the least squares regression and quantile regression (QR) techniques. As the period length increased, the estimation success of the diameter increment models increased while the mean absolute percentage error (MAE) values decreased from 40 to 32%. The best model was the one used for the last 25-year period with the quantile value q = 0.50 which estimated the diameter increment with an RMSE = 1.391 mm/year and MAE = 32.27%. Full article
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<p>The relationship between diameter increments and tree age.</p>
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<p>Comparison of the observed values with the values obtained from the best selected models for each period.</p>
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28 pages, 4502 KiB  
Article
Improved Bacterial Foraging Optimization Algorithm with Machine Learning-Driven Short-Term Electricity Load Forecasting: A Case Study in Peninsular Malaysia
by Farah Anishah Zaini, Mohamad Fani Sulaima, Intan Azmira Wan Abdul Razak, Mohammad Lutfi Othman and Hazlie Mokhlis
Algorithms 2024, 17(11), 510; https://doi.org/10.3390/a17110510 - 6 Nov 2024
Viewed by 635
Abstract
Accurate electricity demand forecasting is crucial for ensuring the sustainability and reliability of power systems. Least square support vector machines (LSSVM) are well suited to handle complex non-linear power load series. However, the less optimal regularization parameter and the Gaussian kernel function in [...] Read more.
Accurate electricity demand forecasting is crucial for ensuring the sustainability and reliability of power systems. Least square support vector machines (LSSVM) are well suited to handle complex non-linear power load series. However, the less optimal regularization parameter and the Gaussian kernel function in the LSSVM model have contributed to flawed forecasting accuracy and random generalization ability. Thus, these parameters of LSSVM need to be chosen appropriately using intelligent optimization algorithms. This study proposes a new hybrid model based on the LSSVM optimized by the improved bacterial foraging optimization algorithm (IBFOA) for forecasting the short-term daily electricity load in Peninsular Malaysia. The IBFOA based on the sine cosine equation addresses the limitations of fixed chemotaxis constants in the original bacterial foraging optimization algorithm (BFOA), enhancing its exploration and exploitation capabilities. Finally, the load forecasting model based on LSSVM-IBFOA is constructed using mean absolute percentage error (MAPE) as the objective function. The comparative analysis demonstrates the model, achieving the highest determination coefficient (R2) of 0.9880 and significantly reducing the average MAPE value by 28.36%, 27.72%, and 5.47% compared to the deep neural network (DNN), LSSVM, and LSSVM-BFOA, respectively. Additionally, IBFOA exhibits faster convergence times compared to BFOA, highlighting the practicality of LSSVM-IBFOA for short-term load forecasting. Full article
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<p>Summary of different types of LF with respective time horizons, domains, inputs, and outputs.</p>
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<p>Framework for electricity load forecasting.</p>
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<p>Structures of LSSVM.</p>
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<p>The flowchart of LSSVM-IBFOA.</p>
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<p>Monthly average electricity load profile in 24 h (2019–2021).</p>
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<p>Typical weekly average load profile in December 2021.</p>
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<p>Visualization of forecasting result for the DNN, LSSVM, LSSVM-BFOA, and LSSVM-IBFOA for (<b>a</b>) Monday; (<b>b</b>) Tuesday–Thursday; (<b>c</b>) Friday; (<b>d</b>) Saturday, and (<b>e</b>) Sunday.</p>
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<p>Visualization of forecasting result for the DNN, LSSVM, LSSVM-BFOA, and LSSVM-IBFOA for (<b>a</b>) Monday; (<b>b</b>) Tuesday–Thursday; (<b>c</b>) Friday; (<b>d</b>) Saturday, and (<b>e</b>) Sunday.</p>
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<p>Visualization of forecasting result for the DNN, LSSVM, LSSVM-BFOA, and LSSVM-IBFOA for (<b>a</b>) Monday; (<b>b</b>) Tuesday–Thursday; (<b>c</b>) Friday; (<b>d</b>) Saturday, and (<b>e</b>) Sunday.</p>
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<p>Illustrations of plots for MAPE and MAE.</p>
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<p>Convergence curve of BFOA and IBFOA for (<b>a</b>) Monday; (<b>b</b>) Tuesday–Thursday; (<b>c</b>) Friday; (<b>d</b>) Saturday; and (<b>e</b>) Sunday.</p>
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10 pages, 260 KiB  
Article
Vox populi (Dei), vox Dei: Pope Francis’ Theology of the People of God, the Priesthood of All Believers and Democracy
by Rudolf von Sinner
Religions 2024, 15(11), 1347; https://doi.org/10.3390/rel15111347 - 5 Nov 2024
Viewed by 1112
Abstract
The Holy See is an absolute monarchy, both as a political and as a spiritual entity. The Second Vatican Council indicated, retrieving biblical terms and metaphors, a new way of giving value to the whole people of God, the laity (laos theou [...] Read more.
The Holy See is an absolute monarchy, both as a political and as a spiritual entity. The Second Vatican Council indicated, retrieving biblical terms and metaphors, a new way of giving value to the whole people of God, the laity (laos theou), constituted by baptism. Rather than a societas perfecta in a pyramidal system, the intention was to declericalise and in this sense democratise the church and its decision-making, not least seeking to secure its witness in an ever more secular world. Even if a sacramental and ontological difference is maintained, this indicates clergy are no longer a first class of believers against which the laity would be a second class; rather, they are rooted and stand with and within the whole people of God with their specific vocation and ordination. The notion of the royal and universal priesthood of believers, taken from 1 Peter 2:9 and emphasised by Luther and other reformers as they distributed power between ordained and not ordained leaders, was visible in the Second Vatican Council and finds new enactment in the synodality process which culminated in the Ordinary Synod in Rome, in October 2024. Based on his own theology of the people of God, developed during the dictatorship and economic oppression in Argentina, with strong cultural and religious connotations, Pope Francis seeks to further major involvement of the laity and especially of women in the church’s administration and transformation processes. Not surprisingly, this process has been receiving criticism both from those who find it is not going far enough and from those who believe the process has already gone far too far. Based on bibliographical and documental research, the intention of this article is to describe and analyse the notion of the people of God as proposed by Pope Francis and its forms of concretisation including its deficiencies, as well as, in dialogue with ongoing debates on populism, highlight the precariousness of any “people” as a concept and as a reality. A dynamic notion of “people” and a theological accountability of the people and the clergy towards each other, towards God and towards the world can do justice to both the ambiguities and the irreplaceability of the people as citizens of the church as well as the world. Full article
15 pages, 7772 KiB  
Article
State of Charge Estimation of Lithium Battery Utilizing Strong Tracking H-Infinity Filtering Algorithm
by Tianqing Yuan, Yang Liu, Jing Bai and Hao Sun
Batteries 2024, 10(11), 388; https://doi.org/10.3390/batteries10110388 - 4 Nov 2024
Viewed by 775
Abstract
The ability to quickly and accurately estimate the state of charge (SOC) of lithium batteries is a key function of the battery management system (BMS). To enhance the accuracy of SOC estimation for lithium batteries, we propose a method that combines the dynamic [...] Read more.
The ability to quickly and accurately estimate the state of charge (SOC) of lithium batteries is a key function of the battery management system (BMS). To enhance the accuracy of SOC estimation for lithium batteries, we propose a method that combines the dynamic factor recursive least squares (DFFRLS) algorithm and the strong tracking H-infinity filtering (STF-HIF) algorithm. To address the issue of fixed forgetting factors in recursive least squares (RLS) that struggle to maintain both fast convergence and stability in battery parameter identification, we introduce dynamic forgetting factors. This approach adjusts the forgetting factor based on the residuals between the model’s estimated and actual values. To improve the H-infinity filtering (HIF) algorithm’s poor performance in tracking sudden state changes, we propose a combined STF-HIF algorithm, integrating HIF with strong tracking filtering (STF). Simulation experiments indicate that, compared to the HIF algorithm, the STF-HIF algorithm achieves a maximum absolute SOC estimation error (MaxAE) of 0.69%, 0.72%, and 1.22%, with mean absolute errors (MAE) of 0.27%, 0.25%, and 0.38%, and root mean square errors (RMSE) of 0.33%, 0.30%, and 0.46% under dynamic stress testing (DST), federal urban driving schedules (FUDS), and Beijing dynamic stress testing (BJDST) conditions, respectively. Full article
(This article belongs to the Section Battery Performance, Ageing, Reliability and Safety)
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<p>Second-order RC Thevenin model.</p>
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<p>(<b>a</b>) Current during the HPPC test; (<b>b</b>) Voltage of HPPC test.</p>
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<p>OCV-SOC curve chart.</p>
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<p>Dynamic forgetting factor parameter identification flowchart.</p>
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<p>Results of battery model parameter identification. (<b>a</b>) <span class="html-italic">R</span><sub>0</sub>; (<b>b</b>) <span class="html-italic">R<sub>P</sub></span><sub>1</sub>; (<b>c</b>) <span class="html-italic">R<sub>p</sub></span><sub>2</sub>; (<b>d</b>) <span class="html-italic">C<sub>P</sub></span><sub>1</sub>; (<b>e</b>) <span class="html-italic">C<sub>P</sub></span><sub>2.</sub></p>
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<p>Flow Chart of the proposed STF-HIF.</p>
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<p>(<b>a</b>) Comparison chart of model terminal voltage; (<b>b</b>) Error curve chart.</p>
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<p>(<b>a</b>) SOC estimation under DST conditions; (<b>b</b>) SOC estimation error under DST conditions.</p>
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<p>(<b>a</b>) SOC estimation under FUDS conditions; (<b>b</b>) SOC estimation error under FUDS conditions.</p>
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<p>(<b>a</b>) SOC estimation under BJDST conditions; (<b>b</b>) SOC estimation error under BJDST conditions.</p>
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27 pages, 2540 KiB  
Article
Forecasting Multi-Step Soil Moisture with Three-Phase Hybrid Wavelet-Least Absolute Shrinkage Selection Operator-Long Short-Term Memory Network (moDWT-Lasso-LSTM) Model
by W. J. M. Lakmini Prarthana Jayasinghe, Ravinesh C. Deo, Nawin Raj, Sujan Ghimire, Zaher Mundher Yaseen, Thong Nguyen-Huy and Afshin Ghahramani
Water 2024, 16(21), 3133; https://doi.org/10.3390/w16213133 - 1 Nov 2024
Viewed by 957
Abstract
To develop agricultural risk management strategies, the early identification of water deficits during the growing cycle is critical. This research proposes a deep learning hybrid approach for multi-step soil moisture forecasting in the Bundaberg region in Queensland, Australia, with predictions made for 1-day, [...] Read more.
To develop agricultural risk management strategies, the early identification of water deficits during the growing cycle is critical. This research proposes a deep learning hybrid approach for multi-step soil moisture forecasting in the Bundaberg region in Queensland, Australia, with predictions made for 1-day, 14-day, and 30-day, intervals. The model integrates Geospatial Interactive Online Visualization and Analysis Infrastructure (Giovanni) satellite data with ground observations. Due to the periodicity, transience, and trends in soil moisture of the top layer, time series datasets were complex. Hence, the Maximum Overlap Discrete Wavelet Transform (moDWT) method was adopted for data decomposition to identify the best correlated wavelet and scaling coefficients of the predictor variables with the target top layer moisture. The proposed 3-phase hybrid moDWT-Lasso-LSTM model used the Least Absolute Shrinkage and Selection Operator (Lasso) method for feature selection. Optimal hyperparameters were identified using the Hyperopt algorithm with deep learning LSTM method. This proposed model’s performances were compared with benchmarked machine learning (ML) models. In total, nine models were developed, including three standalone models (e.g., LSTM), three integrated feature selection models (e.g., Lasso-LSTM), and three hybrid models incorporating wavelet decomposition and feature selection (e.g., moDWT-Lasso-LSTM). Compared to alternative models, the hybrid deep moDWT-Lasso-LSTM produced the superior predictive model across statistical performance metrics. For example, at 1-day forecast, The moDWT-Lasso-LSTM model exhibits the highest accuracy with the highest R20.92469 and the lowest RMSE 0.97808, MAE 0.76623, and SMAPE 4.39700%, outperforming other models. The moDWT-Lasso-DNN model follows closely, while the Lasso-ANN and Lasso-DNN models show lower accuracy with higher RMSE and MAE values. The ANN and DNN models have the lowest performance, with higher error metrics and lower R2 values compared to the deep learning models incorporating moDWT and Lasso techniques. This research emphasizes the utility of the advanced complementary ML model, such as the developed moDWT-Lasso-LSTM 3-phase hybrid model, as a robust data-driven tool for early forecasting of soil moisture. Full article
(This article belongs to the Section Soil and Water)
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<p>Study site geographical location and land use of the region and surrounding areas [<a href="#B41-water-16-03133" class="html-bibr">41</a>].</p>
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<p>Schematic view of the development of benchmark models and proposed 3-phase hybrid moDWT-Lasso-LSTM model for multi-step SM forecasting at <span class="html-italic">t</span> + 1, <span class="html-italic">t</span> + 14 and <span class="html-italic">t</span> + 30 lead times.</p>
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<p>Wavelet and scaling data series resulted from moDWT decomposition process given for the predictor variable: SM10-40 when decomposition level 4 and wavelet filter “haar” is used at <span class="html-italic">t</span> + 1 lead time.</p>
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<p>Heatmap of the Root Mean Square Error (RMSE) and Symmetric Mean Absolute Percentage Error (SMAPE) for the moDWT-Lasso-LSTM model and other benchmark models at <span class="html-italic">t</span> + 1, <span class="html-italic">t</span> + 14 and <span class="html-italic">t</span> + 30 lead time SM forecasting.</p>
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<p>Redar plots for the Mean Absolute Error (MAE) for the moDWT-Lasso-LSTM model and other benchmark models at <span class="html-italic">t</span> + 1, <span class="html-italic">t</span> + 14 and <span class="html-italic">t</span> + 30 lead time SM forecasting.</p>
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<p>Box plot of forecast errors in the testing phase generated by the moDWT-Lasso-LSTM hybrid model and other benchmark models at <span class="html-italic">t</span> + 1, <span class="html-italic">t</span> + 14 and <span class="html-italic">t</span> + 30 lead time SM forecasting.</p>
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<p>Stem plots of the Nash-Sutcliffe Coefficient (<math display="inline"><semantics> <mrow> <mi>N</mi> <mi>S</mi> </mrow> </semantics></math>) for the hybrid moDWT-Lasso-LSTM model and the benchmark models in testing phase at <span class="html-italic">t</span> + 1, <span class="html-italic">t</span> + 14 and <span class="html-italic">t</span> + 30 lead time SM forecasting.</p>
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<p>Scatter plots of moDWT-Lasso-LSTM model and other benchmark models in testing phase at t+30 lead time SM forecasting.</p>
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17 pages, 2705 KiB  
Article
Remaining Service Life Prediction of Lithium-Ion Batteries Based on Randomly Perturbed Traceless Particle Filtering
by Yan Liu, Jun Chen, Jun Yong, Cheng Yang, Liqin Yan and Yanping Zheng
Energies 2024, 17(21), 5482; https://doi.org/10.3390/en17215482 - 1 Nov 2024
Viewed by 730
Abstract
To address the limitations in the prediction accuracy of the remaining useful life (RUL) of lithium-ion batteries, stemming from model accuracy, particle degradation, and insufficient diversity in the particle filter (PF) algorithm, this paper proposes a battery RUL prediction method utilizing a randomly [...] Read more.
To address the limitations in the prediction accuracy of the remaining useful life (RUL) of lithium-ion batteries, stemming from model accuracy, particle degradation, and insufficient diversity in the particle filter (PF) algorithm, this paper proposes a battery RUL prediction method utilizing a randomly perturbed unscented particle filter (RP-UPF) algorithm, based on the constructed battery capacity degradation model. The method utilizes evaluation metrics adjusted R-squared (Radj2) and the Akaike Information Criterion (AIC) to select the battery capacity decline model C5 with a higher goodness of fit. The initial values for constructing the C5 model are obtained using the relevance vector machine (RVM) and nonlinear least squares methods. Based on the constructed battery capacity decline model C5, the RP-UPF algorithm is employed to estimate the posterior parameters and iteratively approach the true battery capacity decline curve, thereby predicting the battery’s RUL. The research results indicate that, using battery B0005 as an example and starting the prediction from the 50th cycle, the RUL prediction results obtained with the RP-UPF algorithm demonstrate reductions in absolute error, relative error, and probability density function (PDF) width of 2%, 2.71%, and 10%, respectively, compared to the PF algorithm. Similar conclusions were drawn for batteries B0006 and B0018. Under the constructed battery capacity degradation model C5, the RP-UPF algorithm shows higher prediction accuracy for battery RUL and a narrower PDF range compared to the PF algorithm. This approach effectively addresses the issue of particle weight degradation in the PF algorithm, providing a more valuable reference for battery RUL prediction. Full article
(This article belongs to the Section D2: Electrochem: Batteries, Fuel Cells, Capacitors)
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<p>Distribution of performance metrics for the seven building models.</p>
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<p>Fitting curves of different batteries using four empirical models.</p>
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<p>Fitting curves of different batteries using four empirical models.</p>
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<p>Comparison between simulation results and test results of the capacity of battery No. B0005.</p>
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<p>B0005 battery RUL prediction results.</p>
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<p>B0006 battery RUL prediction results.</p>
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<p>B0018 battery RUL prediction results.</p>
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