Open AccessArticle

Evaluating High-Precision Machine Learning Techniques for Optimizing Plate Heat Exchangers’ Performance

Gang Hou

¹,

Dong Zhang

^2,*

Zhoujian An

²,

Qunmin Yan

¹,

Meijiao Jiang

²,

Sen Wang

³ and

Liqun Ma

School of Electrical Engineering, Shaanxi University of Technology, Hanzhong 723001, China

School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Lanzhou Lanshi Heat Exchange Equipment Co., Lanzhou 730300, China

Author to whom correspondence should be addressed.

Energies 2025, 18(4), 957; https://doi.org/10.3390/en18040957

Submission received: 7 January 2025 / Revised: 6 February 2025 / Accepted: 10 February 2025 / Published: 17 February 2025

(This article belongs to the Special Issue Development of Thermodynamic Storage Technology)

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Abstract

Plate heat exchangers have the advantages of high heat transfer coefficients and compact structures, and they are widely used in aerospace, nuclear power, and other fields. Nevertheless, several scalability challenges have emerged during the utilization process. If not addressed promptly, the issue will reduce heat transfer efficiency, consequently causing energy waste, diminished production capacity, and a shortened lifespan. In this study, we employed the long short-term memory (LSTM) algorithm model and the multi-layer perceptron (MLP) algorithm model to monitor the health status of plate heat exchangers. This was achieved by fine-tuning the hidden layers and neurons of the models. The individual model exhibiting the highest prediction accuracy was incorporated into a more sophisticated ensemble model to monitor the health status of plate heat exchangers. The study revealed that the MLP 2 × 64 + LSTM 2 × 64 model achieved the highest prediction accuracy, scoring 0.9942. According to the simulation program for plate heat exchangers, the fouling thermal resistance was determined to be 0.0003 m²·K/W when the heat exchange efficiency decreased by 50%. An early warning threshold was established within the health condition value (HCV), triggering an alert when the heat transfer efficiency of the plate heat exchanger fell below 50%. Combining the LSTM and MLP algorithms provides new ideas and technical support for the health assessment and maintenance of plate heat exchangers.

Keywords:

plate heat exchanger; fouling; heat transfer performance; machine learning

1. Introduction

Industrialized civilization represents a significant advancement in human history, characterized primarily by large-scale production and consumption. However, this development paradigm exhibits a significant reliance on fossil fuels, leading to substantial carbon emissions and energy consumption. Consequently, the issue of global warming is escalating [1]. To limit the global temperature rise to 1.5 °C by 2050, the comprehensive utilization of waste heat potential has been widely acknowledged as an effective strategy [2,3,4]. Heat exchangers’ most prevalent practical applications encompass power generation in large-scale thermal power plants, along with heating, cooling, chemical processing, and the electrical and electronics industries [5,6]. As the core equipment for waste heat recovery and utilization, ensuring their long-term stable and efficient operation is paramount [7,8,9]. Compared with the widely utilized tubular heat exchangers, plate heat exchangers exhibit significant advantages due to their compact design and superior performance [10,11]. Consequently, their application in industrial contexts has significantly expanded in recent years. Prashant Saini et al. [12,13,14] introduced a novel configuration of arc-shaped trapezoidal-vane vortex generators (CTWVGs), both with and without circular perforations, to enhance the heat transfer performance of finned-tube heat exchangers. They examined seven distinct CWDWVG configurations, which varied from one to eight waves. The results demonstrated that these configurations can substantially decrease the pressure drop and friction factor of finned heat exchangers across various Reynolds number conditions, thereby enhancing heat transfer efficiency effectively. Feng et al. [15] developed some novel structures aimed to optimize the airside performance of H-type finned tube heat exchangers. The effects of geometric parameters on the heat transfer, flow resistance, and comprehensive thermal–hydraulic performance were investigated by means of the Taguchi method. According to the results, for longitudinal vortex generators, dimples/protrusions, and grooves, the heat transfer characteristics are significantly affected by the winglet type, vertical distance, and groove diameter, while the attack angle, dimple depth, and groove type have prominent impacts on the flow resistance characteristics. Oktarina Heriyani et al. [16] installed perforated concave rectangular winglet pair vortex generators on plates in rectangular ducts to increase the heat transfer through the six heated tubes to the air stream by lowering the enhancement in the pressure drop. The lowest cost–benefit ratio was accompanied by an increase in thermal performance of 1.29.

As a compact heat exchange device, the flow channels of plate heat exchangers are relatively narrow. After prolonged use, the accumulation of fouling can lead to blockages [17], thereby reducing the heat transfer efficiency and increasing flow resistance [18]. This may result in unnecessary economic losses and energy waste. In more severe cases, it can compromise industrial production processes and pose risks to personal safety [19,20]. Due to the prolonged nature of fouling accumulation on the surface of heat exchangers, monitoring the formation process in real time and proposing effective countermeasures is important [21]. Therefore, numerous scholars have forecasted the fouling resistance on the surface of heat exchangers to better understand the fouling formation process. The widely used fouling prediction models are the traditional heat transfer calculation [22], the least squares method [23], and the establishment of a two-dimensional model [24] to analyze the fouling formation mechanism. Alhuthali et al. [25] integrated dynamic modeling, dimensional analysis, and regression modeling to establish the relationship between the adjustable parameters of the soil model. Traditional heat transfer calculations primarily determine fouling thermal resistance using criterion formulas, thermal conductivity resistance, the overall heat transfer coefficient, and thermal resistance equations. The structural block diagram of the fouling monitoring algorithm is presented in Figure 1.

The real-time online monitoring of plate heat exchangers is relatively inadequate. Oddgeir et al. [26] utilized readily available operational measurement data and applied a rapid mathematical model to estimate the total heat transfer coefficient of the heat exchanger. They further employed the Kalman filter method for real-time online monitoring of the plate heat exchanger’s condition. Aminian et al. [27] utilized the flow rate of crude oil, the pipe wall’s surface temperature, and pipe diameter as input variables in a neural network-based model to predict the critical conditions for scaling. A four-layer feed forward neural network estimated the average relative scaling error in the crude oil heat exchanger to be 26.23%. Common approaches to fault monitoring and diagnosis can be categorized into two primary types: the mathematical modeling method and the model-based diagnostic method. These two methods have their advantages and disadvantages, and a comparison of the two methods is shown in Table 1.

Current fouling monitoring technologies predominantly utilize indirect measurement methods, such as assessing the pressure drop and variations in thermal efficiency. These methods are frequently susceptible to fluctuations in other operational parameters, which can compromise the accuracy of the results. The current monitoring methodologies predominantly concentrate on particular types of heat exchangers and specific operating conditions, exhibiting insufficient versatility and adaptability. This limitation restricts their applicability across diverse heat exchanger systems and varying operational scenarios. Domestically and internationally, research concerning the effective integration of machine learning with the health status assessment of plate heat exchanger fouling is relatively inadequate. In light of this, it is imperative to undertake comprehensive research into the application potential of machine learning for assessing fouling and diagnosing performance in plate heat exchangers. This paper employs LSTM and MLP algorithm models with varying hidden layers, dropout rates, and neuron counts. By integrating the LSTM and MLP models, we investigated the fouling assessment and long-term performance diagnosis of plate heat exchangers, thereby enhancing the efficiency and accuracy of health monitoring for these devices.

2. Introduction of the Methods and Principles

2.1. Basic Principles of the LSTM Algorithm

The LSTM neural network model is structurally divided into three layers: the input layer, the implicit layer, and the output layer. The implicit layer, in turn, has a memory unit and a gate structure. The memory unit is used to memorize past information, and the gate structure includes a forgetting gate, an input gate, and an output gate, which are used to control the state of the cell. Firstly, the forgetting gate is utilized to read the last output value h_t−1 and the current input value x_t, which performs a nonlinear mapping and then outputs a vector f_t. The output values are compressed by a sigmoid function between 0 and 1, with values closer to 0 meaning a greater need to be discarded [30,31]. Input gates are used to determine the new information being stored in the cellular state; the output gates determine the value of the next hidden state. By setting the weight matrix W of the three gates to 0 or 1 and dot-multiplying the parameters to add and remove their features, the state of any gate can effectively control the complexity of the algorithm [32]. The concrete components of the structure are illustrated in Figure 2.

2.2. Basic Principle of the MLP Algorithm

A multi-layer perceptron is a hierarchical model that integrates multiple perceptrons, with neurons interconnected between the layers. Given that the MLP model is built through the interconnection of numerous perceptron layers, the output from the first perceptron layer serves as the input to the subsequent perceptron layer. Therefore, the explicit representation of the input layer for the second perceptron can be omitted. In an MLP, in addition to the input and output layers of the model, the intermediate layers are termed hidden layers. The following describes a two-layer perceptron model, consisting of an input layer, a hidden layer, and an output layer. This model is referred to as having a single hidden layer [33]. Figure 3 shows a schematic diagram of the structure of multi-layer sensing.

3. Predictive Model and Data Preprocessing

The trained predictive model generates a function f(x), which can quantify the deviation level at each time point t based on the discrepancy y_t − f(x_t) between the input parameter x and the observed output value y. Machine learning algorithms forecast a system’s output parameters by analyzing a system through an analysis of its input parameters and internal state variables. Taking a fully monitored plate heat exchanger as an example, this study selects key operational parameters, including inlet temperature, inlet pressure, flow rate, and differential pressure to predict the outlet temperature accurately. In the model construction phase, this paper defines two distinct models. Both models ensure identical output parameters while employing different input parameters. The specific input and output parameters are shown in Table 2.

This study employed the interpolation method to address outliers, thereby preserving the uniformity of the time steps. When training the LSTM/MLP algorithm model for signal prediction, the sliding window method [34] is employed to construct the samples. For a long signal within a dataset, a segment of width w is sequentially extracted [28], yielding the following results:

D_{i} = [x_{i}, x_{i + 1}, \dots, x_{i + w - 1}]

(1)

The duration of the window should be determined on the basis of the rate of change in the signal. If the signal exhibits a high rate of change, a shorter sampling sequence may be employed. Considering both the efficiency of model training and the quality of the generated samples, a window cutting length of 12 was selected.

4. Model Construction and Data Preprocessing

4.1. LSTM Model Construction

The core components of the LSTM algorithm are the cell state and hidden state, which enable the transmission of information throughout the network, thereby facilitating long-term memory capabilities. Simultaneously, the LSTM algorithm employs three distinct gates: the input gate, the forgetting gate, and the output gate. The input gate regulates the influx of new information, the forgetting gate manages the discarding of outdated information, and the output gate oversees the selection of output information. The prediction logic of the LSTM algorithm model is shown in Figure 4.

The main functions of the LSTM algorithm model are as follows.

(1): Construction of the LSTM algorithm model: The number of hidden layers is set within the range of 1 to 2. The number of neurons per layer is determined from the set [16, 32, 64, 128].
(2): The activation function, precisely the neuronal activation function utilized in the LSTM model, is the hyperbolic tangent (tanh) function.
(3): The getTestTrainSplit function accepts two parameters to determine the proportions for dividing the dataset into the training and testing subsets. These parameters dictate how the global dataset is partitioned into the training and test sets.

4.2. MLP Model Construction

The MLP employs nonlinear activation functions to propagate signals. The MLP lacks memory of its internal state, as it cannot retain previous information, resulting in its output being solely dependent on the current input and network parameters. Nevertheless, the training process of MLP is more efficient and straightforward than that of LSTM. To address the challenges of memory storage and operational efficiency, this section introduces a regression prediction model based on the MLP algorithm. The logical block diagram illustrating the MLP model’s prediction process is presented in Figure 5.

The main functions used in this model are as follows.

(1): IntiTrainPredict: This function accepts a set of models and determines whether retraining is required, based on predefined criteria. It also accepts facility data and model parameters as inputs. The steps within the function body encompass acquiring configuration information, initializing the data frame, partitioning the test and training sets, and separating the feature and target columns.
(2): The layers parameter is a list wherein each element corresponds to the number of neurons in each layer. By default, the list contains a single component, 128, indicating that the model incorporates one hidden layer comprising 128 neurons. In the MLP model, the number of hidden layers is set within the range of 2 to 3, while the number of neurons per layer is selected from the set [16, 32, 64, 128].
(3): The discard rate parameter is utilized to configure the dropout regularization, which assists in mitigating the overfitting of the model. This parameter is set to a default value of 0.3 in the MLP model.
(4): The activation function, which dictates the nonlinear transformation performed by a neural network layer, is an essential component. In the MLP model, the activation function utilized is Relu.

5. Analysis of the Algorithm’s Prediction Results

The historical operational data of the plate heat exchanger are derived from the operational records collected during the winter heating seasons in a community in Lanzhou, spanning from November 2017 to March 2022. Through analyzing these data, we can gain insights into critical parameters, including the operational status of the plate heat exchanger across various periods and fluctuations in the heating load.

5.1. Temperature Prediction of the Cold Side Outlet of Model A

In the study of predicting the cold-side outlet temperature for Model A, LSTM and MLP algorithm models were selected for comparative analysis. The prediction results when the hidden layers were configured as 2 and 3, with neuron counts of 16, 32, 64, and 128 and a dropout rate of 0.3, are illustrated in the figure below.

For Model A, predictions were generated utilizing the LSTM algorithm, with the training period spanning from November 2017 to November 2020. As illustrated in Figure 6a,b, as the operating time increases, scaling begins to occur within the plate heat exchanger, leading to a reduction in heat exchange efficiency. Consequently, the outlet temperature on the cold side of the plate heat exchanger exhibits a noticeable downward trend. As illustrated in Figure 6c, for the LSTM model, when the number of hidden layers is set to 2 and the number of neurons per layer is 64, the R-squared value of the model reaches 0.9868. When the hidden layer consists of three layers and each layer contains 64 neurons, the R-squared value of the model reaches 0.9735. Regardless of whether the hidden layer consists of two or three neurons, the model’s prediction accuracy initially increases and decreases as the number of neurons grows. The model’s prediction accuracy peaks when the number of neurons is 64. This indicates that an excessive number of hidden layers and neurons may result in overfitting. For Model A, within the LSTM algorithm framework, the prediction performance is notably enhanced when the hidden layer count is set to 2 and the number of neurons per layer is configured to 64.

As illustrated in Figure 7, when the model has 2 hidden layers with 128 neurons each, the prediction accuracy is 0.9433. With an increase to 3 hidden layers, while maintaining 128 neurons per layer, the prediction accuracy improves to 0.9439. Regardless of whether the hidden layer consists of 2 or 3 layers, increasing the number of neurons to 128 results in both configurations achieving their respective peak prediction accuracies.

5.2. Temperature Prediction of the Cold Side Outlet of Model B

For maintaining constant output parameters, Model B incorporates an additional critical variable in its input parameters compared with Model A: the inlet and outlet pressures on the cold side. In the research on predicting the cold side exit temperature for Model B, LSTM and MLP models were compared. The analysis used 2 and 3 hidden layers with neuron counts of 16, 32, 64, and 128 and a dropout rate of 0.3. The results are shown in the figure below.

As illustrated in Figure 8a,b, during the model training process, the predicted values of the cold side outlet temperature of the plate heat exchanger closely align with the measured values. As the operating duration increases, the overall outlet temperature of the plate heat exchanger exhibits a pronounced downward trend. As illustrated in Figure 8c, the LSTM algorithm model achieves its highest prediction accuracy of 0.9942 when the hidden layer count is set to 2 and the number of neurons is 64. It is evident that when the number of hidden layers remains constant, the model’s prediction accuracy initially increases and subsequently decreases as the number of neurons grows. When the number of neurons remains constant, the model’s prediction accuracy tends to decrease as the number of hidden layers increases. Consequently, an excessive number of neurons and hidden layers may potentially compromise the model’s predictive accuracy.

It can be observed from Figure 9a,b that the predicted values of Model B closely align with the measured values during both the prediction and measurement phases. As the operating duration of the plate heat exchanger extends, the discrepancy between the predicted and measured values becomes increasingly significant. As illustrated in Figure 9c, the model with three hidden layers exhibits a lower prediction accuracy than the model with two hidden layers. In Model B, the prediction accuracy peaks at 0.9627 when the hidden layer count is set to 2 and the number of neurons per layer is 64.

5.3. Integrated Model

In Model A and Model B, the optimal MLP algorithm and LSTM algorithm models are integrated to form more sophisticated ensemble models for predicting the temperature at the cold outlet of the plate heat exchanger.

Since integrated models typically exhibit greater complexity compared with single models, this study combines the MLP algorithm model with the LSTM algorithm model. As illustrated in Figure 10, the prediction accuracy of the integrated model surpasses that of the best single model. When the integrated model is configured as MLP + LSTM with two layers of 64 units each and modified Version B, its prediction accuracy reaches 0.9903, the highest among all the tested models. This result unequivocally demonstrates that integrating diverse model types can significantly enhance the prediction accuracy.

A simulation program was developed using MATLAB (R2019a (9.6.0.1072779)) to assess the performance of plate heat exchangers and predict their scaling conditions. In the simulation, thermal resistance was introduced on the cold side of the heat exchanger, and its value was iteratively adjusted until the simulated outlet temperature accurately corresponded to the experimentally measured outlet temperature. At this juncture, the thermal resistance value corresponded to the fouling thermal resistance value. The relationship between temperature difference and fouling thermal resistance has been established, as illustrated in Equation (2). This functional expression not only facilitates the analysis of performance deviations in heat exchangers under varying fouling conditions but also serves as a tool for optimizing the operational performance of heat exchangers.

R_{f} (T_{p r e, o}, T_{a c t u a l, o}) = |T_{p r e, o} - T_{a c t u a l, o}| \times 6 \times 10^{- 5}

(2)

where T_pre_,o is the predicted exit temperature of the cold side, and the unit is °C; T_actual_,o is the actual exit temperature of the cold side, expressed in °C; and the coefficient 6 × 10⁻⁵ m²·K/W is the fouling thermal resistance value corresponding to the obtained data when the temperature difference is 1 °C.

The correlation between the predicted discrepancy in the cold side outlet temperature, as compared with the measured outlet temperature, utilizing the MLP 2 × 64 + LSTM 2 × 64 Mod B model and the inferred fouling coefficient Rf is illustrated in Figure 11.

Figure 11 presents a comparative analysis of the temperature discrepancy between the predicted and actual outlet temperatures, alongside the fouling value derived from the optimal MLP 2 × 64 + LSTM 2 × 64 Mod B model. The fouling factor presented here refers to the value obtained when the heat transfer coefficient of the heat exchanger, as predicted by a MATLAB-based performance simulation program for plate heat exchangers, decreases to 50% of its clean-state value. Compared with the temperature difference predicted by the model, the changing trend of the two values is consistent. Therefore, it is feasible to establish a correlation between fouling and the temperature difference at the cold outlet of the plate heat exchanger.

To more accurately reflect the current health status of the heat exchanger, this paper calculates the HCV of the heat exchanger. The calculation formula is presented in Equation (3).

HCV = 1 - \frac{(1 - {HCV}_{c}) R}{R_{f}}

(3)

In the formula, HCV_c is the fouling warning value of the heat exchanger, and its range is 0–1. The HCV_c value is selected as 0.5. R is the current fouling value, in m²·K/W; R_f is the corresponding fouling heat resistance value when the heat transfer performance decreases by 50%.

In Figure 12, the red dashed line represents a health status warning threshold of 0.5. An alarm will be triggered if the HCV falls below this value, indicating that the heat exchange efficiency has declined to less than 50%, necessitating maintenance and cleaning of the heat exchanger. In the figure, it is evident that HCV levels fell below the warning threshold on two occasions: in November 2021 and March 2022. However, the data from November 2021 indicated an anomaly due to mutations, resulting in a false alarm during this period. However, in March 2022, the data exhibited a gradual transformation, consistent with the actual scaling condition. Consequently, the alert signifies that the heat exchanger’s performance had diminished to the predefined threshold, necessitating a cleaning procedure.

6. Summary

In this study, the LSTM algorithm, the MLP algorithm, and their ensemble model were employed to predict the cold side outlet temperature of a plate heat exchanger. The fouling on the cold side of the plate heat exchanger was assessed by comparing the measured cold side exit temperature against the predicted exit temperature. It primarily comprises the following components.

(1): This paper forecasted a plate heat exchanger’s cold side outlet temperature utilizing individual and ensemble models based on the LSTM and MLP algorithms. We identified the optimal predictive model by systematically evaluating and comparing the prediction performance of Models A and B. For Model A, LSTM 2 × 64 has the highest prediction accuracy, 0.9938. For Model B, LSTM 2 × 64 has the highest prediction accuracy of 0.9942. Consequently, excessive hidden layers and neurons may adversely affect the model’s prediction accuracy. It is crucial to determine an optimal configuration of hidden layers and neurons during the model design phase.
(2): By incorporating LSTM 2 × 64 and MLP 2 × 64 into Model A, the architecture that exhibits a more complex structure and superior prediction accuracy is the MLP + LSTM 2 × 64 configuration, achieving an accuracy of 0.9942. Meanwhile, Model B demonstrates a slightly higher prediction accuracy of 0.9951. The integrated Model B demonstrates superior accuracy in predicting the exit temperature of plate heat exchangers, highlighting its advantages in modeling complex systems. The efficacy of the integrated model in enhancing prediction accuracy has been further substantiated, with Model B’s integrated architecture demonstrating superior performance in this study.
(3): The thermal resistance was incorporated into the cold side of the plate heat exchanger via the simulation software. When the fouling thermal resistance reaches 0.0003 m²·K/W, the heat transfer efficiency of the plate heat exchanger decreases to 50%. By comparing the observed temperature differences with those predicted by the model, it is evident that both exhibit a consistent change trend. The correlation between the temperature differential and the thermal resistance due to fouling offers critical insights for developing a rational cleaning and maintenance strategy.

Author Contributions

Conceptualization, S.W.; Methodology, Z.A.; Software, M.J.; Formal analysis, Q.Y.; Data curation, G.H.; Writing—original draft, G.H.; Writing—review & editing, D.Z.; Visualization, L.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Shaanxi Provincial Department of Education general natural science special project (Development of a Machine Learning-Based System for Monitoring and Diagnosing Heat Exchanger Faults) (No. 24JK0379), the Industrial Support Plan Project of Gansu Provincial Education Department (2025CYZC-034), the Gansu Key Research and Development Program (23YFGA0023), and the Gansu Provincial Youth Talent Program (2025QNTD36).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

Authors Sen Wang and Liqun Ma were employed by the company Lanzhou Lanshi Heat Exchange Equipment Co. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Nomenclature

T_pre,o	The predicted exit temperature of the cold side (°C)
T_actual,o	The actual exit temperature of the cold side (°C)
HCV_c	The fouling warning value of the heat exchanger (%)
R	The current fouling value (m²·K/W)
R_f	The corresponding fouling heat resistance value when the heat transfer performance decreases (m²·K/W)
Abbreviations
LSTM	Long short-term memory
MLP	Multi-layer perceptron
HCV	Health condition value

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Figure 1. Structure block diagram of the fouling monitoring algorithm.

Figure 2. Schematic diagram of the LSTM network structure.

Figure 3. Schematic diagram of the MLP structure.

Figure 4. Prediction logic block diagram of the LSTM algorithm model.

Figure 5. Logic block diagram of the MLP model’s prediction.

Figure 6. Prediction of Model A by the LSTM algorithm model. (a) The predicted and measured temperature of the cold side outlet of Model A when the number of hidden layers is 2. (b) The predicted and measured temperature of the cold side outlet of Model A when the number of hidden layers is 3. (c) Model indicators.

Figure 7. Prediction of the outlet temperature of Model A by MLP. (a) The predicted and measured temperature of the cold side outlet of Model A when the number of hidden layers is 2. (b) The predicted and measured temperature of the cold side outlet of model A when the hidden layer is 3. (c) Model indicators.

Figure 8. LSTM prediction of the exit temperature of Model B. (a) The predicted and measured temperature of the cold side outlet of Model B when the number of hidden layers is 2. (b) The predicted and measured temperature of the cold side outlet of Model B when the number of hidden layer is 3. (c) Model indicators.

Figure 9. MLP prediction of the exit temperature of Model B. (a) The predicted and measured temperature of the cold side outlet of Model B when the number of hidden layers is 2. (b) The predicted and measured temperature of the cold side outlet of Model B when the number of hidden layer is 3. (c) Model indicators.

Figure 10. Prediction of the exit temperature of Model B by the integrated model. (a) The predicted and measured temperature of the cold side outlet of the integrated model. (b) Model indicators.

Figure 11. Temperature difference and fouling value of MLP 2 × 64 + 2 × 64 Mod B.

Figure 12. HCV value of the MLP 2 × 64 + LSTM 2 × 64 Mod B heat exchanger.

Table 1. Comparison of fault monitoring and diagnosis methods.

Type	Method Description	Advantage	Shortcoming
Mathematical model	Modeling of plate heat exchangers using the energy-efficient heat transfer unit method [28].	The structure is simple and the form is intuitive.	Finding appropriate diagnostic rules is relatively difficult in complex systems.
Model-based	Compare and analyze the predicted values of the model with the actual measured values and make a judgment from the degree of deviation [29].	Ideal for equipment or systems with many parameters and high coupling.	Higher complexity of the modeling process.

Table 2. Prediction model.

Name	Input Parameters	Output Parameter
Model A	Hot side fluid volumetric flow rate, hot side inlet and outlet temperatures, cold side inlet temperature, cold side fluid volumetric flow rate	Cold side outlet temperature
Model B	Hot side fluid volumetric flow rate, hot side inlet and outlet temperatures, cold side inlet temperature, cold side inlet flow, cold side inlet and outlet pressure	Cold side outlet temperature

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MDPI and ACS Style

Hou, G.; Zhang, D.; An, Z.; Yan, Q.; Jiang, M.; Wang, S.; Ma, L. Evaluating High-Precision Machine Learning Techniques for Optimizing Plate Heat Exchangers’ Performance. Energies 2025, 18, 957. https://doi.org/10.3390/en18040957

AMA Style

Hou G, Zhang D, An Z, Yan Q, Jiang M, Wang S, Ma L. Evaluating High-Precision Machine Learning Techniques for Optimizing Plate Heat Exchangers’ Performance. Energies. 2025; 18(4):957. https://doi.org/10.3390/en18040957

Chicago/Turabian Style

Hou, Gang, Dong Zhang, Zhoujian An, Qunmin Yan, Meijiao Jiang, Sen Wang, and Liqun Ma. 2025. "Evaluating High-Precision Machine Learning Techniques for Optimizing Plate Heat Exchangers’ Performance" Energies 18, no. 4: 957. https://doi.org/10.3390/en18040957

APA Style

Hou, G., Zhang, D., An, Z., Yan, Q., Jiang, M., Wang, S., & Ma, L. (2025). Evaluating High-Precision Machine Learning Techniques for Optimizing Plate Heat Exchangers’ Performance. Energies, 18(4), 957. https://doi.org/10.3390/en18040957

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