CN118384613B - Bag dust collection state monitoring method and system based on change rate and distance calculation - Google Patents
Bag dust collection state monitoring method and system based on change rate and distance calculation Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B01D—SEPARATION
- B01D46/00—Filters or filtering processes specially modified for separating dispersed particles from gases or vapours
- B01D46/0084—Filters or filtering processes specially modified for separating dispersed particles from gases or vapours provided with safety means
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B01D46/023—Pockets filters, i.e. multiple bag filters mounted on a common frame
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
- B01D—SEPARATION
- B01D46/00—Filters or filtering processes specially modified for separating dispersed particles from gases or vapours
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Abstract
The invention discloses a method and a system for monitoring the state of bag dust collection based on change rate and distance calculation, wherein the method comprises the steps of acquiring a pressure signal at the inlet of the bag dust collection, a dust concentration value at the outlet of the bag dust collection and a pulse valve working signal, and obtaining the bag dust collection fault state and positioning based on the processing of the pressure signal at the bag dust collection inlet, the dust concentration value at the bag dust collection outlet and the pulse valve working signal. The scheme realizes the real-time monitoring, fault early warning, abnormal positioning and other fault monitoring of the dust collection unit, thereby prolonging the service life of the component and reducing the energy efficiency loss.
Description
Technical Field
The invention relates to an intelligent monitoring neighborhood of cloth bag dust removing equipment, in particular to a bag dust collecting state monitoring method based on change rate and distance calculation.
Background
The fault monitoring of the bag-type dust collector generally needs to monitor the blowing electromagnetic pulse valve of the bag-type dust collector and the dust concentration. In the prior art, when a bag-type dust collector blowing electromagnetic pulse valve fails, manual inspection is needed to be conducted one by one, the skill level of the manual inspection is uneven, and inspection quality is uneven. If the electromagnetic pulse valve is leaked, inspection personnel can hardly find in time, the air compressor set is easy to run at full load or even run under pressure, the energy consumption is increased, the pressure difference of the filter bag is increased under the untimely treatment state, and the service life is reduced.
For example, patent application number 202111643592.5 of on-line monitoring method and system of particulate matter concentration and method for judging leakage of cloth bag discloses a monitoring system of particulate matter concentration, which is used for monitoring concentration of dust collecting equipment such as bag dust collection, but the monitoring object is single, the simultaneous monitoring of equipment such as a bag dust collection pulse valve is not realized, and the alarm of discharging according to concentration is intelligently carried out. Therefore, the prior art cannot realize the real-time monitoring, fault early warning, abnormal positioning and other fault monitoring of the dust collection unit.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a bag dust collection state monitoring method based on change rate and distance calculation, which realizes the real-time monitoring, fault early warning, abnormal positioning and other fault monitoring of a dust collection unit, thereby prolonging the service life of components and reducing energy efficiency loss.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the method for monitoring the state of the bag dust collection based on the change rate and the distance calculation comprises the steps of collecting and acquiring a pressure signal at a bag dust collection inlet, a dust concentration value at a bag dust collection outlet and a pulse valve working signal, and obtaining the state and the positioning of the failure of the bag dust collection based on the processing of the pressure signal at the bag dust collection inlet, the dust concentration value at the bag dust collection outlet and the pulse valve working signal.
Based on the real-time acquisition of a pressure signal at a bag dust collecting inlet through a dynamic pressure sensor, monitoring the pressure state of a pulse valve; and when the pulse valve works, N pressure change values are obtained, corresponding N pressure change rates are calculated, probability distribution of the change rates is calculated based on the change rates of the pressure values, and whether the pulse valve has faults or not and the fault degree are judged based on the probability distribution.
And judging the fault alarm degree of the pulse valve at the moment based on the proportion or the number of the negative numbers of the change rate in the distribution probability of the change rate. Based on the fact that the dynamic pressure sensor is used for acquiring the pressure value corresponding to each acquisition time in the working time of each pulse valve in real time, the acquisition time and the pressure value are used as one pressure point, and the Euclidean distance between all the pressure points in the working time of the pulse valve and the pressure point which normally works in preset template data is solved, so that the calculated Euclidean distance corresponding to the pulse valve is obtained.
And judging the fault alarm degree of the pulse valve at the moment by calculating the Euclidean distance value and the distance threshold value together according to the proportion or the number of the negative number of the change rate in the distribution probability of the change rate.
Judging three states of the pulse valve according to the proportion of the change rate value of negative number and the calculated Euclidean distance value and the distance threshold value: normal, early warning, fault alarm conditions.
And judging and positioning the pulse valve corresponding to the detected pressure data according to the time interval and the working time sequence of the pulse valve through the working signal of the pulse valve.
The collected pressure data is subjected to noise and abnormal point removal operation, and the noise and abnormal points are removed and then processed to obtain the bag dust collection fault state and positioning.
The dust concentration value at the dust collection outlet of the bag is obtained through a dust sensor, a dust escape threshold value is set, in an online ash removal mode, if the detection value of the dust sensor is larger than the threshold value after the action of a pulse valve, the dust escape is judged, the leakage phenomenon exists in a blowing cloth bag to which the pulse valve belongs, and if in an offline mode, the detection value of the dust sensor is larger than the threshold value at the moment after the opening of a poppet valve, the leakage of the dust collection bag of the clean air chamber is judged.
Collecting historical data of dust concentration per hour, predicting a predicted value of the dust concentration through a differential autoregressive moving average model, comparing the predicted dust concentration with an actual concentration value, and sending an abnormal alarm signal when the error of the predicted dust concentration and the actual concentration value exceeds a set threshold value.
The utility model provides a bag dust collection state monitoring system, includes sensor, data acquisition ware, edge server, the sensor is used for gathering bag dust collection equipment's pulse valve state and dust concentration data, pulse valve operating signal all send into the edge server into, the edge server operation bag dust collection state monitoring method based on rate of change and distance calculation.
The invention has the advantages that:
1. The efficiency and the productivity of the equipment are improved, namely, the equipment can be ensured to run in the optimal state by monitoring and optimizing the performance of the bag dust collector in real time, so that the efficiency and the productivity of the equipment are improved.
2. The energy consumption and the operation cost are reduced, namely the unnecessary energy waste can be reduced by monitoring and controlling the energy consumption of the bag dust collector in real time, so that the operation cost is reduced.
3. The maintenance and repair costs are reduced, namely, the potential problems can be found and solved in time by monitoring the running state and the potential problems of the equipment in real time, so that the maintenance and repair costs of the equipment are reduced.
4. The safety is improved, namely potential safety hazards can be found in time by monitoring the running state and the emission of the bag dust collector in real time, so that the risk of accidents is reduced.
Drawings
The contents of the drawings and the marks in the drawings of the present specification are briefly described as follows:
FIG. 1 is a schematic diagram of a hardware structure corresponding to a monitoring method of the present invention;
FIG. 2 is a schematic diagram showing the pressure change condition of three pulse valves of the bag dust collecting device in the normal state;
FIG. 3 is a graph of the valve operating pressure values and a distribution chart of the valve operating pressure values, wherein a in FIG. 3 is a schematic diagram of the valve operating pressure values; b is a pulse valve fault work change rate distribution diagram;
FIG. 4 is a diagram of the normal operating pressure value of the pulse valve and a diagram of the normal pressure change rate of the pulse valve according to the present invention, wherein a is a diagram of the normal operating pressure value of the pulse valve in FIG. 4, and b is a diagram of the normal pressure change rate of the pulse valve;
FIG. 5 is a table showing a comparison of fault criteria for different rate of change distribution ranges according to the present invention;
FIG. 6 is a schematic diagram of the data noise reduction processing of the input data according to the present invention;
FIG. 7 is a schematic view of a sensor arrangement of the present invention in a mounted position.
Detailed Description
The following detailed description of the invention refers to the accompanying drawings, which illustrate preferred embodiments of the invention in further detail.
As shown in FIG. 1, the monitoring system of the bag dust collecting equipment provided by the invention comprises a sensor, a data collector, an edge server, an application platform and an intelligent alarm algorithm.
The sensors include a pressure sensor and a dust concentration sensor, which are respectively disposed at the bag dust collection inlet and the bag dust collection outlet, as shown in fig. 7. The data collected by the sensor is uploaded to the edge server through the data collector, the algorithm model is used for denoising some data, and real-time data can be displayed on the application platform. The pulse valve state and the dust concentration of the bag dust collecting equipment are monitored in real time, and intelligent alarm is realized. The real-time monitoring of the operation state of the dust collecting equipment is realized on the application platform, and a friendly man-machine interface is provided, so that operators can intuitively know the operation condition of the equipment. And the control strategy can be further optimized and the equipment efficiency can be improved through the excavation and analysis of a large amount of historical data. The edge server runs an algorithm model to execute an algorithm strategy to perform fault monitoring, positioning and the like and alarms through the application platform. The algorithm model executes strategies including: pulse valve status monitoring and fault location strategy and dust concentration monitoring strategy.
1. Pulse valve condition monitoring and fault locating strategy
The pressure signal at the bag dust collecting inlet is obtained in real time through a dynamic pressure sensor, the pressure state of the pulse valve is monitored, meanwhile, the working signal of the pulse valve is connected to a PLC, and the fault pulse valve is positioned through the signal of the PLC.
The working time of the pulse valve is about 0.1-0.15s, the pressure in the air bag can be instantaneously reduced and slowly increased at the working moment, the pressure fluctuation in the process is monitored by the pressure sensor, 150 pressure change values of each pulse valve during working are finally stored by quantifying the data, and the data are analyzed and displayed. Fig. 2 shows the variation of the pressure values in the 3 pulse valves in the normal operation state.
Statistical analysis of the rate of change shows that there is a transient decrease and a slower rise in pressure values, and we analyze the operating state of the pulse valve by calculating the rate of change for each set of pressure values and calculating the probability distribution of the rate of change. The rate of change is calculated as shown in the following equation, where i represents the pressure value at the i-th point in the set of data and i-1 represents the pressure value at the point before i, thereby calculating the rate of change before each point in the set of pressure values.
。
Wherein, the change rate smaller than 0 represents the process of pressure signal falling, the change rate larger than 0 represents the process of pressure rising, and the magnitude of the change rate represents the speed of pressure value change.
As shown in fig. 3 and 4, when the pulse valve is studied to normally operate in a non-interference environment, the instantaneous pressure value is reduced, the pressure value is slowly increased, and most of the change rate is stabilized within a certain interval range and is distributed on the right. By observing the distribution of the change rate, several processes of the instantaneous pressure reduction of the pulse valve during operation can be analyzed. And the alarm criterion is converted according to the experience of field experts, and whether the pulse valve fails or not and the degree of the failure are determined according to the number of the change rates, so that whether the pulse valve can continue to work or not is judged. The distribution of the change rate means that 150 voltage values are detected by each pulse valve, 150 change rates are calculated by the pressure values, and then the distribution range of the change rates is counted to form a distribution range of the change rate, and in general, most of the change rates are stable in a certain interval range and distributed on the right. That is, the rate of change of less than 0 on the left side is relatively small, and when the pulse valve works normally, the number of the rates of change of less than 0 or the ratio of 150 of the rates of change occupying the whole is smaller than the normal upper limit threshold value, and the pulse valve is judged to be normal; if the number of the change rates smaller than 0 or the ratio of 150 of the change rates occupying all the change rates is larger than a preset alarm threshold, a fault alarm signal is sent out at the moment and used for alarming and reminding the fault of the pulse valve at the moment; when the number of the change rate smaller than 0 or the ratio of 150 of the change rate is between the normal upper limit threshold and the alarm threshold, judging that the state is an early warning state, sending out an early warning signal to remind a user of timely paying attention to the state, and carrying out dust removal, power signal investigation and other treatments on the site.
As shown in fig. 5, for different change rate distribution ranges, the fault degree of the pulse valve can be determined, because the field high dust environment can have a certain influence, and based on 150 change rate values corresponding to 150 pressure data and combined with the actual diagnosis experience of an expert, three fault determination interval ranges are determined according to the number of change rates smaller than 0:
Normal phase: the distribution value with the change rate smaller than 0 is in the range of 1-10, and the pulse valve can be considered to be in a normal state
Early warning stage: the distribution value with the change rate smaller than 0 is in the range of 10-50, the early warning state of the pulse valve can be determined, the pulse valve can be protected under intensive care, dust removal, power signal investigation and other treatments can be implemented on site, when the distribution range of 3-5 times is in the range of 10-50, an alarm can be generated, and the pulse valve is overhauled
Alarming: the distribution value with the change rate smaller than 0 is in the range of more than 50, the pulse valve can be considered to be in a fault state, and the field personnel can stop for maintenance or replacement of the pulse valve.
And meanwhile, in order to further capture the abnormal signal, a template distance matching mode is adopted for verification, and Euclidean distance is adopted for calculating the Euclidean distance of the pulse valve under the normal working condition and the abnormal working condition so as to judge whether the pulse valve works normally. The apparent change in the comparative euclidean distance can be seen in figure 6. Wherein the Euclidean distance formula:
Assume that there are two in the plane ；
Then the distance formula between the two points。
And for the Euclidean distance, calculating the distance between the template data and the measured data, setting a distance threshold value as 2, and generating an early warning signal when the distance between the measured data and the normal template is larger than 2, so as to strengthen the monitoring of the pulse valve. When the pulse valve data are larger than the distance threshold value for 3-5 times, an alarm signal is generated, and on-site personnel stop to overhaul the pulse valve. The Euclidean distance measurement is that the pressure value corresponding to each pulse valve, the template data refers to the pressure curve of the pulse valve in the optimal normal working state is selected by combining with the field actual environment under the guidance of manual experience, when the pressure data of each pulse valve is uploaded, the distance calculation is carried out on each pressure value corresponding to the template, the similarity between the pressure values is reflected, and the formula of the distance calculation is shown in the formula. The method comprises the steps that each pulse valve collects a plurality of real-time pressure data in real time in working time, and meanwhile, a plurality of normal pressure data corresponding to the same time point of each pulse valve in the working time are set; and calculating the Euclidean distance between the normal pressure data and the real-time pressure data, and judging whether to send out an alarm or not based on the Euclidean distance and the change rate. The method comprises the steps of obtaining the Euclidean distance of a single pressure point pressure value by squaring after the pressure of a real-time pressure data point and the pressure of a normal pressure data point in corresponding template data are subjected to difference when the Euclidean distance is calculated because the pressure data point and the template data point which are collected in real time are at the same time point, averaging the Euclidean distances of the pressure values of all the pressure points in the working time of a pulse valve to obtain the Euclidean distance in the re-working time of the pulse valve, and comparing the calculated Euclidean distance with a distance threshold value to judge whether to alarm or not: the pressure data acquired in real time is a series of points related to time, which can be understood as time on the abscissa and pressure value on the ordinate; defining the pressure value point as a real-time pressure value point; the normal pressure point corresponding to each pressure point is set in advance in a template data mode, so that the Euclidean distance between the normal pressure point and the abnormal point can be calculated to carry out deviation evaluation, and the Euclidean distance of each pressure point is firstly calculated when the Euclidean distance is calculated because a plurality of pressure points exist in the working time of the pulse valve, and then the Euclidean distance of each pressure point is summed and then averaged to obtain the Euclidean distance which is used as the calculated Euclidean distance of the pulse valve.
When the ratio or number of the negative number of the change rate of the pressure value meets the fault alarm state and the calculated Euclidean distance of the pressure value meets the alarm state, judging the pressure value to be in the alarm state and sending an alarm signal;
When the ratio or number of the negative number of the change rate of the pressure value meets the fault early warning state and the Euclidean distance of the calculated pressure value meets the early warning state, judging the state as an alarm state and sending out an early warning signal;
Otherwise, judging that the pulse valve is in a normal state.
And a data processing stage: noise and abnormal point removal as shown in fig. 6, noise can be generated on the scene with different collected pulse valve pressure change data, the integral pressure curve trend can be influenced, errors are easy to occur when the distance comparison is carried out, and therefore the pressure curve data after denoising by adopting a preprocessing method is used as the data of the subsequent calculation distance. The denoising processing method comprises the following steps:
1) Wavelet decomposition: selecting a wavelet with the layer number of N (one layer is selected as common data) to carry out wavelet decomposition on the signal;
2) And (3) threshold processing: selecting a threshold value after decomposition, clustering the coefficients after wavelet decomposition by adopting a local distance in a threshold value selection mode, selecting the coefficient with the largest distance in each cluster for zero resetting, removing abnormal noise, and quantizing the coefficient of each layer by using a threshold value function;
3) And (5) denoising signal reconstruction: reconstructing a signal using the processed coefficients
Fault pulse valve positioning: the pulse signal data of the pulse valve work directly passes through the server through the PLC, the pulse valve of work is positioned according to the interval time of each pulse valve work, if the injection interval time is 5s, the pulse valve is positioned according to 5s, if the pressure fluctuation signal is not collected in 5s, the pulse valve is judged to be not work, and the pulse valve signal of the next work is collected after 10 s. The working pulse valve, the pressure data of the corresponding pulse valve and the working state of the corresponding pulse valve which are judged according to the pressure data can be judged according to the working time sequence interval of the pulse valve. A bag collector has a plurality of pulse valves connected in series and operated in a cycle of operation, each pulse valve having a fixed blowing time, the pulse valves being positioned in time series with respect to operation. The pulse valves work according to different time sequences, so that the working time sequence of the pulse valves is known, the detected pressure value is known, and the fault state is judged to be the state of the pulse valve, so that the purpose of fault positioning is achieved.
2. Dust concentration monitoring strategy
And acquiring a dust concentration value at a dust collection outlet of the bag through a dust sensor. Setting a dust escape threshold (the ultra-low emission standard is 10mg/m, and the normal emission is 30 mg/m), judging that dust escapes after a pulse valve acts in an online ash removal mode, if a dust sensor detection value is larger than a threshold, judging that a leakage phenomenon exists in a jetting cloth bag to which the pulse valve belongs, and if the instantaneous dust sensor detection value is larger than the threshold after a poppet valve is opened in an offline mode, judging that the dust collection bag of the clean air chamber leaks. On-line mode: the poppet valve of the bag dust collection device is always opened, when the detected concentration of each pulse valve is operated, the poppet valve of the bag dust collection device can be closed when the pulse valve is operated according to the leakage condition offline mode of the pulse valve corresponding to a certain cloth bag, and when all the pulse valves corresponding to the clean room are opened after the pulse valve is operated, the detection concentration can only judge whether the clean room has leakage condition or not, and the bag cannot be positioned.
And judging the state of the cloth bag every hour according to the data acquired in the past hour. The concentration alarm is carried out according to the cloth bag condition of one hour, and if the concentration exceeds the standard for a plurality of times continuously in one hour, the alarm can be carried out.
Historical data of dust concentration per hour is collected, a predicted value of the dust concentration is predicted through a differential autoregressive moving average model (ARIMA model), the predicted dust concentration is compared with an actual concentration value, and when the error of the predicted dust concentration and the actual concentration value exceeds a specified range, an abnormal alarm is generated. And meanwhile, when the concentration value reaches the standard of ultralow emission, an abnormal dust concentration alarm can be generated. The concentration threshold value is given by dynamic prediction, and the normal concentration threshold value range is obtained in a prediction mode, so that the concentration threshold value is compared with a real-time concentration value, and the concentration abnormal state is judged. And optimizing the concentration threshold, wherein if the concentration threshold is adopted, deviation is easy to generate, so that a prediction model is adopted to predict in real time what range the concentration should be in under the normal state, and if the actual concentration value at the moment is greatly different from the predicted value of normal operation, the problem of concentration is indicated, and alarm information can be generated.
It is obvious that the specific implementation of the present invention is not limited by the above-mentioned modes, and that it is within the scope of protection of the present invention only to adopt various insubstantial modifications made by the method conception and technical scheme of the present invention.
Claims (7)
1. A bag dust collection state monitoring method based on change rate and distance calculation is characterized by comprising the following steps of: acquiring a pressure signal at a bag dust collecting inlet, a dust concentration value at a bag dust collecting outlet and a pulse valve working signal, and processing the pressure signal at the bag dust collecting inlet, the dust concentration value at the bag dust collecting outlet and the pulse valve working signal to obtain a bag dust collecting fault state and positioning;
based on the real-time acquisition of a pressure signal at a bag dust collecting inlet through a dynamic pressure sensor, monitoring the pressure state of a pulse valve; acquiring N pressure change values and calculating corresponding N pressure change rates when the pulse valve works, and calculating probability distribution of the change rates based on the change rates of the pressure values;
Based on the fact that the dynamic pressure sensor is used for acquiring the pressure value corresponding to each acquisition time in the working time of each pulse valve in real time, the acquisition time and the pressure value are taken as one pressure point, and the Euclidean distance between all the pressure points in the working time of the pulse valve and the pressure point which normally works in preset template data is solved, so that the calculated Euclidean distance corresponding to the pulse valve is obtained;
And judging the fault alarm degree of the pulse valve at the moment by calculating the Euclidean distance value and the distance threshold value together according to the proportion or the number of the negative number of the change rate in the distribution probability of the change rate.
2. The method for monitoring the dust collection state of the bag based on the change rate and the distance calculation as claimed in claim 1, wherein the method comprises the following steps: judging three states of the pulse valve according to the proportion of the change rate value of negative number and the calculated Euclidean distance value and the distance threshold value: normal, early warning, fault alarm conditions.
3. The method for monitoring the dust collection state of the bag based on the change rate and the distance calculation as claimed in claim 1, wherein the method comprises the following steps: and judging and positioning the pulse valve corresponding to the detected pressure data according to the time interval and the working time sequence of the pulse valve through the working signal of the pulse valve.
4. The method for monitoring the dust collection state of the bag based on the change rate and the distance calculation as claimed in claim 1, wherein the method comprises the following steps: the collected pressure data is subjected to noise and abnormal point removal operation, and the noise and abnormal points are removed and then processed to obtain the bag dust collection fault state and positioning.
5. The method for monitoring the dust collection state of the bag based on the change rate and the distance calculation as claimed in claim 1, wherein the method comprises the following steps: the dust concentration value at the dust collection outlet of the bag is obtained through a dust sensor, a dust escape threshold value is set, in an online ash removal mode, if the detection value of the dust sensor is larger than the threshold value after the action of a pulse valve, the dust escape is judged, the leakage phenomenon exists in a blowing cloth bag to which the pulse valve belongs, and if in an offline mode, the detection value of the dust sensor is larger than the threshold value at the moment after the opening of a poppet valve, the leakage of the dust collection bag of the clean air chamber is judged.
6. The method for monitoring the dust collection state of the bag based on the change rate and the distance calculation as claimed in claim 1, wherein the method comprises the following steps: collecting historical data of dust concentration per hour, predicting a predicted value of the dust concentration through a differential autoregressive moving average model, comparing the predicted dust concentration with an actual concentration value, and sending an abnormal alarm signal when the error of the predicted dust concentration and the actual concentration value exceeds a set threshold value.
7. A bag dust collection state monitoring system is characterized in that: the method comprises the steps of collecting pulse valve state and dust concentration data of the bag dust collecting equipment, sending pulse valve state and dust concentration data and pulse valve working signals into the edge server, and operating the bag dust collecting state monitoring method based on the change rate and distance calculation according to any one of claims 1-6 by the edge server.
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| CN116510424A (en) * | 2023-04-24 | 2023-08-01 | 东北大学 | Filter bag of dust collector and leakage detection method and preparation method thereof |
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| JP2012071237A (en) * | 2010-09-28 | 2012-04-12 | Technos Serve:Kk | Method and apparatus for monitoring pulse backwashing mechanism in powder collector |
| US9782711B2 (en) * | 2014-01-21 | 2017-10-10 | Covanta Energy, Llc | System and method for automatic control of differential pressure in a baghouse system |
| CN205826222U (en) * | 2016-07-19 | 2016-12-21 | 攀枝花攀钢集团设计研究院有限公司 | Sack cleaner leak-off pocket quickly analyzes inspection system |
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| CN117848713B (en) * | 2024-01-05 | 2024-07-09 | 湖州槐坎南方水泥有限公司 | System and method for monitoring running state of pulse valve of bag-type dust collector |
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| CN113058354A (en) * | 2021-04-09 | 2021-07-02 | 辽宁环宇环保科技股份有限公司 | Pulse valve remote online monitoring system and monitoring method based on bag-type dust collector |
| CN116510424A (en) * | 2023-04-24 | 2023-08-01 | 东北大学 | Filter bag of dust collector and leakage detection method and preparation method thereof |
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