Mobile pollution source location method in confined space based on Gaussian process regression

Abstract

The present invention discloses a method for locating mobile pollution sources in a confined space based on Gaussian process regression, which relates to the technical field of locating mobile pollution sources in a confined space. By adopting the Gaussian process regression algorithm, high-precision positioning of mobile heat sources is achieved in a complex confined space environment. By utilizing the advantages of the Gaussian process regression algorithm, the accuracy and stability of positioning can be maintained even when the data noise is large or the heat source movement path is complex; the present invention is combined with the minimum redundancy maximum correlation algorithm to effectively reduce the number of required measuring points while ensuring positioning accuracy. This measurement point optimization not only reduces the deployment and maintenance costs of the system, but also improves the efficiency of data processing, making the present invention have significant cost-effectiveness advantages in resource-constrained application scenarios.

Description

Technical Field

[0001] The present invention relates to the technical field of positioning mobile pollution sources in confined spaces, and in particular to a method for positioning mobile pollution sources in confined spaces based on Gaussian process regression. Background Art

[0002] In typical confined spaces, such as factory conveyor belts, the cargo holds of roll-on / roll-off ships, underground mines, subways, and highway tunnels, the presence of high-temperature, mobile heat sources can pose a threat to the enclosing structures, as well as the property and safety of personnel. In these unique scenarios, mobile heat sources pose a significant threat to the maintenance structures and the safety of personnel involved in the confined space. Furthermore, these confined spaces may contain electronic equipment, lighting, and other infrastructure that are particularly vulnerable to high temperatures, further exacerbating the risk of compromising the structural integrity and safety of personnel in these typical confined spaces. Therefore, rapid and accurate detection of heat sources within these confined spaces is crucial. This is specifically designed for confined space scenarios involving the presence of high-temperature, mobile heat sources.

[0003] Visual recognition methods and sensors are currently widely used. However, in many real-world scenarios, factors such as lighting conditions, image quality, scene complexity, and other background variables can significantly interfere with visual fire identification. Furthermore, traditional sensors such as smoke alarms, temperature alarms, and infrared alarms can provide alarm functionality but have inherent limitations. First, sensor-triggered responses require the monitored object to exceed a predefined threshold, which often leads to delayed detection and missed opportunities for timely fire extinguishing. Second, smoke alarms are prone to false alarms due to unexpected conditions. Furthermore, the significant installation and maintenance costs of using fiber optic sensors in long tunnels hinder their practical application. Therefore, it is crucial to develop a heat source localization method that is independent of complex fire propagation mechanisms while being economically feasible and applicable to various engineering fields. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a method for locating mobile pollution sources in a confined space based on Gaussian process regression. The following technical solutions are adopted:

[0005] The method for locating mobile pollution sources in a confined space based on Gaussian process regression includes the following steps:

[0006] Step 1: Arrange multiple groups of temperature sensors in the confined space, and the multiple groups of temperature sensors are used to capture temperature distribution change data in the confined space;

[0007] Step 2: The data processing center receives temperature data from multiple sets of temperature sensors, deploys a Gaussian process regression model, and inputs the temperature data from the multiple sets of temperature sensors into the trained Gaussian process regression model for training. The Gaussian process regression model predicts the location of the mobile pollution source in the confined space based on the temperature data from the multiple sets of temperature sensors.

[0008] In step 3, the minimum redundancy maximum correlation algorithm is used to optimize the measuring points. By evaluating the contribution of each measuring point to the heat source positioning and sorting them based on the contribution, the measuring points whose contribution is lower than the set threshold are gradually eliminated.

[0009] Optionally, in step 1, multiple groups of temperature sensors are arranged at equal intervals on the top and sides of the confined space.

[0010] The above-mentioned technical solution, first of all, relies on collecting temperature data from a high-temperature heat source as it moves within a confined space. To this end, a series of temperature sensors are placed on the top and sides of the confined space. These sensors can capture changes in the temperature distribution within the space in real time. As the heat source moves, the temperature data collected by the sensors is transmitted in real time to a data processing center, serving as the basis for training the localization algorithm. This collected temperature data is then fed into a Gaussian process regression model for training. Gaussian process regression is a powerful nonlinear regression tool that predicts temperature values ​​at any location by probabilistically modeling the data and providing an estimate of the uncertainty of the prediction. This method not only handles noise in the data but also adapts to the nonlinear characteristics of the data, thereby accurately predicting the location of a moving heat source. Through model training and optimization, the accuracy and reliability of heat source localization can be continuously improved. To further improve localization efficiency and reduce computational costs, this solution uses the minimum redundancy maximum correlation algorithm to optimize the measurement points. This algorithm evaluates the contribution of each measurement point to heat source localization and ranks them accordingly, identifying the measurement points that have the greatest impact on the localization result. By gradually eliminating measurement points with lower contributions, the number of required measurement points can be significantly reduced while ensuring positioning accuracy. This not only reduces the burden of data processing but also optimizes the overall performance of the system.

[0011] After optimizing the minimum redundancy maximum correlation algorithm, this solution focuses on achieving the optimal balance between the number of measurement points and prediction accuracy. By evaluating the positioning accuracy of different numbers of measurement points, an ideal measurement point configuration can be determined, which minimizes the number of measurement points while maintaining sufficiently high positioning accuracy. Furthermore, this solution takes into account various challenges that may be encountered in practical applications, such as stalling caused by high-temperature mobile heat sources and sensor noise. Therefore, corresponding fault-tolerance mechanisms are introduced into the algorithm design to improve system robustness.

[0012] Optionally, optimize the Gaussian process regression model using the Grey Wolf Optimization algorithm.

[0013] Alternatively, the Gray Wolf Optimization algorithm is used to optimize the Gaussian Process Regression model, which includes the following steps:

[0014] Step a, preprocessing the temperature data;

[0015] Step b: Initially train the Gaussian process regression model using the training data, wherein the Gaussian process regression model establishes the relationship between input and output through kernel functions and basis functions, and continuously updates hyperparameters based on error calculations. This process is repeated until the termination condition is met, and the optimal hyperparameter combination is finally output. The Gaussian process regression model is refitted using the optimal hyperparameter combination, predictions are made on the training set and test set, and the prediction results are denormalized;

[0016] In step c, the mean square error and mean absolute error indicators are calculated through error analysis to evaluate the performance of the model and verify the effectiveness of the Gaussian process regression model optimized by the gray wolf optimization algorithm.

[0017] Optionally, in step b, the termination condition is that the maximum number of iterations is reached or the error is lower than a set threshold.

[0018] Using the above technical solution, data is first preprocessed, including loading, shuffling, and splitting the dataset (80% for training and 20% for testing), as well as normalizing the data. Next, the training data is used to initially train the GPR model. The GPR model uses a kernel function (such as a squared exponential kernel) and a basis function (such as a linear function) to establish the relationship between input and output, and continuously updates hyperparameters based on error calculations. The GWO algorithm plays a key role in this process. It initializes multiple candidate solutions (gray wolf populations) by simulating the hunting behavior of gray wolves, each representing a set of GPR hyperparameters. The algorithm calculates the fitness of each candidate solution (usually measured by model error) and selects the optimal gray wolf (Alpha, Beta, and Delta) based on their fitness ranking. Other gray wolves then update their positions based on the positions of these three optimal individuals, approaching the global optimal solution. This process is repeated until a termination criterion is met (such as reaching a maximum number of iterations or the error falling below a certain threshold), ultimately outputting the optimal hyperparameter combination. Using these optimized parameters, the GPR model was refitted, predictions were made on the training and test sets, and the prediction results were denormalized. Finally, error analysis was performed to evaluate the model's performance using metrics such as mean squared error and mean absolute error, thereby verifying the effectiveness of the GWO-optimized GPR model. The overall process efficiently integrates data preprocessing, model training, optimization, and performance evaluation, significantly improving the predictive capabilities of the GPR model.

[0019] Optionally, in step 3, the minimum redundancy maximum correlation algorithm treats each attribute (sensor measurement value: pollutant concentration value, temperature, humidity, wind speed, and other environmental parameters collected by the sensor. These attributes directly reflect the impact of the pollution source in the current space and are an important basis for locating the pollution source) as a discrete random variable and uses mutual information to measure the similarity between two attributes. The mutual information between two attributes is used to measure the similarity between two attributes X and Y. The mutual information I(X,Y) is calculated as follows:

[0020]

[0021] Where p(x,y) is defined as the joint probability distribution function of X and Y, while p(x) and p(y) represent the marginal probability distribution functions of random variables X and Y respectively;

[0022] Optional, each attribute f i Defined as a vector consisting of N features (f i =f i1 ,f i2 ,···f iN ), attribute f i Considered as an example of a discrete co-occurrence variable, the mutual information between features i and j is expressed as I(F i ,F j ), considering feature x and regression target c, the calculation of mutual information I(x,c) shows that the larger I(x,c), the stronger the correlation between x and c. First, a subset S consisting of m features with the largest mutual information with c is identified from all features. The formula is as follows:

[0023]

[0024] In set S, the redundancy of set S is calculated as follows:

[0025]

[0026] Alternatively, the optimal set S is found considering all 2|Ω| combinations, where Ω is the entire feature set; instead, the mRMR algorithm sorts the features by a forward addition scheme, which requires O(|Ω|·|S|) computations and uses the mutual information quotient MIQ value:

[0027]

[0028] Sort all features in Ω and use the mRMR algorithm to return the index idx of the features sorted by importance. Use a heuristic algorithm to quantify the importance of the features and return a score value. The feature with a large score value indicates that its corresponding predictor variable is important.

[0029] Optionally, a decrease in the feature importance score indicates that the feature's contribution to the model decreases and its influence on the model's predictive ability weakens, and the confidence level also decreases accordingly.

[0030] Optionally, the measurement point arrangement schemes are sorted by contribution, the top three measurement points are extracted to form a new measurement point arrangement scheme, and the stability of the new measurement point arrangement scheme is evaluated to obtain the measurement point arrangement scheme with the highest stability.

[0031] By employing the aforementioned technical solutions, the Minimum Redundancy-Maximum Relevance (mRMR) method is based on the recognition that a combination of variables that performs well individually does not necessarily lead to good classification / prediction performance. To maximize the joint dependence of highly ranked variables on the target variable, the redundancy between them must be reduced. This means incrementally selecting variables with the greatest relevance while avoiding redundancy. This allows for the identification of optimal measurement point solutions, providing more effective data for subsequent localization of mobile pollution sources in confined spaces.

[0032] In summary, the present invention includes at least one of the following beneficial technical effects:

[0033] This invention provides a method for locating mobile pollution sources in confined spaces based on Gaussian process regression. By employing the Gaussian process regression algorithm, this method achieves high-precision positioning of mobile heat sources in complex confined environments. Leveraging the advantages of the Gaussian process regression algorithm, positioning accuracy and stability are maintained even in the presence of high data noise or complex heat source movement paths, significantly outperforming traditional positioning methods.

[0034] Combined with the minimum redundancy maximum correlation algorithm, the number of required measurement points is effectively reduced while ensuring positioning accuracy. This measurement point optimization not only reduces system deployment and maintenance costs, but also improves data processing efficiency, making this invention a significant cost-effectiveness advantage in resource-constrained application scenarios.

[0035] Through advanced data processing and algorithm optimization, the present invention significantly improves the system's resistance to sensor failure, data loss, or external interference. Even in the event of partial sensor failure or poor data quality, it can maintain high positioning accuracy, ensuring stable operation and high reliability of the system.

[0036] The system's maintainability and scalability were fully considered during the design process. The modular algorithm design and flexible measurement point configuration not only facilitate on-site installation and routine maintenance, but also facilitate future technology upgrades and functional expansion, enabling the system to adapt to rapidly changing technical environments and application requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 1 is a flow chart of a method for locating a mobile pollution source in a confined space based on Gaussian process regression according to the present invention;

[0038] Figure 2 This is a schematic diagram of the structure of the experimental cabin in a specific embodiment of the present invention;

[0039] Figure 3 is a schematic structural diagram of a mobile heat source in a specific embodiment of the present invention;

[0040] Figure 4 This is a schematic diagram of the arrangement of top surface measurement points in a specific embodiment of the present invention;

[0041] Figure 5 This is a schematic diagram of the arrangement of side measurement points in a specific embodiment of the present invention;

[0042] Figure 6 2. It is a schematic diagram of the contribution ranking of the top measurement point scheme in a specific embodiment of the present invention;

[0043] Figure 7 2. It is a schematic diagram of the contribution ranking of the side measurement point scheme in a specific embodiment of the present invention;

[0044] Figure 8 Schematic diagram of the arrangement of the top three measurement points in the top contribution ranking according to a specific embodiment of the present invention;

[0045] Figure 9 Schematic diagram of the arrangement of the top three measuring points in the right side contribution ranking in a specific embodiment of the present invention;

[0046] Figure 10 2 is a schematic diagram comparing prediction accuracy under different measurement point schemes in a specific embodiment of the present invention;

[0047] Figure 11 1. It is a schematic diagram of the process of optimizing the GPR model by the GWO algorithm in a specific embodiment of the present invention;

[0048] Figure 12 2 is a schematic diagram of an iteration curve of the GWO algorithm in a specific embodiment of the present invention;

[0049] Figure 13 2 is a schematic diagram of relative error of a test set in a specific embodiment of the present invention;

[0050] Figure 14 2 is a schematic diagram of the prediction results of the test set in a specific embodiment of the present invention;

[0051] Figure 15 2 is a schematic diagram for comparing evaluation indicators in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below with reference to the accompanying drawings.

[0053] The embodiment of the present invention discloses a method for locating a mobile pollution source in a confined space based on Gaussian process regression.

[0054] Reference Figures 1-15 ,A method for locating mobile pollution sources in a restricted space based on Gaussian process regression, includes the following steps:

[0055] Step 1: Arrange multiple groups of temperature sensors in the confined space, and the multiple groups of temperature sensors are used to capture temperature distribution change data in the confined space;

[0056] Step 2: The data processing center receives temperature data from multiple sets of temperature sensors, deploys a Gaussian process regression model, and inputs the temperature data from the multiple sets of temperature sensors into the trained Gaussian process regression model for training. The Gaussian process regression model predicts the location of the mobile pollution source in the confined space based on the temperature data from the multiple sets of temperature sensors.

[0057] In step 3, the minimum redundancy maximum correlation algorithm is used to optimize the measuring points. By evaluating the contribution of each measuring point to the heat source positioning and sorting them based on the contribution, the measuring points whose contribution is lower than the set threshold are gradually eliminated.

[0058] In step 1, multiple groups of temperature sensors are arranged at equal intervals on the top and sides of the confined space.

[0059] First, the foundation of this technical solution lies in collecting temperature data from a high-temperature heat source as it moves within a confined space. To achieve this, a series of temperature sensors are placed on the top and sides of the confined space. These sensors can capture changes in the temperature distribution within the space in real time. As the heat source moves, the temperature data collected by the sensors is transmitted in real time to a data processing center, serving as the basis for subsequent training of the positioning algorithm. This collected temperature data is then fed into a Gaussian process regression model for training. Gaussian process regression is a powerful nonlinear regression tool that predicts the temperature value at any location by probabilistically modeling the data and providing an estimate of the uncertainty of the prediction. This method not only handles noise in the data but also adapts to the nonlinear characteristics of the data, thereby accurately predicting the location of a moving heat source. Through model training and optimization, the accuracy and reliability of heat source positioning can be continuously improved. To further improve positioning efficiency and reduce computational costs, this solution uses the minimum redundancy maximum correlation algorithm to optimize the measurement points. This algorithm evaluates the contribution of each measurement point to heat source positioning and ranks them accordingly, identifying the measurement points that have the greatest impact on the positioning results. By gradually eliminating measurement points with lower contributions, the number of required measurement points can be significantly reduced while ensuring positioning accuracy. This not only reduces the burden of data processing but also optimizes the overall performance of the system.

[0060] After optimizing the minimum redundancy maximum correlation algorithm, this solution focuses on achieving the optimal balance between the number of measurement points and prediction accuracy. By evaluating the positioning accuracy of different numbers of measurement points, an ideal measurement point configuration can be determined, which minimizes the number of measurement points while maintaining sufficiently high positioning accuracy. Furthermore, this solution takes into account various challenges that may be encountered in practical applications, such as stalling caused by high-temperature mobile heat sources and sensor noise. Therefore, corresponding fault-tolerance mechanisms are introduced into the algorithm design to improve system robustness.

[0061] The Gaussian process regression model is optimized using the Grey Wolf Optimization algorithm.

[0062] The Gray Wolf Optimization Algorithm to optimize the Gaussian Process Regression model includes the following steps:

[0063] Step a, preprocessing the temperature data;

[0064] Step b: Initially train the Gaussian process regression model using the training data, wherein the Gaussian process regression model establishes the relationship between input and output through kernel functions and basis functions, and continuously updates hyperparameters based on error calculations. This process is repeated until the termination condition is met, and the optimal hyperparameter combination is finally output. The Gaussian process regression model is refitted using the optimal hyperparameter combination, predictions are made on the training set and test set, and the prediction results are denormalized;

[0065] In step c, the mean square error and mean absolute error indicators are calculated through error analysis to evaluate the performance of the model and verify the effectiveness of the Gaussian process regression model optimized by the gray wolf optimization algorithm.

[0066] In step b, the termination condition is that the maximum number of iterations is reached or the error is lower than the set threshold.

[0067] First, data preprocessing is performed, including loading, shuffling, and splitting the dataset (80% for training and 20% for testing), as well as normalization. Next, the training data is used to initially train the GPR model. The GPR model uses kernel functions (such as squared exponential kernels) and basis functions (such as linear functions) to establish the relationship between input and output, and continuously updates hyperparameters based on error calculations. The GWO algorithm plays a key role in this process. It simulates the hunting behavior of gray wolves to initialize multiple candidate solutions (gray wolf populations), each representing a set of GPR hyperparameters. The algorithm calculates the fitness of each candidate solution (usually measured by model error) and selects the optimal gray wolf (Alpha, Beta, and Delta) based on their fitness ranking. Other gray wolves then update their positions based on the positions of these three optimal individuals, approaching the global optimal solution. This process is repeated until a termination criterion is met (such as reaching a maximum number of iterations or the error falling below a certain threshold), ultimately outputting the optimal hyperparameter combination. Using these optimized parameters, the GPR model was refitted, predictions were made on the training and test sets, and the prediction results were denormalized. Finally, error analysis was performed to evaluate the model's performance using metrics such as mean squared error and mean absolute error, thereby verifying the effectiveness of the GWO-optimized GPR model. The overall process efficiently integrates data preprocessing, model training, optimization, and performance evaluation, significantly improving the predictive capabilities of the GPR model.

[0068] In step 3, the minimum redundancy maximum correlation algorithm treats each attribute (sensor measurement value: pollutant concentration value, temperature, humidity, wind speed and other environmental parameters collected by the sensor. These attributes directly reflect the impact of the pollution source in the current space and are an important basis for locating the pollution source) as a discrete random variable and uses mutual information to measure the similarity between two attributes. The mutual information between two attributes is used to measure the similarity between two attributes X and Y. The mutual information I(X,Y) is calculated as follows:

[0069]

[0070] Where p(x,y) is defined as the joint probability distribution function of X and Y, while p(x) and p(y) represent the marginal probability distribution functions of random variables X and Y respectively;

[0071] Each attribute f i Defined as a vector consisting of N features (f i =f i1 ,f i2 ,···f iN ), attribute f i Considered as an example of a discrete co-occurrence variable, the mutual information between features i and j is expressed as I(F i ,Fj ), considering feature x and regression target c, the calculation of mutual information I(x,c) shows that the larger I(x,c), the stronger the correlation between x and c. First, a subset S consisting of m features with the largest mutual information with c is identified from all features. The formula is as follows:

[0072]

[0073] In set S, the redundancy of set S is calculated as follows:

[0074]

[0075] Finding the optimal set S considers all 2|Ω| combinations, where Ω is the entire feature set; in contrast, the mRMR algorithm sorts the features via a forward addition scheme, which requires O(|Ω|·|S|) computations and uses the mutual information quotient MIQ value:

[0076]

[0077] Sort all features in Ω and use the mRMR algorithm to return the index idx of the features sorted by importance. Use a heuristic algorithm to quantify the importance of the features and return a score value. The feature with a large score value indicates that its corresponding predictor variable is important.

[0078] A decrease in the feature importance score indicates that the feature's contribution to the model decreases and its influence on the model's predictive ability weakens, and the confidence also decreases.

[0079] The measurement point arrangement schemes are ranked by their contribution, and the top three measurement points are extracted to form a new measurement point arrangement scheme. The stability of the new measurement point arrangement scheme is evaluated to obtain the measurement point arrangement scheme with the highest stability.

[0080] The minimum redundancy-maximum relevance (mRMR) method is based on the recognition that a combination of variables that performs well individually does not necessarily lead to good classification / prediction performance. In order to maximize the joint dependence of high-ranking variables on the target variable, the redundancy between them must be reduced. This means incrementally selecting variables with the greatest relevance while avoiding redundancy. This allows the determination of the optimal measurement point plan, providing more effective data for the subsequent localization of mobile pollution sources in confined spaces.

[0081] The following uses a specific embodiment to illustrate the implementation principle of the method for locating a mobile pollution source in a confined space based on Gaussian process regression of the present invention:

[0082] The feasibility of this method was explored by building an experimental platform.

[0083] The experimental cabin is composed of three sections of acrylic panels with dimensions of 2.4m×0.5m×0.4m. Figure 2 As shown, there are free air inlets and outlets on both sides, and guide rails are laid inside to enable the mobile heat source to be carried on a trolley and to make linear motion inside the experimental chamber by pulling the trolley, as shown in the figure. Figure 3 As shown;

[0084] A high-speed hair dryer is used as a mobile heat source. The specific dimensions are shown in the figure. The outer radius of the air outlet is 0.024m, the inner radius is 0.022m, and the length of the air inlet is 0.046m, with a radius of 0.03m. The high-speed hair dryer has two wind temperature settings and two wind speed settings. The specific values ​​are shown in Table 1:

[0085] Table 1 Parameters of gear positions of mobile heat source

[0086]

[0087] Forty K-type thermocouples were arranged according to the following measurement point arrangement diagram and connected to three TSI Fluke 2638A recorders. The K-type thermocouples had an error of ±0.5°C and a recording interval of 1 second.

[0088] Suggestions on the arrangement of top surface measuring points Figure 4 , side measurement point arrangement instructions Figure 5

[0089] At the beginning of the experiment, each Fluke was turned on for data recording. First, the mobile heat source was placed at the starting point of the experimental chamber, the mobile heat source gear corresponding to the working condition was turned on and preheated for 1 minute, and then the mobile heat source was pulled to perform uniform linear motion at the exit of the experimental chamber. When the mobile heat source reached the exit, the mobile heat source was turned off and data recording was stopped at the same time. This completed a working condition experiment. The heat source was tested under four gear combinations with a moving speed of 0.04 m / s.

[0090] The basis of the minimum redundancy-maximum relevance (mRMR) method is the realization that a combination of variables that performs well individually does not necessarily lead to good classification / prediction performance. In other words, in order to maximize the joint dependence of high-ranking variables on the target variable, the redundancy between them must be reduced, which means incrementally selecting variables with maximum relevance while avoiding redundancy. The algorithm treats each attribute as a discrete random variable and uses mutual information to measure the similarity between two attributes. The mutual information between them is used to measure the similarity between two attributes X and Y. The mutual information I(X,Y) is calculated as follows:

[0091]

[0092] In this formula, p(x,y) is defined as the joint probability distribution function of X and Y, while p(x) and p(y) represent the marginal probability distribution functions of random variables X and Y, respectively. For ease of formulation, each attribute f i Defined as a vector consisting of N features (f i =f i1 ,f i2 ,···f iN ). Attribute f i Considered as an example of a discrete co-occurrence variable, the mutual information between features i and j is expressed as I(F i ,F j Considering feature x and regression target c, the calculation of mutual information I(x,c) shows that the larger I(x,c), the stronger the correlation between x and c. We first identify a subset S of m features with the largest mutual information with c from all features, as follows:

[0093]

[0094] In set S, there is redundancy between features because it contains highly correlated features. The redundancy of set S is calculated as follows:

[0095]

[0096] Finding the optimal set S requires considering all 2|Ω| combinations, where Ω is the entire feature set. In contrast, the MRMR algorithm sorts the features via a forward addition scheme, which requires O(|Ω|·|S|) computations and uses the mutual information quotient (MIQ) value:

[0097]

[0098] This function sorts all features in Ω and returns the feature indices (idx) sorted by importance using the mRMR algorithm. Therefore, the computational cost is O(|Ω|2). This function uses a heuristic algorithm to quantify feature importance and returns a score. Features with high scores indicate that their corresponding predictors are important. Furthermore, decreasing feature importance scores indicate confidence in feature selection.

[0099] The contribution of the two measurement point arrangements mentioned above is sorted, and the results are as follows: Figure 6 and Figure 7 As shown in the figure, the top three measurement points in contribution ranking are extracted to form a new measurement point arrangement scheme. The specific measurement points are selected as follows: Figure 8 and Figure 9 shown.

[0100] Figure 10The three schemes (top, side, and optimized) are shown in terms of prediction deviation. The top and side schemes have prediction deviations close to zero, with relatively concentrated performance and few outliers, resulting in relatively stable overall results. The optimized scheme, on the other hand, has a slightly positive prediction deviation, a more dispersed distribution, and the presence of large negative outliers, indicating unstable predictions in some cases. However, the prediction deviation remains within 0.1 m. Overall, by ranking the contribution of measurement points, prediction accuracy is effectively guaranteed while significantly reducing the number of measurement points.

[0101] Next, the GWO algorithm is used to optimize the GPR model. The specific process is as follows Figure 11 As shown in the figure, data preprocessing is performed, including loading, shuffling, and splitting the dataset (80% as a training set and 20% as a test set), as well as normalization. Next, the training data is used to perform initial GPR model training. The GPR model uses kernel functions (such as a squared exponential kernel) and basis functions (such as a linear function) to establish the relationship between input and output, and continuously updates hyperparameters based on error calculations. The GWO algorithm plays a key role in this process. It simulates the hunting behavior of gray wolves to initialize multiple candidate solutions (gray wolf populations), each representing a set of GPR hyperparameters. The algorithm calculates the fitness of each candidate solution (usually measured by model error) and selects the optimal gray wolf (Alpha, Beta, and Delta) based on their fitness ranking. Other gray wolves then update their positions based on the positions of these three optimal individuals, approaching the global optimal solution. This process is repeated until a termination criterion is met (such as reaching a maximum number of iterations or the error falling below a certain threshold), ultimately outputting the optimal hyperparameter combination. Using these optimized parameters, the GPR model was refitted, predictions were made on the training and test sets, and the prediction results were denormalized. Finally, error analysis was performed to evaluate the model's performance using metrics such as mean squared error and mean absolute error, thereby verifying the effectiveness of the GWO-optimized GPR model. The overall process efficiently integrates data preprocessing, model training, optimization, and performance evaluation, significantly improving the predictive capabilities of the GPR model.

[0102] Figure 12This figure shows the variation of the root mean square error (RMSE) with the number of iterations for the Grey Wolf Optimizer (GWO) algorithm in optimizing the parameters of a Gaussian process regression (GPR) model. As can be seen, the RMSE changes little in the first few iterations, exhibiting a relatively stable trend. This indicates that parameter adjustments in the early optimization stages have limited improvement in model error. As the number of iterations increases, the RMSE gradually decreases, with significant step-like decreases occurring at multiple stages, indicating that GWO is continuously finding better parameter combinations, thereby reducing the model's prediction error. Ultimately, the RMSE stabilizes after approximately the 60th iteration, approaching 3.8894655×10⁻³. This indicates that GWO has essentially converged to the optimal solution or a local optimum, and further iterations are no longer significantly beneficial.

[0103] Figure 13 The relative error performance of a standard Gaussian process regression (GPR) model and a Gaussian process regression model with hyperparameters adjusted using the Gray Wolf Optimization (GWO) optimization algorithm (GWO-GPR) on test samples was compared. The GWO-GPR model (orange curve) exhibited lower relative error on most test samples, demonstrating a significant improvement in overall prediction accuracy after the optimization. This demonstrates that the Gray Wolf Optimization algorithm effectively reduces prediction error when selecting hyperparameters for the GPR model, enabling the model to better adapt to the characteristics and trends of the data. However, the GWO-GPR curve exhibits high error spikes at individual sample points (such as around numbers 20 and 100). This is likely due to the unique characteristics of these specific samples, resulting in the optimized model's less stable fit at these points than the unoptimized GPR model. These error spikes may be due to local optima or the model's sensitivity to noise. Overall, the GWO-GPR curve is smoother than the GPR model and exhibits lower error values ​​across the board. This indicates that the optimized model not only improves overall prediction performance but also effectively reduces prediction bias for most samples, although there is still room for improvement at a few extreme points.

[0104] Figure 14This figure shows a comparison of prediction results on the test set for the true value, standard Gaussian process regression, and Gaussian process regression optimized by Gray Wolf. The vertical axis represents the output value, and the horizontal axis represents the test sample number. Overall, the prediction curves of GPR and GWO-GPR closely follow the true value, indicating that both models are relatively accurate in overall prediction. However, the orange line of GWO-GPR is closer to the true value curve for most test samples, demonstrating higher prediction accuracy. In particular, in certain areas with large fluctuations (such as sample numbers around 20 and 60), GWO-GPR better captures the changing trend of the true value. This indicates that the GPR model optimized by Gray Wolf has achieved better results in hyperparameter tuning, further improving its fit to the test set data and prediction accuracy. Overall, GWO-GPR demonstrates more stable and accurate performance than standard GPR.

[0105] Figure 15 The four error metrics of standard Gaussian process regression (GPR) and Gaussian process regression tuned by Grey Wolf Optimization (GWO-GPR) on the test set are compared: mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R 2 As can be seen from the figure, GWO-GPR outperforms GPR (brown columns) in MAE, RMSE, and MAPE, showing lower error values. This shows that after the Gray Wolf optimization, the GWO-GPR model predicts the test data more accurately. In particular, the improvement in RMSE is the most significant, which further verifies the effect of optimization on improving model accuracy. At the same time, in the determination coefficient R 2 In terms of indicators, the performance of GWO-GPR is very close to that of GPR. 2 The value is close to 1, indicating that both models have a good fit, but GWO-GPR still has a slight advantage. Overall, GWO-GPR shows better comprehensive prediction performance than GPR and more accurately captures the changing trend of the data.

[0106] The above are all preferred embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. Therefore, any equivalent changes made based on the structure, shape, and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for locating mobile pollution sources in a confined space based on Gaussian process regression, characterized by: The following steps are involved: Step 1: Arrange multiple groups of temperature sensors in the confined space, and the multiple groups of temperature sensors are used to capture temperature distribution change data in the confined space; Step 2: The data processing center receives temperature data from multiple sets of temperature sensors, deploys a Gaussian process regression model, and inputs the temperature data from the multiple sets of temperature sensors into the trained Gaussian process regression model for training. The Gaussian process regression model predicts the location of the mobile pollution source in the confined space based on the temperature data from the multiple sets of temperature sensors. Step 3: Use the minimum redundancy maximum correlation algorithm to optimize the measurement points. By evaluating the contribution of each measurement point to the heat source location and sorting them based on the contribution, the measurement points with contributions below the set threshold are gradually eliminated. In step 3, the minimum redundancy maximum correlation algorithm treats each attribute as a discrete random variable and uses mutual information to measure the similarity between two attributes. The mutual information between two attributes is used to measure the similarity between two attributes X and Y. The mutual information I(X,Y) is calculated as follows: Where p(x,y) is defined as the joint probability distribution function of random variables X and Y, while p(x) and p(y) represent the marginal probability distribution functions of random variables X and Y respectively; Each attribute f i Defined as a vector consisting of N features (f i =f i1 ,f i2 ,···f iN ), attribute f i Considered as an example of a discrete co-occurrence variable, the mutual information between features i and j is expressed as I(F i ,F j ), considering feature x and regression target c, the calculation of mutual information I(x,c) shows that the larger I(x,c), the stronger the correlation between x and c. First, a subset S consisting of m features with the largest mutual information with c is identified from all features. The formula is as follows: In set S, the redundancy of set S is calculated as follows: Finding the optimal set S considers all 2|Ω| combinations, where Ω is the entire feature set; in contrast, the mRMR algorithm sorts the features via a forward addition scheme, which requires O(|Ω|·|S|) computations and uses the mutual information quotient MIQ value: Sort all features in Ω and use the mRMR algorithm to return the index idx of the features sorted by importance. Use a heuristic algorithm to quantify the importance of the features and return a score value. The feature with a large score value indicates that its corresponding predictor variable is important.

2. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 1, characterized in that: In step 1, multiple groups of temperature sensors are arranged at equal intervals on the top and sides of the confined space.

3. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 1, characterized in that: The Gaussian process regression model is optimized using the Grey Wolf Optimization algorithm.

4. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 3, characterized in that: The Gray Wolf Optimization Algorithm to optimize the Gaussian Process Regression model includes the following steps: Step a, preprocessing the temperature data; Step b: Initially train the Gaussian process regression model using the training data, wherein the Gaussian process regression model establishes the relationship between input and output through kernel functions and basis functions, and continuously updates hyperparameters based on error calculations. This process is repeated until the termination condition is met, and the optimal hyperparameter combination is finally output. The Gaussian process regression model is refitted using the optimal hyperparameter combination, predictions are made on the training set and test set, and the prediction results are denormalized; In step c, the mean square error and mean absolute error indicators are calculated through error analysis to evaluate the performance of the model and verify the effectiveness of the Gaussian process regression model optimized by the gray wolf optimization algorithm.

5. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 4, characterized in that: In step b, the termination condition is that the maximum number of iterations is reached or the error is lower than the set threshold.

6. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 5, characterized in that: A decrease in the feature importance score indicates that the feature's contribution to the model decreases and its influence on the model's predictive ability weakens, and the confidence also decreases.

7. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 6, characterized in that: The measurement point arrangement schemes are ranked by their contribution, and the top three measurement points are extracted to form a new measurement point arrangement scheme. The stability of the new measurement point arrangement scheme is evaluated to obtain the measurement point arrangement scheme with the highest stability.

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