Method for positioning mobile pollution source in restricted space based on Gaussian process regression

Abstract

The invention discloses a method for positioning a mobile pollution source in a confined space based on Gaussian process regression, relates to the technical field of positioning of the mobile pollution source in the confined space, and realizes high-precision positioning of a mobile heat source in a complex confined space environment by adopting a Gaussian process regression algorithm. By utilizing the advantages of the Gaussian process regression algorithm, the accuracy and the stability of positioning can be kept even under the condition that data noise is relatively large or a heat source moving path is complex; according to the method, the minimum redundancy and maximum correlation algorithm is combined, so that the number of required measuring points is effectively reduced, and meanwhile, the positioning precision is ensured. The measurement point optimization not only reduces the deployment and maintenance cost of the system, but also improves the data processing efficiency, so that the method has remarkable cost-benefit advantages in application scenarios with resource limitation.

Description

Technical Field

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

[0002] In typical confined spaces such as factory conveyor belts, cargo holds of roll-on / roll-off ships, underground mines, subways and highway tunnels, once a high-temperature mobile heat source appears, it will cause damage to the enclosure structure of the confined space and the property and safety of personnel. In this special scenario, the mobile heat source will pose a great threat to the safety of the confined space maintenance structure and related personnel. In addition, the interior of these confined spaces may contain electronic equipment, lighting and other infrastructure, which are particularly vulnerable to high temperature damage, which further increases the risk of damage to the structural integrity and personnel safety of these typical confined spaces. Therefore, it is crucial to quickly and accurately detect heat sources in these confined spaces. For confined space scenarios where high-temperature mobile heat sources are moving.

[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 seriously interfere with visual fire recognition. In addition, traditional sensors such as smoke alarms, temperature alarms, and infrared alarms can provide alarm functions, but have inherent limitations. First, the response triggered by the sensor requires 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 also prone to false alarms due to unexpected circumstances. In addition, the installation and maintenance costs of using fiber optic sensors in long tunnels are huge, hindering their practical application. Therefore, it is crucial to develop a heat source localization method that does not rely on 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, arranging multiple groups of temperature sensors in the confined space, wherein 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 value data of multiple groups of temperature sensors, deploys a Gaussian process regression model, inputs the temperature value data of multiple groups of temperature sensors into the trained Gaussian process regression model for training, and the Gaussian process regression model predicts the position of the mobile pollution source in the confined space based on the temperature value data of multiple groups of temperature sensors;

[0008] Step 3: Use the minimum redundancy maximum correlation algorithm 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] By adopting the above technical scheme, first of all, the basis of this technical scheme is to collect temperature data during the movement of high-temperature heat sources in confined spaces. To this end, a series of temperature sensors need to be arranged on the top and sides of the confined space, which can capture the temperature distribution changes in the space in real time. During the movement of the heat source, the temperature data collected by the sensor will be transmitted to the data processing center in real time as the basis for subsequent training of the positioning algorithm. Subsequently, the collected temperature data is input into the Gaussian process regression model for training. Gaussian process regression is a powerful nonlinear regression tool that can predict the temperature value at any position and give an estimate of the uncertainty of the prediction by modeling the probability of the data. This method can not only handle the noise in the data, but also adapt to the nonlinear characteristics of the data, thereby achieving accurate prediction of the position of the mobile heat source. By training and optimizing the model, the accuracy and reliability of heat source positioning can be continuously improved. In order to further improve the positioning efficiency and reduce the computational cost, this scheme uses the minimum redundancy maximum correlation algorithm to optimize the measuring points. The algorithm evaluates the contribution of each measuring point to the heat source positioning and sorts them accordingly, thereby identifying the measuring points that have the greatest impact on the positioning results. By gradually eliminating measurement points with lower contributions, the number of measurement points required 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 the minimum redundancy maximum correlation algorithm optimization, this solution will focus on how to achieve the best balance between the number of measurement points and prediction accuracy. By evaluating the positioning accuracy under different numbers of measurement points, an ideal measurement point configuration scheme can be determined, which can minimize the number of measurement points while ensuring sufficiently high positioning accuracy. In addition, this scheme also takes into account various challenges that may be encountered in practical applications, such as high-temperature mobile heat sources, sensor noise, etc., so corresponding fault-tolerant mechanisms are introduced in the algorithm design to improve the robustness of the system.

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

[0013] Optionally, the Gray Wolf Optimization algorithm is used to optimize the Gaussian process regression model including the following steps:

[0014] Step a, preprocessing the temperature data;

[0015] Step b, using the training data to perform initial Gaussian process regression model training, 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 calculation, and this process is repeated until the termination condition is met, and finally the optimal hyperparameter combination is output, and the Gaussian process regression model is refitted using the optimal hyperparameter combination, and the training set and test set are predicted, and the prediction results are denormalized;

[0016] Step c, calculate the mean square error and mean absolute error indicators through error analysis, 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] By adopting the above technical solution, first, the data is preprocessed, including loading data, shuffling and splitting the data set (80% as a training set and 20% as a test set), and normalizing the data. Next, the training data is used for initial GPR model training, in which the GPR model establishes the relationship between input and output through kernel functions (such as square exponential kernels) and basis functions (such as linear functions), 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, and each solution represents a set of GPR hyperparameters. The algorithm calculates the fitness of each candidate solution (usually measured by the model error) and selects the optimal Alpha, Beta and Delta gray wolves according to the fitness ranking. Other gray wolves update their positions according to the positions of these three optimal individuals to approach the global optimal solution. This process is repeated until the termination condition is met (such as reaching the maximum number of iterations or the error is lower than a certain threshold), and finally outputs the optimal hyperparameter combination. Using these optimized parameters, the GPR model is refitted to predict the training set and test set, and the prediction results are denormalized. Finally, the performance of the model is evaluated by calculating the mean square error, mean absolute error and other indicators through error analysis, thereby verifying the effectiveness of the GPR model optimized by GWO. The overall process efficiently integrates data preprocessing, model training, optimization and performance evaluation steps, significantly improving the prediction ability of the GPR model.

[0019] Optionally, in step 3, the minimum redundancy maximum correlation algorithm regards 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] Among them, 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 denoted 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 search for the optimal set S considers 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. Features with large score values ​​indicate that their corresponding predictor variables are important.

[0029] Optional, A decrease in the feature importance score indicates a decrease in the feature's contribution to the model and its impact on the model's predictive power. The influence of the data is weakened, and the confidence level decreases accordingly. .

[0030] Optionally, the measurement point arrangement schemes are sorted by measurement point contribution, the top three measurement points in the contribution ranking 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 adopting the above technical solutions, the basis of the minimum redundancy-maximum relevance (mRMR) method is to recognize 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, which means that while avoiding redundancy, the variables with the maximum relevance are incrementally selected, which realizes the determination of the optimal measurement point plan and provides more effective data for the subsequent positioning of mobile pollution sources in confined spaces.

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

[0033] The present invention can provide a method for locating mobile pollution sources in a confined space based on Gaussian process regression. By adopting the Gaussian process regression algorithm, the present invention realizes high-precision positioning of mobile heat sources in a complex confined space environment. By taking advantage 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, which is significantly better than the traditional positioning method;

[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 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;

[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 case of partial sensor failure or poor data quality, it can maintain high positioning accuracy, ensuring the stable operation and high reliability of the system;

[0036] The maintainability and scalability of the system are fully considered during the design. The modular algorithm design and flexible measurement point configuration not only facilitates on-site installation and daily maintenance, but also facilitates future technology upgrades and function expansions, allowing the system to adapt to rapidly changing technical environments and application requirements. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0038] Figure 2 It 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 diagram of the structure of a mobile heat source in a specific embodiment of the present invention;

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

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

[0042] Figure 6 1 is a schematic diagram of the ranking of the contribution of the top measuring point scheme in a specific embodiment of the present invention;

[0043] Figure 7 1 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 It is a schematic diagram of the arrangement of the top three measuring points in the order of top contribution in a specific embodiment of the present invention;

[0045] Fig. 9 It is a 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] Fig.10 1 is a schematic diagram showing a comparison of prediction accuracies under different measurement point schemes in a specific embodiment of the present invention;

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

[0048] Fig.12 Schematic diagram of the iteration curve of the GWO algorithm in a specific embodiment of the present invention;

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

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

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

[0052] The present invention is further described in detail below in conjunction with 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 Figure 1-Figure 15 , a method for locating mobile pollution sources in a restricted space based on Gaussian process regression includes the following steps:

[0055] Step 1, arranging multiple groups of temperature sensors in the confined space, wherein 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 value data of multiple groups of temperature sensors, deploys a Gaussian process regression model, inputs the temperature value data of multiple groups of temperature sensors into the trained Gaussian process regression model for training, and the Gaussian process regression model predicts the position of the mobile pollution source in the confined space based on the temperature value data of multiple groups of temperature sensors;

[0057] Step 3: Use the minimum redundancy maximum correlation algorithm 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 of all, the basis of this technical solution is to collect temperature data during the movement of high-temperature heat sources in confined spaces. To this end, a series of temperature sensors need to be arranged on the top and sides of the confined space, which can capture the temperature distribution changes in the space in real time. During the movement of the heat source, the temperature data collected by the sensor will be transmitted to the data processing center in real time as the basis for subsequent training of the positioning algorithm. Subsequently, the collected temperature data is input into the Gaussian process regression model for training. Gaussian process regression is a powerful nonlinear regression tool that can predict the temperature value at any position and give an estimate of the uncertainty of the prediction by modeling the probability of the data. This method can not only handle the noise in the data, but also adapt to the nonlinear characteristics of the data, thereby achieving accurate prediction of the position of the mobile heat source. By training and optimizing the model, the accuracy and reliability of heat source positioning can be continuously improved. In order to further improve the positioning efficiency and reduce the computational cost, this solution uses the minimum redundancy maximum correlation algorithm to optimize the measuring points. The algorithm evaluates the contribution of each measuring point to the positioning of the heat source and sorts them accordingly, thereby identifying the measuring points that have the greatest impact on the positioning results. By gradually eliminating measurement points with lower contributions, the number of measurement points required 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 the minimum redundancy maximum correlation algorithm optimization, this solution will focus on how to achieve the best balance between the number of measurement points and prediction accuracy. By evaluating the positioning accuracy under different numbers of measurement points, an ideal measurement point configuration scheme can be determined, which can minimize the number of measurement points while ensuring sufficiently high positioning accuracy. In addition, this scheme also takes into account various challenges that may be encountered in practical applications, such as high-temperature mobile heat sources, sensor noise, etc., so corresponding fault-tolerant mechanisms are introduced in the algorithm design to improve the robustness of the system.

[0061] The Gaussian process regression model is optimized by 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, using the training data to perform initial Gaussian process regression model training, 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 calculation, and this process is repeated until the termination condition is met, and finally the optimal hyperparameter combination is output, and the Gaussian process regression model is refitted using the optimal hyperparameter combination, and the training set and test set are predicted, and the prediction results are denormalized;

[0065] Step c, calculate the mean square error and mean absolute error indicators through error analysis, 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, the data is preprocessed, including loading data, shuffling and splitting the data set (80% as training set and 20% as test set), and normalizing the data. Next, the training data is used for initial GPR model training, in which the GPR model establishes the relationship between input and output through kernel functions (such as square exponential kernels) and basis functions (such as linear functions), 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, and each solution represents a set of GPR hyperparameters. The algorithm calculates the fitness of each candidate solution (usually measured by model error) and selects the optimal Alpha, Beta and Delta gray wolves according to the fitness ranking. Other gray wolves update their positions according to the positions of these three optimal individuals to approach the global optimal solution. This process is repeated until the termination condition is met (such as reaching the maximum number of iterations or the error is lower than a certain threshold), and finally outputs the optimal hyperparameter combination. Using these optimized parameters, the GPR model is refitted to predict the training set and test set, and the prediction results are denormalized. Finally, the performance of the model is evaluated by calculating the mean square error, mean absolute error and other indicators through error analysis, thereby verifying the effectiveness of the GPR model optimized by GWO. The overall process efficiently integrates data preprocessing, model training, optimization and performance evaluation steps, significantly improving the prediction ability of the GPR model.

[0068] In step 3, the minimum redundancy maximum correlation algorithm regards 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 calculation formula of mutual information I(X,Y) is as follows:

[0069]

[0070] Among them, 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 denoted 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 through 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. Features with large score values ​​indicate that their corresponding predictor variables are 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 according to 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 basis of the minimum redundancy-maximum relevance (mRMR) method is to recognize 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, which means that while avoiding redundancy, the variables with the maximum relevance are incrementally selected, which realizes the determination of the optimal measurement point plan and provides more effective data for the subsequent positioning of mobile pollution sources in confined spaces.

[0081] The following specific embodiments are used 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, so that the mobile heat source can be carried on a trolley and move linearly inside the experimental cabin by towing 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, the length of the air inlet is 0.046m, and the radius is 0.03m. The high-speed hair dryer has 2 wind temperature levels and 2 wind speed levels. The specific values ​​are shown in Table 1:

[0085] Table 1 Parameters of mobile heat source gears

[0086]

[0087] Use 40 K-type thermocouples to arrange the measuring points according to the following measuring point arrangement diagram, and connect to 3 TSI Fluke 2638A to record the data. The error of the K-type thermocouple is ±0.5℃, and the recording interval is 1s.

[0088] Tips on top surface measurement point arrangement Figure 4 , side measurement point arrangement suggestion 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 at the exit of the experimental chamber to make uniform linear motion. 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 and tested the heat sources under four gear combinations at 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 similarity between two attributes X and Y is measured using their mutual information, and 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 denoted 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 consisting 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 the features in Ω and returns the index (idx) of the features sorted by importance using the mRMR algorithm. Therefore, the computational cost is O(|Ω|2). This function quantifies the importance of the features using a heuristic algorithm and returns a score. Features with large scores indicate that their corresponding predictors are important. In addition, a decrease in the feature importance score indicates the confidence of the 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 plan. The specific measurement point selection is as follows: Figure 8 and Fig. 9 shown.

[0100] Fig.10The performance of three schemes (top scheme, side scheme and optimization scheme) in prediction deviation is shown. The prediction deviation of the top scheme and the side scheme is close to zero, the performance is relatively concentrated and there are fewer outliers, and the overall effect is relatively stable. The prediction deviation of the optimization scheme is slightly positive, the distribution is more dispersed, and there are large negative outliers, indicating that its prediction is unstable in some cases, but the prediction deviation is still within the range of 0.1m. Overall, by sorting the contribution of the measuring points, the accuracy of the prediction is effectively guaranteed under the premise of greatly reducing the number of measuring points.

[0101] Next, the GWO algorithm is used to optimize the GPR model. The specific process is as follows Fig.11 As shown. First, the data is preprocessed, including loading data, shuffling and splitting the data set (80% as training set, 20% as test set), and normalizing the data. Next, the training data is used for initial GPR model training, in which the GPR model establishes the relationship between input and output through kernel functions (such as square exponential kernels) and basis functions (such as linear functions), 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, and each solution represents a set of GPR hyperparameters. The algorithm calculates the fitness of each candidate solution (usually measured by model error) and selects the optimal Alpha, Beta and Delta gray wolves according to the fitness ranking. Other gray wolves update their positions according to the positions of these three optimal individuals to approach the global optimal solution. This process is repeated until the termination condition is met (such as reaching the maximum number of iterations or the error is lower than a certain threshold), and finally outputs the optimal hyperparameter combination. Using these optimized parameters, the GPR model is refitted to predict the training set and test set, and the prediction results are denormalized. Finally, the performance of the model is evaluated by calculating the mean square error, mean absolute error and other indicators through error analysis, thereby verifying the effectiveness of the GPR model optimized by GWO. The overall process efficiently integrates data preprocessing, model training, optimization and performance evaluation steps, significantly improving the prediction ability of the GPR model.

[0102] Fig.12The variation of the root mean square error (RMSE) with the number of iterations in the process of optimizing the parameters of the Gaussian process regression (GPR) model by the Grey Wolf Optimizer (GWO) is shown. As can be seen from the figure, the RMSE changes little in the first few iterations, showing a relatively stable trend, which indicates that the improvement of the model error by parameter adjustment in the early optimization stage is relatively limited. As the number of iterations increases, the RMSE gradually decreases, and a significant step-like change occurs in multiple stages, indicating that GWO is constantly finding a better combination of parameters, thereby reducing the prediction error of the model. Finally, the RMSE stabilizes after about the 60th iteration, close to 3.8894655×10-3, which indicates that GWO has basically converged to the optimal solution or the local optimal solution, and the improvement brought by further iterations is no longer obvious.

[0103] Fig.13 The relative error performance of the standard Gaussian process regression (GPR) and the Gaussian process regression (GWO-GPR) after hyperparameter adjustment by Gray Wolf Optimization (GWO) on the test samples is compared. GWO-GPR (orange curve) shows lower relative errors on most test samples, showing a significant improvement in the overall prediction accuracy of the optimized model. This shows that the Gray Wolf Optimization algorithm can effectively reduce the prediction error when selecting the hyperparameters of the GPR model, making the model better adapt to the characteristics and changing trends of the data. However, at individual sample points (such as near numbers 20 and 100), the GWO-GPR curve has higher error spikes, which may be due to the particularity of these specific samples, resulting in the optimized model fitting these points less stably than the unoptimized GPR. These error spikes may be due to local optimal phenomena or the sensitivity of the model to noise. Overall, the GWO-GPR curve is smoother than GPR and most of the error values ​​are lower, which shows that the optimized model not only improves the overall prediction performance, but also more effectively reduces the prediction bias of most samples, although there is still room for improvement at a few extreme points.

[0104] Fig.14The comparison of the prediction results of the true value, standard Gaussian process regression and Gaussian process regression optimized by Gray Wolf on the test set is shown. The vertical axis is the output value and the horizontal axis is 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 in most test samples, showing higher prediction accuracy, especially in some areas with large fluctuations (such as sample numbers around 20 and 60), GWO-GPR better captures the changing trend of the true value. This shows that the GPR model after Gray Wolf optimization has achieved better results in hyperparameter adjustment, thereby further improving the fitting ability and prediction accuracy of the test set data. Overall, GWO-GPR shows more stable and accurate performance than standard GPR.

[0105] Fig.15 Four error metrics on the test set are compared between the standard Gaussian process regression (GPR) and the Gaussian process regression adjusted by Grey Wolf Optimization (GWO-GPR): 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 is better than GPR (brown column) in MAE, RMSE and MAPE indicators, showing lower error values, which 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 good fit, but GWO-GPR is still slightly superior. Overall, GWO-GPR shows better comprehensive prediction performance than GPR and captures the changing trend of the data more accurately.

[0106] The above are all preferred embodiments of the present invention, and are not intended to limit the protection scope 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 protection scope 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, arranging multiple groups of temperature sensors in the confined space, wherein 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 value data of multiple groups of temperature sensors, deploys a Gaussian process regression model, inputs the temperature value data of multiple groups of temperature sensors into the trained Gaussian process regression model for training, and the Gaussian process regression model predicts the position of the mobile pollution source in the confined space based on the temperature value data of multiple groups of temperature sensors; Step 3: Use the minimum redundancy maximum correlation algorithm 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.

2. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 1 is 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 is characterized in that: The Gaussian process regression model is optimized by 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 is 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, using the training data to perform initial Gaussian process regression model training, 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 calculation, and this process is repeated until the termination condition is met, and finally the optimal hyperparameter combination is output, and the Gaussian process regression model is refitted using the optimal hyperparameter combination, and the training set and test set are predicted, and the prediction results are denormalized; Step c, calculate the mean square error and mean absolute error indicators through error analysis, 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 is 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 is characterized in that: In step 3, the minimum redundancy maximum correlation algorithm regards 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 calculation formula of mutual information I(X,Y) is as follows: Among them, 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.

7. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 6 is characterized in that: 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 denoted 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:

8. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 7 is characterized in that: 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 through 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. Features with large score values ​​indicate that their corresponding predictor variables are important.

9. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 8 is 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.

10. The method for locating mobile pollution sources in a confined space based on Gaussian process regression according to claim 9, characterized in that: The measurement point arrangement schemes are ranked according to 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.

Images