A method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron

Abstract

This application discloses a method for deducing the overpressure process of a gas explosion shock wave based on an optimized multilayer perceptron, comprising: obtaining initial parameters and dividing the initial parameters into a training set and a test set; constructing a multilayer perceptron regression model based on the training set and the test set; optimizing the learning rate and regularization factor of the initial parameters of the multilayer perceptron regression model using an improved particle swarm algorithm to obtain a global optimal solution; using a self-help algorithm to output the results of the multilayer perceptron regression model to obtain a confidence interval for the deduced overpressure value; inputting the global optimal solution into the multilayer perceptron regression model to perform overpressure deduction analysis within the obtained confidence interval. This application adaptively optimizes the key hyperparameters of the multilayer perceptron regression model based on data characteristics, improves the model convergence efficiency and accuracy, and provides technical support for being able to grasp the explosion radiation range and intensity in a short period of time after a gas explosion accident occurs.

Description

Technical Field

[0001] The present application relates to a method for deducing a gas explosion shock wave overpressure process based on an optimized multi-layer perceptron, and belongs to the technical field of gas explosion process deduction. Background Art

[0002] Gas explosions are common industrial accidents, often causing incalculable casualties and property losses. Therefore, research on gas explosion process simulation methods is of great practical significance. This method aims to analyze the pressure evolution of the explosion shock wave at the accident site and simulate the location of the potential explosion to accurately determine the explosion radiation range, thereby providing effective support for the formulation of scientific emergency response plans. In recent years, with the continuous maturity of computer technology and the rapid development of intelligent coal mines, various algorithms for disaster prediction, early warning, and simulation analysis have been widely applied in daily coal mine safety production. Numerous machine learning algorithms, such as neural networks, have gradually become more adaptable to data through continuous optimization and iteration, and can explain many nonlinear and complex problems in key scientific issues. However, gas explosion process simulation methods are complex. Existing machine learning algorithms require the establishment of mathematical models to invert the gas explosion process, resulting in a relatively slow acquisition of calculation results. With the development of intelligent coal mines, higher requirements are placed on the ability to quickly obtain and analyze disaster information. How to quickly deduce the explosion process before and after the explosion and provide auxiliary decision-making information for early prevention and rapid formulation of scientific and effective rescue plans after the disaster is a difficult problem that urgently needs to be overcome. Summary of the Invention

[0003] In view of this, this application provides a method for deducing the overpressure process of gas explosion shock waves based on an optimized multi-layer perceptron, which is used to solve the problem in the above-mentioned prior art that the machine learning algorithm model needs to invert the gas explosion process by establishing a mathematical model, resulting in a relatively delayed acquisition of calculation results. The specific solution is as follows:

[0004] A method for deducing a gas explosion shock wave overpressure process based on an optimized multi-layer perceptron comprises the following steps:

[0005] Step 1: Get the initial parameters and divide them into training set and test set;

[0006] Step 2: Build a multi-layer perceptron regression model (MLPRegressor) based on the training set and test set;

[0007] Step 3: Optimize the learning rate and regularization factor (Alpha) of the initial parameters input to the multilayer perceptron regression model (MLPRegressor) through the improved particle swarm optimization (POS) to obtain the global optimal solution;

[0008] Step 4: Use the bootstrap algorithm (BootStrap) to output the results of the multi-layer perceptron regression model (MLPRegressor) to obtain the confidence interval of the deduced overpressure value;

[0009] Step 5: Input the global optimal solution into the multi-layer perceptron regression model (MLPRegressor) to perform overpressure deduction analysis within the obtained confidence interval.

[0010] Preferably, the activation function in the multilayer perceptron regression model is a tanh function;

[0011] The error function uses the mean absolute error (MAE), and the error calculation is done using a back-propagation algorithm.

[0012] Preferably, in the multilayer perceptron regression model, all nodes except the input node are neurons with a nonlinear activation function;

[0013] The initial parameters include: explosion source location coordinates, roadway parameters and explosion initial pressure.

[0014] Preferably, the improved particle swarm optimization algorithm (POS) optimizes the learning rate and regularization factor (Alpha) of the initial parameters input to the multilayer perceptron regression model (MLPRegressor) as follows:

[0015] First, each particle is randomly initialized;

[0016] Subsequently, each particle is evaluated and the global optimal particle is obtained;

[0017] Finally, determine whether the iteration meets the end condition;

[0018] If yes, then end; if no, continue to iterate until the end condition is met and the process ends;

[0019] The value corresponding to when the end condition is met is the global optimal solution.

[0020] Preferably, the iterative process includes the following steps: updating the speed and position of each particle, evaluating the function fitness of each particle, updating the historical optimal position of each particle, and updating the global optimal position of the swarm.

[0021] Preferably, the process of determining whether the iteration meets the end condition is:

[0022] (1) Data preparation: Obtain preprocessed standard data to ensure that the data has been preprocessed; preprocessing includes normalizing or standardizing the feature data to ensure that the model is not sensitive to the data range;

[0023] (2) Import necessary libraries: Import the Scikit-learn library, especially the neural_network module, which contains the MLPRegressor class;

[0024] (3) Define the multilayer perceptron regression model (MLPRegressor): Create an MLPRegressor object and specify the hyperparameters of the multilayer perceptron regression model;

[0025] (4) Train the multilayer perceptron regression model (MLPRegressor): Use the training set (features and target values) to fit the multilayer perceptron regression model;

[0026] (5) Evaluate the MLPRegressor model: Use the test set to evaluate the performance of the MLPRegressor model to select the best hyperparameter combination;

[0027] (6) Prediction of Multilayer Perceptron Regression Model (MLPRegressor): Use the trained multilayer perceptron regression model to predict new data, that is, input the features of the new data into the multilayer perceptron regression model to obtain the prediction results;

[0028] (7) Multilayer Perceptron Regressor (MLPRegressor) optimization: Determine whether the performance of the multilayer perceptron regression model (MLPRegressor) is ideal based on the prediction results. If the performance of the multilayer perceptron regression model (MLPRegressor) is not ideal, try adjusting hyperparameters, increasing the number of hidden layers or neurons, trying different activation functions or optimizers, etc.

[0029] (8) Saving and loading the multilayer perceptron regression model (MLPRegressor). Save the trained multilayer perceptron regression model (MLPRegressor) to a file for subsequent use or deployment. Use libraries such as joblib or pickle to save and load the model.

[0030] Preferably, the improvement process of the particle swarm optimization algorithm (POS) is as follows:

[0031] (1) Analyze the problem: First, analyze the problem to be solved to determine whether there is a risk of premature convergence or falling into a local optimal solution. This can be done by observing the performance of the algorithm in previous iterations;

[0032] (2) Determine the improvement goal: Based on the results of the problem analysis, determine the goal of improving the inertia weight model, which may include improving the global search ability of the algorithm, avoiding premature convergence, or improving the quality of the solution;

[0033] (3) Adopting adaptive inertia weight algorithm to improve particle swarm optimization (POS): According to the fitness of particles or the topological structure of search space, the inertia weight is dynamically adjusted to balance the global search and local search capabilities;

[0034] (4) Implementing the improvement method: Based on the selected improvement method, modify the particle swarm optimization (PSO). This process includes: modifying the particle velocity update equation, adding new parameters, or using different strategies to select the inertia weight value;

[0035] (5) Testing and verification: Use the modified PSO to solve a series of test problems and compare the test results with those of the original algorithm to test and verify the modified PSO. The evaluation indicators of the test results may include convergence speed, solution quality and robustness.

[0036] (6) Based on the test results, further adjust and optimize the parameters or strategies of the improved method in the adaptive inertia weight model to achieve the global optimal solution. This may be an iterative process that requires multiple attempts based on the specific problem and algorithm performance.

[0037] Preferably, in the optimization of the adaptive inertia weight model, after the inertia factor ω is adaptively optimized, the inertia factor ω is associated with the number of iterations and the fitness of each particle:

[0038] 1) Assuming that the problem of finding the minimum fitness value is solved, the fitness expression is formula (1):

[0039]

[0040] 2) Assuming that the problem is to find the maximum fitness, the fitness expression is formula (2):

[0041]

[0042] In formula (1) and formula (2): ω min and ω max is the preset minimum inertia coefficient and maximum inertia coefficient, then the average fitness of all particles at the dth iteration is expressed as formula (3):

[0043]

[0044] The maximum fitness of all particles at the dth iteration It is expressed as formula (4):

[0045]

[0046] Preferably, the deduction and analysis steps are:

[0047] The training is completed to obtain the optimal parameters;

[0048] Input relevant test initial data sets for overpressure simulation analysis;

[0049] At the same time, it is assumed that the deduced initial overpressure value is the maximum value during the explosion process;

[0050] The bootstrap algorithm (BootStrap) is used to estimate the confidence interval of the deduced overpressure value.

[0051] Preferably, the process of obtaining the confidence interval of the deduced overpressure value by the bootstrap algorithm is: The process of obtaining the confidence interval of the deduced overpressure value by the bootstrap algorithm is:

[0052] During the sampling process, the bootstrap algorithm ensures that the probability of each element in the sampling result being drawn is the same. Each time, N elements are drawn and repeated B times to obtain B groups of sample matrices containing N elements. The eigenvalues ​​of each group of samples are calculated to obtain the bootstrap sample probability eigenvalues. Suppose the original sample S is expressed as formula (5):

[0053] S=(S1,S2,S3,…S i ,…,S n ) Formula (5);

[0054] In formula (5): S i is the i-th data of the sample, S n It means there are n elements in total, and B elements are extracted from them, with N data each time. Finally, each sample set P can be expressed as formula (6):

[0055] P=(P1,P2,P3,…P b ,…,P b ) Formula (6);

[0056] In formula (6): P b is the b-th self-service sample set, expressed as formula (7):

[0057] P b =P b (i), i=1,2,…,N Formula (7);

[0058] In formula (7): P b (i) is expressed as P b The i-th element of , so the bootstrap sample set P b The mean The calculation formula is expressed as formula (8):

[0059]

[0060] The bootstrap sample mean It can be expressed as formula (9):

[0061]

[0062] Bootstrap sample variance σ 2 It is expressed as formula (10):

[0063]

[0064] In machine learning, the bootstrap algorithm can be used to solve the confidence interval. By estimating the sample eigenvalues, different confidence intervals can be obtained. Assuming that the bootstrap algorithm is used to obtain the sample parameter estimate, the sample parameter θ is expressed as formula (11):

[0065]

[0066] Arrange them from small to large, and we get formula (12):

[0067]

[0068] Assuming the significance level is α, α∈[0,1], the confidence level is expressed as formula (13):

[0069]

[0070] Let K1 and K2 represent the upper confidence limit and lower confidence limit respectively, see formula (14):

[0071]

[0072] and is the quantile and The estimation of , we can get formula (15):

[0073]

[0074] The final confidence interval is expressed as formula (16):

[0075]

[0076] The beneficial effects of this application include:

[0077] This application uses an improved particle swarm algorithm to optimize the learning rate and regularization factor of the initial parameters input into the multilayer perceptron regression model (MLPRegressor). The appropriate learning rate and regularization factor will enable the algorithm to converge efficiently, increase the robustness of the model, and be more adaptable to data, thereby avoiding overfitting of the model. This can significantly improve the operating efficiency and accuracy of the model. By establishing a correlation between the inertia weight, the number of iterations, and the particle fitness, the key hyperparameters of the multilayer perceptron regression model (MLPRegressor) can be adaptively optimized according to the data characteristics, thereby improving the convergence efficiency and accuracy of the model.

[0078] A self-help algorithm is used to output the results of the multi-layer perceptron regression model (MLPRegressor) to obtain the confidence interval of the deduced overpressure value, and overpressure deduction analysis is performed within the confidence interval to obtain the explosion radiation range and intensity after a gas explosion accident occurs in a coal mine. This application uses an improved particle swarm algorithm to optimize the parameters of the multi-layer perceptron regression model (MLPRegressor), combined with the use of a self-help algorithm to output the results of the multi-layer perceptron regression model (MLPRegressor), to provide certain technical support for being able to grasp the explosion radiation range and intensity in a short time after a gas explosion accident occurs in a coal mine, so that once an accident occurs, the explosion range can be quickly grasped to further judge the degree of underground damage, providing effective support for post-disaster emergency response work. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 This application optimizes the explosion deduction structure diagram of the multi-layer perceptron regression model (MLPRegressor);

[0080] Figure 2 This is a flow chart of the parameter optimization of the self-service algorithm (PSO) in this application;

[0081] Figure 3 is the fitness value corresponding to the global optimal solution of the multilayer perceptron regression model (MLPRegressor);

[0082] Figure 4 This is a diagram of the parameter optimization process of the multilayer perceptron regression model (MLPRegressor);

[0083] Figure 5 This is a visualization diagram of the deduction results of the optimized multilayer perceptron regression model (MLPRegressor) in Example 1;

[0084] Figure 6A comparison chart of the true value, deduced value, and confidence interval of the straight pipe model in Example 1 of the present application;

[0085] Figure 7 Comparison chart of the true value, deduced value and confidence interval of the Chongqing Coal Research Institute pipeline model

[0086] Figure 8 This is a model diagram for the 60° bifurcation pipeline deduction in Example 2;

[0087] Figure 9 This is a schematic diagram of the explosion source location in overpressure deduction in Example 2;

[0088] Figure 10 This is a visualization diagram of the 60° bifurcation pipeline deduction in Example 2. DETAILED DESCRIPTION

[0089] Step 1: Obtain initial parameters and divide them into a training set and a test set in chronological order; in this application, the initial parameters specifically refer to the explosion source location coordinates, roadway parameters, and initial explosion pressure;

[0090] Step 2: Build a multi-layer perceptron regression model (MLPRegressor) based on the training set and test set;

[0091] Step 3: Optimize the learning rate and regularization factor (Alpha) of the initial parameters input to the multilayer perceptron regression model (MLPRegressor) through the improved particle swarm optimization (POS) to obtain the global optimal solution;

[0092] In this application, the purpose of optimizing the learning rate and regularization factor (Alpha) is to: the appropriate learning rate and regularization factor will enable the algorithm to converge efficiently, increase the robustness of the model, and be more adaptable to data, thereby avoiding overfitting of the model and significantly improving the operating efficiency and accuracy of the multilayer perceptron regression model.

[0093] Since the learning rate represents the speed at which information accumulates over time in the algorithm, it is the most critical parameter in the algorithm. A suitable learning rate will enable the algorithm to converge efficiently. The regularization factor (Alpha) is a factor that reduces the overfitting phenomenon of the model. When the parameters in the training set are close to the optimal value, a penalty term will be added to limit the change in the parameters. Selecting a suitable regularization factor (Alpha) can increase the robustness of the model, make it more adaptable to data, and avoid overfitting of the model. Therefore, this application optimizes the learning rate (Learning rate) and regularization factor (Alpha) of the initial parameters through the particle swarm algorithm to avoid overfitting of the multilayer perceptron regression model (MLPRegressor). The specific optimization process is as follows: Figure 2 As shown:

[0094] First, each particle is randomly initialized; then, each particle is evaluated to obtain the global optimum; then, it is determined whether the iteration can reach the end condition. If so, it ends. If not, it repeats the process of updating the speed and position of each particle, evaluating the function fitness of each particle, updating the historical optimal position of each particle, and updating the global optimal position of the group. Finally, the process ends when the judgment result is yes.

[0095] Step 4: Use the bootstrap algorithm (BootStrap) to output the results of the multi-layer perceptron regression model (MLPRegressor) to obtain the confidence interval of the deduced overpressure value;

[0096] Step 5: Input the global optimal solution into the multi-layer perceptron regression model (MLPRegressor) to perform overpressure deduction analysis within the obtained confidence interval. The deduction analysis steps are as follows:

[0097] The training is completed to obtain the optimal parameters;

[0098] Input optimal parameters for overpressure simulation analysis;

[0099] At the same time, it is assumed that the deduced initial overpressure value is the maximum value during the explosion process;

[0100] The confidence interval of the deduced overpressure value is estimated using a bootstrap algorithm.

[0101] It should be noted that:

[0102] In this application:

[0103] The criteria for determining whether an iteration meets the end condition are:

[0104] (1) Data preparation: Obtain preprocessed standard data to ensure that the data has been preprocessed; preprocessing includes normalizing or standardizing the feature data to ensure that the model is not sensitive to the data range;

[0105] (2) Import necessary libraries: Import the Scikit-learn library, especially the neural_network module, which contains the MLPRegressor class;

[0106] (3) Define the multilayer perceptron regression model (MLPRegressor): Create an MLPRegressor object and specify the hyperparameters of the multilayer perceptron regression model (MLPRegressor);

[0107] (4) Train the multilayer perceptron regression model (MLPRegressor): Use the training set (features and target values) to fit the multilayer perceptron regression model (MLPRegressor);

[0108] (5) Evaluate the MLPRegressor model: Use the test set to evaluate the performance of the MLPRegressor model to select the best hyperparameter combination;

[0109] (6) Prediction of Multilayer Perceptron Regression Model (MLPRegressor): Use the trained Multilayer Perceptron Regression Model (MLPRegressor) to predict the new data, that is, input the features of the new data into the Multilayer Perceptron Regression Model (MLPRegressor) to obtain the prediction results;

[0110] (7) Multilayer Perceptron Regressor (MLPRegressor) optimization: Determine whether the performance of the multilayer perceptron regression model (MLPRegressor) is ideal based on the prediction results. If the performance of the multilayer perceptron regression model (MLPRegressor) is not ideal, try adjusting hyperparameters, increasing the number of hidden layers or neurons, trying different activation functions or optimizers, etc.

[0111] (8) Saving and loading the multilayer perceptron regression model (MLPRegressor). Save the trained multilayer perceptron regression model (MLPRegressor) to a file for subsequent use or deployment. Use libraries such as joblib or pickle to save and load the model.

[0112] like Figure 2 The figure shows the optimization flow chart of the particle swarm algorithm (PSO). The improvement process of the particle swarm algorithm (PSO) is as follows:

[0113] (1) Analyze the problem: First, analyze the problem to be solved to determine whether there is a risk of premature convergence or falling into a local optimal solution. This can be done by observing the performance of the algorithm in previous iterations;

[0114] (2) Determine the improvement goal: Based on the results of the problem analysis, determine the goal of improving the inertia weight model, which may include improving the global search ability of the algorithm, avoiding premature convergence, or improving the quality of the solution;

[0115] (3) An adaptive inertia weight model is used to improve the particle swarm optimization (POS): the inertia weight is dynamically adjusted according to the fitness of the particles or the topological structure of the search space to balance the global search and local search capabilities;

[0116] (4) Implementing the improvement method: Based on the selected improvement method, modify the particle swarm optimization (PSO). This process includes: modifying the particle velocity update equation, adding new parameters, or using different strategies to select the inertia weight value;

[0117] (5) Testing and verification: Use the modified PSO to solve a series of test problems and compare the test results with those of the original algorithm to test and verify the modified PSO. The evaluation indicators of the test results may include convergence speed, solution quality and robustness.

[0118] (6) Based on the test results, further adjust and optimize the parameters or strategies of the improved method to achieve the global optimal solution. This may be an iterative process that requires multiple attempts based on the specific problem and algorithm performance.

[0119] In the optimization of the adaptive inertia weight model, after the inertia factor ω is adaptively optimized, the inertia factor ω is associated with the number of iterations and the fitness of each particle:

[0120] 3) Assuming that the problem of finding the minimum fitness value is solved, the fitness expression is formula (1):

[0121]

[0122] 4) Assuming that the problem is to find the maximum fitness, the fitness expression is formula (2):

[0123]

[0124] In formula (1) and formula (2): ω min and ω max is the preset minimum inertia coefficient and maximum inertia coefficient, then the average fitness of all particles at the dth iteration is expressed as formula (3):

[0125]

[0126] The maximum fitness of all particles at the dth iteration It is expressed as formula (4):

[0127]

[0128] In this application, an adaptive inertia weight improvement method is used to improve the particle swarm algorithm (PSO), and the adaptive inertia weight is correlated with the number of iterations and the particle fitness. Furthermore, the purpose of the particle swarm algorithm is to optimize the key hyperparameters of the multilayer perceptron regression model (MLPRegressor), thereby achieving adaptive optimization of the key hyperparameters of the multilayer perceptron regression model (MLPRegressor) according to data characteristics.

[0129] Furthermore, the deduction and analysis steps are:

[0130] The training is completed to obtain the optimal parameters;

[0131] Input relevant test initial data sets for overpressure simulation analysis;

[0132] At the same time, it is assumed that the deduced initial overpressure value is the maximum value during the explosion process;

[0133] The bootstrap algorithm (BootStrap) is used to estimate the confidence interval of the deduced overpressure value.

[0134] Furthermore, the process of obtaining the confidence interval of the deduced overpressure value by the bootstrap algorithm is as follows:

[0135] During the sampling process, the bootstrap algorithm ensures that the probability of each element in the sampling result being drawn is the same. Each time, N elements are drawn and repeated B times to obtain B groups of sample matrices containing N elements. The eigenvalues ​​of each group of samples are calculated to obtain the bootstrap sample probability eigenvalues. Suppose the original sample S is expressed as formula (5):

[0136] S=(S1,S2,S3,…S i ,…,S n ) Formula (5);

[0137] In formula (5): S i is the i-th data of the sample; S n It means there are n elements in total, and B elements are extracted from them, with N data each time. Finally, each sample set P can be expressed as formula (6):

[0138] P=(P1,P2,P3,…P b ,…,P b) Formula (6);

[0139] In formula (6): P b is the b-th self-service sample set, expressed as formula (7):

[0140] P b =P b (i), i=1,2,…,N Formula (7);

[0141] In formula (7): P b (i) is expressed as P b The i-th element of , so the bootstrap sample set P b The mean The calculation formula is expressed as formula (8):

[0142]

[0143] The bootstrap sample mean It can be expressed as formula (9):

[0144]

[0145] Bootstrap sample variance σ 2 It is expressed as formula (10):

[0146]

[0147] In machine learning, the bootstrap algorithm can be used to solve the confidence interval. By estimating the sample eigenvalues, different confidence intervals can be obtained. Assuming that the bootstrap algorithm is used to obtain the sample parameter estimate, the sample parameter θ is expressed as formula (11):

[0148]

[0149] Arrange them from small to large, and we get formula (12):

[0150]

[0151] Assuming the significance level is α, α∈[0,1], the confidence level is expressed as formula (13):

[0152]

[0153] Let K1 and K2 represent the upper confidence limit and lower confidence limit respectively, see formula (14):

[0154]

[0155] and is the quantile and The estimation of , we can get formula (15):

[0156]

[0157] The final confidence interval is expressed as formula (16):

[0158]

[0159] Furthermore, the construction process of the Multi-layer Perceptron Regressor (MLPRegressor) model is as follows:

[0160] like Figure 1 As shown in Figure 1, the Multi-layer Perceptron Regressor (MLPRegressor) model is a feedforward artificial neural network model that maps a set of input vectors to a set of output vectors. It is a directed graph consisting of multiple node layers, with each layer connected to the next. Except for the input nodes, each node is a neuron with a nonlinear activation function, and is trained using a supervised learning method called backpropagation.

[0161] The Multilayer Perceptron Regression model (MLPRegressor) follows the principles of the human nervous system. Its basic structure consists of three layers: input layer, hidden layer (in this application, the hidden layer includes hidden layer 1 and hidden layer 2), and output layer. The product of the input elements and weights is fed back to the summation node with neuron bias. Its main advantage lies in its ability to quickly solve complex problems. It overcomes the weakness of the perceptron that cannot recognize linearly inseparable data and performs well in processing complex and nonlinear data.

[0162] Assume that there are n features in m samples, then the input layer X∈R m×n , assuming there are H neurons, the weight of the hidden layer is W h and deviation b h It can be expressed as W h ∈R h×n , b h ∈R 1×n , if there are q output label values, the weight of the output layer is W o and the bias parameter b h Respectively expressed as W o ∈R h×q , b h ∈R 1×q , then the outputs of the hidden layer and the output layer are expressed as Equation (17) and Equation (18), respectively. This only performs a linear transformation on the data;

[0163] H=XW h +b h Formula (17);

[0164] O=XW o +b o Formula (18);

[0165] After the linear transformation, the data needs to be transformed nonlinearly. Commonly used nonlinear activation functions include the Relu function, the sigmoid function, and the tanh function. The Relu function sets numbers greater than 0 in the output to x and numbers less than 0 to 0; the sigmoid function maps the output to a range between 0 and 1; and the tanh function maps the output to a range between -1 and 1. In this application, the tanh function is used as the activation function.

[0166] Assume that the output of layer l before activation is z l , after activation it is represented as a l , σ is expressed as an activation function, then the output of the previous layer after activation can be set as the input of this layer, and the output of this layer before and after activation is expressed as Equation (19) and Equation (20) respectively:

[0167] z l =W l a l-1 +b l Formula (19);

[0168] a l =σz l Formula (20);

[0169] In formula (19) and formula (20), W l represents the weight of layer l; b l represents the deviation of layer l.

[0170] During the calculation process, the multilayer perceptron regression model (MLPRegressor) uses cross entropy to solve the loss function. Since some data may be close to 0, resulting in large deviations, the mean absolute error (MAE) is used as the error function. The error calculation is a back-propagation algorithm from back to front, as shown in Equation (21):

[0171]

[0172] In formula (21): X represents the matrix; h represents the prediction function; x i represents the true value; y i Represents the predicted value.

[0173] The present application is described in detail below with reference to embodiments, but the present application is not limited to these embodiments.

[0174] The initial data for the following examples are collected from experimental platform data obtained under different operating parameters from the Chongqing Coal Research Institute and the U.S. Bureau of Mines. These platform data have been verified for reliability. In the following implementation, 8 particles were selected for 100 iterations during the initial parameter optimization process. The acceleration factors c1 and c2 were set to 1.1 and 1.3, respectively, and r1 and r2 were set to random numbers in the range [0, 1]. The process of finding the global optimal solution is as shown in the attached figure. Figure 3 As shown in the attached Figure 3 It can be seen that when searching for the global optimal solution during the optimization process, the fitness value shows an overall downward trend. When the global optimal solution appears and remains unchanged, the fitness value is 0.6837.

[0175] The optimization process of the multilayer perceptron regression model (MLPRegressor) is as follows Figure 4 As shown in the figure, it can be seen that the self-service algorithm (PSO) calculates the fitness value every time it sets the learning rate (Learning rate) and regularization factor (Alpha) values. When the global optimal solution appears and remains unchanged, the two parameter values ​​corresponding to the fitness value are optimal. At this time, the learning rate (Learning rate) and regularization factor (Alpha) values ​​are 0.002967 and 0.0001. In the subsequent deduction process, the parameters of the multilayer perceptron regression model (MLPRegressor) are all performed under this value.

[0176] Example 1

[0177] This example performs overpressure analysis on a straight pipeline:

[0178] Overpressure deduction for straight pipelines primarily involves setting an initial overpressure value for the explosion. After training and obtaining optimal parameters, the initial test data set is input for overpressure deduction and analysis, assuming the deduced initial overpressure value is the maximum value during the explosion. Cross-validation was performed using two sets of experimental data: the Chongqing Coal Research Institute model and the optimized multilayer perceptron regression model used in this application. A bootstrap algorithm was used to estimate the confidence intervals for the deduced overpressure values. The results are shown in Tables 1 and 2.

[0179] Tables 1 and 2 show the deduced values, confidence intervals, average absolute errors between the deduced values ​​and the true values, and the maximum absolute error and minimum absolute error within the confidence interval obtained by the deduction explosion of the optimized multilayer perceptron regression model (MLPRegressor) and the Chongqing Coal Research Institute model, respectively.

[0180] Table 1 Optimized multilayer perceptron regression model (MLPRegressor) deduction results

[0181]

[0182] Table 2 Results of Chongqing Institute Model Derivation by Optimized Regression Model (MLPRegressor)

[0183]

[0184] In order to verify the scientificity and effectiveness of the optimized multi-layer perceptron regression model (MLPRegressor), this embodiment visualizes the results of the 9.5% gas concentration explosion in a straight pipeline, as shown in the following example: Figure 5 The figure shows the visualization of the deduction results of the 9.5% gas concentration explosion in a straight pipeline using the optimized multilayer perceptron regression model (MLPRegressor) of this application. Figure 6 and Figure 7 The comparison of the deduced value, true value, upper confidence limit and lower confidence limit results of the multi-layer perceptron regression model (MLPRegressor) optimized in this application and the pipeline model of Chongqing Coal Research Institute is shown in the figure. Figure 5 and Figure 6 It can be seen that the overall error between the deduction results of the optimized multilayer perceptron regression model (MLPRegressor) and the true value is small, and the mean absolute errors of the two groups of results are 0.0722 and 0.032 respectively. It can be seen that the deduced values ​​of each sample can fall within the confidence interval estimated by the bootstrap algorithm (BootStrap), and the minimum mean absolute errors within the confidence interval are 0.1052 and 0.024 respectively, and the maximum mean absolute errors within the confidence interval are 0.2328 and 0.042 respectively. The small error within the interval indicates that the confidence interval is more reasonable and the accuracy is higher. It can be concluded that the confidence interval of the optimized multilayer perceptron regression model (MLPRegressor) is more reasonable and the accuracy is higher.

[0185] Example 2

[0186] This example performs deduction and analysis on a bifurcated pipeline:

[0187] The overpressure deduction method for a pipeline with a bifurcation angle is different from that for a straight pipeline. It is necessary to first determine the bifurcation position and bifurcation angle of the pipeline, so as to determine the attenuation characteristics of the overpressure at different bifurcation angles. This application takes a 60° bifurcation pipeline as an example. First, a bifurcation pipeline coordinate system is established, with the closed end as the coordinate origin O, the direction along the open end of the straight pipe as the x-axis, and the vertical straight pipe section as the y-axis. Figure 8There are two main overpressure propagation paths, which are represented by connecting measuring points: along the straight pipe section: G1 → G2 → G3 → G4 → G5 → G6, and along the branch pipe section: G1 → G2 → G7 → G8. The initial input information for overpressure deduction (specifically, the distance from each measuring point to the explosion source, the coordinates of each point, and pipeline information) is calculated according to the overpressure deduction theoretical model, as shown in Table 3:

[0188] Table 3 Initial input information for overpressure simulation

[0189]

[0190] The overpressure deduction theoretical model is constructed as follows:

[0191] In the overpressure simulation theoretical model, the overpressure propagation path is pre-set and characterized by node connections. Parameters such as the distance between nodes, the bifurcation angle between nodes, and the initial overpressure magnitude are also set.

[0192] For overpressure deduction, the explosion source location must be characterized first, such as Figure 9 As shown, taking the bifurcated angle pipeline in this embodiment as an example, it is necessary to first take the end of the explosion tunnel as the source point, set the direction of shock wave propagation to the right as the positive direction, and establish a one-dimensional coordinate system for the explosion tunnel. The coordinates of each monitoring point can be expressed as g i (i=1,2,3…n), assuming the explosion source position coordinate is f0, the shock wave attenuation distance of each measuring point can be expressed as x i =(g i -f0)m, the overpressure currently monitored at each measuring point can be expressed as p i (i=1,2,3…n).

[0193] Then the attenuation equation of the shock wave with propagation distance can be expressed as formula (22):

[0194]

[0195] In formula (22), y is the volume of gas; L is the propagation distance; A is the cross-sectional area; ρ is the gas density; k is the adiabatic coefficient; and E0 is the released energy. However, this formula fails to clearly characterize the explosion source position. Therefore, the shock wave attenuation distance expressed in coordinates is substituted into formula (22) to obtain the shock wave attenuation theoretical mathematical model with explosion source position coordinate parameters, which is expressed as formula (23):

[0196]

[0197] In formula (23), A is the cross-sectional area; ρ0 is the gas density; k is the adiabatic coefficient; and E0 is the released energy.

[0198] Table 4 shows the deduced values, confidence intervals, mean absolute errors between the deduced values ​​and the true values, and the maximum and minimum absolute errors within the confidence intervals obtained by using the optimized multilayer perceptron regression model (MLPRegressor) to deduce the 60° bifurcation pipe explosion model of this embodiment.

[0199] Table 4. Optimized MLPRegressor model deduction model results

[0200]

[0201] From Table 4, we can see that the average absolute error of the deduced overpressure value is 0.106. The errors at other path points after point G2 are relatively large. Although they all fall within the confidence interval, the confidence interval deviates significantly from the true value. The main reason is that the model training set contains experimental and simulated values ​​of gas explosions in bifurcated pipes with different inner diameters. Due to differences in pipe material and inner diameter, the energy lost by the overpressure when passing through the bifurcation in the gas explosion experiment is also different, resulting in large errors in the deduction after passing through the bifurcation. In view of this, it is necessary to add the overpressure loss coefficient ξ when calculating the bifurcation node in the overpressure deduction theoretical model, ignoring the influence of the experimental pipe material, and assuming that ξ is a power function of the pipe inner diameter r, that is, ξ = r x , where x is a constant. The Matlab fitting results in x = -0.12, i.e. ξ = r -0.12 .

[0202] The overpressure loss coefficient ξ is used to correct the overpressure at the bifurcation node of the model, and the following is obtained: Figure 10 The deduction visualization diagram of the modified model is shown in the figure, and the deduction results of the modified model are shown in Table 5.

[0203] Table 5 Deduction results after model correction

[0204]

[0205]

[0206] Table 5 shows that the error between the deduced results and the true values ​​of the modified model for 60° bifurcated pipelines is relatively small. The mean absolute error between the true and deduced overpressure values ​​is 0.054, respectively. The deduced values ​​for each sample also fall well within the confidence interval estimated by the bootstrap algorithm. The minimum mean absolute error within the confidence interval is 0.02, and the maximum mean absolute error within the confidence interval is 0.08. The small error within the interval demonstrates that the modified model has good applicability in 60° bifurcated pipelines.

[0207] Based on the optimized multi-layer perceptron regression model (MLPRegressor) gas explosion shock wave overpressure deduction model, the overpressure evolution process of the straight pipeline in Example 1 and the pipeline with a 60° angle bifurcation in Example 2 were deduced respectively. The model deduction results were compared with the true values ​​and the average absolute error, maximum and minimum errors of the confidence interval of the deduction results were smaller than those of the true values, which proved the reliability of the calculation results of the proposed gas explosion shock wave overpressure deduction model.

[0208] The above descriptions are merely a few embodiments of the present application and do not constitute any form of limitation to the present application. Although the present application discloses the preferred embodiments as above, they are not intended to limit the present application. Any technical personnel familiar with the present profession, without departing from the scope of the technical solution of the present application, using the technical content disclosed above to make slight changes or modifications are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron, characterized in that: The following steps are involved: Step 1: Obtain initial parameters and divide them into a training set and a test set. The initial parameters include: explosion source location coordinates, roadway parameters, and explosion initial pressure; Step 2: Build a multilayer perceptron regression model based on the training set and test set; Step 3: Optimize the learning rate and regularization factor of the initial parameters input to the multilayer perceptron regression model through the improved particle swarm optimization algorithm to obtain the global optimal solution; Step 4: Use the bootstrap algorithm to output the results of the multilayer perceptron regression model to obtain the confidence interval of the deduced overpressure value; Step 5: Input the global optimal solution into the multi-layer perceptron regression model to perform overpressure deduction analysis within the obtained confidence interval; The improvement process of the particle swarm algorithm is as follows: (1) Analyze the problem to be solved to determine whether there is a risk of premature convergence or falling into a local optimal solution; (2) Determine the goal of improving the inertia weight model based on the results of the problem analysis; (3) Use the adaptive inertia weight model to further improve the particle swarm algorithm; (4) Modify the particle swarm algorithm according to the selected improvement method; (5) Testing and verification: Use the modified particle swarm algorithm to solve a series of test problems and compare the test results with the original algorithm to test and verify the modified particle swarm algorithm; (6) Based on the test results, further adjust and optimize the parameters or strategies of the improved method in the adaptive inertia weight model to obtain the global optimal solution.

2. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 1 is characterized in that: In a multilayer perceptron regression model: The activation function is the tanh function; The error function uses the mean absolute error (MAE), and the error calculation is done using a back-propagation algorithm.

3. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 2, characterized in that: In the multilayer perceptron regression model, all nodes except the input node are neurons with a nonlinear activation function.

4. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 1, characterized in that: The improved particle swarm optimization algorithm optimizes the learning rate and regularization factor of the initial parameters input to the multilayer perceptron regression model as follows: First, each particle is randomly initialized; Subsequently, each particle is evaluated and the global optimal particle is obtained; Finally, determine whether the iteration meets the end condition; If yes, then end; if no, continue to iterate until the end condition is met and the process ends; The value corresponding to when the end condition is met is the global optimal solution.

5. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 4 is characterized in that: The iterative process includes the following steps: updating the speed and position of each particle, evaluating the function fitness value of each particle, updating the historical optimal position of each particle, and updating the global optimal position of the group.

6. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 4, characterized in that: The process of judging whether the iteration meets the end condition is: (1) Obtain preprocessed standard data; (2) Import the Scikit-learn library; (3) Define a multilayer perceptron regression model and specify the model's hyperparameters; (4) fitting a multilayer perceptron regression model using the training set to train the multilayer perceptron regression model; (5) Use the test dataset to evaluate the performance of the multilayer perceptron regression model to select the best hyperparameter combination; (6) Use the trained multilayer perceptron regression model to predict new data to obtain prediction results; (7) Determine whether the performance of the model is ideal based on the prediction results. If the performance of the multilayer perceptron regression model is not ideal, improve the ideality of the multilayer perceptron regression model by adjusting hyperparameters, increasing the number of hidden layers or neurons, or trying different activation functions or optimizers; (8) It is judged that the performance of the multilayer perceptron regression model is ideal, that is, the iteration end condition is met.

7. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 1, characterized in that: In the optimization of the adaptive inertia weight model, after the inertia factor ω is adaptively optimized, the inertia factor ω is associated with the number of iterations and the fitness of each particle: 1) Assuming that the problem of finding the minimum fitness value is solved, the fitness expression is formula (1): 2) Assuming that the problem is to find the maximum fitness, the fitness expression is formula (2): In formula (1) and formula (2): ω min and ω max is the preset minimum inertia coefficient and maximum inertia coefficient, then the average fitness of all particles at the dth iteration is expressed as formula (3): The maximum fitness of all particles at the dth iteration It is expressed as formula (4):

8. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 7, characterized in that: The deduction steps are: The training is completed to obtain the optimal parameters; Input optimal parameters for overpressure simulation analysis; At the same time, it is assumed that the deduced initial overpressure value is the maximum value during the explosion process; A bootstrap algorithm is used to obtain the confidence interval of the deduced overpressure value.

9. The method for deducing the overpressure process of gas explosion shock wave based on optimized multi-layer perceptron according to claim 8, characterized in that: The process of obtaining the confidence interval of the deduced overpressure value through the bootstrap algorithm is as follows: During the sampling process, the bootstrap algorithm ensures that the probability of each element in the sampling result being drawn is the same. Each time, N elements are drawn and repeated B times to obtain B groups of sample matrices containing N elements. The eigenvalues ​​of each group of samples are calculated to obtain the bootstrap sample probability eigenvalues. Suppose the original sample S is expressed as formula (5): S=(S1,S2,S3,…S i ,…,S n ) Formula (5); In formula (5): S i is the i-th data of the sample, S n It means there are n elements in total, and B elements are extracted from them, with N data each time. Finally, each sample set P is expressed as formula (6): P=(P1,P2,P3,…P b ,…,P B ) Formula (6); In formula (6): P b is the b-th self-service sample set, expressed as formula (7): P b = P b (i), i = 1, 2, …, N, Equation (7); In formula (7): P b (i) is expressed as P b The i-th element of , so the bootstrap sample set P b The mean The calculation formula is expressed as formula (8): The bootstrap sample mean It is expressed as formula (9): Bootstrap sample variance σ 2 It is expressed as formula (10): In machine learning, the bootstrap algorithm is used to solve the confidence interval. By estimating the sample eigenvalues, different confidence intervals are obtained. Assuming that the bootstrap algorithm is used to obtain the sample parameter estimate, the sample parameter θ is expressed as formula (11): Arrange them from small to large, and we get formula (12): Assuming the significance level is α, α∈[0,1], the confidence level is expressed as formula (13): Let K1 and K2 represent the upper confidence limit and lower confidence limit respectively, see formula (14): and is the quantile and The estimation of , we get formula (15): The final confidence interval is expressed as formula (16):

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