A penetration depth prediction method based on multi-partition model integration

Abstract

The present invention discloses a penetration depth prediction method based on multi-partition model integration, which divides the evaluation intervals for evaluating engineering algorithms; selects several relatively excellent engineering algorithms; performs batch sample calculations using the selected engineering algorithms to obtain engineering calculation simulation data; in each evaluation interval, uses experimental data and engineering calculation simulation data to establish a dimensionless penetration depth prediction model based on random forest and BP neural network; uses the K-nearest neighbor partition model fusion output for weighted integration to form a fusion model; the input features generate partition prediction results through multiple prediction models, and finally generate a dimensionless penetration depth prediction output through the fusion model. The present invention ensures the accuracy of data and at the same time avoids the influence of the lack of experimental data on the deep learning model; establishes models in intervals, reduces the modeling scope, ensures that the models can reflect the physical characteristics and laws of local areas, generates smaller prediction errors, and obtains a prediction model with higher accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of information processing, and particularly relates to a penetration depth prediction method based on multi-partition model integration. Background Art

[0002] The penetration mechanism of protective material media is revealed through empirical algorithms established based on a large amount of experimental data. The penetration damage problem is a very complex physical process, and existing methods are difficult to accurately and detailedly restore the actual situation. Therefore, in actual processes, engineering algorithms still play an important role. These engineering algorithms are relatively simple to use. By only giving several parameters, a predicted dimensionless penetration depth value can be obtained. The existing engineering algorithms for penetration depth are calculation formulas generated by the inventor of the present invention through fitting and other means based on the experimental data owned by himself. Limited by experimental environments, economic conditions, etc., the experimental data used often can only cover a part of the parameter range, and most of them are scaled-down experiments. This results in each engineering algorithm being able to be used only within a partial parameter range and unable to meet the full parameter region of penetration depth analysis. At the same time, the applicable range of engineering algorithms has no clear measurement standard and is not clear either. Therefore, how to use the experimental data in the hands of each worker in combination with the existing engineering algorithms to establish a penetration depth prediction model, improve the prediction accuracy, and alleviate the difficulties in the selection of numerous engineering algorithms in engineering practical applications has become an important direction in penetration research.

[0003] The penetration process is a highly nonlinear and complex process. The physical laws and mechanisms that may be exhibited in different parameter ranges are different. For example, it behaves like a rigid body at low speeds and like a fluid at ultra-high speeds. Therefore, it is necessary to be able to effectively divide the penetration effect parameter space, try to exhibit different physical mechanisms in different ranges, and independently establish models for prediction in different ranges, rather than using one model to predict in the entire parameter range. Summary of the Invention

[0004] Object of the Invention: In order to overcome the deficiencies existing in the prior art and applications, the present invention provides a penetration depth prediction method based on multi-partition model integration, which gives full play to the advantages of experimental data and the advantages of different engineering algorithms in each parameter range. By narrowing the analysis range, establishing evaluation partitions, and establishing prediction models in the partitions, refined prediction is realized, thereby improving the prediction accuracy of penetration depth.

[0005] Technical Solution: The present invention provides a penetration depth prediction method based on multi-partition model integration, which specifically includes the following steps:

[0006] (1) Through dimensionality reduction and clustering of experimental data, combined with domain expert knowledge, divide the evaluation intervals for evaluating engineering algorithms;

[0007] (2) In each of the divided evaluation intervals, select k engineering algorithms with relatively high calculation accuracy in this evaluation interval;

[0008] (3) In each evaluation interval, use the selected engineering algorithms to perform batch sample calculations to obtain engineering calculation simulation data;

[0009] (4) In each evaluation interval, based on the engineering algorithm simulation data and test data in this interval, use the random forest integration method to integrate the BP neural network, establish the prediction model RF_BP_r for this interval, and realize the prediction of the penetration depth in this interval;

[0010] (5) Use K-nearest neighbor fusion prediction to generate the penetration depth prediction value for the full parameter interval.

[0011] Further, the step (1) includes the following steps:

[0012] (11) Use the manifold learning LLE algorithm to reduce the dimension of the test data: The inputs for penetration depth analysis include 8 characteristic quantities such as impact velocity, projectile mass, projectile diameter, target compressive strength, target material density, CRH, shape factor, and warhead length, and the output is the dimensionless penetration depth. And the international unit is uniformly adopted. The data is organized into the following matrix format:

[0013]

[0014] Among them, d ij is the input quantity, m is the number of input characteristic quantities, the last column is the model output, that is, the dimensionless penetration depth, and the other columns are the inputs of the model. n is the number of data; Use the locally linear embedding manifold learning LLE algorithm for the sample data in the 9-dimensional space described by the matrix M to reduce the dimension to the d-dimensional space. Locally linear embedding attempts to maintain the linear relationship between samples in the neighborhood and maintain this linear relationship in the low-dimensional space, and can be applied to the non-linear dimensionality reduction of high-dimensional data;

[0015] (12) Use the hierarchical clustering algorithm to cluster the data in the reduced d-dimensional space to determine the preliminary range of the evaluation interval. Domain experts analyze different clustering results to determine reasonable clustering levels and results; According to the range of characteristic values of the sample points included in each class, determine the interval of the input characteristic quantities in each class, and the range of values of the characteristic quantities in each class constitutes an evaluation interval;

[0016] (13) Domain experts reasonably expand the intervals of the characteristic quantities, and there can be a certain overlap in the range of values of the characteristic quantities in different evaluation intervals.

[0017] Further, the implementation process of the step (2) is as follows:

[0018] For the evaluation interval r, extract the test data within the evaluation interval r to form a test sample set S r , assuming that g to-be-evaluated engineering algorithms a are selected for r 1 、a 2 、…、a g , use S R and a 1 、a 2 、…、a g to calculate the dimensionless penetration depth, compare it with the actual value, and calculate the algorithm accuracy; use the mean absolute percentage error MAPE as the evaluation criterion for the engineering algorithm calculation accuracy:

[0019]

[0020] where, y i is the true dimensionless penetration depth value, p i is the calculated dimensionless penetration depth value, and m is the total number of samples in this evaluation interval;

[0021] Assume that MAPE 1 、MAPE 2 、…、MAPE g respectively represent the mean absolute percentage errors of the engineering algorithms a 1 、a 2 、…、a g in the analyzed parameter interval. Sort MAPE i (i = 1, …, g) from low to high, and take the algorithms corresponding to the first k errors as the better algorithms in this parameter interval.

[0022] Further, the implementation process of step (3) is as follows:

[0023] Discretize the parameters required for the engineering algorithm calculation within its range in the evaluation interval, then combine them to form a large number of input vectors, and then use the engineering algorithm in this evaluation interval for calculation to obtain engineering calculation simulation data; assume that the current algorithm requires m parameters, and the discretized values of each parameter are p 1 , p 2 , …, p m kinds, then all combinations are kinds, that is, in the current evaluation interval, a batch calculation of an engineering algorithm can generate simulation data; obtain engineering calculation simulation data through batch engineering calculations.

[0024] Further, step (4) includes the following steps:

[0025] (41) Establish a BP neural network model for evaluating partitions using the idea of the random forest algorithm. Each time, randomly select m features from 8 feature vectors as the input of the BP neural network, and the output is the dimensionless penetration depth; randomly select p% of the data S r from S r_p , extract the selected m features of S r_p and the dimensionless penetration depth dimension to form the training set S r_p_train . Use S r_p_train to train a tree, that is, a BP neural network; the value of m is 6 or 7; the setting of p is 70 - 80;

[0026] (42) Construct f trees according to (41), that is, construct f BP neural networks. The number of hidden layers of each BP neural network is , the number of nodes in each layer is 2m, and the activation function is Relu; the training data is standardized using the following formula:

[0027] S r_p_train = (S r_p_train- S r_p_train_ - mean ) / S r_p_train_ ) / std(3)

[0028] where, S r_p_train_ mean represents the vector composed of the mean values of each dimension of S r_p_train , and S r_p_train_ std represents the vector composed of the standard deviations of each dimension of S r_p_train ;

[0029] (44) Use the mean value strategy to calculate the mean of the outputs of f trees as the predicted output of the corresponding partition.

[0030] Further, step (5) includes the following steps:

[0031] (51) Judge the evaluation interval where the input parameter is located according to the input parameter, and select the prediction model of this evaluation interval as the main prediction model to obtain the main predicted value p 1 ;

[0032] (52) Search for the adjacent intervals of the interval where the parameter is located. Assume that k adjacent intervals are found. Each evaluation interval is a hyper-rectangular region. For a certain main evaluation interval r, as long as the evaluation interval that has an intersection or vertex contact with this interval r is an adjacent interval of r;

[0033] (53) Respectively use the prediction models of the adjacent intervals to predict the penetration depth of the input, and calculate the mean of the prediction results to obtain the predicted value p 2 of the adjacent intervals;

[0034] (54) The final prediction result is p = (1 - 1 / (k + 1)) * p1 + p2 / (k + 1); the weight of the main prediction interval is 1 / (k + 1), where k + 1 represents the number of partitions used for this prediction, that is, the weight of the main prediction partition model is inversely proportional to the number of partitions used for prediction; the more the number of evaluation partitions, the finer the interval division, the stronger the independence of each interval, and the higher the weight occupied by the main prediction interval model.

[0035] Advantageous effects: Compared with the prior art, the advantageous effects of the present invention are as follows: Compared with a single engineering algorithm, the present invention can achieve accurate prediction in a relatively wide parameter region; compared with the existing model established only based on experimental data, the present invention can make full use of the advantages of existing engineering algorithms through engineering algorithm pseudo-data to improve the accuracy of the deep learning model; the present invention establishes prediction models targeted in multiple intervals, and each partition model can reflect local physical laws, which can effectively improve prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flowchart of the present invention;

[0037] Figure 2 Adjacent partition retrieval diagram;

[0038] Figure 3 is a MAPE diagram of the test set for different experimental models. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] The present invention will be further described in detail below with reference to the accompanying drawings.

[0040] As Figure 1As shown in the figure, a penetration depth prediction method based on multi-partition model integration disclosed by the present invention reduces the dimension and clusters the experimental data, and then combines the domain expert knowledge to divide the evaluation interval for evaluating the engineering algorithm; in each evaluation area, k engineering algorithms with higher calculation accuracy in this interval are selected; in each evaluation interval, the selected engineering algorithms are used to calculate a batch of samples to obtain engineering calculation simulation data; in each evaluation interval, based on the engineering algorithm simulation data and experimental data in this interval, the random forest integration method is used to integrate the BP neural network to establish the RF_BP_r model of the interval, so as to realize the prediction of the penetration depth in this interval; finally, the prediction results of each partition are weighted and integrated through weight-based fusion to establish the final dimensionless penetration depth prediction output. The present invention uses different engineering algorithms to generate simulation data in different parameter intervals, which not only ensures the accuracy of the data as much as possible, but also avoids the influence of the lack of experimental data on the deep learning model through a large amount of engineering algorithm simulation data. In different intervals, different models are established targeted, which can generate refined interval models, so as to generate a prediction model that can exceed the accuracy of existing engineering algorithms.

[0041] Step 1: Divide the evaluation interval. The evaluation interval for evaluating the engineering algorithm is divided by reducing the dimension and clustering the experimental data and then combining the domain expert knowledge. The following steps are included:

[0042] (1) Use the manifold learning LLE algorithm to reduce the dimension of the experimental data. The inputs for penetration depth analysis include 8 characteristic quantities such as impact velocity, projectile mass, projectile diameter, target compressive strength, target material density, CRH, shape factor, and warhead length, and the output is the dimensionless penetration depth, and the international unit is uniformly used. The data is organized into the following matrix format:

[0043]

[0044] where d ij is the input quantity, m is the number of input characteristic quantities, the last column is the model output, that is, the dimensionless penetration depth, and the other columns are the inputs of the model, and n is the number of data.

[0045] For the sample data in the 9-dimensional space described by the matrix M, use the locally linear embedding manifold learning LLE algorithm to reduce the dimension to the d-dimensional space. The locally linear embedding attempts to maintain the linear relationship between samples in the neighborhood and maintain this linear relationship in the low-dimensional space, and can be applied to the non-linear dimensionality reduction of high-dimensional data.

[0046] (2) Hierarchical clustering algorithm is used to cluster the d-dimensional space data after dimensionality reduction to determine the preliminary evaluation interval range. Domain experts analyze different clustering results to determine reasonable clustering levels and results. According to the characteristic value ranges of the sample points included in each class, the intervals of the input feature quantities in each class are determined. The value ranges of the feature quantities in each class constitute an evaluation interval. For example, (projectile mass: (0 - 100), impact velocity: (0 - 200), projectile shape (0.72 - 0.84), target density: (2.7 - 12.0), CRH: (0.5 - 1.3) …) describes an evaluation interval corresponding to a high-dimensional space, and this clustering result gives a preliminary segmentation of the evaluation interval.

[0047] (3) Domain experts adjust the evaluation intervals. Domain experts reasonably expand the intervals of the feature quantities, and there can be a certain overlap in the value ranges of the feature quantities in different evaluation intervals. The union of the spaces corresponding to all evaluation intervals needs to be able to cover the high-dimensional space composed of the reasonable value ranges of the selected feature quantities. For example, assuming that the feature quantities of the evaluation intervals include three features: projectile mass, impact velocity, and target density, then the union of the ranges of all evaluation intervals needs to be able to cover the three-dimensional space composed of projectile mass, impact velocity, and target density.

[0048] Step 2: Select engineering algorithms. In each of the divided evaluation intervals, k engineering algorithms with higher calculation accuracy in this evaluation interval are selected. The selection method includes two steps:

[0049] (1) According to the existing application practice summary materials, analyze the applicable intervals of various engineering algorithms. For example, for the concrete penetration depth algorithm Young's formula, it generally has better effects in the medium-speed interval.

[0050] (2) On the premise that insufficient information cannot be obtained in (1), use experimental data for calculation accuracy analysis. For the evaluation interval r, extract the experimental data within the evaluation interval r to form the experimental sample set S r , assuming that g engineering algorithms a 1 、a 2 、…、a g are selected for evaluation in r, use S R and a 1 、a 2 、…、a g to calculate the dimensionless penetration depth and compare it with the actual value to calculate the algorithm accuracy. The mean absolute percentage error MAPE is used as the evaluation criterion for the calculation accuracy of engineering algorithms:

[0051]

[0052] Among them, y i is the true dimensionless penetration depth value, p iis the calculated dimensionless penetration depth value, and m is the total number of samples in this evaluation interval.

[0053] Assume MAPE 1 , MAPE 2 , …, MAPE g respectively represent the mean absolute percentage errors of engineering algorithms a 1 , a 2 , …, a g in the analyzed parameter interval. Sort MAPE i (i = 1, …, g) from low to high, and select the first k algorithms corresponding to the errors as the better algorithms in this parameter interval.

[0054] Step 3: In each evaluation interval, use the selected engineering algorithms to perform batch sample calculations to obtain engineering calculation simulation data.

[0055] Perform batch engineering calculations in each evaluation interval to obtain engineering calculation simulation data. Discretize the parameters required for engineering algorithm calculations within their ranges in the evaluation interval, and then combine them to form a large number of input vectors. Then use the engineering algorithms in this evaluation interval for calculations to obtain engineering calculation simulation data. Assume that the current algorithm requires m parameters, and the discretized values of each parameter are p 1 , p 2 , …, p m types respectively. Then all combinations are types, that is, in the current evaluation interval, a batch calculation of an engineering algorithm can generate simulation data. The parameter ranges generally include two types:

[0056] 1) Real number value range. For parameters with real number value ranges, determine the maximum and minimum values of the parameters and the change step size, and then automatically discretize to generate all possible values of the parameters. For example, in the velocity interval [340, 650), the minimum value is 340, the maximum value is 650. Assuming the step size is set to 10, 31 values can be generated.

[0057] 2) Enumerated values. For example, the warhead shape includes flat-nose projectiles, oval projectiles, pointed projectiles, etc. The value setting is of the enumerated type, including: three values of 0.72, 0.8, and 1.14.

[0058] Obtain engineering calculation simulation data through batch engineering calculations. Since engineering algorithms are also generated by fitting a large amount of experimental data, the simulation data obtained by using engineering algorithms in the interval with higher engineering algorithm accuracy has higher accuracy. Mix the engineering simulation data calculated by multiple engineering algorithms in this interval as the dataset for training the model.

[0059] Step 4: Data Partitioning. The experimental data is segmented according to the value range of the characteristic quantities in the evaluation interval, and the data S in each evaluation interval r includes engineering calculation simulation data and experimental data belonging to this evaluation interval. An RF_BP_r model for the evaluation partition is established. A prediction model is established for each evaluation partition based on the random forest algorithm, including the following steps:

[0060] (1) Use the idea of the random forest algorithm to establish a BP neural network model for the evaluation partition. Each time, randomly select m features from 8 feature vectors as the input of the BP neural network, and the output is the dimensionless penetration depth; randomly select p% of the data S r from S r_p , extract the selected m features of S r_p and the dimensionless penetration depth dimension to form the training set S r_p_train , and use S r_p_train to train a tree (i.e., a BP neural network). The value of m is generally between 6 and 7. Since the penetration process is related to many factors, if too few feature quantities are selected each time, it is difficult to establish an appropriate model; the setting of p is generally 70 - 80. If the p value is too small, the amount of data is small, and the training effect of the BP neural network is not good. At the same time, the model differences are large, resulting in large errors. If the p value is too high, such as 100%, then the training data of each model is the same, and the BP neural networks trained have smaller differences and lack diversity;

[0061] (2) Construct f trees according to the idea of (1), that is, construct f BP neural networks. The number of hidden layers of each BP neural network is and the number of nodes in each layer is 2m, and the activation function is Relu. The training data is standardized using the following formula:

[0062] S r_p_train =(S r_p_train- S r_p_train_ mean ) / S r_p_train_ std (3)

[0063] S r_p_train_ mean represents the vector composed of the mean values of each dimension of S r_p_train , and S r_p_train_ std represents the vector composed of the standard deviations of each dimension of S r_p_train .

[0064] (3) Use the average value strategy to calculate the average of the outputs of f trees as the prediction output of the corresponding partition.

[0065] Step 5: Use K-nearest neighbor fusion prediction to predict the penetration depth of the entire parameter interval. The model of each partition may get relatively good results in the prediction of its own partition interval. However, since penetration is a very complex process, in the boundary area of ​​different intervals, the models of adjacent partitions are approximate simulations of the mechanism of the area and may produce similar results. Therefore, when making predictions, the evaluation partition where the input parameters are located is the main focus, and the prediction results of the adjacent partitions are fully utilized for fusion to obtain the final penetration depth prediction result.

[0066] (1) According to the input parameters, the evaluation interval is determined, and the prediction model of the evaluation interval is selected as the main prediction model. The main prediction model is used to predict the input to obtain the main prediction value p 1 ;

[0067] (2) Search for the neighboring intervals of the interval where the parameter is located. Suppose k neighboring intervals are found. Figure 2 As shown in the figure, there are 8 neighboring intervals around the main prediction interval, and each evaluation interval is a super rectangular area. For a certain evaluation interval r, as long as there is an intersection surface (edge) or vertex contact with the interval r, it is a neighboring interval of r. In order to improve efficiency, a list of neighboring intervals for each evaluation interval can be established in advance and stored;

[0068] (3) Use the prediction model of the adjacent interval to predict the penetration depth of the input, and average the prediction results to obtain the prediction value p of the adjacent interval. 2 ;

[0069] (4) The final prediction result is p = (1-1 / (k+1))*p1+p2 / (k+1). The weight of the main prediction interval is 1 / (k+1), where k+1 represents the number of partitions used for this prediction. That is, the weight of the main prediction partition model is inversely proportional to the number of partitions used for prediction. The more evaluation partitions there are, the finer the interval division, the stronger the independence of each interval, and therefore the higher the weight of the main prediction interval model.

[0070] The process of dimensionless penetration depth prediction is as follows: the input vector consisting of eight characteristic quantities, namely, target impact velocity, projectile mass, projectile diameter, target compressive strength, target material density, CRH, shape factor, and warhead length, is used to generate a prediction output through the SF_BP_r model of each partition, and then the final dimensionless penetration depth value is generated through K-nearest neighbor fusion prediction.

[0071] In order to verify the performance of the penetration depth prediction method based on multi-partition model integration, an experiment was conducted using concrete penetration depth prediction as an example to compare the present invention with existing algorithms. The algorithms involved in the comparison include: BP neural network algorithm and existing empirical algorithm.

[0072] For convenient comparison, the experimental data set is divided into a training set and a test set according to a ratio of 7:3. The performance differences between the method proposed in the present invention and the existing methods are compared on the test set, and the evaluation index is the mean absolute percentage error MAPE.

[0073] First, the evaluation interval is divided. First, the existing experimental data is dimensionally reduced using the manifold learning algorithm LLE. When searching for the nearest neighbors, k = 4 is taken, and the data is projected into a 3D space, and the 3D space data is clustered. After adjustment by relevant field personnel, a total of 12 evaluation partitions are finally obtained.

[0074] According to the existing algorithm documents and experimental data, engineering algorithms are selected in 12 intervals, and four engineering algorithms are selected for each interval, as shown in Table 1.

[0075] Table 1 Candidate Table of Engineering Algorithms for Each Evaluation Interval

[0076]

[0077] Batch engineering calculations are performed in each interval. The parameters are discretized in the manner shown in Table 2 to generate combined samples, and the candidate engineering algorithms in each evaluation interval are used for calculation to generate engineering calculation simulation data.

[0078] Table 2 Parameter Table for Generating Pseudo Data Sources of Empirical Algorithms

[0079]

[0080] The MAPE errors of each model and common engineering algorithms on the test set are as Figure 3 shown. BP-exp is the BP neural network model established with experimental data, and BP-cand is the BP neural network model established with engineering calculation simulation data. The dashed line in the figure represents the corresponding lowest MAPE error in the traditional empirical algorithm. It can be seen from the figure that the MAPE errors of the engineering algorithms on the test set are generally higher than those of the neural network models. The MAPE error of the BP-exp model based on the experimental data source is slightly lower than that of the BP-cand model based on the pseudo data source of the empirical algorithm; the MAPE error of the K-nearest neighbor fusion model prediction (K_Fusion) is the lowest.

Claims

1. A penetration depth prediction method based on multi - partition model integration, characterized in that, it includes the following steps: (1) By reducing the dimension and clustering the experimental data, and then combining the domain expert knowledge to divide the evaluation intervals for evaluating the engineering algorithms; (2) In each divided evaluation interval, select k engineering algorithms with higher calculation accuracy in this evaluation interval; (3) In each evaluation interval, use the selected engineering algorithms to perform batch sample calculations to obtain engineering calculation simulation data; (4) In each evaluation interval, based on the engineering algorithm simulation data and experimental data in this interval, use the random forest integration method to integrate the BP neural network, establish the prediction model RF_BP_r of the interval, and realize the penetration depth prediction of this interval; (5) Use the K - nearest neighbor fusion prediction to generate the penetration depth prediction value of the full - parameter interval; The step (1) includes the following steps: (11) Use the manifold learning LLE algorithm to reduce the dimension of the experimental data: The input of the penetration depth analysis includes 8 characteristic quantities such as the impact velocity, projectile mass, projectile diameter, target compressive strength, target material density, CRH, shape factor, and warhead length, and the output is the dimensionless penetration depth, and the international unit is uniformly used. The data is organized into the following matrix format: where d ij is the input quantity, m is the number of input feature quantities, the last column is the model output, i.e., the dimensionless penetration depth, and the other columns are the model inputs. n is the number of data. For the sample data in the 9-dimensional space described by matrix M, the locally linear embedding (LLE) algorithm for manifold learning is used to reduce the dimension to the d-dimensional space. Locally linear embedding attempts to preserve the linear relationship between samples in the neighborhood and maintain this linear relationship in the low-dimensional space, and it can be applied to the nonlinear dimensionality reduction of high-dimensional data. (12) Use the hierarchical clustering algorithm to cluster the data in the d - dimensional space after dimension reduction to determine the preliminary range of the evaluation intervals. The domain experts analyze different clustering results to determine the reasonable clustering level and results; According to the characteristic value range of the sample points included in each class, determine the interval of the input characteristic quantities in each class, and the value range of the characteristic quantities in each class constitutes an evaluation interval; (13) The domain experts reasonably expand the intervals of the characteristic quantities, and there is an overlap in the value ranges of the characteristic quantities in different evaluation intervals.

2. The penetration depth prediction method based on multi - partition model integration according to claim 1, characterized in that, the implementation process of the step (2) is as follows: For the evaluation interval r, extract the test data within the evaluation interval r to form the test sample set S r , assume that g engineering algorithms a to be evaluated are selected for r 1 、a 2 、…、a g , use S R and a 1 、a 2 、…、a g to calculate the dimensionless penetration depth, compare it with the actual value, and calculate the algorithm accuracy; use the mean absolute percentage error MAPE as the evaluation criterion for the calculation accuracy of the engineering algorithm: where y i is the true dimensionless penetration depth value, p i is the calculated dimensionless penetration depth value, and m is the total number of samples in this evaluation interval; Suppose MAPE 1 , MAPE 2 , …, MAPE g respectively represent the mean absolute percentage errors of engineering algorithms a 1 , a 2 , …, a g in the analyzed parameter interval. Let MAPE i , where i = 1, …, g, be sorted from low to high, and take the algorithms corresponding to the first k errors as the better algorithms for this parameter interval.

3. The penetration depth prediction method based on multi - partition model integration according to claim 1, characterized in that, the implementation process of the step (3) is as follows: Discretize the parameters required for engineering algorithm calculation within the range of the evaluation interval, then combine them to form a large number of input vectors, and then use the engineering algorithm in this evaluation interval to perform calculations to obtain engineering calculation simulation data. Assume that the current algorithm requires m parameters, and the discretized values of each parameter are p 1 , p 2 , …, p m types. Then all combinations are types, that is, within the current evaluation interval, the batch calculation of an engineering algorithm generates simulation data; obtain engineering calculation simulation data through batch engineering calculations.

4. The penetration depth prediction method based on multi - partition model integration according to claim 1, characterized in that, the step (4) includes the following steps: (41) Establish a BP neural network model for evaluating partitions using the idea of the random forest algorithm. Each time, randomly select m features from 8 feature vectors as the input of the BP neural network, and the output is the dimensionless penetration depth; randomly select p% of the data S r from S r_p , extract the selected m features of S r_p and the dimensionless penetration depth dimension to form the training set S r_p_train , and use S r_p_train to train a tree, that is, a BP neural network; the value of m is 6 or 7; the setting of p is 70 - 80; (42)Construct f trees according to (41), that is, construct f BP neural networks. The number of hidden layers of each BP neural network is log 2 m , the number of nodes in each layer is 2m, and the activation function is Relu; the training data is standardized using the following formula: S r_p_train＝( S r_p_train- S r_p_train_ mean ) / S r_p_train_ std (3) Among them, S r_p_train_ mean represents S r_p_train the vector formed by the mean values of each dimension, S r_p_train_ std represents S r_p_train the vector formed by the standard deviations of each dimension; (43) Use the average value strategy to calculate the average value of the outputs of f trees as the prediction output of the corresponding partition.

5. The penetration depth prediction method based on multi - partition model integration according to claim 1, characterized in that, the step (5) includes the following steps: (51) Determine the evaluation interval based on the input parameters, and select the prediction model of this evaluation interval as the main prediction model to obtain the main predicted value p 1 ; (52) Search for the adjacent intervals of the interval where the parameter is located. Assume that k adjacent intervals are found. Each evaluation interval is a hyper - rectangular region. For a certain main evaluation interval r, as long as the evaluation interval that has an intersection or vertex contact with this interval r is the adjacent interval of r; (53) The penetration depth is predicted for the input using the prediction models of adjacent intervals respectively, and the average value of the prediction results is calculated to obtain the predicted value p of the adjacent intervals. 2 ; (54) The final prediction result is p = (1 - 1 / (k + 1)) * p1 + p2 / (k + 1); the weight of the main prediction interval is 1 / (k + 1), where k + 1 represents the number of all partitions used for this prediction, that is, the weight of the main prediction partition model is inversely proportional to the number of partitions used for prediction; the more the number of evaluation partitions, the finer the interval division, the stronger the independence of each interval, and the higher the weight of the main prediction interval model.

Images