Variable importance screening method and device based on multi-fidelity sensitivity error

Abstract

The invention discloses a variable importance screening method based on a multi-fidelity sensitivity error, and belongs to the technical field of adapter variable screening. Comprising the following steps: S1, acquiring M variables to be analyzed; S2, respectively collecting a high-fidelity sample set and a low-fidelity sample set as training sets; S3, constructing a multi-fidelity agent model, s4, calculating a contribution value of the high-fidelity sample set to the first importance measurement result; S5, solving a new sample point; S6, respectively calculating error increase amplitudes of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index, s7, updating the multi-fidelity agent model, and calculating a second importance measurement result of the M variables to be analyzed; and S8, taking the second importance measurement result as a target importance measurement result under the condition that the second importance measurement result is convergent, and skipping to S4 under the condition that the second importance measurement result is not convergent. And the adapter variable importance screening efficiency is improved.

Description

Technical Field

[0001] This application belongs to the technical field of adapter variable screening, and particularly relates to a method for screening variable importance based on multi-fidelity sensitivity error. Background Art

[0002] In the mechanical property model of an adapter, the screening of variable importance of the adapter, as a core tool for model optimization, its effectiveness is directly related to the reliability and economy of engineering design. The variable sensitivity differences under the action of multi-variable coupling may cause the mechanical properties output by the mechanical property model of the adapter to be inaccurate, thereby leading to design deviations and resource waste. Therefore, establishing an efficient importance screening method has become a key breakthrough point for improving the cognitive ability of complex systems.

[0003] The existing screening of variable importance of adapters is mainly based on analysis principles, but there are still significant technical bottlenecks. First, the local sensitivity analysis method has insufficient global space representation ability and is difficult to capture the variable interaction effects in nonlinear systems. Second, although the global sensitivity analysis method has the ability of full-space analysis, it will produce the curse of dimensionality when facing high-dimensional variable spaces, resulting in an exponential growth of computational complexity. In addition, the traditional surrogate model technology adopts an architecture that separates offline modeling from online analysis, and lacks a sensitivity feedback mechanism in the process of model iterative optimization, resulting in repeated consumption of computational resources.

[0004] The application of current technologies in the screening of variable importance of adapters faces multiple restrictions. The existing methods are difficult to effectively balance the contradiction between computational accuracy and efficiency, have weak adaptability to nonlinear characteristics, and generally have problems of high computational cost and low screening efficiency. Summary of the Invention

[0005] This application aims to solve at least one of the technical problems existing in the prior art. For this reason, this application proposes a method for screening variable importance based on multi-fidelity sensitivity error, which improves the efficiency of screening variable importance of adapters.

[0006] In a first aspect, this application provides a method for screening variable importance based on multi-fidelity sensitivity error, and the method includes:

[0007] S1 Obtain the distribution characteristics of M variables to be analyzed, where the distribution characteristics include the distribution type and distribution parameters of the variables to be analyzed;

[0008] S2 Based on the distribution characteristics, respectively collect a high-fidelity sample set and a low-fidelity sample set as training sets according to a preset ratio through the Latin hypercube sampling method, and each sample in the training set includes M variables to be analyzed;

[0009] S3 Construct a multi-fidelity surrogate model based on the training set, and calculate the first importance measure results of the M variables to be analyzed based on the multi-fidelity surrogate model;

[0010] S4 Calculate the leave-one-out sensitivity analysis error for each sample in the high-fidelity sample set, and obtain the contribution value of each sample in the high-fidelity sample set to the first importance measure results;

[0011] S5 Construct a mathematical optimization problem for adaptively updating and adding points, and solve it based on the particle swarm optimization algorithm to obtain new sample points;

[0012] S6 Calculate the error improvement amplitudes of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and obtain the fidelity type of the new sample points based on the error improvement amplitudes;

[0013] S7 Add the new sample points to the training set based on the fidelity type of the new sample points, update the multi-fidelity surrogate model, and calculate the second importance measure results of the M variables to be analyzed based on the updated multi-fidelity surrogate model;

[0014] S8 Determine whether the second importance measure results converge. If the second importance measure results converge, use the second importance measure results as the target importance measure results. If the second importance measure results do not converge, jump to S4;

[0015] S9 Rank the importance of the M variables to be analyzed based on the target importance measure results to obtain the importance ranking results of the M variables to be analyzed;

[0016] S10 Screen the M variables to be analyzed based on the importance ranking results and the target problem to obtain a target variable set, where the target variable set includes at least one variable to be analyzed;

[0017] Where M is a positive integer greater than 1.

[0018] According to an embodiment of the present application, the constructing a multi-fidelity surrogate model based on the training set and calculating the first importance measure results of the M variables to be analyzed based on the multi-fidelity surrogate model includes:

[0019] S31 Based on the training set, construct the multi-fidelity surrogate model using the hierarchical Kriging method;

[0020] S32 Based on the multi-fidelity surrogate model, calculate the conditional expected variance and the total output response variance of the M variables to be analyzed respectively;

[0021] S33 obtains the sensitivity indices of the M variables to be analyzed based on the conditional expectation equation and outputs the corresponding total variance;

[0022] S34 obtains the first importance measure result based on the sensitivity indices of the M variables to be analyzed.

[0023] According to an embodiment of the present application, calculating the leave-one-out sensitivity analysis error for each sample in the high-fidelity sample set includes:

[0024] S41 determines whether the number of samples in the high-fidelity sample set is greater than or equal to a first threshold. If the number of samples is greater than or equal to the first threshold, uniformly select the first threshold number of samples from the high-fidelity sample set as the first sample set. If the number of samples is less than the first threshold, use all the samples in the high-fidelity sample set as the first sample set;

[0025] S42 calculates the first total sensitivity index vector of each variable to be analyzed in the first sample set;

[0026] S43 for each sample in the first sample set, after deleting the sample, obtain a second sample set, construct a multi-fidelity surrogate sub-model based on the second sample set, and calculate the second total sensitivity index vector of each variable to be analyzed in the second sample set based on the multi-fidelity surrogate sub-model;

[0027] S44 calculates the leave-one-out sensitivity analysis error for each sample based on the first total sensitivity index vector and the second total sensitivity index vector.

[0028] According to an embodiment of the present application, constructing a mathematical optimization problem for adaptively updating the added points and obtaining new sample points by solving based on the particle swarm optimization algorithm includes:

[0029] S51 constructs a mathematical optimization problem for adaptively updating the added points based on the optimization objective, and the calculation formula is as follows:

[0030]

[0031] where α is a balance factor, d min is the minimum distance between the sample point to be updated and the existing sample points, C(x) is the contribution value of the importance measure result at x, β is a space-filling factor, is the prediction variance of the multi-fidelity surrogate model;

[0032] S52 calculates the space-filling factor and the prediction variance of the multi-fidelity surrogate model;

[0033] S53 calculates the contribution value of the importance measure result of each sample point to be updated based on the weight factor and the leave-one-out sensitivity analysis error, and the calculation formula is as follows:

[0034]

[0035] where C i is the contribution value of the importance measure of the i-th sample point to be updated, N is the number of samples in the first sample set, w k is the weight of the k-th high-fidelity sample, e k is the leave-one-out sensitivity analysis error of the k-th high-fidelity sample, norm(|x i -x j |, 0, 1) is the normalized distance between the i-th sample point to be updated and the high-fidelity sample;

[0036] S54 solves the mathematical optimization problem based on the particle swarm optimization algorithm to obtain new sample points.

[0037] According to an embodiment of the present application, calculating the error improvement amplitudes of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and obtaining the fidelity type of the new sample points based on the error improvement amplitudes includes:

[0038] S61 calculates the error improvement amplitudes of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and the calculation formula is as follows:

[0039]

[0040] where is the value of the j-th variable of the total sensitivity index of the high-fidelity surrogate model established by updating the new sample point x * to the high-fidelity sample set, is the value of the j-th variable of the total sensitivity index of the low-fidelity surrogate model established by updating the new sample point x * to the low-fidelity sample set, S h(j) is the value of the j-th variable of the total sensitivity index of the multi-fidelity surrogate model, IA h is the error improvement amplitude of the new sample point for the high-fidelity sensitivity index, IA l is the error improvement amplitude of the new sample point for the low-fidelity sensitivity index;

[0041] S62 obtains the fidelity type of the new sample point based on the magnitude relationship between the error improvement amplitude of the new sample for the high-fidelity sensitivity index and the error improvement amplitude of the new sample point for the low-fidelity sensitivity index, and the cost ratio of collecting high-fidelity samples and low-fidelity samples.

[0042] According to an embodiment of the present application, determining whether the second importance measure result converges includes:

[0043] S81 Determine whether the total cost of the new sample point is greater than or equal to a second threshold. If the total cost of the new sample point is greater than or equal to the second threshold, determine that the second importance measure result converges. If the number of new sample points is less than the second threshold, jump to S82;

[0044] S82 Calculate the exponential variance, exponential disorder degree, and importance weight of the M variables to be analyzed;

[0045] S83 Based on the exponential variance, exponential disorder degree, and importance weight, obtain the second importance measure convergence error of the M variables to be analyzed;

[0046] S84 Determine whether the second importance measure convergence error is greater than a third threshold. If the second importance measure convergence error is greater than the third threshold, determine that the second importance measure result does not converge. If the second importance measure convergence error is less than or equal to the third threshold, determine that the second importance measure result converges.

[0047] According to an embodiment of the present application, screening the M variables to be analyzed based on the importance ranking result and the target problem to obtain a target variable set includes:

[0048] S101 Calculate the interaction effect of the M variables to be analyzed based on the second importance measure result of the M variables to be analyzed;

[0049] S102 Based on the importance ranking result and the target problem, select the variable with the largest total sensitivity index as the first variable set;

[0050] S103 Calculate the cumulative total sensitivity index of the first variable set, and determine whether the cumulative total sensitivity index is greater than or equal to a fourth threshold. When the cumulative total sensitivity index is greater than or equal to the fourth threshold, use the first variable set as the target variable set. When the cumulative total sensitivity index is less than the fourth threshold, jump to S104;

[0051] S104 Select the variable with the largest total sensitivity index from the remaining variables and add it to the first variable set, then jump to S103.

[0052] In a second aspect, the present application provides a variable importance screening device based on multi-fidelity sensitivity error. The device includes:

[0053] An acquisition module, configured to S1 acquire the distribution characteristics of M variables to be analyzed, where the distribution characteristics include the distribution type and distribution parameters of the variables to be analyzed;

[0054] A first processing module, configured to S2 respectively collect a high-fidelity sample set and a low-fidelity sample set as a training set according to a preset ratio through the Latin hypercube sampling method based on the distribution characteristics, and each sample in the training set includes M variables to be analyzed;

[0055] A second processing module, configured to S3 construct a multi-fidelity surrogate model according to the training set, and calculate a first importance measure result of the M variables to be analyzed based on the multi-fidelity surrogate model;

[0056] A third processing module, configured to S4 calculate the leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set, and obtain the contribution value of each sample in the high-fidelity sample set to the first importance measure result;

[0057] A fourth processing module, configured to S5 construct a mathematical optimization problem for adaptively updating sampling points, and solve to obtain new sample points based on the particle swarm optimization algorithm;

[0058] A fifth processing module, configured to S6 respectively calculate the error improvement amplitude of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index, and obtain the fidelity type of the new sample points based on the error improvement amplitude;

[0059] A sixth processing module, configured to S7 add the new sample points to the training set based on the fidelity type of the new sample points, update the multi-fidelity surrogate model, and calculate a second importance measure result of the M variables to be analyzed based on the updated multi-fidelity surrogate model;

[0060] A judgment module, configured to S8 judge whether the second importance measure result converges. In the case where the second importance measure result converges, use the second importance measure result as the target importance measure result. In the case where the second importance measure result does not converge, jump to S4;

[0061] A sorting module, configured to S9 sort the importance of the M variables to be analyzed based on the target importance measure result, and obtain an importance sorting result of the M variables to be analyzed;

[0062] A screening module, configured to S10 screen the M variables to be analyzed based on the importance sorting result and the target problem, and obtain a target variable set, where the target variable set includes at least one variable to be analyzed;

[0063] Where M is a positive integer greater than 1.

[0064] In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method for screening variable importance based on multi-fidelity sensitivity error as described in the first aspect above is implemented.

[0065] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method for screening variable importance based on multi-fidelity sensitivity error as described in the first aspect above is implemented.

[0066] In a fifth aspect, the present application provides a chip, which includes a processor and a communication interface. The communication interface is coupled to the processor, and the processor is used to run programs or instructions to implement the method for screening variable importance based on multi-fidelity sensitivity error as described in the first aspect.

[0067] In a sixth aspect, the present application provides a computer program product, including a computer program. When the computer program is executed by a processor, the method for screening variable importance based on multi-fidelity sensitivity error as described in the first aspect above is implemented.

[0068] Additional aspects and advantages of the present application will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present application.

[0069] The method for screening variable importance based on multi-fidelity sensitivity error provided by the present invention has the following beneficial effects compared with the prior art:

[0070] (1) By combining the Latin hypercube sampling technique, the multi-fidelity surrogate model, and the sensitivity error analysis framework, and using the dynamic collaborative modeling of high- and low-fidelity samples, the present invention can effectively balance the contradiction between the calculation cost and the model accuracy. The leave-one-out sensitivity analysis error contribution value evaluation and the particle swarm optimization algorithm are used to realize the adaptive update of sample points and the judgment of fidelity types. By introducing the multi-fidelity sensitivity error information, the importance measure process is incorporated into the construction process of the multi-fidelity surrogate model, strengthening the information interaction between the importance measure and the surrogate model, enabling the sensitivity error information to adaptively optimize the multi-fidelity surrogate model, significantly improving the importance measure of adapter variables and the accuracy of the multi-fidelity surrogate model globally, reducing the dependence on high-fidelity samples, and lowering the calculation cost of the adapter mechanical performance model.

[0071] (2) The present invention constructs a multi-fidelity surrogate model through the hierarchical Kriging method. By using high- and low-fidelity data, it can fully integrate the information advantages of samples with different precisions, improving the global approximation ability of the model and the efficiency of capturing local details. By calculating the conditional expected variance and the total variance of the output response, it quantifies the independent contribution of variables to the system response and the influence of interaction effects, enhancing the comprehensiveness and interpretability of variable importance measures. It effectively combines the high- and low-fidelity sensitivity analysis results, fully explores the correlation information between different-fidelity data, and improves the efficiency and robustness of screening important variables of the adapter.

[0072] (3) The present invention calculates the leave-one sensitivity analysis error for the high-fidelity sample set, which can effectively evaluate the influence of each sample on the importance measure results. By calculating the first total sensitivity index vector of each sample and performing a deletion operation on each sample, a new sample set is constructed and the second total sensitivity index vector is calculated, thereby obtaining the leave-one sensitivity analysis error of each sample. It can quantify the contribution of each sample to the importance measure results, help identify the key samples and variables affecting the model performance, and improve the efficiency and robustness of screening important variables of the adapter. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The above and / or additional aspects and advantages of the present application will become apparent and be easily understood from the description of the embodiments in conjunction with the following drawings, where:

[0074] Figure 1 is a schematic flowchart of a method for screening variable importance based on multi-fidelity sensitivity error provided by an embodiment of the present application;

[0075] Figure 2 is a schematic diagram of the final importance measure result of the mechanical properties of a polyurethane metamaterial provided by an embodiment of the present application;

[0076] Figure 3 is a schematic diagram of the verification process of the importance measure result provided by an embodiment of the present application;

[0077] Figure 4 is a schematic structural diagram of a device for screening variable importance based on multi-fidelity sensitivity error provided by an embodiment of the present application;

[0078] Figure 5 is a schematic structural diagram of an electronic device provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0079] Next, the technical solutions in the embodiments of the present application will be clearly described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.

[0080] The terms "first", "second", etc. in the description and claims of the present application are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are usually of the same type, and the number of objects is not limited. For example, the first object can be one or multiple. In addition, "and / or" in the description and claims means at least one of the connected objects, and the character " / " generally means that the related objects before and after are in an "or" relationship.

[0081] Next, in conjunction with the accompanying drawings, the method for screening variable importance based on multi-fidelity sensitivity error, the device for screening variable importance based on multi-fidelity sensitivity error, the electronic device, and the readable storage medium provided by the embodiments of the present application will be described in detail through specific embodiments and their application scenarios.

[0082] Among them, the method for screening variable importance based on multi-fidelity sensitivity error can be applied to a terminal, and can be specifically executed by hardware or software in the terminal.

[0083] The terminal includes, but is not limited to, portable communication devices such as mobile phones or tablets with a touch-sensitive surface (for example, a touch screen display and / or a touchpad). It should also be understood that in some embodiments, the terminal may not be a portable communication device, but a desktop computer with a touch-sensitive surface (for example, a touch screen display and / or a touchpad).

[0084] In the following various embodiments, a terminal including a display and a touch-sensitive surface is described. However, it should be understood that the terminal may include one or more other physical user interface devices such as a physical keyboard, a mouse, and a joystick.

[0085] The variable importance screening method based on multi-fidelity sensitivity error provided by the embodiments of this application. The execution subject of this variable importance screening method based on multi-fidelity sensitivity error can be an electronic device or a functional module or functional entity in the electronic device that can implement the function of this variable importance screening method based on multi-fidelity sensitivity error. The electronic devices mentioned in the embodiments of this application include, but are not limited to, mobile phones, tablet computers, computers, cameras, wearable devices, etc. Here, taking the electronic device as the execution subject as an example, the variable importance screening method based on multi-fidelity sensitivity error provided by the embodiments of this application will be described.

[0086] In the field of engineering design, the modeling and analysis of complex systems usually involve numerous parameters and variables. In these systems, it is crucial to understand the impact of parameters and variables on system performance. Importance measure is one of the important steps to solve uncertainty quantification, which can help analyze the importance degree of system design variables or parameters on the performance of the entire system. Through importance measure, researchers can identify key parameters, optimize the model, reduce the computational cost, and improve the understanding of the system.

[0087] Importance measure methods are mainly divided into local importance measure and global importance measure methods. Local importance measure methods usually evaluate the importance of a variable by analyzing the impact of a certain variable on the system response at a fixed point or within a local range, such as the direct derivative method, finite difference method, etc. These methods are simple to calculate and have high efficiency, but they cannot fully reflect the impact of variables on the system within the entire input range, so there are limitations in the analysis of complex systems. In contrast, global importance measure methods can consider the impact of variables in the entire input space. Common methods include variance decomposition method, moment independence method, etc. These methods can comprehensively evaluate the direct and interaction effects of variables on the system output, but their calculation process usually requires a large number of samples to support, resulting in high computational cost and large time consumption. Especially when dealing with high-dimensional nonlinear problems, it is difficult to meet the actual engineering requirements.

[0088] To solve the problem of high model calculation cost, researchers have introduced surrogate model technology. The surrogate model significantly reduces the computational requirements in the importance measure process by replacing the real model with a low-cost approximate model. However, in existing methods, the construction of the surrogate model and the importance measure process are usually independent of each other. The traditional approach is to first construct a surrogate model that meets the accuracy requirements separately, and then use this model for importance measure analysis. This way does not fully utilize the sensitivity information to optimize the surrogate model, resulting in a lack of information interaction between the two processes and reducing the overall computational efficiency.

[0089] Figure 1 is the schematic flowchart of the variable importance screening method based on multi-fidelity sensitivity error provided by the embodiments of this application, as Figure 1As shown, the variable importance screening method based on multi-fidelity sensitivity error includes: Step 110, Step 120, Step 130, Step 140, Step 150, Step 160, Step 170, Step 180, Step 190, and Step 100.

[0090] Step 110, S1: Obtain the distribution characteristics of M variables to be analyzed, where the distribution characteristics include the distribution type and distribution parameters of the variables to be analyzed;

[0091] It is easy to understand that the electronic device obtains the distribution characteristics of M variables to be analyzed. The distribution characteristics include the distribution type and distribution parameters of the variables to be analyzed. The distribution type is, for example, normal distribution, uniform distribution, exponential distribution, etc., and the distribution parameters are, for example, mean, variance, degrees of freedom, etc.

[0092] Exemplarily, the variables to be analyzed are various geometric features, material properties, process parameters, etc. of the adapter.

[0093] Step 120, S2: Based on the distribution characteristics, respectively collect a high-fidelity sample set and a low-fidelity sample set as the training set according to a preset ratio through the Latin hypercube sampling method. Each sample in the training set includes M variables to be analyzed;

[0094] Optionally, after the electronic device obtains the distribution characteristics of M variables to be analyzed, according to the distribution characteristics, use the Latin hypercube sampling method to respectively collect a high-fidelity sample set with 60% cost and a low-fidelity sample set with 40% cost as the training set according to a preset ratio of 3:2.

[0095] It is easy to understand that the fidelity is the degree to which a certain system, device, or model can faithfully reproduce the original data, signal, or design in a certain process. The higher the fidelity, the closer it is to the real or original state.

[0096] Step 130, S3: Construct a multi-fidelity surrogate model according to the training set, and calculate the first importance measure result of the M variables to be analyzed based on the multi-fidelity surrogate model;

[0097] It is easy to understand that an initial multi-fidelity surrogate model is constructed according to the training set. Based on the constructed multi-fidelity surrogate model, each sample in the training set is predicted to obtain the sensitivity index of the M variables to be analyzed. According to the magnitude relationship of the sensitivity indices of the M variables to be analyzed, the first importance measure result of the M variables to be analyzed is obtained.

[0098] Step 140, S4: Calculate the leave-one sensitivity analysis error of each sample in the high-fidelity sample set, and obtain the contribution value of each sample in the high-fidelity sample set to the first importance measure result;

[0099] It should be noted that the leave-one sensitivity analysis error refers to the difference in the total sensitivity indices of all variables between the re-established multi-fidelity surrogate model and the initial multi-fidelity surrogate model after removing one sample each time during the sensitivity analysis process. This error is used to quantify the contribution value of each sample to the result of the first importance measure.

[0100] Step 150, S5: Construct a mathematical optimization problem for adaptively updating the sampling points, and solve it based on the particle swarm optimization algorithm to obtain new sample points;

[0101] It is worth noting that in order to further improve the importance measure of M variables to be analyzed and the accuracy of the multi-fidelity surrogate model, the initial multi-fidelity surrogate model is updated by adding new sample points.

[0102] Step 160, S6: Calculate the error improvement amplitudes of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and based on the error improvement amplitudes, obtain the fidelity type of the new sample points;

[0103] Furthermore, after obtaining the new sample points, calculate the error improvement amplitudes of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, as well as the cost ratio of collecting high-fidelity samples and low-fidelity samples, and judge the fidelity type of the new sample points.

[0104] Step 170, S7: Based on the fidelity type of the new sample points, add the new sample points to the training set, update the multi-fidelity surrogate model, and calculate the second importance measure result of the M variables to be analyzed based on the updated multi-fidelity surrogate model;

[0105] It is easy to understand that if the new sample point is a high-fidelity sample, add the new sample point to the high-fidelity sample set in the training set; if the new sample point is a low-fidelity sample, add the new sample point to the low-fidelity sample set in the training set and update the multi-fidelity surrogate model.

[0106] Step 180, S8: Judge whether the second importance measure result converges. If the second importance measure result converges, use the second importance measure result as the target importance measure result; if the second importance measure result does not converge, jump to S4;

[0107] It should be noted that after obtaining the second importance measure result of the M variables to be analyzed, judge whether the second importance measure result is stable within a preset range. When the second importance measure result converges, use the second importance measure result as the target importance measure result; when the second importance measure result does not converge, jump to step 140 above.

[0108] Step 190, S9: Based on the target importance measure result, rank the importance of the M variables to be analyzed to obtain the importance ranking result of the M variables to be analyzed;

[0109] Step 100, S10: Based on the importance ranking result and the target problem, screen the M variables to be analyzed to obtain a target variable set, where the target variable set includes at least one variable to be analyzed;

[0110] Where M is a positive integer greater than 1.

[0111] Finally, according to the importance ranking result and the target problem, screen the M variables to be analyzed through the cumulative sensitivity index to obtain the target variable set.

[0112] According to the variable importance screening method based on multi-fidelity sensitivity error provided by the embodiments of the present application, by combining the Latin hypercube sampling technique, the multi-fidelity surrogate model, and the sensitivity error analysis framework, and using the dynamic collaborative modeling of high- and low-fidelity samples, the contradiction between the computational cost and the model accuracy can be effectively balanced. The leave-one sensitivity analysis error contribution value evaluation and the particle swarm optimization algorithm are used to realize the adaptive update of the sample points and the judgment of the fidelity type. By introducing the multi-fidelity sensitivity error information, the importance measure process is incorporated into the construction process of the multi-fidelity surrogate model, strengthening the information interaction between the importance measure and the surrogate model, enabling the sensitivity error information to adaptively optimize the multi-fidelity surrogate model, significantly improving the accuracy of the importance measure of the adapter variables and the multi-fidelity surrogate model globally, reducing the dependence on high-fidelity samples, and reducing the computational cost of the adapter mechanical performance model.

[0113] In some embodiments, the constructing the multi-fidelity surrogate model according to the training set and calculating the first importance measure result of the M variables to be analyzed based on the multi-fidelity surrogate model includes:

[0114] S31: Based on the training set, construct the multi-fidelity surrogate model by using the hierarchical Kriging method;

[0115] S32: Based on the multi-fidelity surrogate model, calculate the conditional expected variance and the total output response variance of the M variables to be analyzed respectively;

[0116] S33: Based on the conditional expected equation and the total output response variance, obtain the sensitivity index of the M variables to be analyzed;

[0117] S34: Based on the sensitivity index of the M variables to be analyzed, obtain the first importance measure result.

[0118] It is easy to understand that first, a low-fidelity Kriging surrogate model is constructed through low-fidelity samples. This surrogate model can estimate the low-fidelity output response of the samples. Then, the hierarchical Kriging method is used to construct the multi-fidelity surrogate model, and the calculation formula is as follows:

[0119]

[0120] where a is the high / low-fidelity correlation coefficient, φ(x) is the correlation vector between x and the high-fidelity sample set, Φ is the correlation vector between samples, y h is the output response of the high-fidelity samples, H is the intermediate regression vector for constructing the low-fidelity model, y mf is the multi-fidelity surrogate model, y lf is the low-fidelity Kriging surrogate model.

[0121] Furthermore, based on the multi-fidelity surrogate model, the conditional expected variance of M variables to be analyzed and the total variance of the output response are calculated, and the sensitivity index of the M variables to be analyzed is calculated according to the ratio of the two.

[0122] In this embodiment, the hierarchical Kriging method is used to construct the multi-fidelity surrogate model. Using high- and low-fidelity data can fully integrate the information advantages of samples with different precisions, improving the global approximation ability of the model and the local detail capture efficiency; by calculating the conditional expected variance and the total variance of the output response, the independent contribution of variables to the system response and the influence of interaction effects are quantified, enhancing the comprehensiveness and interpretability of variable importance measures, effectively combining the high- and low-fidelity sensitivity analysis results, fully exploring the correlation information between different-fidelity data, and improving the efficiency and robustness of variable screening for the adapter.

[0123] In some embodiments, calculating the leave-one sensitivity analysis error for each sample in the high-fidelity sample set includes:

[0124] S41 Determine whether the number of samples in the high-fidelity sample set is greater than or equal to a first threshold. If the number of samples is greater than or equal to the first threshold, uniformly select the first threshold number of samples from the high-fidelity sample set as the first sample set. If the number of samples is less than the first threshold, use all the samples in the high-fidelity sample set as the first sample set;

[0125] S42 Calculate the first total sensitivity index vector for each variable to be analyzed in the first sample set;

[0126] S43 For each sample in the first sample set, after deleting the sample, a second sample set is obtained. Based on the second sample set, a multi-fidelity surrogate sub-model is constructed. Based on the multi-fidelity surrogate sub-model, a second total sensitivity index vector of each variable to be analyzed in the second sample set is calculated.

[0127] S44 Based on the first total sensitivity index vector and the second total sensitivity index vector, the leave-one-out sensitivity analysis error of each sample is calculated.

[0128] In some embodiments, to improve the calculation efficiency, it is necessary to select the high-fidelity sample set. When the number of samples in the high-fidelity sample set is greater than or equal to 50, 50 high-fidelity samples are evenly selected from the high-fidelity sample set as the first sample set. When the number of samples in the high-fidelity sample set is less than 50, all samples in the high-fidelity sample set are used as the first sample set.

[0129] Further, based on the above multi-fidelity surrogate model, a first total sensitivity index vector of each variable to be analyzed in the first sample set is calculated. For the K-th high-fidelity sample point in the first sample set, a multi-fidelity surrogate sub-model excluding the sample point is constructed, and a second total sensitivity index vector of each variable to be analyzed is calculated based on the multi-fidelity surrogate sub-model. According to the first total sensitivity index vector and the second total sensitivity index vector, the leave-one-out sensitivity analysis error of the K-th high-fidelity sample point is calculated. The calculation formula is as follows:

[0130]

[0131] where D is the number of analysis variables, is the value of the j-th variable of the vector S Tk and is the value of the j-th variable of the total sensitivity index constructed by all samples, and e k is the leave-one-out sensitivity analysis error of the k-th high-fidelity sample point.

[0132] In this embodiment, by calculating the leave-one-out sensitivity analysis error of the high-fidelity sample set, the influence of each sample on the importance measure result can be effectively evaluated. By calculating the first total sensitivity index vector of each sample, deleting each sample, constructing a new sample set and calculating the second total sensitivity index vector, the leave-one-out sensitivity analysis error of each sample is obtained. It can quantify the contribution of each sample to the importance measure result, help identify the key samples and variables affecting the model performance, and improve the efficiency and robustness of the adapter importance variable screening.

[0133] In some embodiments, constructing a mathematical optimization problem for adaptively updating sampling points and obtaining new sample points by solving based on a particle swarm optimization algorithm includes:

[0134] S51 Construct a mathematical optimization problem for adaptively updating sampling points based on an optimization objective, and the calculation formula is as follows:

[0135]

[0136] where α is a balance factor, d min is the minimum distance between the sample points to be updated and the existing sample points, C(x) is the contribution value of the importance measure result at x, β is a space filling factor, and is the prediction variance of the multi-fidelity surrogate model;

[0137] S52 Calculate the space filling factor and the prediction variance of the multi-fidelity surrogate model;

[0138] S53 Calculate the contribution value of the importance measure result of each sample point to be updated based on the weight factor and the leave-one-out sensitivity analysis error, and the calculation formula is as follows:

[0139]

[0140] where C i is the importance measure contribution value of the i-th sample point to be updated, N is the number of samples in the first sample set, w k is the weight of the k-th high-fidelity sample, e k is the leave-one-out sensitivity analysis error of the k-th high-fidelity sample, norm(|x i -x j |, 0, 1) is the normalized distance between the i-th sample point to be updated and the high-fidelity sample;

[0141] S54 Solve the mathematical optimization problem based on the particle swarm optimization algorithm to obtain new sample points.

[0142] It is easy to understand that after constructing the mathematical optimization problem for adaptively updating sampling points, first calculate the space filling factor and the prediction variance of the multi-fidelity surrogate model required in the optimization objective. The prediction variance of the multi-fidelity surrogate model can be obtained through the multi-fidelity surrogate model, and the calculation formula of the space filling factor is as follows:

[0143] β = λd ave

[0144] where λ is a scaling factor determining the sample crowding degree, and d ave is the average spatial distance of the existing sample points.

[0145] Further, based on the weight factor and the leave-one-out sensitivity analysis error, calculate the contribution value of the importance measure result of each sample point to be updated, and use the particle swarm intelligent optimization algorithm to solve the mathematical optimization problem to obtain new sample points.

[0146] In some embodiments, the population size is set to 50, the maximum number of iterations is set to 100, the inertia weight and the learning factor are both set to adaptively varying values in the interval [0.5, 2.5]. By initializing the population, updating particle position and velocity parameters, etc., and continuously iterating until convergence, the individual with the largest value of f(x) is calculated as the position of the new sample point.

[0147] In this embodiment, through an adaptive update strategy, a mathematical optimization problem is constructed using sensitivity error information, the fidelity type of the new sample point is dynamically selected and incorporated into the training set, realizing the efficient correction and gradual optimization of the multi-fidelity surrogate model, effectively optimizing the selection of sample points, evaluating the importance of each sample point to be updated and its contribution to the model performance by calculating the space filling factor and the prediction variance of the multi-fidelity surrogate model, combining the leave-one-out sensitivity analysis error and the weight factor, dynamically updating the sample points, and improving the efficiency, robustness, and accuracy of the importance variable screening of the adapter.

[0148] In some embodiments, calculating the error improvement amplitude of the new sample point for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and obtaining the fidelity type of the new sample point based on the error improvement amplitude includes:

[0149] S61 Calculate the error improvement amplitude of the new sample point for the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and the calculation formula is as follows:

[0150]

[0151] Where, is the value of the j-th variable of the total sensitivity index of the high-fidelity sample set established by updating the new sample point x * to the high-fidelity sample set, is the value of the j-th variable of the total sensitivity index of the low-fidelity sample set established by updating the new sample point x * to the low-fidelity sample set, S h(j) is the value of the j-th variable of the total sensitivity index of the multi-fidelity surrogate model, IA h is the error improvement amplitude of the new sample point for the high-fidelity sensitivity index, IA l is the error improvement amplitude of the new sample point for the low-fidelity sensitivity index;

[0152] S62 obtains the fidelity type of the new sample point based on the magnitude relationship between the error improvement amplitude of the high-fidelity sensitivity index with respect to the new sample and the error improvement amplitude of the low-fidelity sensitivity index with respect to the new sample point, as well as the cost ratio of collecting high-fidelity samples and low-fidelity samples.

[0153] It is easy to understand that the error improvement amplitudes of the new sample point with respect to the high-fidelity sensitivity index and the low-fidelity sensitivity index are calculated separately, and in combination with the cost ratio of collecting high-fidelity samples and low-fidelity samples, the fidelity type of the new sample point is determined: when the error improvement amplitude of the new sample point with respect to the high-fidelity sensitivity index is greater than the product of the error improvement amplitude of the new sample point with respect to the low-fidelity sensitivity index and the cost ratio of collecting high- and low-fidelity samples, the fidelity type of the new sample point is determined to be a high-fidelity sample; otherwise, the fidelity type of the new sample point is determined to be a low-fidelity sample.

[0154] In this embodiment, the error improvement amplitudes of the new sample point with respect to the high-fidelity sensitivity index and the low-fidelity sensitivity index are calculated separately, which can effectively evaluate the contribution of new sample points with different fidelities to the importance measure results. Based on the magnitude relationship of the error improvement amplitudes and the cost ratio of collecting high-fidelity and low-fidelity samples, the fidelity type of the new sample point is determined, optimizing the sample point selection strategy, improving the accuracy and calculation efficiency of the importance measure, and reducing the sampling cost.

[0155] In some embodiments, the judging whether the second importance measure result converges includes:

[0156] S81 judges whether the total cost of the new sample points is greater than or equal to a second threshold. If the total cost of the new sample points is greater than or equal to the second threshold, it is determined that the second importance measure result converges; if the number of new sample points is less than the second threshold, it jumps to S82;

[0157] S82 calculates the exponential variance, exponential disorder degree, and importance weights of the M variables to be analyzed;

[0158] S83 obtains the second importance measure convergence error of the M variables to be analyzed based on the exponential variance, exponential disorder degree, and importance weights;

[0159] S84 judges whether the second importance measure convergence error is greater than a third threshold. If the second importance measure convergence error is greater than the third threshold, it is determined that the second importance measure result does not converge; if the second importance measure convergence error is less than or equal to the third threshold, it is determined that the second importance measure result converges.

[0160] It is easy to understand that when the number of new sample points is less than the second threshold, the following steps are continued:

[0161] (1) Calculate the variance of the sensitivity index of the j-th variable, and the calculation formula is as follows:

[0162]

[0163] where m is the number of iterations, and S h(ij) is the value of the j-th variable of the sensitivity index of the multi-fidelity surrogate model in the i-th generation, is the average value of the values of the j-th variable of the sensitivity index of the surrogate models in the previous i generations, is the variance of the sensitivity index.

[0164] (2) Calculate the scrambling degree of the sensitivity index of the j-th variable, and the calculation formula is as follows:

[0165]

[0166] where Noh j and Nol j are the rankings of the j-th variable of the high / low-fidelity sensitivity index respectively, and L is the scrambling degree of the sensitivity index.

[0167] (3) Calculate the importance weight of the j-th variable, and the calculation formula is as follows:

[0168]

[0169] where, and are the average values of the j-th variable of the high / low-fidelity sensitivity index in all iteration processes respectively, and ω is the importance weight.

[0170] Calculate the convergence error of the second importance measure, and the calculation formula is as follows:

[0171]

[0172] where error is the convergence error of the second importance measure, ω is the importance weight, L is the scrambling degree of the sensitivity index, is the variance of the sensitivity index.

[0173] Finally, judge whether the convergence error of the second importance measure is greater than the third threshold. If the convergence error of the second importance measure is greater than the third threshold, it is determined that the result of the second importance measure has not converged, and new sample points need to be solved continuously. If the convergence error of the second importance measure is less than or equal to the third threshold, it is determined that the result of the second importance measure has converged.

[0174] In this embodiment, by judging the relationship between the total cost of the new sample points and the second threshold, the iterative process of the calculation can be effectively controlled. When the total cost reaches a certain threshold, it is determined that the second importance measure result has converged, reducing unnecessary calculations. When the number of new sample points is small, the convergence error of the second importance measure of the variable to be analyzed is calculated through indicators such as exponential variance, exponential disorder degree, and importance weight to determine whether it converges, reducing the calculation cost and time, and improving the efficiency and robustness of the importance variable screening of the adapter.

[0175] In some embodiments, screening the M variables to be analyzed based on the importance ranking result and the target problem to obtain a target variable set, including:

[0176] S101 Calculate the interaction effect of the M variables to be analyzed based on the second importance measure results of the M variables to be analyzed;

[0177] S102 Select the variable with the largest total sensitivity index as the first variable set based on the importance ranking result and the target problem;

[0178] S103 Calculate the cumulative total sensitivity index of the first variable set, and judge whether the cumulative total sensitivity index is greater than or equal to the fourth threshold. When the cumulative total sensitivity index is greater than or equal to the fourth threshold, use the first variable set as the target variable set. When the cumulative total sensitivity index is less than the fourth threshold, jump to S104;

[0179] S104 Select the variable with the largest total sensitivity index from the remaining variables, add it to the first variable set, and jump to S103.

[0180] In some embodiments, ignoring the high-order interaction effects of the analysis problem, calculate the interaction effects of the M variables to be analyzed, and the calculation formula is as follows:

[0181] S c = 1 - ∑S

[0182] where S is the main sensitivity index of the second importance measure result, and S c is the interaction effect.

[0183] Sort the total sensitivity indices of each variable from largest to smallest, select the important variables of this analysis problem according to the sorting, and calculate the cumulative sensitivity index S a , when the cumulative sensitivity index satisfies S a - S c ≥ 0.99, stop selecting important variables. Since the high-order interaction effects are ignored, the second-order interaction effect in the total sensitivity index is calculated twice, so S c; This means that the variables with the top 0.99 influence on the problem are selected, and the influence of the remaining variables will be ignored.

[0184] In some embodiments, the electronic device screens the important variables of the mechanical properties of the metamaterial adapter, the adapter is a polyurethane metamaterial, and the simulation is performed using the finite element software ANSYS19.2. The simulation uses the software's own APDL command stream for automated analysis throughout the simulation, including mesh generation, load setting, constraint setting, calculation evaluation and post-processing. The maximum Y-direction displacement of the upper surface of the polyurethane metamaterial when under pressure is taken to evaluate the mechanical properties. Table 1 shows the six variables to be analyzed and their distribution characteristics of the polyurethane metamaterial. As shown in Table 1, the variables to be analyzed are the radius of the fillet of the horizontal hole, the radius of the fillet of the vertical hole, the center distance of the lower right hole, the center distance of the upper right hole, the center distance of the upper left hole and the center distance of the lower left hole. The Latin hypercube sampling method is used to uniformly collect 6 initial high-fidelity sample points and 24 low-fidelity sample points. The cost ratio of collecting high and low samples in this embodiment is 6:1, the initial high-fidelity sample set cost accounts for 60%, and the low-fidelity sample set cost accounts for 40%.

[0185] Table 1 Distribution characteristics of the variables to be analyzed

[0186]

[0187]

[0188] The variables finally screened out in the above manner are shown in Table 2. The importance of the mechanical properties of the polyurethane metamaterial was measured, and 4 important variables were screened out from the original 6-dimensional variables.

[0189] Table 2. Table of important variables

[0190]

[0191] Figure 2 A schematic diagram of the final importance measurement results of the mechanical properties of the polyurethane metamaterial provided in the embodiment of the present application, such as Figure 2 As shown, the analysis variable x 1 ,x 6 The total sensitivity index of the analysis variable x is very small, only 0.008 and 0.01; 2 ,x 3 showed high sensitivity, with the total sensitivity indexes of 0.441 and 0.559 respectively; the analysis variable x 3 ,x 5 The difference between the total sensitivity index and the main sensitivity index is relatively large, indicating that the two have certain interactions with other variables; according to the importance measurement results in the figure, the importance variables are screened, and S a -S cThe values are shown in Table 3. When the variable is selected to x 5 , stop screening. After screening the important variables for the mechanical properties of the polyurethane metamaterial, x 3 , x 2 , x 5 , x 4 Four important variables can be obtained.

[0192] Table 3 Process table for screening important variables

[0193]

[0194]

[0195] Figure 3 is a schematic diagram of the verification process of the importance measure results provided by the embodiments of the present application. The embodiments of the present solution prove the effectiveness of the present invention by comparing the cumulative distribution functions of the mechanical properties of the polyurethane metamaterial before and after screening; the abscissa in the figure is the maximum Y-direction displacement on the upper surface of the metamaterial structure, and the ordinate is the cumulative distribution probability value. There are three curves in the figure. The solid line represents the output cumulative distribution function of the original simulation model, the dotted line represents the cumulative distribution function of the multi-fidelity surrogate model constructed by using all analysis variables in the present invention, and the dash-dotted line represents removing the variable x 1 , x 6 , and only using the important variables to construct the cumulative distribution function of the multi-fidelity surrogate model; by calculating the lower areas of the three curves as shown in Table 4, it can be known that the error between the adaptive multi-fidelity surrogate model excluding x 1 and x 6 and the original model is only 1.45%, which is only 0.6% higher than the error of directly using all variables for modeling, proving that the variables x 1 , x 6 have little influence on the mechanical properties of the polyurethane metamaterial, and the present invention preferably screens out the important variables of this problem.

[0196] Table 4 Verification of importance measure results

[0197]

[0198] In this embodiment, by calculating the interaction effects of the variables to be analyzed based on the second importance measure results, and combining the importance ranking results and the target problem for variable screening, variables that have a greater impact on the target problem can be effectively identified. Through the judgment of the cumulative total sensitivity index, the selected variable set has sufficient sensitivity, improving the accuracy and pertinence of variable screening, optimizing the target variable set, and improving the efficiency and robustness of the important variable screening of the adapter.

[0199] The variable importance screening method based on multi-fidelity sensitivity error provided by the embodiments of the present application may have an execution entity as the variable importance screening device based on multi-fidelity sensitivity error. In the embodiments of the present application, taking the variable importance screening device based on multi-fidelity sensitivity error as an example to execute the variable importance screening method based on multi-fidelity sensitivity error, the variable importance screening device based on multi-fidelity sensitivity error provided by the embodiments of the present application is described.

[0200] The embodiments of the present application further provide a variable importance screening device based on multi-fidelity sensitivity error, as Figure 4 shown. The variable importance screening device based on multi-fidelity sensitivity error includes: an acquisition module 410, a first processing module 420, a second processing module 430, a third processing module 440, a fourth processing module 450, a fifth processing module 460, a sixth processing module 470, a judgment module 480, a sorting module 490, and a screening module 400.

[0201] The acquisition module 410 is configured to S1 acquire the distribution characteristics of M variables to be analyzed, where the distribution characteristics include the distribution type and distribution parameters of the variables to be analyzed;

[0202] The first processing module 420 is configured to S2 respectively collect a high-fidelity sample set and a low-fidelity sample set as training sets according to a preset ratio by the Latin hypercube sampling method based on the distribution characteristics, and each sample in the training set includes M variables to be analyzed;

[0203] The second processing module 430 is configured to S3 construct a multi-fidelity surrogate model according to the training set, and calculate a first importance measure result of the M variables to be analyzed based on the multi-fidelity surrogate model;

[0204] The third processing module 440 is configured to S4 calculate the leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set, and obtain the contribution value of each sample in the high-fidelity sample set to the first importance measure result;

[0205] The fourth processing module 450 is configured to S5 construct a mathematical optimization problem of adaptively updating and adding points, and solve to obtain new sample points based on the particle swarm optimization algorithm;

[0206] The fifth processing module 460 is configured to S4 respectively calculate the error improvement amplitude of the new sample points for the high-fidelity sensitivity index and the low-fidelity sensitivity index, and obtain the fidelity type of the new sample points based on the error improvement amplitude;

[0207] The sixth processing module 470 is configured to, in S7, add the new sample points to the training set based on the fidelity type of the new sample points, update the multi-fidelity surrogate model, and calculate the second importance measure result of the M variables to be analyzed based on the updated multi-fidelity surrogate model;

[0208] The judgment module 480 is configured to, in S8, judge whether the second importance measure result converges. If the second importance measure result converges, use the second importance measure result as the target importance measure result. If the second importance measure result does not converge, jump to S4;

[0209] The sorting module 490 is configured to, in S9, sort the importance of the M variables to be analyzed based on the target importance measure result to obtain the importance sorting result of the M variables to be analyzed;

[0210] The screening module 400 is configured to, in S10, screen the M variables to be analyzed based on the importance sorting result and the target problem to obtain a target variable set, where the target variable set includes at least one variable to be analyzed;

[0211] Where M is a positive integer greater than 1.

[0212] According to the variable importance screening device based on multi-fidelity sensitivity error provided by the embodiments of the present application, by combining the Latin hypercube sampling technique, the multi-fidelity surrogate model, and the sensitivity error analysis framework, and using the dynamic collaborative modeling of high- and low-fidelity samples, it can effectively balance the contradiction between the calculation cost and the model accuracy. The leave-one sensitivity analysis error contribution value evaluation and the particle swarm optimization algorithm are used to realize the adaptive update of the sample points and the judgment of the fidelity type. By introducing the multi-fidelity sensitivity error information, the importance measure process is incorporated into the construction process of the multi-fidelity surrogate model, strengthening the information interaction between the importance measure and the surrogate model, enabling the sensitivity error information to adaptively optimize the multi-fidelity surrogate model, significantly improving the accuracy of the importance measure of the adapter variables and the multi-fidelity surrogate model globally, reducing the dependence on high-fidelity samples, and reducing the calculation cost of the adapter mechanical performance model.

[0213] The variable importance screening device based on multi-fidelity sensitivity error provided by the embodiments of the present application can implement Figures 1 to 3 Each process implemented by the variable importance screening method embodiment based on multi-fidelity sensitivity error. To avoid repetition, it will not be elaborated here.

[0214] In some embodiments, such as Figure 5As shown in the figure, an embodiment of the present application further provides an electronic device 500, including a processor 501, a memory 502, and a computer program stored on the memory 502 and executable on the processor 501. When the program is executed by the processor 501, it implements each process of the above-described embodiment of the variable importance screening method based on multi-fidelity sensitivity error and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.

[0215] It should be noted that the electronic device in the embodiment of the present application includes the above-mentioned mobile electronic device and non-mobile electronic device.

[0216] An embodiment of the present application further provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements each process of the above-described embodiment of the variable importance screening method based on multi-fidelity sensitivity error and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.

[0217] Among them, the processor is the processor in the electronic device in the above embodiment. The readable storage medium includes computer-readable storage media such as computer read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0218] An embodiment of the present application further provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the above-described variable importance screening method based on multi-fidelity sensitivity error.

[0219] Among them, the processor is the processor in the electronic device in the above embodiment. The readable storage medium includes computer-readable storage media such as computer read-only memory ROM, random access memory RAM, magnetic disk, or optical disk.

[0220] Another embodiment of the present application provides a chip, which includes a processor and a communication interface. The communication interface is coupled to the processor, and the processor is used to run programs or instructions to implement each process of the above-described embodiment of the variable importance screening method based on multi-fidelity sensitivity error and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.

[0221] It should be understood that the chip mentioned in the embodiment of the present application may also be referred to as a system-on-chip, system chip, chip system, or system-on-chip.

[0222] It should be noted that in this text, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of additional identical elements in the process, method, article or device comprising such element. In addition, it should be pointed out that the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, but may also include performing functions in a substantially simultaneous manner or in the reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0223] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described example methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on this understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a computer software product. The computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions for causing a terminal (which can be a mobile phone, computer, server, or network device, etc.) to execute the variable importance screening method based on multi-fidelity sensitivity error in each embodiment of the present application.

[0224] In the description of the present application, the "first feature" and "second feature" may include one or more of such features.

[0225] In the description of the present application, the meaning of "a plurality of" is two or more.

[0226] The embodiments of the present application have been described above in conjunction with the accompanying drawings. However, the present application is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Those of ordinary skill in the art, under the inspiration of the present application and without departing from the spirit and scope protected by the claims of the present application, can still make many forms, all of which fall within the protection scope of the present application.

[0227] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "schematic embodiments", "examples", "specific examples", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0228] Although the embodiments of this application have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of this application, and the scope of this application is defined by the claims and their equivalents.

Claims

1. A variable importance screening method based on multi-fidelity sensitivity error, characterized in that: The method comprises: S1 obtains distribution characteristics of M variables to be analyzed, wherein the distribution characteristics include distribution types and distribution parameters of the variables to be analyzed; S2, based on the distribution characteristics, respectively collects a high-fidelity sample set and a low-fidelity sample set as training sets according to a preset ratio by using a Latin hypercube sampling method, wherein each sample in the training set includes M variables to be analyzed; S3: constructing a multi-fidelity proxy model according to the training set, and calculating the first importance measurement results of the M variables to be analyzed based on the multi-fidelity proxy model; S4: calculating a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set to obtain a contribution value of each sample in the high-fidelity sample set to the first importance measurement result; S5 constructs a mathematical optimization problem for adaptively updating and adding points, and obtains new sample points based on the particle swarm optimization algorithm; S6: respectively calculating the error improvement of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index, and obtaining the fidelity type of the new sample point based on the error improvement; S7: adding the new sample point to the training set based on the fidelity type of the new sample point, updating the multi-fidelity proxy model, and calculating the second importance measurement results of the M variables to be analyzed based on the updated multi-fidelity proxy model; S8: judging whether the second importance measurement result converges. If the second importance measurement result converges, taking the second importance measurement result as the target importance measurement result; if the second importance measurement result does not converge, jumping to S4; S9: sorting the importance of the M variables to be analyzed based on the target importance measurement result to obtain the importance sorting result of the M variables to be analyzed; S10: screening the M variables to be analyzed based on the importance ranking result and the target problem to obtain a target variable set, wherein the target variable set includes at least one variable to be analyzed; Wherein, M is a positive integer greater than 1.

2. The variable importance screening method based on multi-fidelity sensitivity error according to claim 1 is characterized in that: The step of constructing a multi-fidelity proxy model according to the training set and calculating the first importance measurement results of the M variables to be analyzed based on the multi-fidelity proxy model includes: S31 constructing the multi-fidelity proxy model based on the training set using a hierarchical Kriging method; S32, based on the multi-fidelity surrogate model, respectively calculating the conditional expected variance and the total variance of the output response of the M variables to be analyzed; S33 obtains the sensitivity index of the M variables to be analyzed based on the conditional expectation equation and the output corresponding total variance; S34 obtains the first importance measurement result based on the sensitivity indexes of the M variables to be analyzed.

3. The variable importance screening method based on multi-fidelity sensitivity error according to claim 1, characterized in that: The calculating the leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set comprises: S41 determines whether the number of samples in the high-fidelity sample set is greater than or equal to a first threshold. If the number of samples is greater than or equal to the first threshold, uniformly select the first threshold number of samples from the high-fidelity sample set as the first sample set. If the number of samples is less than the first threshold, select all samples in the high-fidelity sample set as the first sample set. S42 calculates a first total sensitivity index vector for each variable to be analyzed in the first sample set; S43, for each sample in the first sample set, deleting the sample to obtain a second sample set, building a multi-fidelity proxy sub-model based on the second sample set, and calculating a second total sensitivity index vector of each variable to be analyzed in the second sample set based on the multi-fidelity proxy sub-model; S44 calculates the leave-one-out sensitivity analysis error of each sample based on the first total sensitivity index vector and the second total sensitivity index vector.

4. The variable importance screening method based on multi-fidelity sensitivity error according to claim 1, characterized in that: The mathematical optimization problem of constructing adaptive update points is solved based on the particle swarm optimization algorithm to obtain new sample points, including: S51 constructs a mathematical optimization problem for adaptively updating and adding points based on the optimization target. The calculation formula is as follows: Among them, α is the balance factor, d min is the minimum distance between the sample point to be updated and the existing sample point, C(x) is the contribution value of the importance measurement result at x, β is the space filling factor, Predicting variance for multi-fidelity surrogate models; S52: calculating the space filling factor and the multi-fidelity proxy model prediction variance; S53 calculates the contribution value of the importance measurement result of each sample point to be updated based on the weight factor and the leave-one-out sensitivity analysis error, and the calculation formula is as follows: Among them, C i is the importance measure contribution value of the i-th sample point to be updated, N is the number of samples in the first sample set, and w k is the weight of the kth high-fidelity sample, e k is the leave-one-out sensitivity analysis error of the kth high-fidelity sample, norm(|x i -x j |,0,1) is the normalized distance between the i-th sample point to be updated and the high-fidelity sample; S54 solves the mathematical optimization problem based on the particle swarm optimization algorithm to obtain new sample points.

5. The variable importance screening method based on multi-fidelity sensitivity error according to claim 1, characterized in that: The respectively calculating the error improvement margins of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index, and obtaining the fidelity type of the new sample point based on the error improvement margins, comprises: S61 calculates the error improvement of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and the calculation formula is as follows: in, is the new sample point x * Update the value of the jth variable of the total sensitivity index of the high-fidelity proxy model established by the high-fidelity sample set, is the new sample point x * Update to the low-fidelity sample set to establish the value of the jth variable of the total sensitivity index of the low-fidelity proxy model, S h(j) is the value of the jth variable of the total sensitivity index of the multi-fidelity surrogate model, IA h is the error improvement of the new sample point on the high-fidelity sensitivity index, IA l is the error improvement of the low-fidelity sensitivity index of the new sample point; S62 obtains the fidelity type of the new sample point based on the relationship between the error improvement margin of the new sample to the high-fidelity sensitivity index and the error improvement margin of the new sample point to the low-fidelity sensitivity index, as well as the cost ratio of collecting high-fidelity samples and low-fidelity samples.

6. The variable importance screening method based on multi-fidelity sensitivity error according to claim 1, characterized in that: The determining whether the second importance measurement result converges includes: S81: determining whether the total cost of the new sample points is greater than or equal to a second threshold value. If the total cost of the new sample points is greater than or equal to the second threshold value, determining that the second importance measurement result converges. If the number of the new sample points is less than the second threshold value, jumping to S82. S82 calculating the exponential variance, exponential disorder degree and importance weight of the M variables to be analyzed; S83, based on the exponential variance, the exponential disorder degree and the importance weight, obtaining a second importance measure convergence error of the M variables to be analyzed; S84 determines whether the convergence error of the second importance measure is greater than a third threshold. When the convergence error of the second importance measure is greater than the third threshold, it is determined that the result of the second importance measure has not converged. When the convergence error of the second importance measure is less than or equal to the third threshold, it is determined that the result of the second importance measure has converged.

7. The variable importance screening method based on multi-fidelity sensitivity error according to claim 1, characterized in that: The M variables to be analyzed are screened based on the importance ranking result and the target problem to obtain a target variable set, including: S101: calculating the interaction effect of the M variables to be analyzed based on the second importance measurement results of the M variables to be analyzed; S102, based on the importance ranking result and the target problem, selecting the variable with the largest total sensitivity index as the first variable set; S103 calculates the cumulative total sensitivity index of the first variable set, and determines whether the cumulative total sensitivity index is greater than or equal to a fourth threshold. When the cumulative total sensitivity index is greater than or equal to the fourth threshold, the first variable set is used as the target variable set. When the cumulative total sensitivity index is less than the fourth threshold, jump to S104. S104 selects the variable with the largest total sensitivity index from the remaining variables, adds it to the first variable set, and jumps to S103.

8. A variable importance screening device based on multi-fidelity sensitivity error, implemented by the variable importance screening method based on multi-fidelity sensitivity error according to any one of claims 1 to 7, characterized in that: The device comprises: An acquisition module, used for S1 acquiring distribution characteristics of M variables to be analyzed, wherein the distribution characteristics include distribution types and distribution parameters of the variables to be analyzed; A first processing module, for S2, based on the distribution characteristics, respectively collecting a high-fidelity sample set and a low-fidelity sample set as a training set according to a preset ratio by using a Latin hypercube sampling method, wherein each sample in the training set includes M variables to be analyzed; A second processing module, configured to construct a multi-fidelity proxy model according to the training set at S3, and calculate a first importance measurement result of the M variables to be analyzed based on the multi-fidelity proxy model; A third processing module, configured to calculate, at S4, a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set to obtain a contribution value of each sample in the high-fidelity sample set to the first importance measurement result; The fourth processing module is used for S5 to construct a mathematical optimization problem for adaptively updating and adding points, and obtain new sample points based on a particle swarm optimization algorithm; A fifth processing module, configured to calculate in S6 the error improvement margins of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index, and obtain the fidelity type of the new sample point based on the error improvement margins; A sixth processing module, configured to add the new sample point to the training set based on the fidelity type of the new sample point, update the multi-fidelity proxy model, and calculate the second importance measurement results of the M variables to be analyzed based on the updated multi-fidelity proxy model. A judging module, configured to judge whether the second importance measurement result converges in S8, and if the second importance measurement result converges, use the second importance measurement result as a target importance measurement result, and if the second importance measurement result does not converge, jump to S4; A sorting module is used for S9 sorting the importance of the M variables to be analyzed based on the target importance measurement results to obtain the importance sorting results of the M variables to be analyzed; A screening module, used for S10 screening the M variables to be analyzed based on the importance ranking result and the target problem to obtain a target variable set, wherein the target variable set includes at least one variable to be analyzed; Wherein, M is a positive integer greater than 1.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the variable importance screening method based on multi-fidelity sensitivity error is implemented as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the variable importance screening method based on multi-fidelity sensitivity error is implemented as described in any one of claims 1 to 7.

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