Variable importance screening method and apparatus based on multifidelity sensitivity error

Abstract

The application discloses a variable importance screening method based on multi-fidelity sensitivity error, and belongs to the technical field of adapter variable screening. S1, M variables to be analyzed are acquired; S2, a high-fidelity sample set and a low-fidelity sample set are respectively collected as a training set; S3, a multi-fidelity proxy model is constructed, and a first importance measure result of the M variables to be analyzed is calculated; S4, a contribution value of the high-fidelity sample set to the first importance measure result is calculated; S5, a new sample point is solved; S6, error improvement amplitudes of the new sample point to a high-fidelity sensitivity index and a low-fidelity sensitivity index are respectively calculated, and a fidelity type of the new sample point is obtained; S7, the multi-fidelity proxy model is updated, and a second importance measure result of the M variables to be analyzed is calculated; S8, in a case that the second importance measure result converges, the second importance measure result is taken as a target importance measure result, and in a case that the second importance measure result does not converge, the step S4 is jumped. The efficiency of adapter variable importance screening is improved.

Description

TECHNICAL FIELD

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

[0002] In the mechanical property model of the adapter, the variable importance screening of the adapter as a core tool for model optimization is directly related to the reliability and economy of engineering design. The variable sensitivity difference under the coupling of multiple variables may cause the mechanical property of the adapter to be inaccurate, thereby causing design deviation and resource waste. Therefore, establishing an efficient importance screening method has become a key breakthrough for improving the cognitive ability of complex systems.

[0003] The existing variable importance screening of the adapter is mainly based on the analysis principle, but there are still significant technical bottlenecks. First, the local sensitivity analysis method has insufficient global spatial representation capability and is difficult to capture the variable interaction effect in nonlinear systems. Second, although the global sensitivity analysis method has global spatial analysis capability, it will produce dimension disaster when facing high-dimensional variable space, resulting in exponential growth of computational complexity. In addition, the traditional proxy model technology adopts an offline modeling and online analysis separation architecture, which lacks sensitivity feedback mechanism in the model iteration optimization process, causing repeated consumption of computing resources.

[0004] The current technology in the application of variable importance screening of the adapter faces multiple constraints. The existing method cannot effectively balance the contradiction between calculation accuracy and efficiency, has weak adaptability to nonlinear characteristics, and generally has the problems of high calculation cost and low screening efficiency. SUMMARY

[0005] The present application aims to at least solve one of the technical problems existing in the prior art. To this end, the present application provides a variable importance screening method based on multi-fidelity sensitivity error, which improves the efficiency of variable importance screening of the adapter.

[0006] In a first aspect, the present application provides a variable importance screening method based on multi-fidelity sensitivity error, which comprises:

[0007] S1, acquiring distribution characteristics of M variables to be analyzed, the distribution characteristics including distribution type and distribution parameters of the variables to be analyzed;

[0008] S2, based on the distribution characteristics, collecting high-fidelity sample set and low-fidelity sample set as training set by Latin hypercube sampling method according to a preset proportion, each sample in the training set comprising M variables to be analyzed;

[0009] S3, constructing a multi-fidelity surrogate model according to the training set, and calculating a first importance measure result of the M variables to be analyzed based on the multi-fidelity surrogate model;

[0010] S4, calculating a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set, and obtaining a contribution value of each sample in the high-fidelity sample set to the first importance measure result;

[0011] S5, constructing a mathematical optimization problem of adaptive update and adding points, and obtaining a new sample point based on a particle swarm optimization algorithm;

[0012] S6, respectively calculating an error improvement amplitude of the new sample point to a high-fidelity sensitivity index and a low-fidelity sensitivity index, and obtaining a fidelity type of the new sample point based on the error improvement amplitudes;

[0013] S7, adding the new sample point to the training set based on the fidelity type of the new sample point, updating the multi-fidelity surrogate model, and calculating a second importance measure result of the M variables to be analyzed based on the updated multi-fidelity surrogate model;

[0014] S8, judging whether the second importance measure result converges, in a case where the second importance measure result converges, taking the second importance measure result as a target importance measure result, and in a case where the second importance measure result does not converge, jumping to S4;

[0015] S9, sorting importance of the M variables to be analyzed based on the target importance measure result, and obtaining an importance sorting result of the M variables to be analyzed;

[0016] S10, screening the M variables to be analyzed based on the importance sorting result and a target problem, and obtaining a target variable set, the target variable set including at least one variable to be analyzed;

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

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

[0019] S31, constructing the multi-fidelity surrogate model by using a hierarchical Kriging method based on the training set;

[0020] S32, respectively calculating a conditional expectation variance and an output response total variance of the M variables to be analyzed based on the multi-fidelity surrogate model;

[0021] S33, based on the conditional expected variance and the total variance of the output response, obtaining a sensitivity index of the M variables to be analyzed;

[0022] S34, based on the sensitivity index of the M variables to be analyzed, obtaining the first importance measure result.

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

[0024] S41, judging whether the number of samples in the high-fidelity sample set is greater than or equal to a first threshold value, in the case where the number of samples is greater than or equal to the first threshold value, uniformly selecting a first threshold value of samples from the high-fidelity sample set as a first sample set, in the case where the number of samples is less than the first threshold value, taking all samples in the high-fidelity sample set as the first sample set;

[0025] S42, calculating a 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, obtaining a second sample set by deleting the sample, constructing 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;

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

[0028] According to an embodiment of the present application, the construction of the mathematical optimization problem of adaptive update adding points is solved based on a particle swarm optimization algorithm to obtain a new sample point, which comprises:

[0029] S51, constructing a mathematical optimization problem of adaptive update adding points based on an optimization objective, and the calculation formula is as follows:

[0030]

[0031] Wherein, α is a 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 measure result at x, β is a space filling factor, is the multi-fidelity proxy model prediction variance;

[0032] S52, calculating the space filling factor and the multi-fidelity proxy model prediction variance;

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

[0034]

[0035] wherein, C i is the importance measure contribution value of the i th to-be-updated sample point, N is the sample number of the first sample set, w k is the weight size 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 k |,0,1) is the normalized distance between the i th to-be-updated sample point and the high-fidelity sample.

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

[0037] According to an embodiment of the present application, the error improvement amplitude of the new sample point on the high-fidelity sensitivity index and the low-fidelity sensitivity index is calculated respectively, and the fidelity type of the new sample point is obtained based on the error improvement amplitude, which comprises:

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

[0039]

[0040] wherein, is the value of the j th variable of the total sensitivity index of the high-fidelity sample set to which the new sample point x * is updated to establish a high-fidelity proxy model, is the value of the j th variable of the total sensitivity index of the low-fidelity sample set to which the new sample point x * is updated to establish a low-fidelity proxy model, S h(j) is the value of the j th variable of the total sensitivity index of the multi-fidelity proxy model, IA h is the error improvement amplitude of the new sample point on the high-fidelity sensitivity index, IA l is the error improvement amplitude of the new sample point on the low-fidelity sensitivity index.

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

[0042] According to one embodiment of the present application, the judging whether the second importance measure result converges comprises:

[0043] S81 judges whether the total cost of the new sample point is greater than or equal to a second threshold value, and in the case that the total cost of the new sample point is greater than or equal to the second threshold value, it is determined that the second importance measure result converges, and in the case that the total cost of the new sample point is less than the second threshold value, it jumps to S82;

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

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

[0046] S84 judges whether the second importance measure convergence error is greater than a third threshold value, and in the case that the second importance measure convergence error is greater than the third threshold value, it is determined that the second importance measure result does not converge, and in the case that the second importance measure convergence error is less than or equal to the third threshold value, it is determined that the second importance measure result converges.

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

[0048] S101 calculates 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 selects a variable with the maximum total sensitivity index as a first variable set based on the importance ranking result and the target problem;

[0050] S103 calculates the cumulative total sensitivity index of the first variable set, and judges whether the cumulative total sensitivity index is greater than or equal to a fourth threshold value, and when the cumulative total sensitivity index is greater than or equal to the fourth threshold value, the first variable set is taken as the target variable set, and when the cumulative total sensitivity index is less than the fourth threshold value, it jumps to S104;

[0051] S104 selects a variable with the maximum total sensitivity index from the remaining variables and adds it to the first variable set, and jumps to S103.

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

[0053] The acquisition module is configured to acquire distribution characteristics of M to-be-analyzed variables, the distribution characteristics including a distribution type and a distribution parameter of the to-be-analyzed variables.

[0054] The first processing module is configured to acquire, based on the distribution characteristics, high-fidelity sample sets and low-fidelity sample sets as training sets by using a Latin hypercube sampling method according to a preset proportion, each sample in the training sets including the M to-be-analyzed variables.

[0055] The second processing module is configured to construct a multi-fidelity proxy model according to the training sets, and calculate a first importance measure result of the M to-be-analyzed variables based on the multi-fidelity proxy model.

[0056] The third processing module is configured to calculate a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample sets, and obtain a contribution value of each sample in the high-fidelity sample sets to the first importance measure result.

[0057] The fourth processing module is configured to construct a mathematical optimization problem of adaptive update and adding points, and obtain a new sample point based on a particle swarm optimization algorithm.

[0058] The fifth processing module is configured to calculate error improvement amplitudes of the new sample point to high-fidelity sensitivity indexes and low-fidelity sensitivity indexes respectively, and obtain a fidelity type of the new sample point based on the error improvement amplitudes.

[0059] The sixth processing module is configured to add the new sample point to the training sets based on the fidelity type of the new sample point, update the multi-fidelity proxy model, and calculate a second importance measure result of the M to-be-analyzed variables based on the updated multi-fidelity proxy model.

[0060] The judgment module is configured to judge whether the second importance measure result converges, and in a case where the second importance measure result converges, take the second importance measure result as a target importance measure result, and in a case where the second importance measure result does not converge, jump to S4.

[0061] The sorting module is configured to sort importance of the M to-be-analyzed variables based on the target importance measure result, and obtain an importance sorting result of the M to-be-analyzed variables.

[0062] The screening module is configured to screen the M to-be-analyzed variables based on the importance sorting result and a target problem, and obtain a target variable set, the target variable set including at least one to-be-analyzed variable.

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

[0064] In a third aspect, the present application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the variable importance screening method based on multi-fidelity sensitivity error according to the first aspect.

[0065] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium, having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the variable importance screening method based on multi-fidelity sensitivity error according to the first aspect.

[0066] In a fifth aspect, the present application provides a chip, comprising a processor and a communication interface, wherein the communication interface is coupled to the processor, and the processor is configured to execute a program or an instruction, and implement the variable importance screening method based on multi-fidelity sensitivity error according to the first aspect.

[0067] In a sixth aspect, the present application provides a computer program product, comprising a computer program, wherein the computer program, when executed by a processor, implements the variable importance screening method based on multi-fidelity sensitivity error according to the first aspect.

[0068] Additional aspects and advantages of the present application will be in part apparent and in part pointed out hereinafter.

[0069] The present application provides a variable importance screening method based on multi-fidelity sensitivity error, which has the following beneficial effects compared with the prior art:

[0070] (1) The present application combines the Latin hypercube sampling technology, the multi-fidelity proxy model and the sensitivity error analysis framework, utilizes the dynamic collaborative modeling of high-fidelity and low-fidelity samples, can effectively balance the contradiction between the calculation cost and the model accuracy, adopts the leave-one-out sensitivity analysis error contribution value evaluation and the particle swarm optimization algorithm to realize the adaptive updating of the sample points and the judgment of the fidelity type, introduces the multi-fidelity sensitivity error information, integrates the importance measure process into the construction process of the multi-fidelity proxy model, strengthens the information interaction between the importance measure and the proxy model, makes the sensitivity error information adaptively optimize the multi-fidelity proxy model, significantly improves the importance measure of the adapter variables and the accuracy of the multi-fidelity proxy model in the global range, reduces the dependence on the high-fidelity samples, and reduces the calculation cost of the adapter mechanical performance model.

[0071] (2) The application constructs a multi-fidelity proxy model by a hierarchical Kriging method, uses high and low fidelity data to fully integrate the information advantages of different precision samples, improves the global approximation ability and local detail capture efficiency of the model, calculates the conditional expectation variance and the total variance of the output response, quantifies the independent contribution and interaction influence of variables on the system response, enhances the comprehensiveness and interpretability of the variable importance measure, effectively combines the high and low fidelity sensitivity analysis results, fully excavates the correlation information between different fidelity data, and improves the efficiency and robustness of the importance variable screening of the adapter.

[0072] (3) The application can effectively evaluate the influence of each sample on the importance measure result by calculating the leave-one-out sensitivity analysis error of the high-fidelity sample set. 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. The contribution of each sample to the importance measure result can be quantified, which helps to identify the key samples and variables affecting the model performance, and improves the efficiency and robustity of the importance variable screening of the adapter. BRIEF DESCRIPTION OF DRAWINGS

[0073] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:

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

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

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

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

[0078] Figure 5 is a structural schematic diagram of the electronic device provided by the embodiments of the present application. DETAILED DESCRIPTION

[0079] With reference to the drawings and the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly described. Obviously, the described embodiments are only some of the embodiments of the present application, but not all of the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art are within the scope of the present application.

[0080] The terms "first", "second", and the like in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way 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 generally a category, and do not limit the number of objects, for example, the first object can be one or more. In addition, "and / or" in the specification and claims indicates at least one of the connected objects, and the character " / ", generally indicates that the front and rear associated objects are in a "or" relationship.

[0081] The multi-fidelity sensitivity error based variable importance screening method, multi-fidelity sensitivity error based variable importance screening device, electronic equipment and readable storage medium provided by the embodiments of the present application will be described in detail below in combination with the drawings, through specific embodiments and application scenarios.

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

[0083] The terminal includes, but is not limited to, a portable communication device such as a mobile phone or a tablet computer having a touch-sensitive surface (e.g., a touchscreen display and / or a touchpad). It should also be understood that in some embodiments, the terminal can not be a portable communication device, but a desktop computer having a touch-sensitive surface (e.g., a touchscreen 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 can 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 in the embodiments of the present application can be executed by an electronic device or a functional module or functional entity capable of implementing the variable importance screening method based on multi-fidelity sensitivity error in the electronic device. The electronic device mentioned in the embodiments of the present application includes but is not limited to a mobile phone, a tablet computer, a computer, a camera, a wearable device, and the like. The variable importance screening method based on multi-fidelity sensitivity error provided in the embodiments of the present application is described below by taking an electronic device as an example.

[0086] In the field of engineering design, the modeling and analysis of complex systems often involve numerous parameters and variables. In these systems, it is crucial to understand the impact of parameters and variables on system performance. Importance measures are an important step in quantifying uncertainty, which can help analyze the importance of system design variables or parameters on the overall system performance. Through importance measures, researchers can identify key parameters, optimize models, and reduce computational costs to improve the understanding of the system.

[0087] Importance measure methods can be mainly divided into local importance measure methods and global importance measure methods. Local importance measure methods usually evaluate the importance of a variable by analyzing its impact on system response at a fixed point or in a local range, such as direct differentiation method, finite difference method, etc. These methods are simple to calculate and efficient, but they cannot fully reflect the impact of variables on the system in the entire input range, so they have limitations in complex system analysis. 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 interactive effects of variables on system output, but their calculation process usually requires a large number of samples, resulting in high computational cost and time consumption, especially when dealing with high-dimensional nonlinear problems, it is difficult to meet the practical needs of engineering.

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

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

[0090] Step 110, S1, acquires distribution characteristics of M variables to be analyzed, the distribution characteristics including a distribution type and a distribution parameter of the variables to be analyzed;

[0091] It is easy to understand that the electronic device acquires the distribution characteristics of the M variables to be analyzed, and the distribution characteristics include the distribution type and the distribution parameter of the variables to be analyzed. The distribution type is, for example, a normal distribution, a uniform distribution, an exponential distribution, etc., and the distribution parameter is, for example, a mean, a variance, a degree of freedom, etc.

[0092] For example, the variables to be analyzed are various geometric characteristics, material properties, process parameters, etc. of an adapter.

[0093] Step 120, S2, based on the distribution characteristics, acquires a high-fidelity sample set and a low-fidelity sample set as a training set by a Latin hypercube sampling method according to a preset proportion, each sample in the training set including the M variables to be analyzed;

[0094] Optionally, after the electronic device acquires the distribution characteristics of the M variables to be analyzed, the Latin hypercube sampling method is used to acquire a 60% cost high-fidelity sample set and a 40% cost low-fidelity sample set as the training set according to the distribution characteristics and the preset proportion 3:2.

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

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

[0097] It is easy to understand that an initial multi-fidelity proxy model is constructed according to the training set, each sample in the training set is predicted based on the constructed multi-fidelity proxy model, a sensitivity index of the M variables to be analyzed is obtained, and a first importance measure result of the M variables to be analyzed is obtained according to the size relationship of the sensitivity index of the M variables to be analyzed.

[0098] Step 140, S4, calculates a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set, and obtains a 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 between the total sensitivity index of all variables of the re-established multi-fidelity surrogate model and the initial multi-fidelity surrogate model after removing one sample each time during the sensitivity analysis. This error is used to quantify the contribution value of each sample to the first importance measure result.

[0100] Step 150, S5, constructs a mathematical optimization problem of adaptive update adding points, and solves a new sample point based on a particle swarm optimization algorithm;

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

[0102] Step 160, S6, respectively calculates the error improvement amplitude of the new sample point on the high-fidelity sensitivity index and the low-fidelity sensitivity index, and obtains the fidelity type of the new sample point based on the error improvement amplitude;

[0103] Further, after obtaining the new sample point, the error improvement amplitude of the new sample point on the high-fidelity sensitivity index and the low-fidelity sensitivity index is respectively calculated, and the cost ratio of the high-fidelity sample and the low-fidelity sample is collected, to determine the fidelity type of the new sample point.

[0104] Step 170, S7, adds the new sample point to the training set based on the fidelity type of the new sample point, updates the multi-fidelity surrogate model, and calculates 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, the new sample point is added to the high-fidelity sample set in the training set, if the new sample point is a low-fidelity sample, the new sample point is added to the low-fidelity sample set in the training set, and the multi-fidelity surrogate model is updated.

[0106] Step 180, S8, judges whether the second importance measure result converges, in the case that the second importance measure result converges, takes the second importance measure result as the target importance measure result, and in the case that the second importance measure result does not converge, jumps to S4;

[0107] Notably, after obtaining the second importance measure result of the M variables to be analyzed, it is judged whether the second importance measure result is stable within a preset range, in the case that the second importance measure result converges, the second importance measure result is taken as the target importance measure result, and in the case that the second importance measure result does not converge, jumps to the above step 140.

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

[0109] Step 100, S10, screening the M variables to be analyzed based on the importance ranking result and a target problem, to obtain a target variable set, the target variable set including at least one variable to be analyzed;

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

[0111] Finally, according to the importance ranking result and the target problem, the M variables to be analyzed are screened by accumulating the sensitivity index, to obtain the target variable set.

[0112] According to the variable importance screening method based on multi-fidelity sensitivity error provided in the embodiments of the present application, by combining the Latin hypercube sampling technology, the multi-fidelity proxy model and the sensitivity error analysis framework, the dynamic collaborative modeling of high-fidelity and low-fidelity samples is used, which 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 updating of the sample points and the judgment of the fidelity type. By introducing the multi-fidelity sensitivity error information, the importance measure process is integrated into the construction process of the multi-fidelity proxy model, the information interaction between the importance measure and the proxy model is strengthened, the sensitivity error information is used for adaptive optimization of the multi-fidelity proxy model, the importance measure of the adapter variable and the accuracy of the multi-fidelity proxy model in the global range are significantly improved, the dependence on the high-fidelity samples is reduced, and the calculation cost of the adapter mechanical performance model is reduced.

[0113] In some embodiments, the multi-fidelity proxy model is constructed according to the training set, and the first importance measure result of the M variables to be analyzed is calculated based on the multi-fidelity proxy model, including:

[0114] S31, constructing the multi-fidelity proxy model by using a hierarchical Kriging method based on the training set;

[0115] S32, calculating the conditional expectation variance and the total output response variance of the M variables to be analyzed based on the multi-fidelity proxy model;

[0116] S33, obtaining the sensitivity index of the M variables to be analyzed based on the conditional expectation variance and the total output response variance;

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

[0118] It is easy to understand that a low-fidelity Kriging surrogate model is first constructed by using low-fidelity samples, the surrogate model can predict the low-fidelity output response of the samples, and then a multi-fidelity Kriging method is used to construct a multi-fidelity surrogate model, and the calculation formula is as follows:

[0119]

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

[0121] Further, the conditional expectation variance of M variables to be analyzed and the total variance of the output response are calculated based on the multi-fidelity surrogate model, 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 multi-fidelity surrogate model is constructed by using the hierarchical Kriging method, the high-fidelity and low-fidelity data can fully integrate the information advantages of different precision samples, and the global approximation ability and local detail capture efficiency of the model are improved; by calculating the conditional expectation variance and the total variance of the output response, the independent contribution and interaction influence of the variables on the system response are quantified, the comprehensiveness and interpretability of the variable importance measure are enhanced, the high-fidelity and low-fidelity sensitivity analysis results are effectively combined, the correlation information between different fidelity data is fully mined, and the efficiency and robustness of the importance variable screening of the adapter are improved.

[0123] In some embodiments, the calculation of the leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set comprises:

[0124] S41 judges whether the number of samples in the high-fidelity sample set is greater than or equal to a first threshold value, in the case that the number of samples is greater than or equal to the first threshold value, uniformly selects a first threshold value of samples from the high-fidelity sample set as a first sample set, and in the case that the number of samples is less than the first threshold value, all samples in the high-fidelity sample set are used as the first sample set;

[0125] S42 calculates a first total sensitivity index vector of each variable to be analyzed in the first sample set;

[0126] S43For each sample in the first sample set, a second sample set is obtained by deleting the sample, a multi-fidelity proxy sub-model is constructed based on the second sample set, and a second total sensitivity index vector of each variable to be analyzed in the second sample set is calculated based on the multi-fidelity proxy sub-model;

[0127] S44Based on the first total sensitivity index vector and the second total sensitivity index vector, a leave-one-out sensitivity analysis error of each sample is calculated.

[0128] In some embodiments, in order to improve the efficiency of calculation, 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 uniformly 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 taken as the first sample set.

[0129] Further, based on the above multi-fidelity proxy model, a first total sensitivity index vector of each variable to be analyzed in the first sample set is calculated, for the Kth high-fidelity sample point in the first sample set, a multi-fidelity proxy 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 proxy sub-model, and a leave-one-out sensitivity analysis error of the Kth high-fidelity sample point is calculated according to the first total sensitivity index vector and the second total sensitivity index vector, and the calculation formula is as follows:

[0130]

[0131] Wherein, D is the number of analysis variables, is the value of the jth variable of the vector S Tk , is the value of the jth variable of the total sensitivity index constructed by all samples, e k is the leave-one-out sensitivity analysis error of the kth 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, and deleting each sample, a new sample set is constructed and the second total sensitivity index vector is calculated, so as to obtain the leave-one-out sensitivity analysis error of each sample. The contribution of each sample to the importance measure result can be quantified, which helps to identify the key samples and variables affecting the model performance, and improves the efficiency and robustness of the adapter importance variable screening.

[0133] In some embodiments, the mathematical optimization problem of adaptive updating sampling points is constructed based on a particle swarm optimization algorithm to obtain new sample points, including:

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

[0135]

[0136] Wherein, α is a 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 measure result at x, β is a space filling factor, is the multi-fidelity proxy model prediction variance;

[0137] S52, the space filling factor and the multi-fidelity proxy model prediction variance are calculated;

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

[0139]

[0140] Wherein, C i is the importance measure contribution value of the i-th sample point to be updated, N is the number of samples of the first sample set, w k is the weight size 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 k |,0,1) is the normalized distance between the i-th sample point to be updated and the high-fidelity sample;

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

[0142] It is easy to understand that after the mathematical optimization problem of adaptive updating sampling points is constructed, the space filling factor and the multi-fidelity proxy model prediction variance required in the optimization objective are calculated first, wherein the multi-fidelity proxy model prediction variance can be obtained through the multi-fidelity proxy model, and the calculation formula of the space filling factor is as follows:

[0143] β=λd ave

[0144] Wherein, λ is a scaling factor that determines the crowding degree of samples, d ave is the average spatial distance of the existing sample points.

[0145] Further, based on the weight factor and the leave-one-sensitivity analysis error, a contribution value of an importance measure result of each to-be-updated sample point is calculated, a particle swarm intelligent optimization algorithm is used to solve a mathematical optimization problem, and a new sample point is obtained.

[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 adaptive change values in the interval [0.5, 2.5], and by initializing the population, updating the particle position and speed parameters, etc., the convergence is constantly iterated until the individual with the maximum value of f(x) is calculated as the position of the new sample point.

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

[0148] In some embodiments, the respectively calculating the error improvement amplitude of the new sample point on 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 amplitude, comprises:

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

[0150]

[0151] wherein, is the value of the jth variable of the total sensitivity index of the high-fidelity proxy model updated to the high-fidelity sample set, * is the value of the jth variable of the total sensitivity index of the high-fidelity proxy model updated to the high-fidelity sample set, is the value of the jth variable of the total sensitivity index of the low-fidelity proxy model updated to the low-fidelity sample set, * is the value of the jth variable of the total sensitivity index of the low-fidelity proxy model updated to the low-fidelity sample set, h(j) is the value of the jth variable of the total sensitivity index of the multi-fidelity proxy model, h is the error improvement amplitude of the new sample point on the high-fidelity sensitivity index, l is the error improvement amplitude of the new sample point on the low-fidelity sensitivity index;

[0152] S62 obtains the fidelity type of the new sample point based on a size relationship between an error promotion amplitude of the high-fidelity sensitivity index based on the new sample point and an error promotion amplitude of the low-fidelity sensitivity index based on the new sample point, and a cost ratio of collecting high-fidelity samples and low-fidelity samples.

[0153] It is easy to understand that the error promotion amplitudes of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index are calculated respectively, and the cost ratio of collecting high-fidelity samples and low-fidelity samples is combined to determine the fidelity type of the new sample point: when the error promotion amplitude of the new sample point to the high-fidelity sensitivity index is greater than the product of the error promotion amplitude of the new sample point to the low-fidelity sensitivity index and the cost ratio of collecting high-fidelity samples and low-fidelity samples, it is determined that the fidelity type of the new sample point is a high-fidelity sample, otherwise, it is determined that the fidelity type of the new sample point is a low-fidelity sample.

[0154] In this embodiment, the error promotion amplitudes of the new sample point to the high-fidelity sensitivity index and the low-fidelity sensitivity index are calculated respectively, which can effectively evaluate the contribution of the new sample point with different fidelity to the importance measure result. The fidelity type of the new sample point is determined based on the size relationship between the error promotion amplitudes and the cost ratio of collecting high-fidelity samples and low-fidelity samples, which optimizes the selection strategy of the sample point, improves the precision and calculation efficiency of the importance measure, and reduces the sampling cost.

[0155] In some embodiments, the determining whether the second importance measure result converges comprises:

[0156] S81 determines whether the total cost of the new sample point is greater than or equal to a second threshold value, and in the case that the total cost of the new sample point is greater than or equal to the second threshold value, it is determined that the second importance measure result converges, and in the case that the total cost of the new sample point is less than the second threshold value, it is jumped to S82;

[0157] S82 calculates the exponential variance, the exponential disorder degree and the importance weight 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, the exponential disorder degree and the importance weight;

[0159] S84 determines whether the second importance measure convergence error is greater than a third threshold value, and in the case that the second importance measure convergence error is greater than the third threshold value, it is determined that the second importance measure result does not converge, and in the case that the second importance measure convergence error is less than or equal to the third threshold value, it is determined that the second importance measure result converges.

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

[0161] (1) The sensitivity index variance of the jth variable is calculated, and the calculation formula is as follows:

[0162]

[0163] Wherein, m is the number of iterations, S h(ij) is the jth variable value of the sensitivity index of the i-generation multi-fidelity surrogate model, is the average value of the jth variable value of the sensitivity index of the previous i-generation surrogate model, is the sensitivity index variance.

[0164] (2) The sensitivity index disorder degree of the jth variable is calculated, and the calculation formula is as follows:

[0165]

[0166] Wherein, Noh j and Nol j are the rankings of the jth variable of the high / low fidelity sensitivity index, and L is the sensitivity index disorder degree.

[0167] (3) The importance weight of the jth variable is calculated, and the calculation formula is as follows:

[0168]

[0169] Wherein, and are the average values of the jth variable of the high / low fidelity sensitivity index of all iterations, and ω is the importance weight.

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

[0171]

[0172] Wherein, error is the second importance measure convergence error, ω is the importance weight, L is the sensitivity index disorder degree, is the sensitivity index variance.

[0173] Finally, it is judged whether the second importance measure convergence error is greater than the third threshold value. In the case that the second importance measure convergence error is greater than the third threshold value, it is determined that the second importance measure result has not converged, and a new sample point needs to be solved. In the case that the second importance measure convergence error is less than or equal to the third threshold value, it is determined that the second importance measure result converges.

[0174] In the embodiment, by judging the relationship between the total cost of the new sample point and the second threshold value, the iterative process of calculation can be effectively controlled, and when the total cost reaches a certain threshold value, it is determined that the second importance measure result has converged, thereby reducing unnecessary calculation. When the number of new sample points is small, by judging whether the second importance measure of the variable to be analyzed converges or not through indicators such as exponential variance, exponential disorder degree and importance weight, the calculation cost and time are reduced, and the efficiency and robustness of the importance variable screening of the adapter are improved.

[0175] In some embodiments, 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:

[0176] S101, based on the second importance measure result of the M variables to be analyzed, calculating the interaction effect of the M variables to be analyzed;

[0177] S102, based on the importance ranking result and the target problem, selecting a variable with the maximum total sensitivity index as a first variable set;

[0178] S103, calculating the cumulative total sensitivity index of the first variable set, and judging whether the cumulative total sensitivity index is greater than or equal to a fourth threshold value; when the cumulative total sensitivity index is greater than or equal to the fourth threshold value, the first variable set is taken as the target variable set; when the cumulative total sensitivity index is less than the fourth threshold value, jumping to S104;

[0179] S104, selecting a variable with the maximum total sensitivity index from the remaining variables and adding it to the first variable set, and jumping to S103.

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

[0181] S c =1-∑S

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

[0183] The total sensitivity index of each variable is sorted from large to small, the importance variable of the analysis problem is selected according to the sorting, and the cumulative sensitivity index S a is calculated. a When the cumulative sensitivity index satisfies S c -S cAt this time, it means that the variables with an impact degree of 0.99 before the problem are selected, and the impact of the remaining variables is ignored.

[0184] In some embodiments, the electronic device performs importance variable screening on the mechanical properties of the metamaterial adapter, the adapter is a polyurethane metamaterial, and the simulation is performed by using the finite element software ANSYS19.2. The APDL command stream form provided by the software is used for automatic 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 under pressure is used to evaluate the mechanical properties. Table 1 shows the distribution characteristics of the six variables to be analyzed, as shown in Table 1. The variables to be analyzed are the horizontal hole round corner radius, the vertical hole round corner radius, the right lower hole center distance, the right upper hole center distance, the left upper hole center distance and the left lower hole center distance. 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 high and low samples in this embodiment is 6:1. The cost ratio of the initial high-fidelity sample set is 60%, and the cost ratio of the low-fidelity sample set is 40%.

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

[0186]

[0187]

[0188] According to the above manner, the variables finally screened are shown in Table 2, and the importance measure of the mechanical properties of the polyurethane metamaterial is performed. Four important variables are selected from the original 6-dimensional variables.

[0189] Table 2 shows the importance variable table

[0190]

[0191] Figure 2 The schematic diagram of the final importance measure result of the mechanical properties of the polyurethane metamaterial provided by the embodiments of the present application is shown in Figure 2 As shown in the figure, the total sensitivity index of the analysis variables x1 and x6 is very small, only 0.008 and 0.01; while the analysis variables x2 and x3 show higher sensitivity, and the total sensitivity index is 0.441 and 0.559 respectively; the difference between the total sensitivity index and the main sensitivity index of the analysis variables x3 and x5 is relatively large, indicating that there is a certain interaction between the two and the remaining variables; according to the importance measure result value in the figure, the importance variable screening can be obtained S a -S c The value is shown in Table 3. When the variable is selected to x5, the screening is stopped, and after the importance variable screening of the mechanical properties of the polyurethane metamaterial, four important variables x3, x2, x5 and x4 can be obtained.

[0192] Table 3 important variable screening process table

[0193]

[0194]

[0195] Figure 3 The schematic diagram of the verification process of the importance measure result provided by the embodiment of the application, the embodiment of the scheme proves the effectiveness of the application 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 of 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 proxy model constructed by using all the analysis variables, and the dotted line represents the cumulative distribution function of the multi-fidelity proxy model constructed by removing the variables x1 and x6; by calculating the lower areas of the three curves as shown in Table 4, it can be seen that the error of the adaptive multi-fidelity proxy model removing x1 and x6 is only 1.45% compared with the original model, which only increases by 0.6% compared with the error of directly using all the variables to build a model, proving that the variables x1 and x6 have little effect on the mechanical properties of the polyurethane metamaterial, and the important variables of the problem are better screened out.

[0196] Table 4 importance measure result verification

[0197]

[0198] In this embodiment, by calculating the interaction effect of the to-be-analyzed variables based on the second importance measure result, and combining the importance ranking result and the target problem to screen the variables, the 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, which improves the accuracy and pertinence of variable screening, optimizes the target variable set, and improves the efficiency and robustness of the importance variable screening of the adapter.

[0199] The variable importance screening method based on multi-fidelity sensitivity error provided by the embodiment of the application can be executed by a variable importance screening device based on multi-fidelity sensitivity error. In the embodiment of the application, the variable importance screening device based on multi-fidelity sensitivity error is taken as an example to execute the variable importance screening method based on multi-fidelity sensitivity error, and the variable importance screening device based on multi-fidelity sensitivity error provided by the embodiment of the application is described.

[0200] The embodiment of the application also provides a variable importance screening device based on multi-fidelity sensitivity error, which comprises Figure 4As shown, the variable importance screening device based on the 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 acquire, at S1, distribution characteristics of M to-be-analyzed variables, the distribution characteristics including a distribution type and a distribution parameter of the to-be-analyzed variables.

[0202] The first processing module 420 is configured to acquire, at S2, a high-fidelity sample set and a low-fidelity sample set as training sets based on the distribution characteristics by using a Latin hypercube sampling method at a preset proportion, each sample in the training set including the M to-be-analyzed variables.

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

[0204] The third processing module 440 is configured to calculate, at S4, a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set, and obtain a 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 construct, at S5, a mathematical optimization problem of adaptive update and point addition, and obtain a new sample point based on a particle swarm optimization algorithm.

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

[0207] The sixth processing module 470 is configured to add, at S7, 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 a second importance measure result of the M to-be-analyzed variables based on the updated multi-fidelity proxy model.

[0208] The judgment module 480 is configured to judge, at S8, whether the second importance measure result converges, in a case where the second importance measure result converges, take the second importance measure result as a target importance measure result, and in a case where the second importance measure result does not converge, jump to S4.

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

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

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

[0212] According to the variable importance screening method and device based on multi-fidelity sensitivity error provided in the embodiments of the present application, by combining the Latin hypercube sampling technology, the multi-fidelity proxy model and the sensitivity error analysis framework, the dynamic collaborative modeling of the high-fidelity samples and the low-fidelity samples can effectively balance the contradiction between the calculation cost and the model accuracy, the sample point adaptive updating and the fidelity type judgment are realized by using the leave-one-out sensitivity analysis error contribution value evaluation and the particle swarm optimization algorithm, by introducing the multi-fidelity sensitivity error information, the importance measure process is integrated into the construction process of the multi-fidelity proxy model, the information interaction between the importance measure and the proxy model is strengthened, the sensitivity error information is used for adaptive optimization of the multi-fidelity proxy model, the importance measure of the adapter variable and the accuracy of the multi-fidelity proxy model in the global range are significantly improved, the dependence on the high-fidelity samples is reduced, and the calculation cost of the adapter mechanical performance model is reduced.

[0213] The variable importance screening device based on multi-fidelity sensitivity error provided in the embodiments of the present application can realize the variable importance screening method based on multi-fidelity sensitivity error Figures 1 to 3 The variable importance screening device based on multi-fidelity sensitivity error provided in the embodiments of the present application can realize the variable importance screening method based on multi-fidelity sensitivity error

[0214] In some embodiments, as shown in Figure 5 The embodiments of the present application also provide an electronic device 500, including a processor 501, a memory 502, and a computer program stored in the memory 502 and executable on the processor 501, which realizes each process of the above-mentioned variable importance screening method based on multi-fidelity sensitivity error when executed by the processor 501, and can achieve the same technical effects, and details are not repeated here.

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

[0216] The embodiment of the present application further provides a non-transitory computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement each process of the variable importance screening method based on the multi-fidelity sensitivity error and achieve the same technical effects. To avoid repetition, details are not described herein.

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

[0218] The embodiment of the present application further provides a computer program product, which includes a computer program, and the computer program is executed by a processor to implement the variable importance screening method based on the multi-fidelity sensitivity error.

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

[0220] The embodiment of the present application further provides a chip, which includes a processor and a communication interface. The communication interface is coupled with the processor. The processor is configured to execute a program or an instruction to implement each process of the variable importance screening method based on the multi-fidelity sensitivity error and achieve the same technical effects. To avoid repetition, details are not described herein.

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

[0222] It should be noted that, in the present document, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises a", "comprising", or "includes a", does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. Additionally, it should be noted that the scope of the methods and apparatus of the present embodiments are not limited by the order of the steps or the sequence for performing the steps, as some steps can occur simultaneously, in other steps can occur sequentially, or in between other steps can occur, as can be readily appreciated by those skilled in the art. Further, the features of the various examples described can be combined, in other examples.

[0223] From the above description of the embodiments, it is clear that the above-described method of the embodiments can be realized by means of software and the necessary universal hardware platform, of course, it can also be realized by hardware, but in many cases, the former is a better embodiment. Based on such understanding, the technical solutions of the present application can be embodied in the form of a computer software product in essence or the part of the prior art that contributes to the present application, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a plurality of instructions for making a terminal (which can be a mobile phone, computer, server, or network device, etc.) execute the variable importance screening method based on multi-fidelity sensitivity error of each embodiment of the present application.

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

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

[0226] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-described specific embodiments, and the above-described specific embodiments are only illustrative, not restrictive, and those skilled in the art can make many forms under the inspiration of the present application without departing from the scope of the present application and the scope protected by the claims.

[0227] In the description of the application, reference has been made to descriptive terms such as "one embodiment", "some embodiments", "an embodiment", "example", "specific example" or "some examples" etc. It is emphasized that each of these terms refers to a specific feature, structure, material or characteristic described in connection with a particular embodiment or example. The descriptive terms are not necessarily referring to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0228] While embodiments of the application have been shown and described, it is to be understood that the application is not limited to the details of the embodiments described, since the scope of the application is defined with respect to the appended claims.

Claims

1. A variable importance screening method based on multifidelity sensitivity error, used for importance variable screening of mechanical properties of metamaterial adapters, characterized in that, The method comprises: S1, acquiring distribution characteristics of M variables to be analyzed, the distribution characteristics comprising a distribution type and a distribution parameter of the variables to be analyzed; the variables to be analyzed comprising respective geometric characteristics, material properties and process parameters of an adapter; S2, based on the distribution characteristics, collecting a high-fidelity sample set and a low-fidelity sample set as a training set by a Latin hypercube sampling method according to a preset proportion, each sample in the training set comprising M variables to be analyzed; S3, constructing a multi-fidelity surrogate model according to the training set, and calculating a first importance measure result of the M variables to be analyzed based on the multi-fidelity surrogate model; S4, calculating a leave-one-out sensitivity analysis error of each sample in the high-fidelity sample set, and obtaining a contribution value of each sample in the high-fidelity sample set to the first importance measure result; S5, constructing a mathematical optimization problem of adaptive update and adding points, and obtaining a new sample point based on a particle swarm optimization algorithm; S6, respectively calculating error improvement amplitudes of the new sample point on a high-fidelity sensitivity index and a low-fidelity sensitivity index, and obtaining a fidelity type of the new sample point based on the error improvement amplitudes; S7, adding the new sample point to the training set based on the fidelity type of the new sample point, updating the multi-fidelity surrogate model, and calculating a second importance measure result of the M variables to be analyzed based on the updated multi-fidelity surrogate model; S8, judging whether the second importance measure result converges, in a case where the second importance measure result converges, taking the second importance measure result as a target importance measure result, and in a case where the second importance measure result does not converge, jumping to S4; S9, sorting importance of the M variables to be analyzed based on the target importance measure result, and obtaining an importance sorting result of the M variables to be analyzed; S10, screening the M variables to be analyzed based on the importance sorting result and a target problem, and obtaining a target variable set comprising at least one variable to be analyzed; wherein M is a positive integer greater than 1.

2. The variable importance screening method based on multifaithful sensitivity error according to claim 1, wherein, The method comprises: S31, constructing the multi-fidelity surrogate model by a hierarchical Kriging method based on the training set; S32, respectively calculating a conditional expectation variance and an output response total variance of the M variables to be analyzed based on the multi-fidelity surrogate model; S33, obtaining a sensitivity index of the M variables to be analyzed based on the conditional expectation variance and the output response total variance; S34, obtaining the first importance measure result based on the sensitivity index of the M variables to be analyzed.

3. The variable importance screening method based on multifaithful sensitivity error of claim 1, wherein, The method comprises: S41 judges whether the number of samples in the high-fidelity sample set is greater than or equal to a first threshold value, and in the case where the number of samples is greater than or equal to the first threshold value, a first threshold value of samples are uniformly selected from the high-fidelity sample set as a first sample set, and in the case where the number of samples is less than the first threshold value, all samples in the high-fidelity sample set are taken as the first sample set; S42 calculates a first total sensitivity index vector of each variable to be analyzed in the first sample set; S43, for each sample in the first sample set, obtains a second sample set by deleting the sample, constructs a multi-fidelity proxy sub-model based on the second sample set, and calculates 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 a 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 multifaithful sensitivity error of claim 1, wherein, The mathematical optimization problem of adaptive updating and adding points is solved based on a particle swarm optimization algorithm to obtain a new sample point, and includes: S51 constructs a mathematical optimization problem of adaptive updating and adding points based on an optimization target, and the calculation formula is as follows: wherein a is a balancing 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 multi-fidelity proxy model prediction variance; S52 calculates the space filling factor and the multi-fidelity proxy model prediction variance; S53 calculates a contribution value of an importance measure result of each sample point to be updated based on a weight factor and the leave-one-out sensitivity analysis error, and the calculation formula is as follows: wherein C i is the importance measure contribution value of the i-th to-be-updated sample point, N is the number of samples of the first sample set, w k is the weight size occupied by 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 k |,0,1) is the normalized distance between the i-th to-be-updated sample point and the high-fidelity sample. S54 solves the mathematical optimization problem based on the particle swarm optimization algorithm to obtain a new sample point.

5. The method of variable importance screening based on multifaithful sensitivity error of claim 1, wherein, The error improvement amplitude of the new sample point on the high-fidelity sensitivity index and the low-fidelity sensitivity index is calculated respectively, and the fidelity type of the new sample point is obtained based on the error improvement amplitude, and includes: S61 calculates the error improvement amplitude of the new sample point on the high-fidelity sensitivity index and the low-fidelity sensitivity index respectively, and the calculation formula is as follows: wherein, is the value of the jth variable of the total sensitivity index of the high-fidelity proxy model for the new sample point x * is the value of the jth variable of the total sensitivity index of the high-fidelity proxy model for the new sample point x is the value of the jth variable of the total sensitivity index of the low-fidelity proxy model for the new sample point x * is the value of the jth variable of the total sensitivity index of the low-fidelity proxy model for the new sample point x h(j) is the value of the jth variable of the total sensitivity index of the multi-fidelity proxy model for the new sample point x h is the error boost of the high-fidelity sensitivity index for the new sample point x l is the error boost of the low-fidelity sensitivity index for the new sample point x S62 obtains the fidelity type of the new sample point based on the size relationship between the error improvement amplitude of the new sample on the high-fidelity sensitivity index and the error improvement amplitude of the new sample point on the low-fidelity sensitivity index, and the cost proportion of collecting high-fidelity samples and low-fidelity samples.

6. The variable importance screening method based on multifaithful sensitivity error of claim 1, wherein, The judgment of whether the second importance measure result converges includes: S81 judges whether the total cost of the new sample point is greater than or equal to a second threshold value, and in the case where the total cost of the new sample point is greater than or equal to the second threshold value, it is determined that the second importance measure result converges, and in the case where the total cost of the new sample point is less than the second threshold value, it is jumped to S82; S82 calculates the index variance, index disorder degree and importance weight of the M variables to be analyzed; S83 obtains a second importance measure convergence error of the M variables to be analyzed based on the index variance, index disorder degree and importance weight; S84 judges whether the second importance measure convergence error is greater than a third threshold value, and in the case that the second importance measure convergence error is greater than the third threshold value, it is determined that the second importance measure result does not converge, and in the case that the second importance measure convergence error is less than or equal to the third threshold value, it is determined that the second importance measure result converges.

7. The variable importance screening method based on a multi-fidelity sensitivity error of claim 1, wherein, The screening of the M variables to be analyzed based on the importance ranking result and the target problem to obtain a target variable set comprises: S101, based on the second importance measure result of the M variables to be analyzed, calculating an interaction effect of the M variables to be analyzed; S102, based on the importance ranking result and the target problem, selecting a variable with the maximum total sensitivity index as a first variable set; S103, calculating a cumulative total sensitivity index of the first variable set, and judging whether the cumulative total sensitivity index is greater than or equal to a fourth threshold value, when the cumulative total sensitivity index is greater than or equal to the fourth threshold value, the first variable set is taken as the target variable set, and when the cumulative total sensitivity index is less than the fourth threshold value, jumping to S104; S104, selecting a variable with the maximum total sensitivity index from the remaining variables and adding it to the first variable set, and jumping to S103.

8. A device for screening the importance of variables based on the multi-fidelity sensitivity error, using the method for screening the importance of variables based on the multi-fidelity sensitivity error according to any one of claims 1 to 7, for screening the importance of variables of the mechanical properties of metamaterial adapters, characterized in that, The device comprises: An acquisition module configured to acquire, at S1, distribution characteristics of M variables to be analyzed, the distribution characteristics comprising a distribution type and a distribution parameter of the variables to be analyzed, and the variables to be analyzed comprising various geometric characteristics, material properties and process parameters of an adapter; A first processing module configured to acquire, at S2, a high-fidelity sample set and a low-fidelity sample set as training sets by Latin hypercube sampling method according to a preset proportion based on the distribution characteristics, each sample in the training set comprising the M variables to be analyzed; A second processing module configured to construct, at S3, a multi-fidelity proxy model according to the training set, and to calculate, based on the multi-fidelity proxy model, a first importance measure result of the M variables to be analyzed; 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, and to obtain a contribution value of each sample in the high-fidelity sample set to the first importance measure result; A fourth processing module configured to construct, at S5, a mathematical optimization problem of adaptive update and adding points, and to solve the mathematical optimization problem based on a particle swarm optimization algorithm to obtain a new sample point; A fifth processing module configured to calculate, at S6, an error improvement amplitude of the new sample point to a high-fidelity sensitivity index and a low-fidelity sensitivity index respectively, and to obtain a fidelity type of the new sample point based on the error improvement amplitude; A sixth processing module configured to add, at S7, 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, based on the updated multi-fidelity proxy model, a second importance measure result of the M variables to be analyzed. a judging module configured to judge, at S8, whether the second importance measure result converges, and in a case where the second importance measure result converges, take the second importance measure result as a target importance measure result, and in a case where the second importance measure result does not converge, jump to S4; a sorting module configured to sort, at S9, the importance of the M variables to be analyzed based on the target importance measure result, to obtain an importance sorting result of the M variables to be analyzed; a screening module configured to screen, at S10, the M variables to be analyzed based on the importance sorting result and a target problem, to obtain a target variable set, the target variable set including 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 on the memory and executable on the processor, characterized in that, The processor executes the program to implement the variable importance screening method based on multi-fidelity sensitivity error according to any one of claims 1 to 7. 10.A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the variable importance screening method based on multi-fidelity sensitivity error according to any one of claims 1 to 7.

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