A structure dynamics model correction method, device and equipment considering non-probabilistic uncertainty and correlation, and a medium

Abstract

The application discloses a structure dynamics model correction method and device considering non-probabilistic uncertainty and correlation, equipment and medium, relates to the model correction technical field, obtains the parameter interval and parameter correlation coefficient of the to-be-solved parameter; calculates the interval error of the first interval boundary of the predicted response and the second interval boundary of the measured response under the parameter interval and the correlation coefficient error of the first correlation coefficient of the predicted response and the second correlation coefficient of the measured response under the parameter correlation coefficient; constructs a target function for minimizing the interval error and the correlation coefficient error; fixes the parameter correlation coefficient to obtain the updated parameter interval; then fixes the updated parameter interval to obtain the updated correlation coefficient; obtains the total error according to the updated parameter interval and the correlation coefficient; if the total error is greater than or equal to the preset error, the first interval boundary of the predicted response and the first non-probabilistic correlation coefficient are recalculated. The method can accurately correct the non-probabilistic structure dynamics model.

Description

Technical Field

[0001] This application relates to the field of model correction technology, and in particular to a method, apparatus, device and medium for correcting structural dynamics models that consider non-probabilistic uncertainties and correlations. Background Technology

[0002] The finite element method (FEM) has been widely applied in fields such as mechanical, aerospace, and civil engineering. Correcting the initial finite element model based on measured data is a crucial step in structural dynamics research. However, engineering structures are generally subject to uncertainties such as material property fluctuations, geometric tolerances, boundary condition variations, and measurement noise, which often cause the corrected deterministic model results to deviate from the actual physical state. Therefore, how to conduct structural dynamics model correction under uncertain conditions has become an urgent problem to be solved in this field.

[0003] To address the aforementioned issues, existing technologies mainly fall into three categories. Probabilistic methods quantify uncertainty by constructing probability distribution functions of the parameters, but their accuracy is highly dependent on a large amount of sample data, making it difficult to guarantee correction effects under small sample conditions. Fuzzy methods describe uncertainty through membership functions; however, the construction of membership functions is highly subjective and lacks objective basis. Non-probabilistic convex model methods only require knowledge of the parameter boundaries to conduct analysis, showing significant advantages under small sample conditions. Among these, the hyperrectangular interval model cannot characterize the correlation between parameters, and while the multidimensional ellipsoidal model can introduce correlation, its boundary representation lacks flexibility, easily leading to over-expansion or conservatism of the uncertainty domain.

[0004] This shows that existing technical methods cannot accurately correct non-probabilistic structural dynamics models. Summary of the Invention

[0005] This application provides a method, apparatus, device, and medium for correcting structural dynamics models that consider non-probabilistic uncertainties and correlations, which can accurately correct non-probabilistic structural dynamics models.

[0006] To achieve the above objectives, this application adopts the following technical solution: Firstly, this application provides a method for modifying structural dynamics models that considers non-probabilistic uncertainties and correlations, including: Obtain the parameter range and non-probabilistic correlation coefficient of the parameters to be solved in structural dynamics; Calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the parameter interval; calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the parameter non-probability correlation coefficient. Construct an objective function that minimizes the interval error and the correlation coefficient error; First, fix the current non-probability correlation coefficients of the parameters and solve for the parameter range in the objective function to obtain the updated parameter range; then fix the updated parameter range and solve for the non-probability correlation coefficients of the parameters in the objective function to obtain the updated non-probability correlation coefficients of the parameters. The total error is obtained by comparing the updated parameter range, the updated non-probability correlation coefficient of the parameters with the measured parameter range and the measured non-probability correlation coefficient of the parameters. If the total error is greater than or equal to the preset error, the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response are recalculated. If the total error is less than the preset error, then output the updated parameter range and the updated parameter non-probability correlation coefficient.

[0007] Optionally, the first interval boundary for predicting the structural dynamic response and the first non-probabilistic correlation coefficient for predicting the structural dynamic response are obtained in the following way: Based on the selected sample set of parameters to be solved, a Kriging surrogate model is established; By inputting the parameter range into the Kriging surrogate model and propagating the positive uncertainty, the first interval boundary of the predicted structural dynamic response under the parameter range is obtained. By inputting the non-probability correlation coefficient of the parameters into the Kriging surrogate model and propagating through non-probability correlation, the first non-probability correlation coefficient of the predicted structural dynamic response under the non-probability correlation coefficient of the parameters is obtained.

[0008] Optionally, the filtered sample set of parameters to be solved is obtained in the following way: Obtain the candidate parameter vector sample set; Calculate the overall sensitivity index of each candidate parameter sample based on the candidate parameter vector sample set; The total sensitivity indices are sorted in descending order, and the candidate parameter samples corresponding to the top n total sensitivity indices are selected as the filtered parameter sample set to be solved.

[0009] Optionally, the step of establishing a Kriging surrogate model based on the filtered sample set of parameters to be solved includes: The filtered sample set of parameters to be solved is divided into an initial training set and a candidate sample pool; Based on the initial training set, a Kriging surrogate model is constructed. The Kriging surrogate model includes a regression coefficient vector and a zero-mean stationary Gaussian random process. The covariance matrix of the zero-mean stationary Gaussian random process is characterized by a correlation function.

[0010] Optionally, if the total error is greater than or equal to a preset error, the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response are recalculated, including: An adaptive acquisition function is obtained based on the local uncertainty term and the updated importance term of the candidate samples in the candidate sample pool; Add the candidate sample with the highest score of the adaptive acquisition function to the initial training set to obtain the updated training set; The Kriging proxy model is reconstructed based on the updated training set; Using the reconstructed Kriging surrogate model, the first interval boundary and the first nonprobabilistic correlation coefficient of the predicted structural dynamic response are recalculated.

[0011] Optionally, the step of obtaining the adaptive acquisition function based on the local uncertainty term and the updated importance term of the candidate samples in the candidate sample pool includes: The initial value of the local uncertainty term is obtained based on the candidate samples in the candidate sample pool and the training samples in the initial training set; The initial values ​​of the importance terms are obtained based on the deviation between the predicted structural dynamic response and the midpoint of the measured response interval of the Kriging surrogate model at the candidate sample, and the distance between the candidate sample and the midpoint of the parameter interval of the current parameter to be solved. The initial values ​​of the local uncertainty term and the updated importance term are normalized in the candidate sample pool space to obtain the local uncertainty term and the updated importance term. The local uncertainty term and the updated importance term are weighted and summed to obtain the adaptive acquisition function.

[0012] Optionally, the step of obtaining the total error based on the updated parameter range, the updated non-probability correlation coefficient of the parameters, the measured parameter range, and the measured non-probability correlation coefficient of the parameters includes: Calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the updated parameter interval; Calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the updated parameter non-probability correlation coefficient; The total error is obtained by adding the interval error to the correlation coefficient error.

[0013] Secondly, this application provides a structural dynamics model correction device that considers non-probabilistic uncertainties and correlations, comprising: The acquisition module is used to obtain the parameter range and non-probabilistic correlation coefficient of the parameters to be solved in structural dynamics; The processing module is used to calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the parameter interval; calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the parameter non-probability correlation coefficient; construct an objective function that minimizes the interval error and the correlation coefficient error; first, fix the current parameter non-probability correlation coefficient and solve the parameter interval in the objective function to obtain the updated parameter interval; then fix the updated parameter interval and solve the parameter non-probability correlation coefficient in the objective function to obtain the updated parameter non-probability correlation coefficient. The judgment module is used to recalculate the first interval boundary and the first non-probability correlation coefficient of the predicted structural dynamic response if the total error is greater than or equal to the preset error; if the total error is less than the preset error, it outputs the updated parameter interval and the updated parameter non-probability correlation coefficient.

[0014] Thirdly, this application provides a computing device, including a memory and a processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of the first aspects.

[0015] Fourthly, this application provides a computer-readable storage medium for storing a computer program for performing the method as described in any one of the first aspects.

[0016] As can be seen from the above technical solution, this application has at least the following beneficial effects: This application employs a multidimensional parallelepiped model to handle structural dynamics model correction under uncertainty. This eliminates the need for a large number of samples, avoiding the requirement for sufficient samples in probabilistic methods, and also avoids manually setting membership functions, reducing subjective biases introduced by fuzzy methods. Furthermore, this model can simultaneously represent parameter intervals and non-probabilistic correlation coefficients, better reflecting the correlation between parameters compared to hyperrectangular interval models, and allowing for flexible setting of uncertainty domain boundaries compared to multidimensional ellipsoidal models, reducing the risk of excessive expansion of the uncertainty domain and overly conservative results. This method calculates the interval error between the first interval boundary of the predicted structural dynamics response and the second interval boundary of the measured response, as well as the correlation coefficient error between the first non-probabilistic correlation coefficient of the predicted structural dynamics response and the second non-probabilistic correlation coefficient of the measured response, constructing a model based on the minimum sum of these two types of errors. The objective function is defined by the parameter interval, which is solved by fixing the non-probability correlation coefficient. Then, the parameter interval is fixed and the non-probability correlation coefficient is solved by the parameter interval, which is then solved by the parameter interval. This reduces the difficulty of solving each optimization. The total error is calculated by combining the interval error and the correlation coefficient error and compared with the preset error. When the total error is greater than or equal to the preset error, the prediction model (Kriging surrogate model) is updated to recalculate the first interval boundary and the first non-probability correlation coefficient of the predicted structural dynamic response. The parameter interval and the parameter non-probability correlation coefficient are continuously adjusted iteratively. When the total error is less than the preset error, the corresponding parameter interval and parameter non-probability correlation coefficient are output. The parameter interval and parameter non-probability correlation coefficient obtained through iterative optimization can achieve a higher degree of matching with the measured response.

[0017] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description

[0018] Figure 1 A flowchart illustrating a method for correcting a structural dynamics model that considers non-probabilistic uncertainties and correlations, provided in an embodiment of this application; Figure 2A first comparison diagram of two-dimensional projection of MP convex model, which considers non-probabilistic uncertainty and correlation, and the true value of the structural dynamics model correction result, is provided for embodiments of this application. Figure 3 is a second comparison diagram of the two-dimensional projection of the MP convex model, which considers non-probabilistic uncertainty and correlation, and the true value of the structural dynamics model correction result and the actual value provided in the embodiment of this application. Figure 4 A third comparison diagram of the two-dimensional projection of the MP convex model, which considers non-probabilistic uncertainties and correlations, and the true values, is provided for embodiments of this application. Figure 5 A first comparison diagram of the two-dimensional projection of the MP convex model with the corrected result of the nonprobabilistic structural dynamics model based on the Monte Carlo method and the true value is provided for the embodiments of this application. Figure 6 A second comparison diagram of the two-dimensional projection of the MP convex model with the corrected result of the nonprobabilistic structural dynamics model based on the Monte Carlo method and the true value is provided for an embodiment of this application. Figure 7 A third comparison diagram of the two-dimensional projection of the MP convex model with the corrected result of the nonprobabilistic structural dynamics model based on the Monte Carlo method and the true value is provided for the embodiments of this application. Figure 8 A schematic diagram of a structural dynamics model correction device considering non-probabilistic uncertainties and correlations provided in this application embodiment; Figure 9 This is a schematic diagram of a computing device provided in an embodiment of this application. Detailed Implementation

[0019] The terms "first," "second," and "third," etc., used in this application specification and accompanying drawings are used to distinguish different objects, not to limit a specific order.

[0020] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0021] The correction of finite element models involves various uncertainties, including those related to materials, geometry, boundaries, and measurements. Deterministic correction methods produce results that deviate from actual working conditions. Existing methods for handling three types of uncertainties all have shortcomings: probabilistic methods rely on a large number of samples, fuzzy methods are subject to subjective bias, and traditional non-probabilistic convex models struggle to simultaneously consider parameter ranges and parameter correlations, easily leading to distortions in the uncertainty domain description. The root cause of these problems lies in the fact that existing solutions cannot simultaneously correct the parameter value ranges and the degree of correlation between parameters. The optimization process does not treat these two types of correction variables separately, making it difficult to simultaneously reduce response interval deviations and response correlation deviations. Furthermore, the lack of iterative verification logic to continuously adjust parameter ranges and non-probabilistic correlation coefficients ultimately prevents effective correction of the non-probabilistic structural dynamics model.

[0022] In view of this, embodiments of this application provide a method for correcting structural dynamics models that considers non-probabilistic uncertainties and correlations. This method can be executed by a processing device. The processing device can be a terminal or a server. Terminals include, but are not limited to, smartphones, tablets, laptops, personal digital assistants, or smart wearable devices. Servers can be cloud servers, such as central servers in a central cloud computing cluster or edge servers in an edge cloud computing cluster. Of course, servers can also be servers in a local data center. A local data center refers to a data center directly controlled by the user.

[0023] This application relies on a multidimensional parallelepiped model to simultaneously describe the parameter range and non-probability correlation coefficient of the parameters to be solved. It simultaneously measures the deviation between the predicted response and the measured response in terms of both range and correlation. It calculates the range error and correlation coefficient error separately and constructs corresponding objective functions. It updates the parameter range and non-probability correlation coefficient in batches using an alternating optimization approach. It integrates the two types of errors to obtain the total error. It iteratively updates the first range boundary and the first non-probability correlation coefficient of the predicted response based on the relationship between the total error and the preset error. After the total error meets the requirements, it outputs the corrected parameter range and non-probability correlation coefficient. This improves the problem that traditional schemes have difficulty in simultaneously correcting the parameter value range and parameter correlation.

[0024] To make the technical solution of this application clearer and easier to understand, the following describes, in conjunction with the accompanying drawings, a method for correcting a structural dynamics model that considers non-probabilistic uncertainties and correlations, as provided in the embodiments of this application. Figure 1 As shown, this figure is a flowchart of a structural dynamics model correction method considering non-probabilistic uncertainties and correlations provided in an embodiment of this application. In this embodiment, the method includes: S201. The processing equipment obtains the parameter range and non-probabilistic correlation coefficient of the parameters to be solved in the structural dynamics.

[0025] Structural dynamics studies the response characteristics of structures under dynamic loads, including the variation patterns of physical quantities such as displacement, velocity, and acceleration. Unsolved parameters refer to uncertain parameters in the structural dynamics model that require correction, such as Young's modulus, Poisson's ratio, and density of materials, and tooth clearance in transmission systems. The parameter range refers to the possible values ​​of the unsolved parameter, defined by its lower and upper bounds, characterizing the magnitude of its uncertain variation. The non-probabilistic correlation coefficient is a numerical value used to quantitatively describe the degree of linear correlation between any two unsolved parameters within a non-probabilistic framework; its value ranges from -1 to 1.

[0026] The processing device reads the pre-defined initial parameter range and non-probability correlation coefficients of the parameters to be solved from external input or internal storage. Further, the processing device constructs a multidimensional parallelepiped model based on the initial parameter range and non-probability correlation coefficients of the parameters to be solved, to simultaneously characterize the uncertainty boundaries of the parameters and the correlations between the parameters.

[0027] The processing device constructs a multidimensional parallelepiped nonprobabilistic uncertainty model to characterize the uncertainty domain of the parameters to be solved, based on the parameter range and nonprobabilistic correlation coefficient of the parameters.

[0028] S202, the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the calculation parameter interval of the processing equipment; the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the non-probability correlation coefficient of the calculation parameters.

[0029] The predicted structural dynamic response refers to the output response of the structure under dynamic loads, such as displacement response, calculated by the processing device through the Kriging surrogate model. The first interval boundary refers to the lower and upper bounds of the predicted structural dynamic response interval, calculated by the Kriging surrogate model based on interval propagation of the current parameters. The measured response refers to the actual output response of the structure under dynamic loads, such as displacement response, obtained by the processing device through experimental measurements. The second interval boundary refers to the lower and upper bounds of the measured response interval, obtained by the processing device based on statistical analysis of experimental measurement sample data. The interval error refers to the degree of difference between the first and second interval boundaries. The first non-probability correlation coefficient refers to the non-probability correlation coefficient between any two predicted structural dynamic responses calculated by the processing device through propagation of the Kriging surrogate model based on the non-probability correlation coefficient of the current parameters. The second non-probability correlation coefficient refers to the non-probability correlation coefficient between any two measured responses constructed by the processing device through a multidimensional parallelepiped convex model based on experimental measurement response samples. The correlation coefficient error refers to the degree of difference between the first and second non-probability correlation coefficients.

[0030] In some embodiments, the processing device establishes a Kriging surrogate model based on a filtered set of parameters to be solved. The filtered set of parameters to be solved refers to the parameters that play a dominant role in the structural dynamic response, selected from the candidate parameter vector sample set after non-probabilistic sensitivity analysis.

[0031] The filtered sample set of parameters to be solved is obtained in the following way: The processing device acquires a sample set of candidate parameter vectors; based on the sample set of candidate parameter vectors, it calculates the total sensitivity index of each candidate parameter sample; the total sensitivity indices are sorted in descending order, and the candidate parameter samples corresponding to the top n total sensitivity indices are selected as the filtered sample set of parameters to be solved.

[0032] A candidate parameter vector sample set refers to multiple parameters selected from the structure that may have uncertainties and have limited value ranges, along with several specific numerical points of these parameters within their respective value ranges. The overall sensitivity index is a numerical value used to measure the degree of influence of a single candidate parameter sample on the overall structural dynamic response; a larger value indicates a greater influence of the parameter on the response.

[0033] Specifically, the processing device takes the acquired candidate uncertain but bounded parameter samples as input, assuming the candidate parameter vector sample set before sensitivity analysis is . ,in The number of candidate parameter samples. Indicates the first A number of candidate parameter samples were analyzed. First, a multi-input, multi-output non-probabilistic sensitivity analysis was performed on the structure based on a multidimensional parallelepiped convex model. In this analysis, the processing device quantified the total contribution of each candidate parameter sample to the structural dynamic response into two parts: independent contribution and correlated contribution, using variance decomposition.

[0034] The nonprobability variance of any response is calculated using the following formula:

[0035] in, Indicates the output response The non-probability variance, This represents the first constant coefficient, which is related to the dimension of the uncertain input parameters. This indicates the total number of output responses. Represents the matrix determinant operator. This represents the diagonal normalized matrix of the output response. The correlation matrix represents the output response and is used to describe the non-probabilistic correlation coefficients between different output responses. This represents the second constant coefficient, used to adjust the proportional relationships in the formula. This represents the interval radius vector of the output response. This represents the vector of first-order partial derivatives of the output response function at the midpoint of the parameters. This represents the diagonal normalized matrix of the input parameters. This represents the Hessian matrix of the second-order partial derivatives of the output response function at the midpoint of the parameters. Represents the matrix trace operator.

[0036] To eliminate the influence of differences in the dimensions of different output responses on the sensitivity analysis results, the first... The output response is normalized to:

[0037] in, Indicates the first The normalized output response Indicates the first One output response, Indicates the first Output response The non-probability variance.

[0038] Let the first Each output response satisfies:

[0039] in, Indicates the first Each output response and The response mapping function between them.

[0040] Then the first The normalized output response can be expressed as:

[0041] The total variance vector of the system is obtained by assembling the normalized output responses:

[0042] in, Represents the total variance vector of the system. Indicates the first The non-probabilistic variance of the normalized output response Indicates the first The unit vector corresponding to the normalized output response.

[0043] Furthermore, the first The candidate parameter sample pair of the th... The independent variance contribution and the correlated variance contribution of each normalized output response are expressed as follows:

[0044]

[0045] in, Indicates the first The candidate parameter for the th... The independent variance contribution of each normalized output response. Indicates the third constant coefficient. Indicates the first The interval radius of a normalized output response. Indicates the first The normalized output response mapping function corresponding to each normalized output response. Indicates the first A sample of candidate parameters, Indicates the first Diagonal normalized coefficients of candidate parameter samples Indicates the first The non-probability variance of the candidate parameter samples Indicates the first A sample of candidate parameters, Indicates the first Diagonal normalized coefficients of candidate parameter samples Indicates the first The non-probability variance of the candidate parameter samples; Indicates the first The candidate parameter for the th... The correlation variance contribution of the normalized output response Indicates the first The candidate parameter sample and the first Non-probability covariance among candidate parameter samples Indicates the first A sample of candidate parameters, Indicates the first A sample of candidate parameters, Indicates the first Diagonal normalized coefficients of candidate parameter samples Indicates the first Diagonal normalized coefficients of candidate parameter samples Indicates the first The candidate parameter sample and the first Non-probabilistic covariance among candidate parameter samples.

[0046] The first The independent variance contribution and correlated variance contribution of each candidate parameter sample to each normalized output response are assembled into an independent variance contribution vector and a correlated variance contribution vector, respectively. Further, the independent variance contribution vector and the correlated variance contribution vector are projected onto the total system variance vector to obtain the i-th... Independent sensitivity indices and related sensitivity indices for each candidate parameter sample:

[0047] in, Indicates the first Independent sensitivity index for each candidate parameter sample. Indicates the first The independent variance contribution vector of each candidate parameter sample. This represents the vector dot product operator. Indicates the first The relevant sensitivity index of each candidate parameter Indicates the first The correlation variance contribution vector of each candidate parameter.

[0048] The independent sensitivity index is added to the relevant sensitivity index to obtain the total sensitivity index. All candidate parameter samples are then sorted in descending order based on the total sensitivity index, and the candidate parameter samples corresponding to the top n total sensitivity indices are selected as the filtered set of parameters to be solved. The final sorting result in this embodiment is: .in, Indicates the Young's modulus of the internal gear ring, Indicates transmission clearance, This indicates the Poisson's ratio of the internal gear ring. This indicates the density of the internal gear ring. This represents the Young's modulus of the pinion shaft. This represents the Poisson's ratio of the pinion shaft. This indicates the density of the pinion shaft.

[0049] Based on the sensitivity ranking results, this embodiment selects three key parameters (i.e., n=3) that play a dominant role in the structural dynamics response: Young's modulus of the internal gear ring. Transmission clearance and Poisson's ratio of internal gear ring Successfully achieved parameter dimensionality reduction, only requiring model correction for the aforementioned three parameters.

[0050] The Kriging surrogate model is a surrogate model based on Gaussian processes, used to establish an approximate mapping relationship between input parameters and output response, replacing the high-cost finite element simulation calculation.

[0051] In this embodiment, the steps for constructing the Kriging proxy model are as follows: The processing device divides the filtered sample set of parameters to be solved into an initial training set and a candidate sample pool; based on the initial training set, a Kriging surrogate model is constructed. The Kriging surrogate model contains a regression coefficient vector and a zero-mean stationary Gaussian random process. The covariance matrix of the zero-mean stationary Gaussian random process is characterized by a correlation function.

[0052] In this embodiment, the filtered sample set of parameters to be solved consists of three key parameters (Young's modulus of the internal gear ring). Transmission clearance and Poisson's ratio of internal gear ring The processing device extracts sample components corresponding to the three key parameters from 100 sets of candidate parameter samples, forming a three-dimensional key parameter sample set. Further, this 100 sets of key parameter sample sets are divided into 18 initial training samples and 82 candidate samples. The initial training set is used to establish a Kriging surrogate model as a forward solver, while the candidate sample pool is used for subsequent adaptive sampling and updates.

[0053] Specifically, taking the sample points in the initial training set corresponding to the filtered sample set vector of parameters to be solved as input, and the predicted structural dynamic response corresponding to the sample points as output, Kriging surrogate models corresponding to each output response are established respectively. The mathematical expression corresponding to the Kriging proxy model of each output response is:

[0054] in, Indicates the first The output response at the sample point Kriging prediction at that location Indicates the first The basis function regression vector of each output response. Indicates the first The vector of regression coefficients corresponding to each output response. Indicates the first The output response is defined as a zero-mean stationary Gaussian random process in the key parameter space, and its covariance matrix is ​​expressed as:

[0055] in, The covariance operator is represented. Indicates the first The output response at the sample point A Gaussian random process at that location, Indicates the first The output response at the sample point A Gaussian random process at that location, Indicates the first The variance of the Gaussian process corresponding to each output response Indicates the first Two sample points corresponding to each output response and The correlation function of spatial distance between them.

[0056] The processing device assembles a multi-output predicted structural dynamics response model from the Kriging surrogate models of each output response. This multi-output Kriging surrogate model is used to replace the original structural dynamics model and participates in subsequent processes such as calculating the marginal intervals of the predicted output responses, propagating the non-probabilistic correlations of the predicted output responses, correcting the interval boundaries of key parameters, and correcting the non-probabilistic correlation coefficients of key parameters.

[0057] In this embodiment, the processing device inputs the parameter range into the Kriging surrogate model and obtains the first interval boundary of the predicted structural dynamic response under the parameter range through forward uncertainty propagation; it also inputs the non-probability correlation coefficient of the parameters into the Kriging surrogate model and obtains the first non-probability correlation coefficient of the predicted structural dynamic response under the non-probability correlation coefficient of the parameters through non-probability correlation propagation.

[0058] For the current parameter range, the processing device uses the sub-interval decomposition method to calculate the first interval boundary for predicting the structural dynamic response.

[0059] Assume the first The vector of the sample set of parameters to be solved after the next iteration The lower and upper bounds of the interval of the sample set vector of the parameters to be solved are respectively and The corresponding center vector and radius matrix of the parameter interval are respectively and .in, This represents the total number of parameter samples to be solved in the filtered parameter sample set. Indicates the first A sample of filtered parameters to be solved Indicates the first In the nth iteration The lower bound of the interval for each filtered sample of parameters to be solved. Indicates the first In the nth iteration The upper bound of the interval of the filtered sample of parameters to be solved.

[0060] Processing equipment for the first The current interval of the filtered sample of parameters to be solved is divided into sub-intervals, let the division be as follows: There are 10 sub-intervals, among which Let be a preset positive integer, the value of which is determined according to the requirements of calculation precision and efficiency. Then the th... The filtered sample of parameters to be solved is in the th... The th iteration Each sub-interval node is represented as:

[0061] in, Indicates the first The filtered sample of parameters to be solved is in the th... The th iteration The values ​​of each sub-interval node Indicates the first In the nth iteration The lower bound of the interval for each filtered sample of parameters to be solved. Indicates the first In the nth iteration The length of the sub-interval of the filtered sample of parameters to be solved.

[0062] The processing equipment is based on the established first The Kriging agent model is constructed to build the first... A one-dimensional nonlinear surrogate subsystem along the direction of the filtered sample parameters to be solved. In this one-dimensional nonlinear surrogate subsystem, only the first... The selected sample of parameters to be solved takes the node value of the sub-interval, and the remaining selected sample of parameters to be solved takes the center value of the current interval, that is, constructing a one-dimensional subsystem sampling point:

[0063] in, This represents the sampling point of a one-dimensional subsystem. Indicates the first In the nth iteration To the The interval center values ​​of the filtered sample of parameters to be solved Indicates the first In the nth iteration The filtered sample of parameters to be solved is in the th... The values ​​at the nodes of each sub-interval Indicates the first In the nth iteration To the The interval center value of the filtered sample of parameters to be solved.

[0064] The processing device inputs the sampling points of the one-dimensional subsystem into the first... The Kriging proxy model is obtained from the first... Approximate response values ​​for the predicted structural dynamic response:

[0065] in, Indicates the first In the nth iteration The predicted structural dynamic response in the sub-interval node combination The approximate response value is obtained by sub-interval decomposition at the given location. Indicates the first The predicted structural dynamic response at the ... The filtered sample of parameters to be solved is taken from the first... The response value calculated by the Kriging surrogate model when the sub-interval node values ​​and the remaining filtered parameter samples are taken as the center value of the current interval. Indicates the first The predicted structural dynamic response is the response value calculated by the Kriging surrogate model when all the filtered sample parameters to be solved take the center value of the current interval.

[0066] Processing equipment for the first The approximate response values ​​of the predicted structural dynamic response at all sub-interval nodes of all filtered parameter samples are used to perform an interval union operation, that is, to take the minimum and maximum values ​​among all approximate response values ​​to obtain the i-th... The lower and upper bounds of the first interval boundary for predicting the structural dynamic response:

[0067] in, Indicates the first In the nth iteration The lower bound of the first interval boundary for predicting the structural dynamic response. Indicates the first In the nth iteration The upper bound of the first interval boundary for predicting structural dynamic response. Indicates the first The total number of subintervals in the current interval division of the filtered parameter sample to be solved.

[0068] Next, the processing device inputs the non-probabilistic correlation coefficient of the parameters into the Kriging surrogate model. Through non-probabilistic correlation propagation, it obtains the first non-probabilistic correlation coefficient of the predicted structural dynamic response under the non-probabilistic correlation coefficient of the parameters. Specifically, it is assumed that the first... The non-probability correlation coefficient matrix of the filtered parameter samples after the next iteration is: Then the non-probability covariance between any two filtered parameter samples is:

[0069] in, Indicates the first In the nth iteration The filtered sample of parameters to be solved and the first The non-probabilistic covariance among the filtered samples of parameters to be solved Indicates the first In the nth iteration The filtered sample of parameters to be solved and the first Non-probabilistic correlation coefficients among the filtered samples of parameters to be solved. Indicates the first In the nth iteration The interval radius of the filtered sample of parameters to be solved Indicates the first In the nth iteration The interval radius of the filtered sample of parameters to be solved.

[0070] Based on the established current Kriging surrogate model, the processing device calculates the first and second partial derivatives of the predicted structural dynamic response with respect to the filtered sample of parameters to be solved at the midpoint of the current parameter interval, and substitutes them into the non-probabilistic correlation propagation formula to calculate the first non-probabilistic correlation coefficient between any two predicted structural dynamic responses:

[0071] in, Indicates the first In the nth iteration The predicted structural dynamic response and the first The first non-probabilistic correlation coefficient between the predicted structural dynamic responses Indicates the first In the nth iteration The vector of first-order partial derivatives of the predicted structural dynamic response at the midpoint of the parameter interval. Indicates the first In the nth iteration The vector of first-order partial derivatives of the predicted structural dynamic response at the midpoint of the parameter interval. Indicates the first In the nth iteration The second-order partial derivative Hessian matrix of the predicted structural dynamic response at the midpoint of the parameter interval. Indicates the first In the nth iteration The second-order partial derivative Hessian matrix of the predicted structural dynamic response at the midpoint of the parameter interval.

[0072] After calculating the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response, the processing device needs to construct an objective function to quantify the degree of difference between the predicted and experimentally measured structural dynamic responses. The objective function consists of two parts: interval error and correlation coefficient error. The interval error measures the deviation between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the experimentally measured structural dynamic response. The correlation coefficient error measures the deviation between the first non-probabilistic correlation coefficient of the predicted structural dynamic response and the second non-probabilistic correlation coefficient of the experimentally measured structural dynamic response.

[0073] The expression for calculating interval error is:

[0074] in, Indicates interval error. The second interval boundary represents the measured response. This represents the first interval boundary for predicting the structural dynamic response. This indicates the total number of output responses. Indicates the first The upper bound of the first interval boundary of the output response. Indicates the first The upper bound of the second interval boundary of the output response. Indicates the first The lower bound of the first interval boundary of the output response. Indicates the first The lower bound of the second interval boundary of the output response. Indicates the parameter range.

[0075] The expression for calculating the correlation coefficient error is:

[0076] in, This indicates the correlation coefficient error. The second non-probability correlation coefficient represents the measurement response. This represents the first non-probabilistic correlation coefficient used to predict the structural dynamic response. Indicates the first The output response and the first The first non-probabilistic correlation coefficient between the output responses Indicates the first The output response and the first The second non-probabilistic correlation coefficient between the output responses.

[0077] S203. The processing device constructs an objective function that minimizes the interval error and the correlation coefficient error.

[0078] To simultaneously correct the parameter ranges and non-probability correlation coefficients of the filtered parameter samples, the processing device constructs an objective function that minimizes the sum of the range error and the correlation coefficient error. The expression for the objective function is as follows:

[0079] in, Describe the objective function. Indicates the parameter range. This indicates the lower bound of the parameter range. This represents the upper bound of the parameter interval. This represents the non-probability correlation coefficient of the parameters. This represents the minimum allowed lower bound of the parameter range. This represents the maximum allowed upper bound of the parameter range.

[0080] S204. The processing device first fixes the current non-probability correlation coefficient of the parameters and solves the parameter interval in the objective function to obtain the updated parameter interval; then fixes the updated parameter interval and solves the non-probability correlation coefficient of the parameters in the objective function to obtain the updated non-probability correlation coefficient of the parameters.

[0081] The processing device first fixes the current non-probability correlation coefficient of the parameters to a constant. At this time, the objective function only uses the parameter interval as the optimization variable. The processing device solves for the parameter interval to obtain the updated parameter interval. Then, the processing device fixes the updated parameter interval obtained in the first step to a constant. At this time, the objective function only uses the non-probability correlation coefficient of the parameters as the optimization variable. The processing device solves for this univariate optimization problem to obtain the updated non-probability correlation coefficient of the parameters.

[0082] The above two steps constitute a complete cycle of alternating updates. The updated parameter interval represents the range of parameter uncertainty that minimizes the interval error between the predicted structural dynamic response and the experimentally measured structural dynamic response under the current non-probabilistic correlation coefficient. The updated parameter non-probabilistic correlation coefficient represents the correlation between parameters that minimizes the correlation coefficient error between the predicted structural dynamic response and the experimentally measured structural dynamic response under the current parameter interval.

[0083] S205. The processing equipment obtains the total error based on the updated parameter range, the updated parameter non-probability correlation coefficient, the measured parameter range, and the measured parameter non-probability correlation coefficient.

[0084] In some embodiments, the processing device calculates the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the updated parameter interval; calculates the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the updated parameter non-probability correlation coefficient; and adds the interval error and the correlation coefficient error to obtain the total error.

[0085] The processing equipment uses the same method as described above to calculate the interval error under the updated parameter interval and the correlation coefficient error under the updated non-probability correlation coefficient. The two are then summed to obtain the current total error. This total error value characterizes the overall deviation between the predicted structural dynamic response and the experimentally measured structural dynamic response in terms of interval range and correlation characteristics under the current updated parameter interval and non-probability correlation coefficient.

[0086] S206. The processing equipment determines whether the total error is greater than or equal to the preset error.

[0087] If the total error is greater than or equal to the preset error, execute S207; if the total error is less than the preset error, execute S208.

[0088] S207. If the total error is greater than or equal to the preset error, the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response shall be recalculated.

[0089] In some embodiments, the processing device obtains an adaptive acquisition function based on the local uncertainty term and the updated importance term of the candidate samples in the candidate sample pool.

[0090] Specifically, the processing device obtains the initial value of the local uncertainty term based on the candidate samples in the candidate sample pool and the training samples in the initial training set; it obtains the initial value of the updated importance term based on the deviation between the predicted structural dynamic response and the midpoint of the measured response interval of the Kriging surrogate model at the candidate sample, and the distance between the candidate sample and the midpoint of the parameter interval of the current parameter to be solved; it normalizes the initial values ​​of the local uncertainty term and the updated importance term in the candidate sample pool space to obtain the local uncertainty term and the updated importance term; and it performs a weighted summation of the local uncertainty term and the updated importance term to obtain the adaptive acquisition function.

[0091] The initial value of the local uncertainty term is obtained by calculating the minimum Euclidean distance between the candidate sample and all training samples in the initial training set in the normalized space. A larger value indicates that the candidate sample is farther from existing training samples, and the higher the uncertainty of the surrogate model in that region. The expression for the initial value of the local uncertainty term is:

[0092] in, Indicates the first The initial values ​​of the local uncertainty term for each candidate sample. Represents the normalized i-th The parameter vector of each candidate sample, Represents the first normalized training set. The parameter vector of each training sample This represents the total number of training samples in the initial training set.

[0093] The denominator of the initial value for updating the importance term consists of two parts: response bias and spatial distance. Response bias reflects the degree of deviation between the predicted response at a candidate sample and the midpoint of the measured response interval; a larger deviation indicates a more important candidate sample. Spatial distance reflects the distance of a candidate sample from the midpoint of the current parameter interval; a larger distance indicates a more important candidate sample. The weighted sum of these two factors, followed by the reciprocal, means that candidate samples with larger response bias and spatial distances have smaller initial values ​​for updating the importance term. The expression for the initial value of the importance term is:

[0094]

[0095]

[0096] in, Indicates the first The initial values ​​of the updated importance terms for each candidate sample. Indicates the first The deviation between the predicted structural dynamic response and the midpoint of the experimentally measured structural dynamic response interval at each candidate sample. Indicates the weighting coefficient. This represents a very small positive number, used to prevent the denominator from being zero. Indicates the first The standard Euclidean distance from each candidate sample to the midpoint of the current parameter interval. This indicates that according to the Kriging agent model, in the first... The predicted structural dynamics response at each candidate sample Indicates the midpoint of the measured response interval. Indicates the first candidate sample in the pool The parameter vector of each candidate sample, This represents the center vector of the current parameter interval. This represents the radius vector of the current parameter interval. This represents the 2-norm of a vector.

[0097] The processing device normalizes the initial values ​​of the local uncertainty term and the initial values ​​of the updated importance term for all candidate samples in the candidate sample pool, respectively, to obtain... and This brings the two to the same order of magnitude. Finally, the processing device performs a weighted summation of the normalized local uncertainty term and the update importance term to obtain an adaptive acquisition function. This score is used to measure the contribution of each candidate sample to the update of the surrogate model.

[0098] The expressions for the local uncertainty term and the updated importance term are:

[0099] in, This represents a local uncertainty term. This indicates that the importance item has been updated. This represents the minimum initial value of the local uncertainty term for all candidate samples in the candidate sample pool. This represents the maximum initial value of the local uncertainty term for all candidate samples in the candidate sample pool. This represents the minimum initial value of the update importance term for all candidate samples in the candidate sample pool. This represents the maximum value of the initial value of the update importance term for all candidate samples in the candidate sample pool.

[0100]

[0101] in, Indicates the first An adaptive acquisition function for candidate samples. This represents the weighting coefficient of the local uncertainty term.

[0102] The processing device adds the candidate sample with the highest score of the adaptive acquisition function to the initial training set to obtain the updated training set; based on the updated training set, the Kriging surrogate model is reconstructed; using the reconstructed Kriging surrogate model, the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response are recalculated.

[0103] The processing device first calculates the adaptive acquisition function score of all candidate samples in the candidate sample pool, selects the candidate sample with the highest score, and adds it to the initial training set to obtain the updated training set. Then, the processing device reconstructs the Kriging surrogate model based on the updated training set, i.e., it retrains the surrogate model using the sample points in the updated training set to reflect the information brought by the newly added sample points. Finally, the processing device uses the reconstructed Kriging surrogate model to recalculate the first interval boundary and the first non-probability correlation coefficient for predicting the structural dynamic response in the same manner as described above. The recalculated first interval boundary and the first non-probability correlation coefficient characterize the current estimation results of the updated Kriging surrogate model for the uncertainty and correlation features of the predicted structural dynamic response after the addition of candidate samples.

[0104] S208. If the total error is less than the preset error, output the updated parameter range and the updated parameter non-probability correlation coefficient.

[0105] The processing device compares the currently calculated total error with a pre-set preset error. If the total error is less than the preset error, it indicates that the overall deviation between the currently predicted structural dynamic response and the experimentally measured structural dynamic response has met the accuracy requirements. The processing device then stops iterative updates and outputs the updated parameter range and the updated non-probability correlation coefficients as the final correction results. The final parameter range characterizes the uncertainty range of the selected parameter samples after model correction; the final non-probability correlation coefficients characterize the direction and strength of the pairwise correlation between the selected parameter samples after model correction.

[0106] In this embodiment, the entire model correction framework adaptively supplements the initial 18 sets of samples with 3 sets of high-value training samples in the core dynamic optimization region, resulting in a final training sample size of only 21 sets. At this point, the total error between the predicted structural dynamic response MP model and the experimentally measured structural dynamic response MP model meets the preset accuracy convergence condition. The processing device stops iterative updates and outputs the final corrected parameter range and parameter non-probability correlation coefficients, along with Table 1. Figure 2 The final key uncertainty parameter is shown as the corrected interval boundary and non-probabilistic correlation coefficient.

[0107] The true uncertainty ranges for the three key parameters are as follows: Young's modulus of the internal gear ring. for MPa, transmission clearance for mm, Poisson's ratio of internal gear ring for The actual non-probability correlation coefficients are as follows: , , The initial search interval and correlation coefficient, the final correction results, and the correction errors of each parameter are detailed in Table 1.

[0108] Table 1. Corrected results of key structural parameter ranges and non-probabilistic correlation coefficients for 4.55 MW wind turbine gearboxes.

[0109] To clearly demonstrate the identification effect of the uncertain topological domain, the projected boundaries (i.e., the final MP convex model boundaries) of the key parameter three-dimensional domain after the modification of the present invention framework are shown on various two-dimensional planes. Figures 2-4 The specific values ​​of the corrected key parameter interval boundaries and non-probability correlation coefficients are listed in Table 1. Meanwhile, to provide an objective performance benchmark, a traditional Monte Carlo inverse model correction method (MCS-NPMU, which uniformly samples 200,000 parameter points from the initial model for forward response evaluation) is introduced as a benchmark for comparison. Its corrected topological boundary projection is shown in Table 1. Figures 5-7 The results of the correction using the traditional fixed training set surrogate model method (ordinary Kriging) are listed in Table 2.

[0110] Table 2. Gearbox parameter correction results based on the ordinary Kriging proxy model

[0111] Combining Table 1 and Table 2 with Figures 2-7 The comparison clearly shows that, in terms of correction accuracy, the multidimensional parallelepiped plane tilted boundary (red solid line in the figure) obtained by the method of this invention is highly consistent with the real physical boundary (blue solid line in the figure), completely and compactly enclosing the actual sample area. Its identification accuracy is comparable to that of the traditional MCS method that calls 200,000 parameter samples. Figures 5-7The method achieves perfect equivalence—the maximum relative error of the boundary of the marginal interval is only 0.2889%, and the maximum relative error of the non-probability correlation coefficient is only 2.0000%. In contrast, the traditional fixed-train-set Kriging method, lacking local blind-filling updates within the dynamic search region through inverse optimization, suffers from a correlation coefficient identification error exceeding 44.20%. In terms of computational cost, the method of this invention requires only 21 training samples to achieve the aforementioned accuracy, while the traditional MCS method requires forward evaluation of 200,000 parameter points. In solving the high-dimensional matrix of the finite element method for large and complex wind turbine gearboxes, its computational cost is completely unacceptable in practical engineering. The above comparison fully verifies the effectiveness of the method of this invention in simultaneously achieving accurate correction of parameter interval boundaries and non-probability correlation coefficients under limited sample conditions.

[0112] Table 4 shows the gearbox parameter correction results obtained based on the MCS method. The specific values ​​are listed in Table 4 as a reference. Figures 5-7 Supplementary explanation of the numerical values ​​corresponding to the projected boundaries shown.

[0113] Table 4. Gearbox parameter correction results obtained based on the MCS method

[0114] Based on the above description, this application has the following beneficial effects: This application employs a multidimensional parallelepiped model to correct nonprobabilistic structural dynamics models. It describes uncertainty solely based on the parameter intervals and nonprobabilistic correlation coefficients of the parameters to be solved, eliminating the need for sufficient sample support and avoiding the requirement for large-scale experimental samples in probabilistic methods. Furthermore, it eliminates the need for manually setting membership functions, reducing subjective interference from fuzzy methods. This model can simultaneously carry both parameter intervals and nonprobabilistic correlation coefficients, better reflecting the relationships between parameters compared to hyperrectangular interval models, and more flexibly constraining the uncertainty domain compared to multidimensional ellipsoidal models, reducing the conservatism problem caused by excessive expansion of the uncertainty domain. This method separately calculates the interval error formed by the first interval boundary of the predicted structural dynamics response and the second interval boundary of the measured response, as well as the first nonprobabilistic correlation coefficient of the predicted structural dynamics response and the measured response... The correlation coefficient error formed by the second non-probability correlation coefficient is used to construct an optimization objective function. The solution operations for the two types of variables are completed step by step. First, the parameter non-probability correlation coefficient is locked to solve the parameter interval, and then the updated parameter interval is locked to solve the parameter non-probability correlation coefficient. The optimization calculations for the two types of variables are completed separately to reduce the solution difficulty of a single optimization operation. After the interval error and the correlation coefficient error are superimposed to obtain the total error, it is compared with the preset error. If the total error does not reach the preset error standard, the first interval boundary and the first non-probability correlation coefficient of the predicted structural dynamic response are recalculated. The parameter interval and the parameter non-probability correlation coefficient are continuously iterated and adjusted until the total error meets the standard. Then, the corresponding parameter interval and the parameter non-probability correlation coefficient are output. The iteratively adjusted parameter interval and parameter non-probability correlation coefficient can reduce the deviation between the predicted response and the measured response.

[0115] The above text combined Figure 1 The structural dynamics model correction method considering non-probabilistic uncertainties and correlations provided in the embodiments of this application has been described in detail. The apparatus and equipment provided in the embodiments of this application will be described below with reference to the accompanying drawings.

[0116] like Figure 8 As shown in the figure, this is a schematic diagram of a structural dynamics model correction device that considers non-probabilistic uncertainties and correlations according to an embodiment of this application. The device includes: The acquisition module 301 is used to acquire the parameter range and non-probability correlation coefficient of the parameters to be solved in structural dynamics; Processing module 302 is used to calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the parameter interval; calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the parameter non-probability correlation coefficient; construct an objective function that minimizes the interval error and the correlation coefficient error; first, fix the current parameter non-probability correlation coefficient and solve the parameter interval in the objective function to obtain the updated parameter interval; then fix the updated parameter interval and solve the parameter non-probability correlation coefficient in the objective function to obtain the updated parameter non-probability correlation coefficient. The judgment module 303 is used to recalculate the first interval boundary and the first non-probability correlation coefficient of the predicted structural dynamic response if the total error is greater than or equal to the preset error; and to output the updated parameter interval and the updated parameter non-probability correlation coefficient if the total error is less than the preset error.

[0117] Optionally, the processing module 302 is specifically used to establish a Kriging surrogate model based on the filtered sample set of parameters to be solved; By inputting the parameter range into the Kriging surrogate model and propagating the positive uncertainty, the first interval boundary of the predicted structural dynamic response under the parameter range is obtained. By inputting the non-probability correlation coefficient of the parameters into the Kriging surrogate model and propagating through non-probability correlation, the first non-probability correlation coefficient of the predicted structural dynamic response under the non-probability correlation coefficient of the parameters is obtained.

[0118] Optionally, the processing module 302 is specifically used to obtain a sample set of candidate parameter vectors; Calculate the overall sensitivity index of each candidate parameter sample based on the candidate parameter vector sample set; The total sensitivity indices are sorted in descending order, and the candidate parameter samples corresponding to the top n total sensitivity indices are selected as the filtered parameter sample set to be solved.

[0119] Optionally, the processing module 302 is specifically used to divide the filtered sample set of parameters to be solved into an initial training set and a candidate sample pool; Based on the initial training set, a Kriging surrogate model is constructed. The Kriging surrogate model includes a regression coefficient vector and a zero-mean stationary Gaussian random process. The covariance matrix of the zero-mean stationary Gaussian random process is characterized by a correlation function.

[0120] Optionally, the processing module 302 is specifically used to obtain an adaptive acquisition function based on the local uncertainty term and the updated importance term of the candidate samples in the candidate sample pool; Add the candidate sample with the highest score of the adaptive acquisition function to the initial training set to obtain the updated training set; The Kriging proxy model is reconstructed based on the updated training set; Using the reconstructed Kriging surrogate model, the first interval boundary and the first nonprobabilistic correlation coefficient of the predicted structural dynamic response are recalculated.

[0121] Optionally, the processing module 302 is specifically used to obtain the initial value of the local uncertainty term based on the candidate samples in the candidate sample pool and the training samples in the initial training set; The initial values ​​of the importance terms are obtained based on the deviation between the predicted structural dynamic response and the midpoint of the measured response interval of the Kriging surrogate model at the candidate sample, and the distance between the candidate sample and the midpoint of the parameter interval of the current parameter to be solved. The initial values ​​of the local uncertainty term and the updated importance term are normalized in the candidate sample pool space to obtain the local uncertainty term and the updated importance term. The local uncertainty term and the updated importance term are weighted and summed to obtain the adaptive acquisition function.

[0122] Optionally, the processing module 302 is specifically used to calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the updated parameter interval. Calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the updated parameter non-probability correlation coefficient; The total error is obtained by adding the interval error to the correlation coefficient error.

[0123] The structural dynamics model correction device considering non-probabilistic uncertainties and correlations according to the embodiments of this application can correspond to the execution of the method described in the embodiments of this application, and the other operations and / or functions of the various modules / units of the structural dynamics model correction device considering non-probabilistic uncertainties and correlations are respectively for the purpose of implementing Figure 1 For the sake of brevity, the corresponding processes of each method in the illustrated embodiments will not be described in detail here.

[0124] This application also provides a computing device. For example... Figure 9 As shown in the figure, this is a schematic diagram of a computing device provided in an embodiment of this application. The computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other via the bus 401.

[0125] Bus 401 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 9 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0126] Processor 402 can be any one or more of the following processors: central processing unit (CPU), graphics processing unit (GPU), microprocessor (MP), or digital signal processor (DSP).

[0127] Communication interface 403 is used for communication with external devices.

[0128] Memory 404 may include volatile memory, such as random access memory (RAM). Memory 404 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0129] The memory 404 stores executable code, which the processor 402 executes to perform the aforementioned structural dynamics model correction method that considers non-probabilistic uncertainties and correlations.

[0130] Specifically, in achieving Figure 8 In the case of the illustrated embodiment, and Figure 8 When the modules or units of the structural dynamics model correction device considering non-probabilistic uncertainties and correlations described in the embodiments are implemented by software, the following steps are performed: Figure 8 The software or program code required for the functions of each module / unit can be partially or entirely stored in memory 404. Processor 402 executes the program code corresponding to each unit stored in memory 404, and executes the aforementioned structural dynamics model correction method that considers non-probabilistic uncertainties and correlations.

[0131] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a computing device can store, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct the computing device to execute the above-described structural dynamics model correction method that considers non-probabilistic uncertainties and correlations.

[0132] This application also provides a computer program product comprising one or more computer instructions. When the computer instructions are loaded and executed on a computing device, all or part of the processes or functions described in this application are generated.

[0133] The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0134] When the computer program product is executed by a computer, the computer performs any of the aforementioned methods for correcting structural dynamics models that consider non-probabilistic uncertainties and correlations. The computer program product can be a software installation package; when any of the aforementioned methods for correcting structural dynamics models that consider non-probabilistic uncertainties and correlations needs to be used, the computer program product can be downloaded and executed on the computer.

[0135] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0136] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in this application should be covered within the scope of protection of this application.

Claims

1. A method for correcting structural dynamics models considering non-probabilistic uncertainties and correlations, characterized in that, The method includes: Obtain the parameter range and non-probabilistic correlation coefficient of the parameters to be solved in structural dynamics; Calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the parameter interval; calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the parameter non-probability correlation coefficient. Construct an objective function that minimizes the interval error and the correlation coefficient error; First, fix the current non-probability correlation coefficients of the parameters and solve for the parameter range in the objective function to obtain the updated parameter range; then fix the updated parameter range and solve for the non-probability correlation coefficients of the parameters in the objective function to obtain the updated non-probability correlation coefficients of the parameters. The total error is obtained by comparing the updated parameter range, the updated non-probability correlation coefficient of the parameters with the measured parameter range and the measured non-probability correlation coefficient of the parameters. If the total error is greater than or equal to the preset error, the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response are recalculated. If the total error is less than the preset error, then output the updated parameter range and the updated parameter non-probability correlation coefficient.

2. The method according to claim 1, characterized in that, The first interval boundary for predicting the structural dynamic response and the first non-probabilistic correlation coefficient for predicting the structural dynamic response are obtained in the following way: Based on the selected sample set of parameters to be solved, a Kriging surrogate model is established; By inputting the parameter range into the Kriging surrogate model and propagating the positive uncertainty, the first interval boundary of the predicted structural dynamic response under the parameter range is obtained. By inputting the non-probability correlation coefficient of the parameters into the Kriging surrogate model and using the non-probability correlation propagation formula, the first non-probability correlation coefficient of the predicted structural dynamic response under the non-probability correlation coefficient of the parameters is obtained.

3. The method according to claim 2, characterized in that, The filtered sample set of parameters to be solved is obtained in the following way: Obtain the candidate parameter vector sample set; Calculate the overall sensitivity index of each candidate parameter sample based on the candidate parameter vector sample set; The total sensitivity indices are sorted in descending order, and the candidate parameter samples corresponding to the top n total sensitivity indices are selected as the filtered parameter sample set to be solved.

4. The method according to claim 2, characterized in that, The step of establishing a Kriging surrogate model based on the filtered sample set of parameters to be solved includes: The filtered sample set of parameters to be solved is divided into an initial training set and a candidate sample pool; Based on the initial training set, a Kriging surrogate model is constructed. The Kriging surrogate model includes a regression coefficient vector and a zero-mean stationary Gaussian random process. The covariance matrix of the zero-mean stationary Gaussian random process is characterized by a correlation function.

5. The method according to claim 4, characterized in that, If the total error is greater than or equal to the preset error, the first interval boundary and the first non-probabilistic correlation coefficient of the predicted structural dynamic response are recalculated, including: An adaptive acquisition function is obtained based on the local uncertainty term and the updated importance term of the candidate samples in the candidate sample pool; Add the candidate sample with the highest score of the adaptive acquisition function to the initial training set to obtain the updated training set; The Kriging proxy model is reconstructed based on the updated training set; Using the reconstructed Kriging surrogate model, the first interval boundary and the first nonprobabilistic correlation coefficient of the predicted structural dynamic response are recalculated.

6. The method according to claim 5, characterized in that, The adaptive acquisition function is obtained based on the local uncertainty term and the updated importance term of the candidate samples in the candidate sample pool, including: The initial value of the local uncertainty term is obtained based on the candidate samples in the candidate sample pool and the training samples in the initial training set; The initial values ​​of the importance terms are obtained based on the deviation between the predicted structural dynamic response and the midpoint of the measured response interval of the Kriging surrogate model at the candidate sample, and the distance between the candidate sample and the midpoint of the parameter interval of the current parameter to be solved. The initial values ​​of the local uncertainty term and the updated importance term are normalized in the candidate sample pool space to obtain the local uncertainty term and the updated importance term. The local uncertainty term and the updated importance term are weighted and summed to obtain the adaptive acquisition function.

7. The method according to claim 1, characterized in that, The total error is obtained by comparing the updated parameter range, the updated non-probability correlation coefficient of the parameters with the measured parameter range and the measured non-probability correlation coefficient, including: Calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the updated parameter interval; Calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the updated parameter non-probability correlation coefficient; The total error is obtained by adding the interval error to the correlation coefficient error.

8. A structural dynamics model correction device considering non-probabilistic uncertainties and correlations, characterized in that, The device includes: The acquisition module is used to obtain the parameter range and non-probabilistic correlation coefficient of the parameters to be solved in structural dynamics; The processing module is used to calculate the interval error between the first interval boundary of the predicted structural dynamic response and the second interval boundary of the measured response under the parameter interval; calculate the correlation coefficient error between the first non-probability correlation coefficient of the predicted structural dynamic response and the second non-probability correlation coefficient of the measured response under the parameter non-probability correlation coefficient; construct an objective function that minimizes the interval error and the correlation coefficient error; first, fix the current parameter non-probability correlation coefficient and solve the parameter interval in the objective function to obtain the updated parameter interval; then fix the updated parameter interval and solve the parameter non-probability correlation coefficient in the objective function to obtain the updated parameter non-probability correlation coefficient. The judgment module is used to recalculate the first interval boundary and the first non-probability correlation coefficient of the predicted structural dynamic response if the total error is greater than or equal to the preset error; if the total error is less than the preset error, it outputs the currently updated parameter interval and the updated parameter non-probability correlation coefficient.

9. A computing device, characterized in that, Including memory and processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program for performing the method as described in any one of claims 1 to 7.

Images