Aviation precision transmission part dynamic sensitivity rapid evaluation method based on hidden space mapping

Abstract

The invention provides an aviation precision transmission part dynamic sensitivity rapid evaluation method based on hidden space mapping, comprising the following steps: step 1, determining aviation precision transmission part dynamic performance indexes and an uncertainty parameter set, and extracting dynamic performance response time-varying data; step 2, sampling to generate an unconditional sample set of the uncertainty parameters and corresponding sample data; uncertain sources are stripped one by one, and a condition sample set and corresponding sample data are generated; 3, allocating a category label # imgabs0 # to the sample data, converting the category label # imgabs0 # into a binary vector, projecting the binary vector to a low-dimensional hidden space, and generating a hidden variable # imgabs1 #; and step 4, by taking the hidden variable # imgabs2 # corresponding to the unconditional sample data as a reference, calculating the Euclidean distance # imgabs5 # of the hidden variables # imgabs3 # and # imgabs4 # corresponding to the conditional sample data, and carrying out importance sorting on each uncertainty source according to # imgabs6 #. According to the method, the time-varying response data is compressed into the two-dimensional vector # imgabs7 # through hidden space mapping, high-dimensional calculation can be avoided only by calculating the distance # imgabs10 # from the # imgabs8 # and the # imgabs9 #, and the complexity of dynamic sensitivity analysis is reduced.

Description

Technical Field

[0001] The present invention relates to the field of dynamic system sensitivity analysis, and more particularly to a dynamic sensitivity rapid evaluation method based on latent space mapping. Background Art

[0002] The service performance and functionality of precision aircraft transmission components, such as bearings and gears, are affected by multiple sources of uncertainty, including material dispersion, manufacturing tolerances, interface nonlinearities, and the randomness of the load environment. These factors lead to insufficient precision and increased damage to transmission components, severely impacting the reliability and service life of aircraft transmission systems. Therefore, effective sensitivity analysis methods are essential to quantify the impact of these multiple sources of uncertainty and identify the sources of uncertainty that most significantly impact key performance indicators of transmission components, providing technical support for performance improvement and optimized design of transmission systems.

[0003] Precision transmission components in aviation withstand and transmit complex dynamic cyclic loads, and their key performance indicators exhibit significant dynamic and time-varying characteristics. Existing uncertainty sensitivity analysis methods primarily focus on static responses. While a small number of dynamic sensitivity analysis methods exist, these methods typically transform dynamic problems into static ones through feature extraction or time-domain discretization. Consequently, they exhibit significant limitations in analyzing the sensitivity of actual system dynamic responses, primarily manifested in the following three key aspects: First, while existing methods extend the static sensitivity analysis framework, they often struggle to fully characterize the time-dependence of transmission component performance and the complex coupling effects between various uncertainties. Second, existing dynamic sensitivity analysis methods generally rely on frequently invoking costly simulation models to acquire large amounts of discrete system response data. These methods then derive sensitivity indices based on variance estimation, probability distributions, or distance metrics. However, these sensitivity indices exhibit discrete and time-varying characteristics within the analyzed time interval, making it difficult to formulate a unified and comprehensive parameter importance ranking, which in turn hinders accurate understanding of the overall dynamic behavior of the system. Third, since the performance / function evaluation model of aircraft control system transmission components involves multi-variable and multi-moment responses under dynamic loading, existing methods often face the problem of a sharp increase in computational complexity during the evaluation process, resulting in heavy computational burden and low efficiency.

[0004] In summary, facing the complex coupling problems caused by multiple sources of uncertainty in aviation precision transmission components, existing dynamic sensitivity analysis methods remain insufficient in fully reflecting temporal correlations, capturing the combined effects of multiple factors, and overcoming the computational challenges posed by high-dimensional data. Developing a new and efficient method for rapid dynamic sensitivity assessment has become an urgent challenge for those skilled in the art. Summary of the Invention

[0005] To overcome the problems of high computational cost and insufficient interpretability of the existing dynamic sensitivity assessment of aviation precision transmission components, this paper proposes a rapid dynamic sensitivity assessment method based on latent space mapping, which can efficiently and interpretably quantify the sensitivity of input parameters / variables to the uncertainty of the dynamic time-varying response of the transmission system.

[0006] The technical solutions of the present invention are as follows:

[0007] A method for rapid dynamic sensitivity evaluation of aviation precision transmission components based on latent space mapping includes the following steps:

[0008] Step 1: Determine the dynamic performance indicators and uncertainty parameter sets of aviation precision transmission components, establish a simulation model interface, and extract time-varying data of dynamic performance response; Step 2: Generate an unconditional sample set of uncertainty parameters through high-dimensional sampling , in order to reflect the full uncertainty impact, input the simulation model to obtain the unconditional sample data of the dynamic response; use the factor fixing method to remove the uncertainty source one by one and generate the conditional sample set , obtain conditional sample data to provide input for latent space mapping; Step 3, assign category labels to the unconditional sample data and conditional sample data , use one-hot encoding to convert discrete category labels Convert to binary vector , through the mapping matrix Will Projecting into low-dimensional latent space to generate continuous latent variables , to establish a mapping relationship from label to latent variable; Step 4, the latent variable corresponding to the unconditional sample data As a benchmark, calculate the latent variables corresponding to the conditional sample data and Euclidean distance ,according to Rank the importance of each uncertainty source to achieve a unified importance ranking.

[0009] As a preference, in step 2, the factor fixing method is: for any input parameter , , in turn In each sample The corresponding random sampling value is fixed to its expected value , obtained in the peeling In the case of uncertainty, the conditional sample set of input parameters , thereby eliminating the uncertainty of any single / combination of parameters and constructing a conditioned sample set of the corresponding input parameters.

[0010] Preferably, in step 2, the expected value is the mean of the probability distribution of the input parameters.

[0011] Preferably, in step 3, Number the tags The corresponding sample set, Corresponding to unconditional sample data, Corresponding to the conditional sample data from which the uncertainty sources 1 to k are stripped; based on the one-hot encoding, the category labels Numerical mapping to high-dimensional binary vectors , When , it is constrained to be the origin in the latent space, hour, In the The first component is 1, and the rest are 0.

[0012] As a preference, set the hidden space dimension , using the mapping matrix Will Mapped to a low-dimensional latent space, generating latent variables, expressed as , where 、 Respectively The first and second dimension coordinate components in the two-dimensional latent space.

[0013] Preferably, in step 4, the latent variable vector difference is quantified by constructing a latent mapping Gaussian process proxy model, and its kernel function is defined as: , where the input of the proxy model is defined as , is the label difference term, is the time difference term.

[0014] As a preference, in step 4, the latent space mapping matrix parameters are optimized by maximum likelihood estimation. and temporal roughness parameter : , where is the prediction variance of the Gaussian process model, R is the co-correlation matrix based on the kernel function, is the total amount of training data, the superscript ^ is the optimal estimate; the optimal mapping matrix is determined by optimizing the parameter A , by optimizing the parameters Improve the accuracy of latent space modeling.

[0015] As a preference, in step 4, Group Euclidean distance Expressed as: , superscript Indicates the Group.

[0016] As a preference, by The latent space distance index is calculated by taking the mean of the Euclidean distance of the group sample data, which is expressed as , the importance of each input parameter is ranked based on the latent space distance index. The larger the distance value, the greater the influence of the corresponding input parameter.

[0017] Beneficial effects

[0018] (1) This paper proposes a new solution for the dynamic sensitivity assessment of aviation precision transmission components. It labels the uncertainty sources and constructs a low-dimensional latent space to quickly evaluate the sensitivity of the dynamic response of the transmission components. This method avoids the repeated use of high-precision and expensive simulation models and sensitivity index calculations in traditional variance decomposition-based methods, significantly reducing computational costs and analysis time. It is suitable for the scenario of rapid sensitivity analysis of dynamic systems in actual engineering.

[0019] (2) Compared with the existing sensitivity analysis methods, the present invention simultaneously performs dynamic response modeling and uncertainty difference measurement of transmission components in the latent space. Finally, by comparing the Euclidean distances between the latent variables in the latent space, a unified and comprehensive variable importance ranking is given within the analyzed time interval, so that the sensitivity analysis results have visualization and physical interpretation capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0022] Figure 2 A structural diagram of a self-lubricating spherical plain bearing for an aircraft flap provided by an embodiment of the present invention;

[0023] Figure 3 A visualization diagram of the stress cloud diagram of the pad component of the bearing provided by an embodiment of the present invention;

[0024] Figure 4 A maximum stress uncertainty measurement diagram for a bearing pad component provided by an embodiment of the present invention;

[0025] Figure 5 This is a result diagram obtained by the latent space-based dynamic sensitivity rapid evaluation method provided by an embodiment of the present invention;

[0026] Figure 6 A variable sensitivity ranking diagram obtained by a dynamic sensitivity rapid evaluation method based on latent space provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0027] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many different ways than those described herein, and those skilled in the art can make similar modifications without violating the scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The following embodiments of the present invention are further described in detail with reference to the accompanying drawings.

[0028] like Figures 1 to 6 As shown, this embodiment discloses a method for rapid dynamic sensitivity evaluation of aviation precision transmission components based on latent space mapping. Taking the sensitivity analysis of the dynamic load response of the self-lubricating spherical bearing of an aircraft flap during operation as an example, the method includes the following steps:

[0029] Step 1: Use ABAQUS software to establish a finite element simulation model for the flap self-lubricating spherical bearing, a key component in the flap transmission mechanism.

[0030] The self-lubricating spherical plain bearing consists of a metal inner ring, an outer ring and a self-lubricating fabric lining. The inner ring material is an elastic modulus of 193 , Poisson's ratio is 0.4, and density is 7930 Special stainless steel; the outer ring material is an elastic modulus of 200 , Poisson's ratio is 0.4, and density is 7800 The self-lubricating liner material is an anisotropic woven composite material. The material parameters are shown in Table 1 below:

[0031] Table 1 Material parameters of self-lubricating gasket .

[0032] The load setting of the flap joint bearing is: the reciprocating motion time is 4 seconds, and the first swing reciprocating angle is , radial load force is 3500 Transformed to 5000 , the axial load force changes from 3500 to 8000 , the axial load is 100 Transformed to 220 The second swing reciprocating angle is , radial load force is 3500 Transformed to 8000 , the axial load is 100 Transformed to 350 . Figure 3 The Von Mises stress distribution cloud diagram of the bearing pad component under the above parameter settings and loading conditions is shown.

[0033] Step 2: Flap bearings are subject to numerous sources of uncertainty during operation, and their mechanical response characteristics are influenced by a variety of structural parameters. In this example, the maximum von Mises stress experienced by the self-lubricating fabric pad during motion is used as the dynamic output response. The contribution of the uncertainty of each structural parameter to the uncertainty of the dynamic output response is analyzed. The uncertainty metrics for each input parameter are shown in Table 2 below:

[0034] Table 2 Uncertainty measures of input parameters .

[0035] Under the combined effect of all uncertainty sources, the maximum stress borne by the bearing pad component shows significant uncertainty, and its uncertainty measurement results are as follows: Figure 4 shown.

[0036] In order to quantify the impact of uncertainty, it is necessary to define the sample set structure:

[0037] Sample set: A complete data set corresponding to a specific uncertainty scenario, including an unconditional sample set and conditional sample set Among them, the unconditional sample set Contains dynamic response data of all uncertainty sources; conditional sample set It is the dynamic response data after removing a specific uncertainty source (such as fixing an input parameter).

[0038] Sample group: The smallest unit in a sample set. Each sample group is a complete parameter sampling value and the corresponding dynamic response time-varying data. The data is generated through the following process:

[0039] Step 2.1: Generate data and obtain unconditional samples.

[0040] Based on the joint probability density function of the input parameters, Latin hypercube sampling technology is used to generate a sample set of input parameters (in is the number of sample groups, is the dimension of the input variable). After multiple pre-experimental verifications, in this embodiment, , which can ensure the convergence of the subsequent dynamic sensitivity evaluation results. Establish the interface between the aircraft flap bearing simulation model and the sensitivity evaluation calculation program, and realize the transfer of input parameter uncertainty to the flap bearing dynamic output response through batch processing. Write a python script and use the ABAQUS secondary development interface to transfer the sample set to the Each set of parameter sampling values in the simulation model is loaded into the flap bearing finite element model for simulation. The mesh corresponding to the maximum Von Mises stress of the self-lubricating fabric lining component in the simulation model is searched frame by frame and the data is extracted. Ultimately, unconditional sample data of the maximum Von Mises stress response of the flap bearing during the 0-4 second run time is obtained. Figure 2 It shows that under the combined influence of various uncertainty sources, the maximum Von Mises stress borne by the self-lubricating fabric lining component has great uncertainty during operation.

[0041] Step 2.2: Remove uncertainty sources to generate a conditional sample set.

[0042] In order to quantify the contribution of each uncertainty source to the uncertainty of dynamic output, based on the idea of “stripping” the uncertainty sources one by one, the factor fixing method is used to strip each uncertainty source: for any input parameter , in turn In each sample The corresponding random sampling value is fixed to its expected value , you can get the peeling In the case of uncertainty, the conditional sample set of input parameters By analogy, the uncertainty of any single / combination parameter can be eliminated, and a conditional sample set of the corresponding input parameters can be constructed. As shown in Table 2, 11 uncertainty sources (input parameters) are defined in this embodiment. The uncertainty of each input parameter is eliminated in turn, without involving the elimination of the uncertainty of the combination parameter. A total of 11 conditional sample sets of input parameters are constructed. ~ . ABAQUS is also used to perform parametric modeling with the help of Python scripts to obtain the conditional sample data of the maximum Von Mises stress response of the flap bearing.

[0043] So far, this embodiment has obtained a total of 12 unconditional sample sets and conditional sample sets of the maximum Von Mises stress response of the flap bearing. Each sample set contains 100 groups of time-varying data, and the category label is defined as Number the tags The corresponding sample set, Corresponding to unconditional sample data, This corresponds to the conditional sample data with the 1st to kth uncertainty sources removed. In addition, a separate set of experiments was conducted in which each input parameter took the expected value and was input into the aircraft flap bearing simulation model. The maximum Von Mises stress response corresponding to the elimination of all uncertainty sources was obtained for benchmark comparison.

[0044] Step 3: Construct the latent space.

[0045] In order to distinguish the dynamic response data from different sources, each set of time-varying data is given a unique category label, which is:

[0046] ,

[0047] in, Defined as the sample group number; Defined as tag number; Defined as tag number The corresponding sample set; 、 Defined as tag number The corresponding sample set The group response time-varying data, i.e. For the Labels in group samples The corresponding time point, For a specific time point The corresponding output dynamic response value, in this embodiment, is the maximum Von Mises stress value of the flap bearing.

[0048] For the above discrete labels , using One-Hot encoding (single hot encoding), the category label Convert to a sparse binary vector , which is defined as follows:

[0049]

[0050] Among them, the numbered labels Corresponding One-Hot encoding In the The first component is 1, and the rest are 0.

[0051] In order to fuse the discrete One-Hot vector with the continuous time-varying response data in the same model, it is necessary to project it into a preset low-dimensional continuous latent space. , let the mapping matrix is the matrix to be learned, then the binary prior representation of each category is After mapping, the corresponding latent variable vector (posterior potential representation) can be obtained:

[0052] ,

[0053] That is, extract the mapping matrix No. Row, each category Fixed corresponding to a two-dimensional vector (mapping matrix No. OK).

[0054] To ensure that the unconditional response (label encoding is 0) is located at the reference point in the latent space, it is necessary to Apply a constraint so that it is fixed to the origin: .

[0055] In summary, the discrete labels can be transformed into Mapping to two-dimensional latent variables , used for subsequent Gaussian process modeling.

[0056] Step 4: Based on Gaussian process regression and implicit mapping technology, an implicit mapping Gaussian process regression proxy model is established to model the unconditional sample data and conditional sample data of the flap bearing dynamic response respectively, and to quantify the differences in the impact of different uncertainty sources on the dynamic response uncertainty.

[0057] For the Group dynamic response to time-varying data , the input of the implicit mapping Gaussian process surrogate model is defined as , the latent variables in the continuous low-dimensional latent space are obtained Plugging into the standard Gaussian kernel:

[0058] ,

[0059] Where, is the time dimension, is the roughness parameter. By embedding discrete labels into functions, the model can simultaneously integrate the influence of time and uncertainty sources.

[0060] The maximum likelihood estimation (MLE) To optimize:

[0061] ,

[0062] Where, Defined as the Euclidean distance, , is the roughness or scale parameter, yes dimensional correlation matrix, It's a process difference.

[0063] After training, the mapping matrix can be obtained And each category of latent variables ,in In order to quantify the “uncertainty impact difference” between the conditional dynamic response and the unconditional dynamic response in the latent space, we define Euclidean distance of class-conditioned dynamic response:

[0064] ,

[0065] The Euclidean distance Responded to the A set of unconditional and conditional response time-varying data, in the latent space The influence degree of the quasi-conditional response on the uncertainty of the dynamic response is shown in the figure. The larger the distance value, the smaller the uncertainty of the dynamic response of the flap bearing is after the corresponding uncertainty source is stripped away, and the influence of this uncertainty source is significant.

[0066] In this step, we construct (In this embodiment ) Implicit mapping Gaussian process proxy model, get 100 sets of Euclidean distance. Based on 100 sets of Euclidean distance, get the latent space distance index , sort the importance of each input parameter (uncertainty source). The latent space distance index of each input parameter calculated in this embodiment is shown in Table 3.

[0067] Table 3 Dynamic sensitivity analysis results of aviation bearings based on latent space mapping .

[0068] Figure 5 It reflects the positions of various conditional dynamic responses and unconditional dynamic responses in the latent space. The figure shows that the latent mapping Gaussian process proxy model is more interpretable in dynamic sensitivity analysis. Figure 6 It shows the sensitivity ranking of each variable.

[0069] The importance ranking of the variables is:

[0070] ,

[0071] The number of times the implicit mapping Gaussian process proxy model established in this embodiment calls the metamodel evaluation is: ,Right now This demonstrates the high efficiency of the method proposed in this invention.

[0072] In this example, the parameter with the greatest impact is and The parameters with greater influence are 、 、 、 , the effects of other parameters are small.

[0073] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for rapid dynamic sensitivity evaluation of aviation precision transmission components based on latent space mapping, characterized in that: The following steps are involved: Step 1: Determine the dynamic performance index and uncertainty parameter set of aviation precision transmission components, establish a simulation model interface, and extract the time-varying data of dynamic performance response; Step 2: Generate an unconditional sample set of uncertainty parameters through high-dimensional sampling , input the simulation model to obtain unconditional sample data of dynamic response; Use the factor fixing method to remove the uncertainty sources one by one and generate the conditional sample set , obtain conditional sample data; Step 3: assign category labels to the unconditional sample data and conditional sample data , use one-hot encoding to convert discrete category labels Convert to binary vector , through the mapping matrix Will Projecting into low-dimensional latent space to generate continuous latent variables ; Step 4: Use the hidden variables corresponding to the unconditional sample data As a benchmark, calculate the latent variables corresponding to the conditional sample data and Euclidean distance ,according to Rank the importance of each uncertainty source.

2. The method according to claim 1, characterized in that In step 2, the factor fixing method is: for any input parameter , , in turn In each sample The corresponding random sampling value is fixed to its expected value , obtained in the peeling In the case of uncertainty, the conditional sample set of input parameters , thereby eliminating the uncertainty of any single / combination of parameters and constructing a conditioned sample set of the corresponding input parameters.

3. The method according to claim 2, characterized in that In step 2, the expected value is the mean of the probability distribution of the input parameters.

4. The method according to claim 1, wherein In step 3, Number the tags The corresponding sample set, Corresponding to unconditional sample data, Corresponding to the conditional sample data from which the uncertainty sources 1 to k are stripped; based on the one-hot encoding, the category labels Numerical mapping to high-dimensional binary vectors , When , it is constrained to be the origin in the latent space, hour, In the The first component is 1, and the rest are 0.

5. The method according to claim 4, characterized in that Hidden space dimension , using the mapping matrix Will Mapped to a low-dimensional latent space, generating latent variables, expressed as , where 、 Respectively The first and second dimension coordinate components in the two-dimensional latent space.

6. The method according to claim 1, characterized in that In step 4, the latent variable vector difference is quantified by constructing a latent mapping Gaussian process proxy model, and its kernel function is defined as: , where the input of the proxy model is defined as , is the label difference term, is the time difference term.

7. The method according to claim 6, characterized in that In step 4, the latent space mapping matrix parameters are optimized by maximum likelihood estimation and temporal roughness parameter : , where is the prediction variance of the Gaussian process model, R is the co-correlation matrix based on the kernel function, is the total amount of training data, the superscript ^ is the optimal estimate; the optimal mapping matrix is determined by optimizing the parameter A , by optimizing the parameters Improve the accuracy of latent space modeling.

8. The method according to any one of claims 1 to 7, characterized in that In step 4, Group Euclidean distance Expressed as: , superscript Indicates the Group.

9. The method according to claim 8, characterized in that pass The latent space distance index is calculated by taking the mean of the Euclidean distance of the group sample data, which is expressed as , the importance of each input parameter is ranked based on the latent space distance index. The larger the distance value, the greater the influence of the corresponding input parameter.

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