A rapid evaluation method for the dynamic sensitivity of aerospace precision transmission components based on latent space mapping

Abstract

This invention provides a rapid assessment method for the dynamic sensitivity of aerospace precision transmission components based on latent space mapping. The method includes: Step 1, determining the dynamic performance indicators and uncertainty parameter set of the aerospace precision transmission components, and extracting time-varying data of the dynamic performance response; Step 2, sampling to generate an unconditional sample set of uncertainty parameters and corresponding sample data; stripping uncertainty sources one by one to generate a conditional sample set and corresponding sample data; Step 3, assigning category labels to the sample data, converting it into binary vectors, and projecting it onto a low-dimensional latent space to generate latent variables; Step 4, using the latent variables corresponding to the unconditional sample data as a benchmark, calculating the Euclidean distance between the latent variables corresponding to the conditional sample data and the vectors, and ranking the importance of each uncertainty source. This application compresses the time-varying response data into a two-dimensional vector through latent space mapping, requiring only the calculation of the distance between the vectors and the vectors to avoid high-dimensional calculations, thus reducing the complexity of dynamic sensitivity analysis.

Description

Technical Field

[0001] This invention relates to the field of sensitivity analysis of dynamic systems, and more specifically to a method for rapid assessment of dynamic sensitivity based on latent space mapping. Background Technology

[0002] The service performance / function of precision transmission components in aerospace, such as bearings and gears, is affected by multiple uncertainties, including material dispersion, manufacturing tolerances, interface nonlinear effects, and the randomness of the load environment. These factors lead to insufficient precision and accelerated damage in transmission components, severely impacting the reliability and service life of aircraft transmission systems. Therefore, it is essential to develop effective sensitivity analysis methods to quantify the impact of these multiple uncertainties, identify the most significant sources of uncertainty affecting the key performance indicators of transmission components, and provide technical support for performance improvement and optimized design of transmission systems.

[0003] Precision transmission components in aerospace systems bear and transmit complex dynamic cyclic loads, and their key performance indicators exhibit significant dynamic and time-varying characteristics. Existing uncertainty sensitivity analysis methods are mostly geared towards static responses. Although a few dynamic sensitivity analysis methods exist, these methods typically transform dynamic problems into static ones through feature extraction or time-domain discretization, resulting in significant limitations in analyzing the sensitivity of real-world system dynamic responses. These limitations manifest in three main ways: First, while extending the framework of static sensitivity analysis, existing methods often fail to comprehensively characterize the time-dependent performance of transmission components and the complex coupling effects between various uncertainties. Second, existing dynamic sensitivity analysis methods generally rely on frequent and costly calls to simulation models to obtain large amounts of discrete system response data, then deriving 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 establish a unified and comprehensive ranking of parameter importance, thus affecting the accurate understanding of the overall dynamic behavior of the system. Third, since the performance / functional evaluation model of the transmission components of the aircraft control system involves multiple variables and multi-moment response under dynamic loading, existing methods often face the problem of a sharp increase in computational complexity during the evaluation process, resulting in a heavy computational burden and low efficiency.

[0004] In summary, existing dynamic sensitivity analysis methods are still insufficient in comprehensively reflecting time correlation, capturing the combined effects of multiple factors, and overcoming the computational challenges posed by high-dimensional data when dealing with the complex coupling problems of precision aerospace transmission components under the influence of multiple uncertainties. Developing a novel and efficient method for rapid assessment of dynamic sensitivity has become an urgent problem for those skilled in the art. Summary of the Invention

[0005] To overcome the problems of high computational cost and insufficient interpretability of evaluation results in the current dynamic sensitivity assessment of precision aerospace transmission components, this invention proposes a fast dynamic sensitivity assessment method based on latent space mapping, which can efficiently and interpretably quantify the sensitivity influence of input parameters / variables on the uncertainty of the dynamic time-varying response of the transmission system.

[0006] The technical solution of the present invention is as follows:

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

[0008] Step 1: Determine the dynamic performance indicators and uncertainty parameter set of aerospace precision transmission components, establish a simulation model interface, and extract time-varying data of dynamic performance response;

[0009] Step 2: Generate an unconditional sample set X0 of uncertainty parameters through high-dimensional sampling to reflect the effects of total uncertainty. Input this set into the simulation model to obtain unconditional sample data of the dynamic response. Then, use the factor fixing method to remove uncertainty sources one by one to generate a conditional sample set X. i , i = 1, 2, ..., to obtain conditional sample data, providing input for latent space mapping;

[0010] Step 3: Assign category labels to the unconditional sample data and the conditional sample data. m The subscript m represents the label number, m = 0, 1, 2, ... , and the discrete category labels l are encoded using one-hot encoding. m Convert to binary vector e m e is mapped through the mapping matrix M m Projecting onto a low-dimensional latent space generates continuous latent variables, where the latent variable corresponding to the unconditional sample data is denoted as z0, and the latent variable corresponding to the conditional sample data is denoted as z... m (m≠0) to establish a mapping relationship between labels and latent variables;

[0011] Step 4: Using the latent variable z0 corresponding to the unconditional sample data as a benchmark, calculate the latent variable z corresponding to the conditional sample data. m The Euclidean distance D between (m≠0) and z0 m According to D m The importance of each uncertainty source is ranked to achieve a unified importance ranking.

[0012] Preferably, in step 2, the factor fixing method is as follows: for any input parameter x i Let i = 1, 2, ..., and sequentially select x from each sample group in X0. i The corresponding random sample value is fixed at its expected value. Obtain in stripping xi Under uncertainty, the conditional sample set X of the input parameters i This eliminates the uncertainty of any single or combined parameters and constructs a conditional sample set of the corresponding input parameters.

[0013] Preferably, in step 2, the expected value The mean of the probability distribution of the input parameters.

[0014] Preferably, in step 3, l m Let m be the sample set corresponding to label number m, where m = 0 corresponds to unconditional sample data, and m = 1, 2, ..., k corresponds to conditional sample data where the first to k uncertainty sources are removed; based on one-hot encoding, the category label l m Numerical mapping to a high-dimensional binary vector e m When m = 0, the constraint in the latent space is the origin; when m ≠ 0, e m It is 1 for the m-th component and 0 for the remaining components.

[0015] As a preferred option, let the dimension of the latent space be d. z =2, using the mapping matrix M to transform e m Mapping to a low-dimensional latent space generates latent variables, represented as In the formula They represent e respectively m The first and second dimension coordinate components in the two-dimensional implicit space.

[0016] Preferably, in step 4, the differences in latent variable vectors are quantified by constructing a latent mapping Gaussian process surrogate model, the kernel function of which is defined as:

[0017]

[0018] The input to the proxy model is defined as w = [t, l]. For label differences, This represents the time difference term.

[0019] Preferably, in step 4, the latent space mapping matrix parameter A and the time roughness parameter ω are optimized by maximum likelihood estimation:

[0020]

[0021] In the formula, Let be the prediction variance of the Gaussian process model, R be the cocorrelation matrix based on the kernel function, n be the total amount of training data, and the superscript ^ be the optimal estimate. The optimal mapping matrix M is determined by optimizing parameter A, and the latent space modeling accuracy is improved by optimizing parameter ω.

[0022] Preferably, in step 4, the j-th group of Euclidean distances Represented as: The superscript j indicates the j-th group.

[0023] Preferably, the latent space distance index is calculated using the mean Euclidean distance of N sets of sample data, and expressed as follows: 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.

[0024] Beneficial effects

[0025] (1) This invention proposes a novel solution for the dynamic sensitivity assessment of precision transmission components in aerospace. It labels the uncertainty sources and constructs a low-dimensional latent space to rapidly assess the sensitivity of the transmission components' dynamic response. This method avoids the extensive repetitive calls to high-precision, costly simulation models and the complex sensitivity index calculations required by traditional variance decomposition-based methods, significantly reducing computational costs and analysis time. It is suitable for scenarios requiring rapid sensitivity analysis of dynamic systems in practical engineering applications.

[0026] (2) Compared with existing sensitivity analysis methods, this invention simultaneously models the dynamic response of transmission components and measures the uncertainty difference in the latent space. Finally, by comparing the Euclidean distance between each latent variable in the latent space, a unified and comprehensive ranking of variable importance is given within the analyzed time interval, so that the sensitivity analysis results have visualization and physical interpretation capabilities. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A flowchart of the method provided in an embodiment of the present invention;

[0029] Figure 2 A structural diagram of a self-lubricating joint bearing for an aircraft flap provided in an embodiment of the present invention;

[0030] Figure 3 Stress cloud diagram of the bearing liner component provided in an embodiment of the present invention;

[0031] Figure 4 A graph showing the maximum stress uncertainty of the bearing liner component provided in this embodiment of the invention;

[0032] Figure 5 The result diagram is obtained by the method for rapid evaluation of dynamic sensitivity based on latent space provided in the embodiments of the present invention.

[0033] Figure 6 The variable sensitivity ranking diagram is obtained by the dynamic sensitivity fast evaluation method based on latent space provided in the embodiments of the present invention. Detailed Implementation

[0034] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many different ways as described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention; therefore, the present invention is not limited to the specific embodiments disclosed below. Embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0035] like Figures 1 to 6 As shown, this embodiment discloses a rapid evaluation method for the dynamic sensitivity of aerospace precision transmission components based on latent space mapping. Taking the sensitivity analysis of the dynamic load response during the operation of an aircraft flap self-lubricating spherical bearing as an example, the method includes the following steps:

[0036] Step 1: For the key component in the flap transmission mechanism—the flap self-lubricating spherical bearing—a finite element simulation model is established using ABAQUS software.

[0037] This self-lubricating spherical plain bearing consists of a metal inner ring, an outer ring, and a self-lubricating fabric liner. The inner ring material has an elastic modulus of 193 GPa, a Poisson's ratio of 0.4, and a density of 7930 kg / m³. 3 Special stainless steel; the outer ring material has an elastic modulus of 200 GPa, a Poisson's ratio of 0.4, and a density of 7800 kg / m³. 3 Special precipitation-hardening steel. The self-lubricating gasket material is anisotropic woven composite material; material parameters are shown in Table 1 below:

[0038] Table 1 Material parameters of self-lubricating gaskets

[0039]

[0040] The loading settings for the flap spherical bearing are as follows: one reciprocating motion takes 4 seconds, with the first reciprocating angle being 17.5°, the radial load changing from 3500N to 5000N, the axial load changing from 3500N to 8000N, and the axial load changing from 100N to 220N. The second reciprocating angle is 35°, the radial load changing from 3500N to 8000N, and the axial load changing from 100N to 350N. Figure 3 The Von Mises stress distribution contour map of the bearing liner component is shown under the above parameter settings and loading conditions.

[0041] Step 2: The flap bearing experiences numerous uncertainties during operation, and its mechanical response characteristics are influenced by various structural parameters. In this embodiment, the maximum Von Mises stress borne by the self-lubricating fabric liner during operation is used as the dynamic output response to analyze the contribution of the uncertainties of each structural parameter to the uncertainty of the dynamic output response. The uncertainty measures of each input parameter are shown in Table 2 below:

[0042] Table 2 Uncertainty Measures of Input Parameters

[0043]

[0044]

[0045] Under the combined effect of all uncertainty sources, the maximum stress borne by the bearing liner component exhibits significant uncertainty, as shown in the uncertainty measurement results. Figure 4 As shown.

[0046] To quantify the impact of uncertainty, the sample set structure needs to be defined:

[0047] Sample set: A complete dataset corresponding to a specific uncertainty scenario, including the unconditional sample set X0 and the conditional sample set X. i The unconditional sample set X0 contains dynamic response data resulting from the combined effects of all uncertainty sources; the conditional sample set X... i This refers to dynamic response data after removing specific sources of uncertainty (such as fixing an input parameter).

[0048] Sample set: The smallest unit in a sample set. Each sample set consists of a complete parameter sample value and its corresponding time-varying dynamic response data. Data is generated through the following process:

[0049] Step 2.1: Generate data and obtain unconditional samples.

[0050] Based on the joint probability density function of the input parameters, a sample set of the input parameters is generated using the Latin hypercube sampling technique. (Where N is the number of sample groups, and d is the dimension of the input variables). After multiple preliminary experiments, setting N=100 in this embodiment ensures the convergence of subsequent dynamic sensitivity assessment results. An interface is established between the aircraft flap bearing simulation model and the sensitivity assessment calculation program. Batch processing is used to transfer the uncertainty of input parameters to the dynamic output response of the flap bearing. A Python script is written to load the sampled values ​​of each parameter set X0 into the flap bearing finite element model through the ABAQUS secondary development interface for simulation calculation. The mesh corresponding to the maximum Von Mises stress borne by the self-lubricating fabric lining component in the simulation model is searched frame by frame, and this data is extracted. Finally, unconditional sample data of the maximum Von Mises stress response of the flap bearing within the 0–4s running time can be obtained. Figure 2 This demonstrates that, under the combined influence of various uncertainties, the maximum Von Mises stress borne by the self-lubricating fabric lining component exhibits significant uncertainty during operation.

[0051] Step 2.2: Remove uncertainty sources to generate a conditional sample set.

[0052] To quantify the contribution of each uncertainty source to the uncertainty of the dynamic output, a factor-fixed method is used to isolate each uncertainty source based on the idea of ​​"stripping away" the uncertainty sources one by one: for any input parameter x i ,i=1,2,...,11,, and sequentially select x from each sample group in X0. i The corresponding random sample value is fixed at its expected value. This will allow you to obtain the result of peeling x i In the case of uncertainty, a conditional sample set of input parameters is constructed. Similarly, the uncertainty of any single / combined parameter can be eliminated, constructing the corresponding conditional sample set of input parameters. As shown in Table 2, this embodiment defines 11 uncertainty sources (input parameters), and eliminates the uncertainty of each input parameter sequentially, without involving the elimination of uncertainty of combined parameters, thus constructing a total of 11 conditional sample sets X1 to X... 11 Similarly, a Python script was used to perform parametric modeling of ABAQUS to obtain conditional sample data of the maximum Von Mises stress response of the flap bearing.

[0053] Thus far, this embodiment has obtained a total of 12 unconditional and conditional sample sets of the maximum Von Mises stress response of the flap bearing. Each sample set contains 100 sets of time-varying data, and a category label is defined. mLet m be the sample set corresponding to label number m, where m = 0 corresponds to unconditional sample data, and m = 1, 2, ..., k corresponds to conditional sample data where the first to k uncertainty sources are removed. In addition, another set of experiments is set up, in which the expected value of each input parameter is taken and input into the aircraft flap bearing simulation model to obtain the maximum Von Mises stress response under the condition of eliminating all uncertainty sources, for benchmark comparison.

[0054] Step 3: Construct the hidden space.

[0055] To distinguish dynamic response data from different sources, each set of time-varying data is assigned a unique category label, then:

[0056]

[0057] Where j is defined as the sample group number; m is defined as the label number; l m Defined as the sample set corresponding to label number m; Defined as the j-th group of time-varying response data in the sample set corresponding to label number m, i.e. For the label l in the j-th sample m 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.

[0058] Regarding the aforementioned discrete label l m One-Hot encoding is used to encode the category label l m Convert to a sparse binary vector e m ∈{0,1} 11 Its definition is as follows:

[0059]

[0060] Among them, the One-Hot code e corresponding to the number label m m It is 1 for the m-th component and 0 for the remaining components.

[0061] To fuse discrete One-Hot vectors with continuous time-varying response data in the same model, they need to be projected into a pre-defined low-dimensional continuous latent space. Let the dimension of the latent space be d. z =2, let the mapping matrix M (j) Given the matrix to be learned, the binary prior representation e for each category is... m After mapping, the corresponding latent variable vector (posterior latent representation) can be obtained:

[0062]

[0063] That is, extract the mapping matrix M (j) In the m-th row, each category m is fixed to correspond to a two-dimensional vector (matrix M). (j) (the mth line).

[0064] To ensure that the unconditional response (label encoded as 0) is located at the reference point in the latent space, a constraint needs to be imposed on z0 during training to fix it at the origin:

[0065] In summary, by multiplying the One-Hot encoding with the mapping matrix, the discrete label l can be... m Mapped to a two-dimensional hidden variable z m This is used for subsequent Gaussian process modeling.

[0066] Step 4: Based on Gaussian process regression and implicit mapping techniques, establish an implicit mapping Gaussian process regression surrogate model to model the unconditional sample data and conditional sample data of the dynamic response of the flap bearing, and quantify the differences in the impact of different uncertainty sources on the uncertainty of the dynamic response.

[0067] For the j-th group of dynamic response time-varying data The input to the implicit mapping Gaussian process surrogate model is defined as w = [t, l], and the latent variable z in the obtained continuous low-dimensional latent space is... m Insert into the standard Gaussian kernel function:

[0068]

[0069] The input to the proxy model is defined as w = [t, l]. For label differences, This represents the time difference term.

[0070] A and ω are optimized using maximum likelihood estimation (MLE):

[0071]

[0072] In the formula, ||·||² is defined as the Euclidean distance, R is an n×n dimensional correlation matrix, and σ 2 It's a difference in process.

[0073] After training, the mapping matrix M can be obtained. (j) and latent variables of each category in To quantify the difference in "uncertainty impact" between conditional and unconditional dynamic responses in the latent space, the Euclidean distance for the m-th type of conditional dynamic response is defined as follows:

[0074]

[0075] Euclidean distance This reflects the influence of the m-th type of conditional response on the uncertainty of the dynamic response in the latent space for the j-th group of unconditional and conditional time-varying data. The larger the distance value, the smaller the uncertainty of the flap bearing dynamic response after removing the corresponding uncertainty source, and the more significant the influence of this uncertainty source.

[0076] In this step, a total of N latent mapping Gaussian process surrogate models are constructed (N=100 in this embodiment), resulting in 100 sets of Euclidean distances. The latent space distance index is then obtained based on these 100 sets of Euclidean distances. The importance of each input parameter (uncertainty source) is ranked. The latent space distance index of each input parameter calculated in this embodiment is shown in Table 3.

[0077] Table 3 Results of Dynamic Sensitivity Analysis of Aircraft Bearings Based on Latent Space Mapping

[0078]

[0079] Figure 5 This figure illustrates the positions of various conditional and unconditional dynamic responses in the latent space, demonstrating that the latent mapping Gaussian process surrogate model is more interpretable in dynamic sensitivity analysis. Figure 6 This shows the sensitivity ranking of each variable.

[0080] The importance ranking of the variables is as follows:

[0081] E2>μ>G 12 >E outer >G 13 >G 23 >E1>v outer >v 12 >E inner ≈v inner ,

[0082] In this embodiment, the number of times the implicit mapping Gaussian process proxy model calls the meta-model evaluation is: N call = N×k+1, that is, N×k+1=100×12+1=1201. This demonstrates the high efficiency of the method proposed in this invention.

[0083] In this embodiment, the parameters with the greatest impact are E2 and μ, and the parameter with a relatively large impact is G. 12 E outer G 13 G 23 The influence of the other parameters is minimal.

[0084] 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 foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rapid evaluation method for the dynamic sensitivity of aerospace precision transmission components based on latent space mapping, characterized in that, Includes the following steps: Step 1: Determine the dynamic performance indicators and uncertainty parameter set of aerospace precision transmission components, establish a simulation model interface, and extract time-varying data of dynamic performance response; Step 2: Generate an unconditional sample set X0 of uncertain parameters through high-dimensional sampling, and input it into the simulation model to obtain unconditional sample data of dynamic response; The uncertainty sources are removed one by one using the factor fixation method to generate the conditional sample set X. i , i = 1, 2, ..., to obtain conditional sample data; Step 3: Assign category labels to the unconditional sample data and the conditional sample data. m The subscript m represents the label number, where m = 0, 1, 2, ..., m = 0 corresponds to unconditional sample data, and m = 1, 2, ..., k corresponds to conditional sample data where the first to k uncertainty sources are removed. One-hot encoding is used to encode the discrete category labels l. m Convert to binary vector e m e is mapped through the mapping matrix M m Projecting onto a low-dimensional latent space generates continuous latent variables, where the latent variable corresponding to the unconditional sample data is denoted as z0, and the latent variable corresponding to the conditional sample data is denoted as z... m m≠0; Step 4: Using the latent variable z0 corresponding to the unconditional sample data as a benchmark, calculate the latent variable z corresponding to the conditional sample data. m The Euclidean distance D between m≠0 and z0 m According to D m Rank the sources of uncertainty by importance.

2. The method according to claim 1, characterized in that, In step 2, the factor fixing method is as follows: for any input parameter x i Let i = 1, 2, ..., and sequentially select x from each sample group in X0. i The corresponding random sample value is fixed at its expected value. Obtain in stripping x i Under uncertainty, the conditional sample set X of the input parameters i This eliminates the uncertainty of any single parameter or combination of parameters, and constructs a conditional sample set of the corresponding input parameters.

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

4. The method according to claim 1, characterized in that, In step 3, based on one-hot encoding, the category label l is... m Numerical mapping to a high-dimensional binary vector e m When m = 0, the constraint in the latent space is the origin; when m ≠ 0, e m It is 1 for the m-th component and 0 for the remaining components.

5. The method according to claim 4, characterized in that, Let the dimension of the hidden space be d. z =2, using the mapping matrix M to transform e m Mapping to a low-dimensional latent space generates latent variables, represented as In the formula They represent e respectively m The first and second dimension coordinate components in the two-dimensional latent space, with the superscript j representing the sample group number.

6. The method according to claim 1, characterized in that, In step 4, the differences in latent variable vectors are quantified by constructing a latent mapping Gaussian process surrogate model.

7. The method according to claim 6, characterized in that, In step 4, the latent space mapping matrix parameter A and the time roughness parameter ω are optimized using maximum likelihood estimation: In the formula, Let be the prediction variance of the Gaussian process model, R be the cocorrelation matrix based on the kernel function, n be the total amount of training data, and the superscript ^ be the optimal estimate. The optimal mapping matrix M is determined by optimizing parameter A, and the latent space modeling accuracy is improved by optimizing parameter ω.

8. The method according to any one of claims 1-7, characterized in that, In step 4, the j-th group of Euclidean distances Represented as: The superscript j indicates the j-th group.

9. The method according to claim 8, characterized in that, The latent space distance index is calculated using the mean Euclidean distance of N sets of sample data, and is expressed as follows: 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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