Analysis method of aero-engine turbine shaft under uncertain distribution parameters and product

Abstract

The invention discloses a method and a product for analyzing a turbine shaft of an aero-engine under uncertain distribution parameters, and belongs to the technical field of analysis of the turbine shaft of the aero-engine. According to the method, a two-stage self-adaptive POD-Kriging agent is constructed, wherein in the first stage, based on a left singular vector of a snapshot matrix and an improved LOOCV error criterion, modeling is conducted with distribution parameters as input, and the snapshot matrix is efficiently expanded and transmitted to the second stage; in the second stage, on the basis of a right singular vector of an extended snapshot matrix and an improved U learning function criterion, a standard normal sample is used as input for modeling, the first stage model is nested in the self-adaptive updating process to improve efficiency, and the failure probability under a distribution parameter implementation value can be rapidly and accurately calculated in combination with Monte Carlo simulation. According to the method, through two-stage adaptive modeling, huge calculation cost needed by traditional nested Monte Carlo simulation is remarkably reduced, efficient estimation of the failure probability is achieved, and the bottleneck that engineering application is difficult due to expensive calculation in the prior art is overcome.

Description

Technical Field

[0001] This invention relates to the field of aero-engine turbine shaft analysis technology, specifically to an analysis method and product for aero-engine turbine shafts under conditions of uncertain distributed parameters. Background Technology

[0002] As a core load-bearing and power transmission component, the turbine shaft of an aero-engine bears the crucial function of transmitting the mechanical work provided by the turbine to drive the high-speed rotation of the compressor system. Simultaneously, it must withstand various complex loads generated by the rotor system, including gravity, inertial forces, and torque. Failure of this structure, especially fatigue fracture, can lead to serious consequences such as loss of engine thrust, posing a direct threat to flight safety. Therefore, ensuring high reliability and stability of the turbine shaft throughout its entire lifecycle is of paramount importance for the safe operation of aero-engines.

[0003] However, the performance and lifespan of turbine shafts in actual operation are affected by a variety of uncertainties. These uncertainties mainly stem from the microscopic non-uniformity of materials, inherent tolerances in the manufacturing and assembly processes, and variations in service loads and the environment. In engineering practice, due to design and testing costs, these uncertainties are usually characterized as random variables with specific probability distributions, while also considering the uncertainty of their distribution parameters (also known as statistical uncertainty or second-order uncertainty). This ensures that the established probability model can cover as many potential operating conditions as possible, and on this basis, the reliability assessment of the fatigue life of the turbine shaft can be achieved. The existence of uncertainty in the distribution parameters means that the probability distribution of the input variables is not deterministic, making the failure probability of the structure no longer a fixed value, but typically a failure probability interval. A precise description of this interval mathematically usually involves a computationally intensive double-nested loop process: the outer loop samples the distribution parameters, while the inner loop, based on the realized value of each distribution parameter, samples a large number of input variables to calculate the failure probability under that realized value. Clearly, this process requires calling tens of thousands of structural response functions (such as finite element analysis), resulting in extremely high computational costs, which severely limits its application in practical engineering. Furthermore, in structural reliability optimization design, the reliability analysis problem obtained after decoupling can also be formally reduced to a type of reliability analysis problem under uncertainty in the distribution parameters.

[0004] In summary, the main bottleneck of the existing technology lies in the lack of a practical method that can efficiently and accurately estimate the fatigue life failure probability of turbine shafts under arbitrary distributed parameter values. This will limit the realization of reliability design and optimization of turbine shafts considering the uncertainty of distributed parameters. Summary of the Invention

[0005] The purpose of this invention is to provide an analysis method and product for aero-engine turbine shafts under uncertain distributed parameters, so as to overcome the problem in the prior art that it is impossible to quickly and accurately evaluate the fatigue life reliability of turbine shafts under arbitrary distributed parameter values.

[0006] The present invention solves the above-mentioned technical problems through the following technical solution: This invention provides an analysis method for aero-engine turbine shafts under conditions of uncertain distributed parameters, comprising the following steps: Based on the hybrid sampling scheme, the distribution parameter interval of each dimension of the aero-engine turbine shaft input variable is discretized and randomly recombined to construct a distribution parameter sample pool. A standard normal sample set is generated based on the standard normal probability density function. Initial training samples of the distribution parameters and the standard normal sample set are extracted from the distribution parameter sample pool and the standard normal sample set, respectively, and the function values ​​are calculated to construct a snapshot matrix. Perform singular value decomposition on the snapshot matrix and extract the previous... L One left singular vector is used as the POD basis to obtain the first-stage POD coefficients. The first-stage POD-Kriging model between the first-stage POD coefficients and the distribution parameters is constructed. Based on the improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model until the first preset accuracy condition is met. Based on the first-stage POD-Kriging model that meets the first preset accuracy condition, the snapshot matrix is ​​expanded; singular value decomposition is performed on the expanded snapshot matrix to extract the previous snapshot matrix. L Two right singular vectors are used as POD bases to obtain the second-stage POD coefficients. A second-stage POD-Kriging model is constructed between the second-stage POD coefficients and the standard normal variables. Based on the U learning function criterion, new standard normal samples are adaptively selected to update the second-stage POD-Kriging model until the second preset accuracy condition is met. Based on the second-stage POD-Kriging model that meets the second preset accuracy condition, combined with Monte Carlo simulation, the failure probability range is obtained by calculating the failure probability of the fatigue life of the turbine shaft of the aero-engine in the distributed parameter sample pool.

[0007] A further improvement of this invention lies in that, based on a hybrid sampling scheme, the distribution parameter range of each dimension of the aero-engine turbine shaft input variable is discretized and randomly recombined to construct a distribution parameter sample pool, specifically including: For each distribution parameter with interval uncertainty, discrete sampling is performed within its interval, and then the sampling points of all distribution parameters are randomly recombined to form a distribution parameter sample pool.

[0008] A further improvement of this invention lies in that, based on an improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model, specifically including: Calculate the average leave-one-out cross-validation error for all training points of the current first-stage POD-Kriging model; If the maximum value of the average leave-one-out cross-validation error exceeds the preset error threshold, an auxiliary Kriging model is constructed between the distribution parameters and the leave-one-out cross-validation error. Using the auxiliary Kriging model, candidate distribution parameter samples that maximize the maximum value of the leave-one-out cross-validation error are predicted from the distribution parameter sample pool. These candidate distribution parameter samples are then added as new distribution parameter samples to the distribution parameter training samples to update the first-stage POD-Kriging model.

[0009] A further improvement of this invention lies in adaptively selecting new standard normal samples based on the U learning function criterion to update the second-stage POD-Kriging model, specifically including: Calculate the U-function value of the current second-stage POD-Kriging model at each sample point in the standard normal sample set; If the minimum U-function value is less than a preset threshold, the corresponding standard normal sample is added to the standard normal training sample. The newly added standard normal samples are combined with the current distribution parameter training samples. The first-stage POD-Kriging model that meets the first preset accuracy condition is reconstructed and invoked. The snapshot matrix is ​​then expanded and the second-stage POD-Kriging model is updated.

[0010] A further improvement of this invention is that, when expanding the snapshot matrix, the previously calculated function values ​​are reused, and new function values ​​are calculated only for the combination of newly added standard normal samples and current distribution parameter training samples. A further improvement of the present invention is that it also includes a failure probability interval visualization output step: presenting the failure probabilities corresponding to different combinations of distribution parameters in the form of a two-dimensional function graph or a histogram, wherein the two-dimensional function graph uses color mapping to represent the magnitude of the failure probability, and the histogram displays the distribution characteristics of each distribution parameter according to the failure probability interval.

[0011] This invention also provides an analysis system for aero-engine turbine shafts under conditions of uncertain distributed parameters, comprising: The first module is used to discretize and randomly recombine the distribution parameter intervals of each dimension of the aero-engine turbine shaft input variable based on a hybrid sampling scheme, construct a distribution parameter sample pool, generate a standard normal sample set based on the standard normal probability density function, extract initial training samples of distribution parameters and initial training samples of standard normal from the distribution parameter sample pool and the standard normal sample set respectively, and calculate the function value to construct a snapshot matrix. The second module is used to perform singular value decomposition on the snapshot matrix and extract the previous... L One left singular vector is used as the POD basis to obtain the first-stage POD coefficients. The first-stage POD-Kriging model between the first-stage POD coefficients and the distribution parameters is constructed. Based on the improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model until the first preset accuracy condition is met. The third module is used to expand the snapshot matrix based on the first-stage POD-Kriging model that meets the first preset accuracy condition; and to perform singular value decomposition on the expanded snapshot matrix to extract the previous snapshot matrix. L Two right singular vectors are used as POD bases to obtain the second-stage POD coefficients. A second-stage POD-Kriging model is constructed between the second-stage POD coefficients and the standard normal variables. Based on the U learning function criterion, new standard normal samples are adaptively selected to update the second-stage POD-Kriging model until the second preset accuracy condition is met. The fourth module is used to obtain the failure probability range by calculating the failure probability of the fatigue life of the aero-engine turbine shaft in the distributed parameter sample pool based on the second-stage POD-Kriging model that meets the second preset accuracy condition and combined with Monte Carlo simulation.

[0012] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the analysis method for aero-engine turbine shaft under uncertain distributed parameters as described above.

[0013] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the analysis method for aero-engine turbine shaft under uncertain distributed parameters as described above.

[0014] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the analysis method for aero-engine turbine shafts under uncertain distributed parameters as described above.

[0015] Compared with the prior art, the positive and progressive effects of the present invention are as follows: The present invention provides an analysis method for aero-engine turbine shafts under uncertain distributed parameters. It constructs a sample pool of distributed parameters through a hybrid sampling scheme and establishes a unified random variable sampling mechanism by combining probability transformation, avoiding redundant calculations due to repeated sampling under different distributed parameters. Simultaneously, it employs a two-stage POD-Kriging surrogate model, utilizing the dimensionality reduction characteristics of POD technology to extract data features, fitting POD coefficients through the high-precision mapping capability of the Kriging model, and then accurately supplementing training samples using adaptive sample selection criteria (leave-one-out cross-validation error criterion and U-learning function criterion), without blindly expanding the sample size. Finally, it combines Monte Carlo simulation to calculate the failure probability. This significantly reduces the number of calls to the structural response function, greatly reducing computational complexity and cost, and solving the core problem of existing technologies being difficult to apply in engineering due to excessive computational load. Through a two-stage... The collaborative optimization of the POD-Kriging model involves two phases. The first phase focuses on global coverage of the distributed parameters, employing an improved leave-one-out cross-validation error criterion to ensure global prediction accuracy and provide a reliable foundation for snapshot matrix expansion. The second phase addresses the core requirement of failure probability prediction, enhancing prediction accuracy in key areas through an improved U-learning function criterion. The update process involves the reuse of information from the first phase modeling and the reconstruction and updating of the first phase model, enabling rapid expansion of the snapshot matrix. Furthermore, the hybrid sampling scheme ensures comprehensiveness of the distributed parameter samples through interval discretization and random recombination, avoiding accuracy loss due to incomplete sample coverage. This accurately captures the impact of distributed parameter uncertainty on failure probability, precisely outputs the failure probability range, and significantly improves the accuracy and reliability of turbine shaft fatigue life reliability analysis under scenarios of uncertain distributed parameters. Attached Figure Description

[0016] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0017] Figure 1 To simplify the model of an aircraft engine turbine shaft; Figure 2 for Figure 1 Equivalent stress cloud diagrams under different conditions; Figure (a) is the equivalent stress cloud diagram under the maximum speed condition; Figure (b) is the equivalent stress cloud diagram under the cruise speed condition; Figure 3 The failure probability function graph corresponding to the distribution parameters of any two-dimensional input variable; Figure 4 Histograms of the distribution parameters of input variables under different failure probability intervals; Figure 5 This is a flowchart illustrating the analytical method for aero-engine turbine shafts under uncertain distributed parameters according to the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0020] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0021] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0022] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This is an explanation of the present invention and not a limitation thereof.

[0024] The turbine shaft, as a core component of an aero-engine, connects the compressor and the turbine, and is a key component for power transmission. The turbine shaft geometry studied in this invention is as follows: Figure 1As shown, it mainly consists of a spline, a flange, and an intermediate connecting shaft. The vent holes and connecting holes on the spline and flange are prone to stress concentration, which may lead to fatigue failure. Therefore, they are identified as dangerous parts.

[0025] The load spectrum of the turbine shaft over 750 hours is shown in Table 1, which includes two types of periodic loads: the main cycle (start-maximum speed-start) and the secondary cycle (cruise-maximum speed-cruise), and two working states: maximum speed and cruising speed.

[0026] Table 1 Turbine shaft load spectrum

[0027] The turbine shaft structure was analyzed using ABAQUS software under maximum and cruising speed conditions, and the equivalent stress contour plot is shown below. Figure 2 As shown, the maximum equivalent stress in both states occurs at the vent at the spline root, thus this location is identified as a key point for fatigue life assessment. Factors influencing the maximum stress at this location include structural geometry, material properties, and load conditions, specifically the radius of the vent. r Distance of ventilation holes from the root h elastic modulus E Poisson's ratio v Speed ​​at maximum speed n 1 and torque T 1. Speed ​​during cruising n 2 and torque T 2. Due to the influence of manufacturing and control precision, the above input parameters... It exhibits randomness, and its distribution type and parameters are shown in Table 2.

[0028] Table 2 Distribution Types of Turbine Shaft Input Variables

[0029] Due to insufficient experimental data, the mean of the input variable distribution is limited. The variables are statistically classified as interval variables, and their upper and lower bounds are shown in Table 3.

[0030] Table 3 Distribution parameters of the means of input variables

[0031] Based on the Manson-Coffin formula and the Morrow modified model, the fatigue life prediction model for the turbine shaft can be expressed as:

[0032] in, The total strain amplitude, For average stress, For fatigue life, For elastic modulus, The fatigue strength coefficient, The fatigue strength index. The fatigue ductility coefficient, The fatigue ductility index is [value missing], the turbine shaft material is GH4169, and the operating temperature is 650℃. According to the "Materials Data Sheet for Aircraft Engine Design," the parameter values ​​are [value missing]. , , , Material strain amplitude With stress amplitude The relationship between them is as follows:

[0033] In the formula, For cyclical reinforcement index, The cyclic strain strengthening index is given. Based on the nonlinear damage accumulation theory, the formula for predicting the composite fatigue life of the turbine shaft is:

[0034] in, Indicates the stress amplitude of the main cyclic load. Indicates the stress amplitude of the secondary cyclic load. The ratio of the number of cycles for the primary and secondary cyclic loads. This indicates the fatigue life under the main cyclic load. This represents the combined fatigue life under the combined effects of the main cycle and the secondary cycle of periodic loads. is a material constant, which is taken as 1.5 in this embodiment.

[0035] Therefore, it is only necessary to analyze and calculate the turbine shaft under two operating conditions—maximum speed and cruising speed—using Abaqus. and The fatigue life can be calculated using the following set of equations. :

[0036] because and It's about input variables. The function of composite fatigue life, therefore Also about random input variables The function, i.e. Define the threshold for the combined fatigue life of the turbine shaft. The fatigue life reliability analysis model is defined as follows:

[0037] The aforementioned calculation of composite fatigue life requires repeated solving of the exponential equation, which leads to a large computational load and low computational efficiency. Therefore, the composite fatigue life reliability analysis model based on inverse strain amplitude proposed by Yun et al. can be used, and its expression is as follows:

[0038] Based on the above formula, the turbine shaft fatigue life function can be transformed as follows:

[0039] The corresponding expression for the fatigue life failure probability of the turbine shaft is as follows: .

[0040] Among them, input parameters The distribution form is determined by the distribution parameters. Control, based on the laws of uncertainty propagation, when the distribution parameters... When there is subjective uncertainty (following an interval distribution), the uncertainty of the distribution parameters will be passed on to the failure probability. Therefore, the uncertainty of the distribution parameters will lead to the uncertainty of the failure probability. The failure probability under the uncertainty of the distribution parameters can be described as the distribution parameter... implicit function form

[0041] To effectively estimate the upper and lower bounds of the failure probability, the distribution parameters are... A hybrid sampling scheme was adopted, the core idea of ​​which is to discretize each distribution parameter interval separately, that is, to generate each dimension. Each set of sample points is used, and then all the samples of distribution parameters are randomly recombined to form a unified sample set of distribution parameters. To some extent, this is similar to a random search for the extreme values ​​of the predicted response.

[0042] For any parameter implementation value The following is a sample of random variables used to calculate the corresponding failure probability. It can be based on the same set of standard normal space samples. The result obtained after the corresponding transformation is, i.e.

[0043] in, This indicates the probability transformation relationship used, such as the Rosenblatt transform, Nataf transform, etc. Therefore, it corresponds to the realized value of the input variable. Fatigue life can be converted into

[0044] The failure probability can then be transformed into

[0045] in, .

[0046] Furthermore, for The distribution parameter realizes the value The snapshot matrix of the simulation output can be calculated and constructed as follows:

[0047] in, , . It is a real-valued snapshot matrix whose rank satisfies Based on the fundamental principles of POD, the response function The POD representation can be based on The eigenvalues ​​are obtained by the eigenvalue decomposition, i.e.

[0048] in, and They are The equations above contain eigenvectors and eigenvalues, where each eigenvalue represents the average energy captured by its corresponding eigenvector, and the total energy is given by the sum of the eigenvalues. The eigenvalue problem in the above equations relates to the matrix. It is related to singular value decomposition (SVD), that is

[0049] in, Includes singular values , Represents a matrix of appropriate dimensions with zero elements. A matrix that is a left singular vector. It is a matrix of right singular vectors, and both are orthogonal matrices. Let and They are and The l Column vectors, then and They are and The eigenvectors of , with eigenvalues ​​. .

[0050] According to the Schmidt-Eckart-Young theorem, from the matrix The former L The basis formed by the left singular vectors is in all L In an orthogonal basis, the projection error of the snapshot can be minimized, therefore the rank is... L The basis of POD is taken as a matrix The former L Columns, Functions The POD model can be represented as:

[0051] in, and ,gather Indicates from the previous L POD basis functions consisting of 1 left singular vectors These are the coefficients corresponding to these basis functions; they are distribution parameters. The function, This refers to the number of eigenvectors (i.e., POD basis functions) retained. The squared error represented by the POD above is defined by the sum of the eigenvalues ​​of the eigenvectors corresponding to those not selected into the POD basis in the eigenvalue problem. Therefore, the number of POD basis functions can be selected according to the following criteria:

[0052] in, This is a user-defined tolerance, typically set to 10. -3 Or smaller.

[0053] Note that each coefficient in the POD model above is a distribution parameter. The function is such that the mapping between each POD coefficient and the distribution parameter can be constructed using the Kriging model. The Kriging model is a statistical interpolation and surrogate modeling method widely used in engineering optimization, uncertainty analysis, and computer experimental design. Its core idea is to make optimal unbiased predictions of the response at unknown locations by considering the spatial correlation between sample points; therefore, the individual POD coefficients... The Kriging model can be represented as

[0054] Based on this, the POD-Kriging model can be obtained, which can be used to approximate the function under parameter uncertainty:

[0055] Since the approximation on the right-hand side of the equation is a linear combination of the Kriging model, and the Kriging model is a Gaussian process, the POD-Kriging model used to estimate the response function is also a Gaussian process model. For any distribution parameter implementation value... The POD-Kriging model works on any standard normal sample. The predicted response function follows a normal distribution, i.e.

[0056] The mean and standard deviation are estimated by the following formula:

[0057]

[0058] Therefore, based on the above POD-Kriging model combined with the Monte Carlo method, the realized values ​​of arbitrary distribution parameters can be estimated. The following failure probability:

[0059] in, .

[0060] However, estimating the failure probability based on the above formula still requires calling a large number of function calls to construct the snapshot matrix. In fact, based on the same theory, the response function... The POD-Kriging model can also be expressed as:

[0061] in, yes The former L A right singular vector, These are the corresponding POD coefficients represented by the Kriging model. The two POD-Kriging models described above extract the most characteristic structure functions from the response space in different ways. Based on these characteristics of the POD-Kriging model, a two-stage POD-Kriging model can be established to calculate the failure probability for any realized value of the distribution parameters. Specifically, this involves first using a small number of distribution parameter samples... and a small number of standard normal samples Constructing a snapshot matrix An initial POD-Kriging model is established on its left singular vector. The model was then used to... Expand to .

[0062] Next, in the snapshot matrix Establish another POD-Kriging model on the right singular vector. Based on this model, the corresponding sample set can be obtained. and The response function values ​​corresponding to all samples in the dataset.

[0063] It is worth noting that the purpose of the first phase of POD-Kriging is to extend the snapshot matrix obtained in the second phase. Therefore, a learning function that improves global prediction accuracy should be adopted to ensure the global prediction accuracy of the POD-Kriging model in the first stage. Here, an improved version of leave-one-out cross-validation (LOOCV) error is used. This error index is obtained as a byproduct of Kriging model construction, and its expression is as follows:

[0064] in, Is it excluding the first training points The first one is built on all training points A Kriging model with 1 coefficient, This indicates that the current model is at point Mean prediction at [location] These are training coefficient samples. It is the correlation matrix in the Kriging model. It is a regression function matrix. , , and They represent and The i OK, express The i List, and They represent and The diagonal elements on the graph. The average LOOCV error (ELOO) can be obtained as follows: .

[0065] Because in the POD-Kriging model, there exists Each of the Kriging models corresponds to... Each model has a corresponding ELOO error, and therefore, the maximum error is selected. and compare it with a preset error threshold. If a comparison is made, If the model fails to update, new sample implementations are selected from the sampling pool. Ideally, the sample implementations that produce the largest LOOCV error should be included in the training set. To facilitate this process, a coarse Kriging model is constructed to approximate the distribution parameters. With LOOCV error The mapping relationship between them enables efficient estimation of the LOOCV error of all candidate implementations in the distributed parameter sample pool. Then, for any sample in the distributed parameter sample pool... ,there will be The corresponding LOOCV errors, with the maximum error Corresponding samples These will be used as new training samples in the training set to update the model, that is:

[0066] The goal of the second-stage POD is to obtain a convergent failure probability function. Therefore, the second-stage POD-Kriging employs an adaptive construction of an improved U-learning function to ensure high accuracy of the model in predicting failure probabilities. Its expression is as follows:

[0067] In this process, the standard normal sample that minimizes the U value is included in the training set to update the POD-Kriging model. The update process terminates when the minimum U value exceeds a given threshold or the maximum number of iterations is reached. In the second phase... During adaptive update, snapshot matrix After continuous dimensional expansion, in order to achieve [something] with fewer response function calls. Efficient expansion, snapshot matrix The information is reused and updated, while the auxiliary Kriging model is also updated. Ultimately, it is based on the second-stage POD-Kriging model. Efficiently calculate the realized values ​​of parameters with arbitrary distributions The following failure probability:

[0068] Based on the above-mentioned inventive concept, the present invention provides an analysis method for aero-engine turbine shafts under conditions of uncertain distributed parameters, comprising the following steps: Based on the hybrid sampling scheme, the distribution parameter interval of each dimension of the aero-engine turbine shaft input variable is discretized and randomly recombined to construct a distribution parameter sample pool. A standard normal sample set is generated based on the standard normal probability density function. Initial training samples of the distribution parameters and the standard normal sample set are extracted from the distribution parameter sample pool and the standard normal sample set, respectively, and the function values ​​are calculated to construct a snapshot matrix. Perform singular value decomposition on the snapshot matrix and extract the previous... L One left singular vector is used as the POD basis to obtain the first-stage POD coefficients. The first-stage POD-Kriging model between the first-stage POD coefficients and the distribution parameters is constructed. Based on the improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model until the first preset accuracy condition is met. Based on the first-stage POD-Kriging model that meets the first preset accuracy condition, the snapshot matrix is ​​expanded; singular value decomposition is performed on the expanded snapshot matrix to extract the previous snapshot matrix. L Two right singular vectors are used as POD bases to obtain the second-stage POD coefficients. A second-stage POD-Kriging model is constructed between the second-stage POD coefficients and the standard normal variables. Based on the U learning function criterion, new standard normal samples are adaptively selected to update the second-stage POD-Kriging model until the second preset accuracy condition is met. Based on the second-stage POD-Kriging model that meets the second preset accuracy condition, combined with Monte Carlo simulation, the failure probability range is obtained by calculating the failure probability of the fatigue life of the turbine shaft of the aero-engine in the distributed parameter sample pool.

[0069] For details, see Figure 5 An analytical method for aero-engine turbine shafts under uncertain distributed parameters includes the following steps: Step S1: Obtain the sample pool of distribution parameters based on the mixed sampling method. Standard normal samples are obtained based on the standard normal probability density function. .

[0070] Step S2: Extract initial training samples for distribution parameters from the corresponding sample pools. and standard normal variables initial training samples .

[0071] Step S3: Construct the first-stage POD-Kriging model Step S31: Initialize the iteration counter k =0 Step S32, let k = k +1, based on and , obtain the snapshot matrix ,in, , .

[0072] Step S33, for Perform SVD decomposition to obtain the first L 1 left singular matrix and the corresponding POD coefficient , construct a reflection and distribution parameters The Kriging model of the mapping relationship between them yields the first-stage POD-Kriging model. .

[0073] Step S34, Calculation LOOCV error corresponding to training samples and ELOO error ,when or If the condition is met, proceed to step S4; otherwise, proceed to step S35.

[0074] Step S35, Use and As a dataset, construct parameters that reflect the distribution. and The Kriging model between them, calculation LOOCV error for all samples in the dataset. ,make .

[0075] (3-6) Calculation ,in ,make , Return to step S32.

[0076] Step S4: Construct the second-stage POD-Kriging model Step S41: Using the POD-Kriging model trained in step S3 Estimate the output response corresponding to the sample of distribution parameters to obtain a new snapshot matrix. ,in ,

[0077] Step S42: Initialize the iteration counter k =0.

[0078] Step S43, for Perform SVD decomposition to obtain the first L 2 right singular matrices and the corresponding POD coefficient , construct a reflection and standard normal variables The Kriging model of the mapping relationship between them yields the POD-Kriging model. .

[0079] Step S44: Calculate the corresponding and The response matrix is ​​obtained by taking the U-function values ​​of all sample points. ,in ,from Determine the minimum value and the corresponding standard normal samples ,if If the condition is met, proceed to step S5; otherwise, proceed to step S45.

[0080] Step S45: Train the standard normal variable training sample pool Updated to Repeat step S3. To avoid redundant calculations, in step S32, when... k When =1, the snapshot matrix Update directly to ,in , , This represents the number of training samples for the distribution parameters after the previous execution of step S3, at which point the POD-Kriging model in the first stage... It was reconstructed again.

[0081] Step S46: Update the snapshot matrix ,in , .

[0082] Step S5: Based on the POD-Kriging model finally obtained in step S4 Calculate the failure probability function in the distributed parameter sample pool:

[0083]

[0084]

[0085] For the distribution parameter interval of each dimension of the aero-engine turbine shaft input variable, it is uniformly discretized into 10,000 sample points of distribution parameters, and then randomly recombine them into a sample set containing 10,000 distribution parameter samples. 10 samples are then extracted based on the standard normal probability density function. 5 A standard normal sample set is constructed using standard normal variables to estimate the failure probability. Thirteen distribution parameter samples and thirteen standard normal variable samples are selected as initial training samples for the distribution parameters and standard normal variables, respectively. Based on step S3, the first-stage POD-Kriging model is constructed. At this point, the response function call count is 13×17, meaning that through adaptive learning, three distribution parameter samples are added to the distribution parameter training sample set for model training. Furthermore, a snapshot matrix is ​​calculated based on the first-stage POD-Kriging model. Step S4 is executed to construct the second-stage POD-Kriging model. In this process, to achieve sample reuse and reduce computational costs, the first-stage POD-Kriging model is reconstructed for the snapshot matrix. The total number of calls to the final response function was 52×26, meaning that a total of 39 standard normal samples and 13 distribution parameter samples were selected to update all POD-Kriging models during the two-stage modeling process.

[0086] Based on the POD-Kriging model obtained in the second stage, the failure probability corresponding to all distribution parameter samples in the distribution parameter sample pool is predicted, and the final failure probability range is [5.7×10]. -4 [0.9275], to clearly illustrate the relationship between the failure probability and the distribution parameters of the input variables, Figure 3 This displays a graph of the failure probability function corresponding to the distribution parameters of any two-dimensional input variable, where colors map to the corresponding failure probability values. Furthermore... Figure 4 Histograms of the distribution parameters of each input variable were plotted under different failure probability intervals, taking into account... Figure 3 and Figure 4 As can be seen from the radius of the vent... r Torque T 1、 Distance from vent to root h The change in the value of the distribution parameter results in a significant fluctuation in the failure probability, which indicates that the distribution parameters corresponding to these three input parameters are key factors affecting the fatigue life reliability of the engine turbine shaft, and should be given more attention during the design, optimization, and manufacturing of the turbine shaft.

[0087] To address the reliability analysis of complex structures under uncertain distributed parameters, this invention employs the surrogate models POD (Proper Orthogonal Decomposition) and Kriging, which are used to achieve an efficient and high-precision calculation method for reliability indices of complex structures under uncertain distributed parameters at different realized values ​​of distributed parameters. The main technologies used are POD model, Kriging model, and Monte Carlo simulation.

[0088] The core of this invention lies in the following: First, through probability transformation, a set of random variable samples that can be used for reliability estimation under different distribution parameter samples are generated, and a snapshot matrix with correlation is constructed by combining a set of distribution parameter samples; then, a POD-Kriging model can be established to efficiently predict the structural response values ​​corresponding to different distribution parameter samples; to minimize computational costs and fully utilize the characteristics of the POD-Kriging model, a two-stage adaptive surrogate model is constructed to accelerate the computation process; finally, by combining the Monte Carlo simulation method, a rapid and accurate assessment of the fatigue life reliability of the turbine shaft under arbitrary distribution parameter values ​​is achieved, and the distribution parameters that have a significant impact on the failure probability value can be effectively identified.

[0089] Based on the same inventive concept, this application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of an analysis method for aero-engine turbine shafts under uncertain distributed parameters. The memory may include main memory, such as high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device. The processor, network interface, and memory are interconnected via an internal bus, which may be an industry-standard architecture bus, a peripheral component interconnection standard bus, an extended industry-standard architecture bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. The memory stores the program; specifically, the program may include program code, which includes computer operation instructions. The memory may include main memory and non-volatile memory, and provides instructions and data to the processor.

[0090] Based on the same inventive concept, embodiments of this application provide a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the steps of the analysis method for aero-engine turbine shafts under uncertain distributed parameters. Specifically, the computer-readable storage medium includes, but is not limited to, volatile memory and / or non-volatile memory. The volatile memory may include RAM (Random Access Memory) and / or cache memory, etc. The non-volatile memory may include ROM (Read-Only Memory), hard disk, flash memory, optical disk, magnetic disk, etc.

[0091] Based on the same inventive concept, this application provides a computer program product, which includes a computer program stored on a computer-readable storage medium. The computer program includes program instructions, which, when executed by a computer device, cause the computer device to perform the steps of the above-described analysis method for aero-engine turbine shafts under uncertain distribution parameters.

[0092] Those skilled in the art will understand that embodiments of the present invention can be provided as methods or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM (Compact Disc Read-Only Memory), optical storage, etc.) containing computer-usable program code.

[0093] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer apparatus or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0094] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer device or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0095] These computer program instructions may also be loaded onto a computer device or other programmable data processing equipment to cause a series of operational steps to be performed on the computer device or other programmable equipment to produce a process implemented by the computer device, thereby providing instructions that execute on the computer device or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0096] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0097] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. An analytical method for aero-engine turbine shafts under uncertain distributed parameters, characterized in that, Includes the following steps: Based on the hybrid sampling scheme, the distribution parameter interval of each dimension of the aero-engine turbine shaft input variable is discretized and randomly recombined to construct a distribution parameter sample pool. A standard normal sample set is generated based on the standard normal probability density function. Initial training samples of the distribution parameters and the standard normal sample set are extracted from the distribution parameter sample pool and the standard normal sample set, respectively, and the function values ​​are calculated to construct a snapshot matrix. Perform singular value decomposition on the snapshot matrix and extract the previous... L One left singular vector is used as the POD basis to obtain the first-stage POD coefficients. The first-stage POD-Kriging model between the first-stage POD coefficients and the distribution parameters is constructed. Based on the improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model until the first preset accuracy condition is met. Based on the first-stage POD-Kriging model that meets the first preset accuracy condition, the snapshot matrix is ​​expanded; singular value decomposition is performed on the expanded snapshot matrix to extract the previous snapshot matrix. L Two right singular vectors are used as POD bases to obtain the second-stage POD coefficients. A second-stage POD-Kriging model is constructed between the second-stage POD coefficients and the standard normal variables. Based on the U learning function criterion, new standard normal samples are adaptively selected to update the second-stage POD-Kriging model until the second preset accuracy condition is met. Based on the second-stage POD-Kriging model that meets the second preset accuracy condition, combined with Monte Carlo simulation, the failure probability range is obtained by calculating the failure probability of the fatigue life of the turbine shaft of the aero-engine in the distributed parameter sample pool.

2. The method for analyzing aero-engine turbine shafts under uncertain distributed parameters according to claim 1, characterized in that, Based on a hybrid sampling scheme, the distribution parameter range of each dimension of the aero-engine turbine shaft input variable is discretized and randomly recombined to construct a distribution parameter sample pool, specifically including: For each distribution parameter with interval uncertainty, discrete sampling is performed within its interval, and then the sampling points of all distribution parameters are randomly recombined to form a distribution parameter sample pool.

3. The method for analyzing aero-engine turbine shafts under uncertain distributed parameters according to claim 1, characterized in that, Based on the improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model, specifically including: Calculate the average leave-one-out cross-validation error for all training points of the current first-stage POD-Kriging model; If the maximum value of the average leave-one-out cross-validation error exceeds the preset error threshold, an auxiliary Kriging model is constructed between the distribution parameters and the leave-one-out cross-validation error. Using the auxiliary Kriging model, candidate distribution parameter samples that maximize the maximum value of the leave-one-out cross-validation error are predicted from the distribution parameter sample pool. These candidate distribution parameter samples are then added as new distribution parameter samples to the distribution parameter training samples to update the first-stage POD-Kriging model.

4. The method for analyzing aero-engine turbine shafts under uncertain distributed parameters according to claim 1, characterized in that, Based on the U-learning function criterion, new standard normal samples are adaptively selected to update the second-stage POD-Kriging model, specifically including: Calculate the U-function value of the current second-stage POD-Kriging model at each sample point in the standard normal sample set; If the minimum U-function value is less than a preset threshold, the corresponding standard normal sample is added to the standard normal training sample. The newly added standard normal samples are combined with the current distribution parameter training samples. The first-stage POD-Kriging model that meets the first preset accuracy condition is reconstructed and invoked. The snapshot matrix is ​​then expanded and the second-stage POD-Kriging model is updated.

5. The method for analyzing aero-engine turbine shafts under uncertain distributed parameters according to claim 4, characterized in that, When expanding the snapshot matrix, the previously calculated function values ​​are reused, and new function values ​​are calculated only for the combination of newly added standard normal samples and current distribution parameter training samples.

6. The method for analyzing aero-engine turbine shafts under uncertain distributed parameters according to claim 1, characterized in that, It also includes a failure probability interval visualization output step: presenting the failure probability corresponding to different combinations of distribution parameters in the form of a two-dimensional function graph or a histogram. The two-dimensional function graph uses color mapping to represent the magnitude of the failure probability, and the histogram displays the distribution characteristics of each distribution parameter according to the failure probability interval.

7. An analysis system for aero-engine turbine shafts under uncertain distributed parameters, characterized in that, include: The first module is used to discretize and randomly recombine the distribution parameter intervals of each dimension of the aero-engine turbine shaft input variable based on a hybrid sampling scheme, construct a distribution parameter sample pool, generate a standard normal sample set based on the standard normal probability density function, extract initial training samples of distribution parameters and initial training samples of standard normal from the distribution parameter sample pool and the standard normal sample set respectively, and calculate the function value to construct a snapshot matrix. The second module is used to perform singular value decomposition on the snapshot matrix and extract the previous... L One left singular vector is used as the POD basis to obtain the first-stage POD coefficients. The first-stage POD-Kriging model between the first-stage POD coefficients and the distribution parameters is constructed. Based on the improved leave-one-out cross-validation error criterion, new distribution parameter samples are adaptively selected to update the first-stage POD-Kriging model until the first preset accuracy condition is met. The third module is used to expand the snapshot matrix based on the first-stage POD-Kriging model that meets the first preset accuracy condition; and to perform singular value decomposition on the expanded snapshot matrix to extract the previous snapshot matrix. L Two right singular vectors are used as POD bases to obtain the second-stage POD coefficients. A second-stage POD-Kriging model is constructed between the second-stage POD coefficients and the standard normal variables. Based on the U learning function criterion, new standard normal samples are adaptively selected to update the second-stage POD-Kriging model until the second preset accuracy condition is met. The fourth module is used to obtain the failure probability range by calculating the failure probability of the fatigue life of the aero-engine turbine shaft in the distributed parameter sample pool based on the second-stage POD-Kriging model that meets the second preset accuracy condition and combined with Monte Carlo simulation.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the analysis method for the turbine shaft of an aero-engine under uncertain distributed parameters as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the analysis method for the turbine shaft of an aero-engine under uncertain distributed parameters as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the analysis method for the turbine shaft of an aero-engine under uncertain distributed parameters as described in any one of claims 1 to 6.

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