Engine turbine disc uncertainty optimization method based on radial basis function neural network

Abstract

The invention discloses an engine turbine disk uncertainty optimization method based on a radial basis function neural network, and the method comprises the steps: constructing a safe cycle life model of an engine turbine disk in a service period based on a cumulative damage theory; constructing an uncertainty optimization design model of the fatigue-creep life of the turbine disc by taking the expected value of the safe cycle life as a target; constructing an initial training set by using a Latin hypercube sampling method; constructing a radial basis function neural network by adopting the training set; and searching the current design point by using an expectation improvement criterion, and if the current design point meets a preset threshold requirement, taking the current design point as an optimal design point to obtain a specific value of the design variable. According to the method, the expectation improvement criterion is provided for model dynamic updating and design, unnecessary sampling is avoided, meanwhile, the numerical integration method is used for converting the uncertainty optimization process with the coupling relation into deterministic optimization, and the solving efficiency of the uncertainty optimization design problem is improved.

Description

Technical Field

[0001] The present invention relates to the field of performance optimization design of aircraft engine turbine disks, and specifically relates to an uncertainty optimization method for engine turbine disks based on a radial basis neural network. Background Art

[0002] The main function of an aircraft engine is to provide propulsion power or support force for the aircraft, and it is known as the "heart" of the aircraft. Its performance and quality are directly related to the safety and economy of the aircraft. Therefore, the structural optimization design of aircraft engines is of great significance. The rotating components of the engine need to adapt to the requirements of high thrust-to-weight ratio, high speed, and high temperature development of aircraft engines. Their operating environment has become increasingly harsh, and the loads they need to bear have also become higher. Therefore, when designing the structure of the turbine disk, it is necessary to consider both its anti-fatigue and creep resistance performance.

[0003] Due to the influence of uncertainties, the fatigue and creep lives of engine turbine disks may have large dispersions, resulting in the problem that the actual fatigue-creep life is far lower than the expected fatigue life. Considering that uncertainties widely exist in material properties, working environments, and model parameters, how to comprehensively consider the influence of various uncertainty factors on fatigue life in the structural design of engine turbine disks, pursue lightweight design under the condition of meeting fatigue-creep life performance, and shorten the design cycle at the same time is an urgent problem to be solved currently.

[0004] Considering the coupling of outer-layer design optimization and inner-layer uncertainty analysis in the uncertainty optimization design problem, the patent application with the publication number CN113626942A: A reliability optimization method for the fatigue creep life of a double-amplitude turbine disk based on a surrogate model uses a Kriging approximation surrogate model to establish the relationship between uncertainty variables and the fatigue-creep life of the turbine disk, and transforms the uncertainty optimization problem into a deterministic optimization problem through a decoupling algorithm.

[0005] Although the decoupling method of the existing technology reduces the complexity of solving the uncertainty optimization design problem, the approximation errors in the early cycles of deterministic optimization and uncertainty analysis may cause the search direction of the optimal solution of the decoupling method to be incorrect. When the initial value of the design variable is far from the optimal solution or facing a highly nonlinear functional function, it may lead to the inability to converge to the optimal solution. Summary of the Invention

[0006] The purpose of the present invention is to provide an uncertainty optimization method for engine turbine disks based on a radial basis neural network to solve the problems that it is difficult to obtain the optimal solution and the solution efficiency is low in the existing technology during the solution process.

[0007] To achieve the above tasks, the present invention adopts the following technical solutions:

[0008] An uncertainty optimization method for engine turbine disks based on a radial basis neural network, comprising:

[0009] Based on the cumulative damage theory, construct a safety cycle life model for the engine turbine disk during the service period;

[0010] With the expected value of the safety cycle life as the objective, construct an uncertainty optimization design model for the fatigue-creep life of the turbine disk;

[0011] Use the Latin hypercube sampling method to construct an initial training set;

[0012] Construct a radial basis neural network using the training set;

[0013] Use the expected improvement criterion to find the current design point. If the current design point meets the preset threshold requirements, then take the current design point as the optimal design point to obtain the specific values of the design variables.

[0014] Furthermore, the constructing of the safety cycle life model for the engine turbine disk during the service period based on the cumulative damage theory includes:

[0015] Use the Coffin-Manson model to establish the relationship between the material strain and fatigue life of the turbine disk;

[0016] Use the Larson-Miller model to establish the relationship between the material strain, temperature and creep life of the turbine disk material;

[0017] Construct a linear cumulative damage form of the turbine disk based on fatigue damage and creep damage, and then according to the linear cumulative damage theory, obtain the safety cycle life model of the turbine disk during the service period required by the design; this model is a function of the uncertainty variable vector and the design variable vector.

[0018] Furthermore, with the expected value of the safety cycle life as the objective, the constructing of the uncertainty optimization design model for the fatigue-creep life of the turbine disk includes:

[0019] Construct the uncertainty variables and design variables in the design process of the turbine disk;

[0020] According to the design requirements of the turbine disk, construct an uncertainty optimization design model for the fatigue-creep life, expressed as:

[0021]

[0022] s.t.W(x)≤W * ,x≤[x L ,x U

[0023] ​Among them, \(x\) is the design variable vector composed of design variables, \(p\) is the uncertainty variable vector composed of uncertainty variables, and \(N\) fc (\(x,p\)) represents the safe cyclic life \(N\) fc is a function of the uncertainty variables and design variables; \(E\) p [·] represents the expectation operation considering the uncertainty variable vector \(p\), \(W(x)\) represents the total weight of the turbine disk, which is a constraint function related to \(x\), and \(W\) * is the constraint threshold, and \(x\) L and \(x\) U respectively represent the lower and upper boundaries of the design space \([x\) L , \(x\) U where the design variable vector \(x\) is located;

[0024] The uncertainty optimization design model is converted into a deterministic optimization problem through the numerical integration method, which is expressed as:

[0025]

[0026] s.t. \(W(x)\leq W\) *

[0027] where \(f\) P (\(p\)) represents the probability density function of the uncertainty variable vector; at this time, \(M(x)\) is the objective function related only to the design variable vector \(x\).

[0028] Furthermore, the Latin hypercube sampling method is used to construct the initial training set, including:

[0029] Using the Latin hypercube sampling method to extract a set of design variable vectors \(x\) within \([x\) L , \(x\) U as training samples, denoted as \(x\) D =\{x\) (1) ,…, \(x\) (N) \} T , where \(x\) (N) represents the \(N\)th extracted design variable vector. At the same time, \(f\) P (\(p\)) is used to obtain a set of training samples of the uncertainty variable vector \(p\), denoted as \(p\) D =\{p\) (1) ,…, \(p\) (M) \} T , where \(p\) (M) represents the \(M\)th extracted uncertainty variable vector. Combine \(x\) ( \(_i\) ) (\(i = 1,...,N\)) and \(p\) (j) to obtain \(N\times M\) groups of training samples. Substitute each group of training samples \((x\) (i) , \(p\) (j) ) into \(N\) fc(x, p) gives the output response y of the safe cyclic life (i,j) = N fc (x (i) , p (j) ) and the output response z of the constraint function (i) = W(x (i) ), thereby generating two training sets of the radial basis neural network and

[0030] Furthermore, a radial basis neural network is constructed using the training sets, including:

[0031] Normalize the training sets of the radial basis neural network to obtain the normalized training sets;

[0032] The radial basis neural network includes an input layer, a hidden layer, and an output layer; the training process of the radial basis neural network includes two stages: unsupervised learning and supervised learning;

[0033] In the unsupervised learning stage, the k-means clustering method is used to initialize the centers and widths of the radial basis functions in the hidden layer; when training the radial basis neural network, the training samples in the training set are first grouped so that the center of each group can be used as the center of the radial basis function, and the width of each radial basis function can be determined according to the Euclidean distance from the training samples to the center of each group;

[0034] Cross-validation randomly divides the training sets S and D into K sub-training sets, denoted as S( k ) and D( k ), and repeats training the radial basis neural network on these subsets to evaluate the performance of each radial basis neural network, thereby constructing K radial basis neural networks, denoted as and

[0035] In the supervised learning stage, the training samples (x (i) , p (j) ) are provided to the radial basis neural network and The predicted values are calculated using the radial basis functions and The predicted values and The predicted values are then compared with the true output responses y (i,j) and z (i) to establish the training error, and then the gradient descent algorithm is used to adjust the weights connecting the neurons in the hidden layer and the output layer.

[0036] Furthermore, the expected improvement criterion is used to find the current design point, including:

[0037] The estimated value of the k-th objective function M(x) and the estimated value of the k-th constraint function obtained by the Monte Carlo method; based on the estimated values, use a radial basis neural network to obtain the predicted mean values of the objective function and the constraint function and the predicted variance

[0038] Let M min represent the currently observed minimum value of the objective function;

[0039] The expected improvement criterion hopes to find training samples other than the current training sample x L , x U in the design space [x D = {x (1) , …, x (N)} T as the current design point x * ;

[0040] The expected improvement criterion is expressed as:

[0041]

[0042] where Φ(·) and represent the cumulative distribution function and the probability density function of the standard normal distribution respectively;

[0043] Due to the existence of constraints, the expected improvement criterion also needs to consider the feasible probability index:

[0044]

[0045] Combining EI(x) and PI(x), the final expected improvement criterion is obtained:

[0046] Use the particle swarm optimization algorithm to maximize the expected improvement criterion to obtain the current design point.

[0047] Furthermore, if the difference between the current design point and the current design point of the previous iteration is less than the preset tolerance, the iteration ends and the current design point x * is output as the optimal design point x ** .

[0048] Furthermore, if the difference between the current design point and the current design point of the previous iteration exceeds the preset tolerance, the training set needs to be updated using the current design point, and the updated training set is used to reconstruct the radial basis neural network and perform the next iteration.

[0049] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the uncertainty optimization method for the engine turbine disk based on the radial basis neural network is implemented.

[0050] A computer-readable storage medium stores a computer program therein; when the computer program is executed by a processor, the uncertainty optimization method of the engine turbine disk based on the radial basis neural network is implemented.

[0051] Compared with the prior art, the present invention has the following technical features:

[0052] The present invention first constructs an uncertainty optimization design model for the fatigue-creep life of the turbine disk; at the same time, a radial basis neural network is used to accurately predict the fatigue-creep life of the turbine disk, and the extended expected improvement criterion is used to avoid the uncertainty analysis calculation in the uncertainty optimization design problem, realizing deterministic optimization. The present invention updates and designs the model using the expected improvement criterion, avoiding unnecessary sampling. At the same time, the numerical integration method is used to transform the uncertainty optimization process with coupling relationships into a deterministic optimization, improving the solution efficiency of the uncertainty optimization design problem, and having strong engineering significance for the life design of the engine turbine disk structure. Description of the Drawings

[0053] Figure 1 is a schematic flow chart of the method of the present invention;

[0054] Figure 2 shows the cyclic load spectrum selected in the embodiment of the present invention;

[0055] Figure 3 shows the schematic diagram of the parametric model established in the embodiment of the present invention. Detailed Embodiments

[0056] Figure 1 Schematically shows an uncertainty optimization design method for an aircraft engine turbine disk based on a radial basis neural network in an embodiment of the present invention, including:

[0057] S01, based on the cumulative damage theory, construct a safety cyclic life model of the engine turbine disk during the service period T.

[0058] The fatigue-creep life refers to the life in which creep deformation and fatigue damage occur simultaneously in the material under the combined action of high temperature and cruise load and affect each other, resulting in material failure; this life prediction is a unique fatigue phenomenon of high-temperature structures and is particularly important for structural components operating in high-temperature environments. The cumulative damage theory can study the cumulative law of fatigue-creep damage under variable working conditions. This theory is divided into two categories: linear cumulative damage theory and non-linear cumulative damage theory; compared with the non-linear cumulative damage theory, the linear cumulative damage theory does not require a large amount of experimental data support and is more suitable for dealing with the common small-sample problems in engineering.

[0059] In some embodiments of the present invention, step S01 includes:

[0060] S011. Establish the relationship between the material strain and fatigue life of the turbine disk using the Coffin-Manson model.

[0061] The Coffin-Manson fatigue life model is an empirical model known for predicting the fatigue life of turbine disk materials under cyclic loading. This model combines the description of Basquin's law (describing the relationship between elastic strain and fatigue life) and Coffin-Manson's law (describing the relationship between plastic strain and fatigue life) to predict fatigue life.

[0062] In the embodiment of the present invention, the Coffin-Manson model used to represent the functional relationship between strain and fatigue life is:

[0063]

[0064] where ε pl is the plastic strain of the turbine disk, N f is the fatigue life (number of cycles), E' is the elastic modulus of the turbine disk material, σ′ f and ε′ f are the fatigue strength coefficient and fatigue plasticity coefficient respectively, c is the fatigue ductility exponent, and b is the fatigue strength exponent.

[0065] S012. Establish the relationship between the stress, temperature and creep life of the turbine disk using the Larson-Miller model.

[0066] The Larson-Miller creep life model is a mathematical model used to describe the high-temperature creep behavior of turbine disk materials. By comprehensively considering the influence of temperature and stress on the creep rate, this model provides a simple method for predicting the creep performance of turbine disk materials.

[0067] In the embodiment of the present invention, the Larson-Miller creep life model describing the functional relationship between life and stress, temperature is:

[0068]

[0069] where T c is the rupture time (h), T E is the rupture time temperature (K); C0 is a coefficient related to the material persistence, [a0, a1, a2, a3] T are coefficients related to the stress S, which can be obtained by solving using the least squares method.

[0070] S013. Obtain the interaction life under the fatigue-creep load spectrum of the turbine disk by the linear cumulative damage method.

[0071] The linear cumulative damage theory holds that under cyclic loading, the relationship between fatigue-creep damage and the number of load cycles is linear, and the damage can accumulate linearly. When the accumulated damage reaches a certain value, the turbine disk undergoes fatigue or creep failure.

[0072] In the embodiments of the present invention, considering the "start-up - maximum - start-up" working condition, the form of linear cumulative damage is:

[0073]

[0074] where D f is the fatigue damage, D c is the creep damage, n f is the number of cycles under the i-th strain condition, t c is the holding time under the stress S; in the example shown in Figure 2 , n f = 2249, t c = 241.34 h.

[0075] According to the linear cumulative damage theory, the safe cycle life model N fc of the turbine disk within the service period T required by the design requirements is expressed as:

[0076]

[0077] In the process of carrying out uncertainty-based optimal design, the evaluation of the safe cycle life needs to comprehensively consider various types of variables such as material properties, load conditions, environmental factors, and model uncertainties. These variables can be divided into uncertainty variables and design variables. Therefore, in the subsequent steps, the safe cycle life N fc is expressed as a function of the uncertainty variable vector and the design variable vector.

[0078] S02. Taking the expected value of the safe cycle life as the objective, an uncertainty-based optimal design model for the fatigue-creep life of the turbine disk is constructed.

[0079] The uncertainty-based optimal design model for the fatigue-creep life is a mathematical model that takes into account uncertainty factors during the design stage, aiming to improve the robustness and reliability of the design results of the turbine disk in the face of multi-source uncertainties.

[0080] In some embodiments of the present invention, step S02 includes:

[0081] S021, identifying uncertainty variables and design variables.

[0082] In the uncertainty optimization design model, the distinction between uncertainty variables and design variables is very important. Uncertainty variables refer to variables whose values exhibit random characteristics due to factors such as data missing, measurement errors, or uncertainty of model parameters in the optimization design model. The randomness of these variables will affect the final design result. Common sources of uncertainty include the distribution of material properties, errors in manufacturing precision, and changes in loads / environments, etc. Such variables can be described by probability density functions.

[0083] Design variables are parameters that need to be selected during the optimization process. The values of these parameters are adjustable and are usually optimized to meet the design objectives. Design variables can be geometric parameters such as dimensions and shapes, or physical quantities such as strength and weight.

[0084] In the embodiment of the present invention, the uncertainty variables are shown in Table 1.

[0085] Table 1 Uncertainty variables in the embodiment

[0086]

[0087] In the embodiment of the present invention, referring to Figure 3 , the design variables are shown in Table 2.

[0088] Table 2 Design variables in the embodiment

[0089]

[0090] S022, according to the design requirements of the turbine disk, construct the corresponding optimization design model.

[0091] The purpose of the turbine disk optimization design is to take the mean value of the safe cyclic life as the optimization objective under the condition of meeting the structural weight constraint.

[0092] In the embodiment of the present invention, the turbine disk is machined from DZ125 superalloy, and the established fatigue-creep life optimization design model of the turbine disk is as follows:

[0093]

[0094] s.t.W(x)≤W * ,x≤[x L ,x U

[0095] Among them, x is the design variable vector composed of design variables, p is the uncertainty variable vector composed of uncertainty variables, N fc (x,p) represents the safe cyclic life N fc as a function of uncertainty variables and design variables; E p [N fc ​(x,p)] represents the expectation of the safe cycle life within 1000 hours of service with respect to the uncertainty variable p, E p [·] represents the expectation operation considering the uncertainty variable vector p, W(x) represents the total weight of the turbine disk, which is a constraint function related to x, W * is the constraint threshold, x L and x U respectively represent the lower and upper bounds of the design space [x L ,x U where the design variable vector x is located.

[0096] S023, convert the uncertain optimization problem into a deterministic optimization problem through numerical integration method.

[0097] The uncertain optimization design model contains both uncertainty variables and design variables. The uncertainty analysis process usually requires multiple calls to time-consuming simulation analysis models, resulting in an increase in the complexity of the optimization problem. Using the numerical integration method can transform the uncertain optimization design problem into a deterministic optimization design problem to improve the optimization efficiency.

[0098] In the embodiment of the present invention, the optimization design model obtained through the numerical integration method is:

[0099]

[0100] s.t.W(x)≤W *

[0101] where, f P (p) represents the probability density function of the uncertainty variable vector; at this time, M(x) is the objective function related only to the design variable vector x.

[0102] S03, construct the initial training set using the Latin hypercube sampling method.

[0103] Use the Latin hypercube sampling method to extract a set of design variable vectors x within [x L ,x U as training samples, denoted as x D ={x (1) ,…,x (N)} T , the superscript T represents the transpose; where x (N) represents the Nth extracted design variable vector, N represents the number of training samples of the design variable vector, and at the same time use f P (p) to obtain a set of training samples of the uncertainty variable vector p, denoted as p D ={p (1) ,…,p (M)} T , where p(M) represents the Mth extracted uncertainty variable vector, where M represents the number of training samples of the uncertainty variable vector. Let x (i) (i = 1,..., N) and p (j) (j = 1,..., M) are combined to obtain N×M groups of training samples. Substitute each group of training samples (x (i) , p (j) ) into N fc (x, p) to obtain the output response y of the safe cyclic life (i,j) = N fc (x (i) , p (j) ) and the output response z of the constraint function (i) = W(x (i) ). Thus, two training sets of the radial basis neural network are generated and

[0104] S04. Use the training sets to construct the radial basis neural network.

[0105] The radial basis neural network is a feedforward neural network, consisting of an input layer, a hidden layer, and an output layer. The input layer receives the input sample points of the uncertainty variables and design variables. The hidden layer processes the sample points through the radial basis function and passes them to the output layer. The neurons in the output layer generate the final prediction results based on the weighted sum of the sample points and the output of the hidden layer. Due to its excellent non-linear mapping ability and approximation performance, the radial basis neural network is widely used in engineering fields such as pattern classification, function approximation, and data mining.

[0106] In some embodiments of the present invention, step S04 includes:

[0107] S041, perform normalization processing on the training sets.

[0108] When constructing the radial basis neural network, performing normalization processing on the training sets and is a very important step. Training set normalization is a commonly used processing method to reduce the data magnitude difference and ensure that each feature has the same importance. During the normalization process, first determine the maximum and minimum values of the training samples and the corresponding output responses in each training set, and then apply the normalization formula to process the training samples and output responses in the training sets.

[0109] S042, define the neural network architecture.

[0110] The architecture of a radial basis neural network usually consists of three layers: an input layer, a hidden layer, and an output layer. The input layer directly passes the training samples to the hidden layer without any calculation or transformation; for each set of training samples, each node in the hidden layer calculates its distance from the center of the node and applies a radial basis function (such as a Gaussian function) to determine the activation degree; the output layer usually uses a linear combination method to multiply the output of the hidden layer by the weights and sum them to obtain the final prediction value of the radial basis neural network.

[0111] S043, the radial basis neural network is trained using the cross-validation method.

[0112] The training process of a radial basis neural network usually includes two stages: unsupervised learning and supervised learning.

[0113] In the unsupervised learning stage, the k-means clustering method is used to initialize the centers and widths of the radial basis functions in the hidden layer; when training the radial basis neural network, the training samples in the training set are first grouped so that the center of each group can be used as the center of the radial basis function, and the width of each radial basis function can be determined according to the Euclidean distance from the training samples to the center of each group.

[0114] Cross-validation evaluates the performance of each radial basis neural network by dividing the training sets S and D into multiple subsets and repeating the training of the radial basis neural network on these subsets; K-fold cross-validation is the most common cross-validation method in the field of machine learning. K-fold cross-validation randomly divides the training set into K sub-training sets, where the k-th subset is denoted as S (k) (k = 1,..., K) and D (k) (k = 1,..., K), from which K radial basis neural networks can be constructed respectively, and the k-th one is denoted as and

[0115] In the supervised learning stage, the training samples (x (i) , p (j) ) are provided to the radial basis neural network and The predicted values are calculated using the radial basis function and The predicted values and Subsequently, they are compared with the true output responses y (i,j) and z (i) to establish the training error, and then the gradient descent algorithm is used to adjust the weights connecting the neurons in the hidden layer and the output layer to minimize the error between the calculated output and the target output.

[0116] S05, the expected improvement criterion is used to find the current design point.

[0117] The expected improvement criterion is a commonly used sampling criterion in deterministic global optimization algorithms, especially in global optimization design based on surrogate models. Its core idea is to select a new sample point at each iteration, which can maximize the expected improvement between the current best point and the predicted best point.

[0118] In some embodiments of the present invention, step S05 includes:

[0119] S051, obtaining the predicted mean and predicted variance of the objective function and the constraint function using a radial basis neural network.

[0120] In the embodiments of the present invention, the predicted mean of the objective function is obtained through a radial basis neural network and the predicted variance are expressed as:

[0121]

[0122] where represents the estimated value of the k-th objective function M(x) obtained by the Monte Carlo method:

[0123]

[0124] Similarly, the predicted mean of the constraint function and the predicted variance are expressed as:

[0125]

[0126] where represents the estimated values of the k constraint functions.

[0127] S052, establishing an expected improvement criterion using the predicted mean and the predicted variance.

[0128] Let M min represent the currently observed minimum value of the objective function, that is:

[0129]

[0130] Assuming that M(x) is a Gaussian process, the expected improvement criterion hopes to find a training sample of the design variable vector x other than x L , x U in [x D = {x (1) , …, x (N)} T as the current design point x * .

[0131] In the embodiments of the present invention, the expected improvement criterion is expressed as:

[0132]

[0133] where Φ(·) and respectively represent the cumulative distribution function and the probability density function of the standard normal distribution.

[0134] Due to the existence of constraints, the expected improvement criterion also needs to consider the feasible probability index:

[0135]

[0136] Combining EI(x) and PI(x), the final expected improvement criterion is obtained:

[0137] EIPI(x) = EI(x)PI(x)

[0138] S053, Use the particle swarm optimization algorithm to maximize the expected improvement criterion to obtain the current design point.

[0139] The particle swarm optimization algorithm is an optimization algorithm based on swarm intelligence. It is inspired by the foraging behavior of bird flocks and finds the optimal solution by simulating the cooperation and information sharing among individuals in the bird flock.

[0140] In some embodiments of the present invention, the particle swarm optimization algorithm is used to maximize the expected improvement criterion EIPI(x) to obtain the current design point x * :

[0141] x * = argmax EIPI(x)

[0142] subject to x ∈ [x L , x U

[0143] S06, Compare the current design point and the iterative design point:

[0144] If ||current design point - iterative design point|| ≤ the preset tolerance, it means that the current design point x * is close to the iterative design point (i.e., the previous current design point), then the iteration ends, and the current optimal design point x * can be determined as the optimal design point x ** , that is, x * = x ** ;

[0145] If ||current design point - iterative design point|| > the preset tolerance, it means that the current design point x * differs greatly from the iterative design point (i.e., the previous current design point), then the training set needs to be updated using the current design point, which is expressed as:

[0146]

[0147] At this time, go to step S04 to construct a radial basis neural network using the training set and perform the next iteration.

[0148] In the embodiment, it is iterated 10 times in total to meet the convergence condition || current design point - iterative design point || ≤ preset tolerance (10 -4 ).

[0149] The obtained optimal design points are shown in Table 3.

[0150] Table 3 Optimal design results in the embodiment

[0151]

[0152] The present invention provides a desired improvement criterion for model dynamic update and design, avoiding unnecessary sampling. At the same time, the numerical integration method is used to transform the uncertainty optimization process with coupling relationships into a deterministic optimization, improving the solution efficiency of the uncertainty optimization design problem.

[0153] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. An uncertainty optimization method for an engine turbine disk based on a radial basis neural network, characterized in that, Including: Based on the cumulative damage theory, construct a safety cyclic life model of the engine turbine disk during the service period; Taking the expected value of the safety cyclic life as the goal, construct an uncertainty optimization design model for the fatigue-creep life of the turbine disk; Use the Latin hypercube sampling method to construct an initial training set; Adopt the training set to construct a radial basis neural network; Use the expected improvement criterion to find the current design point. If the current design point meets the preset threshold requirements, then take the current design point as the optimal design point to obtain the specific values of the design variables.

2. The uncertainty optimization method for an engine turbine disk based on a radial basis neural network according to claim 1, wherein The construction of the safety cyclic life model of the engine turbine disk during the service period based on the cumulative damage theory includes: Use the Coffin-Manson model to establish the relationship between the material strain and fatigue life of the turbine disk; Use the Larson-Miller model to establish the relationship between the material strain, temperature and creep life of the turbine disk material; Construct the linear cumulative damage form of the turbine disk based on fatigue damage and creep damage, and then according to the linear cumulative damage theory, obtain the safety cyclic life model of the turbine disk during the service period required by the design; this model is a function of the uncertainty variable vector and the design variable vector.

3. The engine turbine disk uncertainty optimization method based on a radial basis neural network according to claim 1, characterized in that Taking the expected value of the safety cyclic life as the goal, constructing an uncertainty optimization design model for the fatigue-creep life of the turbine disk includes: Construct the uncertainty variables and design variables in the design process of the turbine disk; According to the design requirements of the turbine disk, construct an uncertainty optimization design model for the fatigue-creep life, expressed as: s.t. W(x) ≤ W * , x ≤ [x L , x U ​ where x is the design variable vector composed of design variables, p is the uncertainty variable vector composed of uncertainty variables, and N fc (x, p) represents the safe cyclic life N fc is a function of the uncertainty variables and design variables; E p [·] represents the expectation operation considering the uncertainty variable vector p, W(x) represents the total weight of the turbine disk, which is a constraint function related to x, and W * is the constraint threshold, x L and x U respectively represent the lower and upper bounds of the design space [x L , x U where the design variable vector x is located; Convert the uncertainty optimization design model into a deterministic optimization problem through numerical integration method, expressed as: s.t. W(x) ≤ W * where, f P (p) represents the probability density function of the uncertainty variable vector; at this time, M(x) is an objective function related only to the design variable vector x.

4. The uncertainty optimization method for an engine turbine disk based on a radial basis neural network according to claim 1, characterized in that Using the Latin hypercube sampling method to construct an initial training set includes: Use the Latin hypercube sampling method to extract a set of design variable vectors x within [x L , x U as training samples, denoted as x D = {x (1) , …, x (N)} T , where x (N) represents the Nth extracted design variable vector. At the same time, use f P (p) to obtain a set of training samples of the uncertainty variable vector p, denoted as p D = {p (1) , …, p (M)} T , where p (M) represents the Mth extracted uncertainty variable vector. Combine x ( i ) (i = 1, …, N) and p (j) to obtain N × M groups of training samples. Substitute each group of training samples (x (i) , p (j) ) into N fc (x, p) to obtain the output response y (i,j) = N fc (x (i) , p (j) ) and the output response z (i) = W(x (i) ), thus generating two training sets for the radial basis neural network and 5. The uncertainty optimization method for the engine turbine disk based on the radial basis neural network according to claim 1, wherein Adopting the training set to construct a radial basis neural network includes: Normalize the training set of the radial basis neural network to obtain the normalized training set; The radial basis neural network includes an input layer, a hidden layer and an output layer; the training process of the radial basis neural network includes two stages: unsupervised learning and supervised learning; In the unsupervised learning stage, use the k-means clustering method to initialize the centers and widths of the radial basis functions in the hidden layer; when training the radial basis neural network, first group the training samples in the training set so that the center of each group can be used as the center of the radial basis function, and the width of each radial basis function can be determined according to the Euclidean distance from the training sample to the center of each group; Cross-validation randomly divides the training sets S and D into K sub-training sets, denoted as S( k ) and D( k ), and repeats the training of the radial basis neural network on these subsets to evaluate the performance of each radial basis neural network. Thus, K radial basis neural networks can be constructed respectively, denoted as and In the supervised learning stage, the training samples (x (i) , p (j) ) are provided to the radial basis neural network and The predicted values are calculated using the radial basis function and The predicted values and are then compared with the true output responses y (i,j) and z (i) to establish the training error, and then the gradient descent algorithm is used to adjust the weights connecting the neurons in the hidden layer and the output layer.

6. The method for optimizing the uncertainty of an engine turbine disk based on a radial basis neural network according to claim 1, wherein Using the expected improvement criterion to find the current design point includes: The estimated value of the k-th objective function M(x) and the estimated value of the k-th constraint function obtained by the Monte Carlo method; based on the estimated values, use a radial basis neural network to obtain the predicted mean values of the objective function and the constraint function and the predicted variances Let M min represent the minimum value of the objective function currently observed; The aspiration improvement criterion aims to find training samples other than the current training samples x L , x U in the design space [x D = {x (1) , …, x (N)}, T as the current design point x * ; The expected improvement criterion is expressed as: where, Φ(·) and represent the cumulative distribution function and the probability density function of the standard normal distribution, respectively; Due to the existence of constraints, the expected improvement criterion also needs to consider the feasible probability index: Combine EI(x) and PI(x) to obtain the final expected improvement criterion: Use the particle swarm optimization algorithm to maximize the expected improvement criterion to obtain the current design point.

7. The method for optimizing the uncertainty of an engine turbine disk based on a radial basis neural network according to claim 1, wherein If the difference between the current design point and the current design point of the previous iteration is less than the preset tolerance, the iteration ends and the current design point x is output * is the optimal design point x ** .

8. The uncertainty optimization method of an engine turbine disk based on a radial basis neural network according to claim 1, characterized in that If the difference between the current design point and the current design point of the previous iteration exceeds the preset tolerance, then it is necessary to update the training set with the current design point, and the updated training set is used to reconstruct the radial basis neural network and perform the next iteration.

9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it realizes the uncertainty optimization method of the engine turbine disk based on the radial basis neural network according to any one of claims 1-8.

10. A computer-readable storage medium storing a computer program therein; characterized in that, When the computer program is executed by a processor, it implements the optimization method for engine turbine disks with uncertainty based on a radial basis neural network according to any one of claims 1-8.

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