Method for solving failure probability function of turbine blade system based on sample information sharing

Abstract

The present disclosure relates to a turbine blade system failure probability function solving method based on sample information sharing, and relates to the technical field of reliability analysis, and the method comprises the following steps: constructing a unified sampling density function independent of distribution parameters according to the distribution parameters of input variables of a turbine blade system, and constructing an alternative sample pool for solving the failure probability function of the turbine blade system according to the distribution parameters; extracting first training sample points from the alternative sample pool according to the unified sampling density function, and constructing initial Kriging surrogate models under different failure modes according to the first training sample points; selecting second training sample points according to the system state misjudgment probability of the turbine blade system, and updating the initial Kriging surrogate models based on the second training sample points to obtain converged Kriging surrogate models; and using the converged Kriging surrogate models to solve the failure probability function of the turbine blade system. The present disclosure improves the calculation efficiency of the failure probability function.

Description

Technical Field

[0001] This disclosure relates to the field of reliability analysis technology, and more specifically, to a method for solving the failure probability function of a turbine blade system based on sample information sharing. Background Technology

[0002] Solving for the failure probability function can quantify the impact of input variable distribution parameters on the safety level of a structural system, and can also decouple the reliability optimization design model under failure probability constraints. As a core component that converts the internal energy of the working fluid into kinetic energy, the turbine blade system bears enormous mechanical loads under high-speed conditions, and its reliability is crucial to the safety of the entire engine and aircraft. Therefore, solving for the failure probability function of the turbine blade system is essential for understanding the overall reliability level of an aero-engine.

[0003] Existing methods for calculating the failure probability function of turbine blade systems can be based on a double-loop algorithm; however, this method suffers from problems such as large computational load and poor computational efficiency in solving the failure probability function of turbine blade systems.

[0004] Therefore, there is still a lack of efficient and accurate methods for solving the system failure probability function of turbine blades under high-speed environments.

[0005] It should be noted that the information in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this disclosure is to provide a method for solving the failure probability function of a turbine blade system based on sample information sharing, thereby overcoming, to at least some extent, the problems of large computational load and poor computational efficiency caused by the limitations and defects of related technologies.

[0007] According to one aspect of this disclosure, a method for solving the failure probability function of a turbine blade system based on sample information sharing is provided, including:

[0008] Based on the distribution parameters of the input variables of the turbine blade system, a unified sampling density function independent of the distribution parameters is constructed, and based on the distribution parameters, a candidate sample pool for solving the failure probability function of the turbine blade system is constructed.

[0009] The first training sample points are extracted from the candidate sample pool according to the unified sampling density function, and the initial Kriging proxy model under different failure modes is constructed based on the first training sample points.

[0010] The second training sample point is selected based on the system state misjudgment probability of the turbine blade system, and the initial Kriging surrogate model is updated based on the second training sample point to obtain a converged Kriging surrogate model.

[0011] The failure probability function of the turbine blade system is solved using a convergent Kriging surrogate model.

[0012] In one exemplary embodiment of this disclosure, a uniform sampling density function independent of the distribution parameters of the input variables of the turbine blade system is constructed, including:

[0013] Obtain the input variables of the turbine blade system; wherein, the input variables include multiple of the following: the first elastic modulus along the tangent, the second elastic modulus along the radial direction, the third elastic modulus along the circumferential direction of the turbine blade model corresponding to the turbine blade system, and the maximum rotational speed of the turbine blade model;

[0014] Calculate the distribution parameters of the input variables; wherein the distribution parameters include the mean and standard deviation of the input variables;

[0015] Determine the threshold range of the distribution parameters, and determine the conditional probability density function of the input variable and the prior density function of the distribution parameters;

[0016] Integrating the product of the conditional probability density function and the prior density function over the threshold interval yields a unified sampling density function independent of the distribution parameters.

[0017] In one exemplary embodiment of this disclosure, constructing a candidate sample pool for solving the failure probability function of the turbine blade system based on the distribution parameters includes:

[0018] A sample pool of distribution parameters is generated based on the prior density function of the distribution parameters, and a sample of the input variable is determined from the sample pool of distribution parameters based on the conditional probability density function of the input variable.

[0019] Based on the input variable samples, a candidate sample pool is constructed to solve the failure probability function of the turbine blade system.

[0020] In one exemplary embodiment of this disclosure, a first training sample point is drawn from the candidate sample pool according to the uniform sampling density function, and an initial Kriging surrogate model for different failure modes is constructed based on the first training sample point, including:

[0021] According to the unified sampling density function, a first training sample point with a first preset number is drawn from the candidate sample pool;

[0022] Based on the first training sample points and the failure modes of the turbine blade system, an initial training sample set is constructed under different failure modes; wherein, the failure modes include a first failure mode, a second failure mode, ..., the m-th failure mode, where m is the number of failure modes of the turbine blade system; the initial training sample set includes a first initial sample set corresponding to the first failure mode, a second initial sample set corresponding to the second failure mode, ..., the m-th initial sample set corresponding to the m-th failure mode;

[0023] Based on the initial training sample sets under different failure modes and the failure modes of the turbine blade system, initial Kriging surrogate models under different failure modes are constructed; the initial Kriging surrogate models include a first initial Kriging surrogate model, a second initial Kriging surrogate model, ..., the m-th initial Kriging surrogate model.

[0024] In one exemplary embodiment of this disclosure, a second training sample point is selected based on the system state misjudgment probability of the turbine blade system, and the initial Kriging surrogate model is updated based on the second training sample point to obtain a converged Kriging surrogate model, including:

[0025] Based on the initial Kriging proxy model, predict the predicted mean and predicted standard deviation of the input variable samples in the candidate sample pool in the turbine blade system;

[0026] Based on the predicted mean and predicted standard deviation, the probability of misjudging the system state of the input variable sample in the turbine blade system is determined, and a second training sample point is selected based on the probability of misjudging the system state.

[0027] The failure mode to which the second training sample point belongs is determined based on the predicted mean and predicted standard deviation of the second training sample point, and the second training sample point is added to the initial training sample set corresponding to the failure mode based on the failure mode to obtain the target training sample set.

[0028] The initial Kriging proxy model is updated based on the target training sample set to obtain a converged Kriging proxy model.

[0029] In one exemplary embodiment of this disclosure, determining the system state misjudgment probability of the turbine blade system based on the predicted mean and the predicted standard deviation includes:

[0030] Determine the connection method of the turbine blade system mode; wherein, the connection method of the system mode includes a series model or a parallel model;

[0031] Based on the connection method of the turbine blade system mode and the predicted mean, the calculation rules for the system state misjudgment probability are determined;

[0032] Substituting the predicted mean and predicted standard deviation into the calculation rule, the system state misjudgment probability of the turbine blade system is obtained.

[0033] In one exemplary embodiment of this disclosure, selecting a second training sample point based on the system state misjudgment probability includes:

[0034] Based on the unified sampling density function and the system state misjudgment probability, determine the probability that the input variable sample will cause the turbine blade system to misjudge its state.

[0035] The input variable samples are sorted based on the probability of generating a state misjudgment, and the second training sample is selected from the input variable samples in the candidate sample pool based on the sorting result.

[0036] In one exemplary embodiment of this disclosure, determining the failure mode to which the second training sample point belongs based on the predicted mean and predicted standard deviation of the second training sample point includes:

[0037] Based on the predicted mean and predicted standard deviation of the second training sample points, the U learning function values ​​of the second training sample points under different failure modes are determined.

[0038] The failure mode to which the second training sample point belongs is determined based on the value of the U learning function.

[0039] In one exemplary embodiment of this disclosure, updating the initial Kriging proxy model based on the target training sample set to obtain a converged Kriging proxy model includes:

[0040] The initial Kriging proxy model is updated based on the target training sample set to obtain the updated Kriging proxy model. Based on the updated Kriging proxy model, the first system expansion failure probability of the target sample points in the target training sample set is predicted.

[0041] Obtain the predicted mean of the target sample points, and determine the second system extended failure probability of the target sample points based on the predicted mean;

[0042] Based on the first system expansion failure probability and the second system expansion failure probability, determine whether the updated Kriging proxy model satisfies the model convergence condition.

[0043] If the updated Kriging surrogate model satisfies the model convergence condition, then the updated Kriging surrogate model is taken as the converged Kriging surrogate model; if the updated Kriging surrogate model does not satisfy the model convergence condition, then the model update steps are repeated until the updated Kriging surrogate model satisfies the model convergence condition, so as to obtain the converged Kriging surrogate model.

[0044] In one exemplary embodiment of this disclosure, determining whether the updated Kriging proxy model satisfies the model convergence condition based on the first system extended failure probability and the second system extended failure probability includes:

[0045] Calculate the first difference between the extended failure probability of the first system and the extended failure probability of the second system, and calculate the first ratio between the first difference and the extended failure probability of the second system.

[0046] Calculate the first expected value of the absolute value of the first ratio, and determine whether the updated Kriging proxy model satisfies the model convergence condition based on the first expected value.

[0047] This disclosure provides an example embodiment of a method for solving the failure probability function of a turbine blade system based on sample information sharing. On one hand, it constructs a unified sampling density function independent of the distribution parameters of the input variables of the turbine blade system, and builds a candidate sample pool for solving the failure probability function of the turbine blade system based on the distribution parameters. Then, it extracts first training sample points from the candidate sample pool according to the unified sampling density function, and constructs initial Kriging surrogate models for different failure modes based on the first training sample points. Next, it selects second training sample points based on the system state misjudgment probability of the turbine blade system, and updates the initial Kriging surrogate model based on the second training sample points to obtain a converged Kriging surrogate. The model is then used to solve for the failure probability function of the turbine blade system. Since a convergent Kriging surrogate model can be obtained based on the distribution parameters of the input variables of the turbine blade system, and the failure probability function can be solved based on this model, there is no need to use a double-loop algorithm to calculate the failure probability function. This solves the problems of high computational cost and poor computational efficiency caused by using a double-loop algorithm, thus improving computational efficiency while reducing computational cost. Furthermore, the accuracy of the obtained failure probability function is improved because a convergent Kriging surrogate model can be used to solve for it.

[0048] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0049] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0050] Figure 1 The flowchart illustrates a method for solving the failure probability function of a turbine blade system based on sample information sharing, according to an exemplary embodiment of the present disclosure.

[0051] Figure 2 An example diagram schematically illustrates a turbine blade model in a turbine blade system according to an exemplary embodiment of the present disclosure.

[0052] Figure 3 The diagram schematically illustrates specific tangential, radial, and circumferential directions of the input variables of a turbine blade system according to an exemplary embodiment of the present disclosure.

[0053] Figure 4 The flowchart illustrates a method for constructing an initial Kriging proxy model under different failure modes based on a first training sample point, according to an example embodiment of the present disclosure.

[0054] Figure 5 The flowchart illustrates a method for updating an initial Kriging proxy model based on a second training sample point, according to an exemplary embodiment of the present disclosure, to obtain a converged Kriging proxy model.

[0055] Figure 6 An example diagram illustrating a failure probability function of a turbine blade system according to an exemplary embodiment of the present disclosure is shown.

[0056] Figure 7 The diagram schematically illustrates a block diagram of an apparatus for solving the failure probability function of a turbine blade system based on sample information sharing, according to an exemplary embodiment of the present disclosure.

[0057] Figure 8 An electronic device is illustrated according to an example embodiment of the present disclosure for implementing the above-described method for solving the failure probability function of a turbine blade system based on sample information sharing. Detailed Implementation

[0058] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this disclosure more comprehensive and complete, and to fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced with one or more of the specific details omitted, or other methods, components, apparatus, steps, etc., can be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0059] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0060] This exemplary embodiment first provides a method for solving the failure probability function of a turbine blade system based on sample information sharing. This method can run on a server, server cluster, or cloud server, etc. Of course, those skilled in the art can also run the method disclosed herein on other platforms as needed, and this exemplary embodiment does not impose any special limitations on this. Specifically, refer to... Figure 1 As shown, the method for solving the failure probability function of a turbine blade system based on sample information sharing may include the following steps:

[0061] Step S110. Based on the distribution parameters of the input variables of the turbine blade system, construct a unified sampling density function independent of the distribution parameters, and based on the distribution parameters, construct a candidate sample pool for solving the failure probability function of the turbine blade system.

[0062] Step S120. Extract the first training sample points from the candidate sample pool according to the unified sampling density function, and construct the initial Kriging proxy model under different failure modes based on the first training sample points.

[0063] Step S130. Select a second training sample point based on the system state misjudgment probability of the turbine blade system, and update the initial Kriging surrogate model based on the second training sample point to obtain a converged Kriging surrogate model.

[0064] Step S140. Solve the failure probability function of the turbine blade system using a convergent Kriging surrogate model.

[0065] In the aforementioned method for solving the failure probability function of a turbine blade system based on sample information sharing, on the one hand, a unified sampling density function independent of the distribution parameters of the input variables of the turbine blade system is constructed, and a candidate sample pool for solving the failure probability function of the turbine blade system is built based on the distribution parameters; then, a first training sample point is extracted from the candidate sample pool according to the unified sampling density function, and an initial Kriging surrogate model under different failure modes is constructed based on the first training sample point; then, a second training sample point is selected according to the system state misjudgment probability of the turbine blade system, and the initial Kriging surrogate model is updated based on the second training sample point to obtain a converged Kriging surrogate model; finally... The failure probability function of the turbine blade system is solved using a convergent Kriging surrogate model. Since a convergent Kriging surrogate model can be obtained based on the distribution parameters of the input variables of the turbine blade system, and then the failure probability function is solved based on this model, there is no need to use a double-loop algorithm to calculate the failure probability function. This solves the problems of high computational cost and poor computational efficiency caused by using a double-loop algorithm, thus improving computational efficiency while reducing computational cost. Furthermore, the accuracy of the obtained failure probability function is improved because a convergent Kriging surrogate model can be used.

[0066] The following will provide a detailed explanation and description of the method for solving the failure probability function of a turbine blade system based on sample information sharing, as described in the exemplary embodiments of this disclosure, with reference to the accompanying drawings.

[0067] First, the turbine blade model of the turbine blade system described in the exemplary embodiments of this disclosure will be explained and described. Specifically, the turbine blade model of the turbine blade system described herein can be referred to... Figure 2 As shown.

[0068] Secondly, the input variables of the turbine blade system described in the exemplary embodiments of this disclosure will be explained and described. Specifically, the input variables of the turbine blade system may include a first elastic modulus along the tangential direction of the turbine blade model, a second elastic modulus along the radial direction, a third elastic modulus along the circumferential direction, and the maximum rotational speed of the turbine blade model; wherein, the first elastic modulus along the tangential direction, the second elastic modulus along the radial direction, and the third elastic modulus along the circumferential direction can be specifically referred to... Figure 3 As shown; meanwhile, the maximum rotational speed of the turbine blade model represents the maximum rotational speed of the turbine blade system during operation.

[0069] Furthermore, the distribution parameters of the input variables described in the exemplary embodiments of this disclosure will be explained and illustrated. Specifically, the distribution form and distribution parameters of the input variables of the turbine blade system are shown in Table 1 below:

[0070] Table 1

[0071]

[0072]

[0073] Specifically, based on the content shown in Table 1 above, it can be seen that the first elastic modulus along the tangential direction, the second elastic modulus along the radial direction, the third elastic modulus along the circumferential direction, and the maximum rotational speed recorded in the example embodiments of this disclosure all exhibit a normal distribution. Furthermore, the first distribution parameter corresponding to the first elastic modulus may include the first variable mean and the first variable standard deviation; the second distribution parameter corresponding to the second elastic modulus may include the second variable mean and the second variable standard deviation; the third distribution parameter corresponding to the third elastic modulus may include the third variable mean and the third variable standard deviation; and the fourth distribution parameter corresponding to the maximum rotational speed may include the fourth variable mean and the fourth variable standard deviation.

[0074] The following will combine Figure 2 as well as Figure 3 right Figure 1 The method for solving the failure probability function of a turbine blade system based on sample information sharing, as shown in the example, will be further explained and illustrated. Specifically:

[0075] In step S110, a unified sampling density function independent of the distribution parameters of the input variables of the turbine blade system is constructed based on the distribution parameters, and a candidate sample pool for solving the failure probability function of the turbine blade system is constructed based on the distribution parameters.

[0076] In the exemplary embodiments of this disclosure, firstly, a unified sampling density function independent of the distribution parameters of the input variables of the turbine blade system is constructed. Specifically, the construction process of the unified sampling density function can be as follows: First, the input variables of the turbine blade system are obtained; wherein, the input variables include multiple of the following: a first elastic modulus along the tangent of the turbine blade model corresponding to the turbine blade system, a second elastic modulus along the radial direction, a third elastic modulus along the circumferential direction, and the maximum rotational speed of the turbine blade model; second, the distribution parameters of the input variables are calculated; wherein, the distribution parameters include the mean and standard deviation of the input variables; then, a threshold interval of the distribution parameters is determined, and the conditional probability density function of the input variables and the prior density function of the distribution parameters are determined; finally, the product of the conditional probability density function and the prior density function is integrated over the threshold interval to obtain the unified sampling density function independent of the distribution parameters.

[0077] Specifically, in practical applications, the calculation process of the unified sampling density function can be achieved through the following formula (1):

[0078]

[0079] in, To unify the sampling density function, θ is the distribution parameter of the input variable, [θ L ,θ U ] represents the threshold interval for the distribution parameter, θ L θ is the lower threshold. U f is the upper threshold; X (x|θ) is the conditional probability density function of the input variable x when the distribution parameter is θ. Let θ be the prior density function for the distribution parameter θ; where the uniform sampling density function described here is independent of the distribution parameter.

[0080] Secondly, based on the distribution parameters, a candidate sample pool for solving the failure probability function of the turbine blade system is constructed. Specifically, the construction process of the candidate sample pool can be implemented as follows: First, a distribution parameter sample pool is generated based on the prior density function of the distribution parameters, and input variable samples are determined from the distribution parameter sample pool based on the conditional probability density function of the input variables; secondly, based on the input variable samples, a candidate sample pool for solving the failure probability function of the turbine blade system is constructed.

[0081] Specifically, in practical applications, the construction process of the candidate sample pool can be as follows: First, based on the prior density function of the distribution parameter θ... Generate a sample pool of size N for the distributed parameters; secondly, for a given distribution parameter θi (i = 1, 2, ..., N), according to f X (x|θ i ) produces the corresponding θ i Input variable sample x i (i = 1, 2, ..., N) to form a uniform sampling density function alternative sample pool S x ={x1,x2,...,x N} T Where N represents the sample pool size; meanwhile, f X (x|θ i ) indicates that the distribution parameter of the input variable x takes the value θ. i The conditional probability density function when.

[0082] In step S120, a first training sample point is extracted from the candidate sample pool according to the unified sampling density function, and an initial Kriging surrogate model for different failure modes is constructed based on the first training sample point.

[0083] For details, please refer to Figure 4 As shown, the process of extracting first training sample points from the candidate sample pool according to the unified sampling density function, and constructing initial Kriging surrogate models under different failure modes based on the first training sample points, may include the following steps:

[0084] Step S410: Extract a first training sample point with a first preset number from the candidate sample pool according to the unified sampling density function;

[0085] Step S420: Based on the first training sample points and the failure modes of the turbine blade system, construct initial training sample sets for different failure modes; wherein, the failure modes include a first failure mode, a second failure mode, ..., the m-th failure mode, where m is the number of failure modes of the turbine blade system; the initial training sample sets include a first initial sample set corresponding to the first failure mode, a second initial sample set corresponding to the second failure mode, ..., the m-th initial sample set corresponding to the m-th failure mode;

[0086] Step S430: Based on the initial training sample sets under different failure modes and the failure modes of the turbine blade system, construct initial Kriging surrogate models under different failure modes; the initial Kriging surrogate models include a first initial Kriging surrogate model, a second initial Kriging surrogate model, ..., the m-th initial Kriging surrogate model.

[0087] The following will explain and illustrate steps S410-S430. Specifically, in the process of constructing the initial Kriging surrogate model, firstly, the first training sample points can be randomly selected from the candidate sample pool with a uniform sampling density function; the first preset number recorded here can be determined according to actual needs; for example, 10, 15, or 20 sample points can be selected; the first preset number here only needs to satisfy a small number; secondly, based on the failure modes of the turbine blade system, the initial training sample set T of the response is constructed. j (j = 1, 2, ..., m); where m is the number of failure modes in the turbine blade system; that is, each failure mode requires an initial training sample set; assuming the failure modes include a first failure mode, a second failure mode, ..., the mth failure mode, where m is the number of failure modes in the turbine blade system; then the initial training sample set includes a first initial sample set corresponding to the first failure mode, a second initial sample set corresponding to the second failure mode, ..., the mth initial sample set corresponding to the mth failure mode; furthermore, the initial training sample set is used to construct an initial Kriging surrogate model; wherein, the initial Kriging surrogate model... It can also include m; that is, the number of initial Kriging agent models corresponds to the number of failure modes.

[0088] It should be added that the reason for randomly selecting the first training sample point from the candidate sample pool with a uniform sampling density function is that, since the prior density of the distribution parameter is uniformly distributed, random sampling can ensure that the selected first training sample point can cover the entire parameter space as much as possible, and prevent the training sample points from being too concentrated or too scattered, which would lead to poor accuracy of the resulting Kriging surrogate model.

[0089] In step S130, a second training sample point is selected based on the system state misjudgment probability of the turbine blade system, and the initial Kriging surrogate model is updated based on the second training sample point to obtain a converged Kriging surrogate model.

[0090] For details, please refer to Figure 5 As shown, selecting a second training sample point based on the system state misjudgment probability of the turbine blade system, and updating the initial Kriging surrogate model based on the second training sample point to obtain a converged Kriging surrogate model, may include the following steps:

[0091] Step S510: Based on the initial Kriging proxy model, predict the predicted mean and predicted standard deviation of the input variable samples in the candidate sample pool in the turbine blade system.

[0092] Step S520: Based on the predicted mean and predicted standard deviation, determine the system state misjudgment probability of the input variable sample in the turbine blade system, and select a second training sample point based on the system state misjudgment probability.

[0093] Step S530: Determine the failure mode to which the second training sample point belongs based on the predicted mean and predicted standard deviation of the second training sample point, and add the second training sample point to the initial training sample set corresponding to the failure mode based on the failure mode to obtain the target training sample set.

[0094] Step S540: Update the initial Kriging proxy model based on the target training sample set to obtain a converged Kriging proxy model.

[0095] In one example embodiment, the probability of misjudging the system state of the turbine blade system based on the predicted mean and the predicted standard deviation can be achieved as follows: First, determine the connection method of the turbine blade system modes; wherein, the connection method of the system modes includes a series model or a parallel model; second, determine the calculation rule for the probability of misjudging the system state based on the connection method of the turbine blade system modes and the predicted mean; then, substitute the predicted mean and the predicted standard deviation into the calculation rule to obtain the probability of misjudging the system state of the turbine blade system.

[0096] In one example embodiment, selecting a second training sample point based on the system state misjudgment probability can be achieved as follows: First, determine the probability that the input variable sample will cause the turbine blade system to misjudge its state based on the unified sampling density function and the system state misjudgment probability; second, sort the input variable samples based on the probability of the sample point causing state misjudgment, and select the second training sample from the candidate sample pool based on the sorting result.

[0097] In one example embodiment, determining the failure mode to which the second training sample point belongs based on the predicted mean and predicted standard deviation of the second training sample point can be achieved as follows: First, based on the predicted mean and predicted standard deviation of the second training sample point, determine the U learning function value of the second training sample point under different failure modes; second, based on the U learning function value, determine the failure mode to which the second training sample point belongs.

[0098] In one example embodiment, updating the initial Kriging surrogate model based on the target training sample set to obtain a converged Kriging surrogate model can be achieved as follows: First, the initial Kriging surrogate model is updated based on the target training sample set to obtain an updated Kriging surrogate model, and based on the updated Kriging surrogate model, a first system expansion failure probability is predicted for the target sample points in the target training sample set; second, the predicted mean of the target sample points is obtained, and a second system expansion failure probability of the target sample points is determined based on the predicted mean; then, the updated Kriging surrogate model is judged to meet the model convergence condition based on the first system expansion failure probability and the second system expansion failure probability; finally, if the updated Kriging surrogate model meets the model convergence condition, the updated Kriging surrogate model is used as the converged Kriging surrogate model; if the updated Kriging surrogate model does not meet the model convergence condition, the model update steps are repeated until the updated Kriging surrogate model meets the model convergence condition to obtain a converged Kriging surrogate model.

[0099] In one example embodiment, determining whether the updated Kriging surrogate model satisfies the model convergence condition based on the first system extended failure probability and the second system extended failure probability can be achieved as follows: First, calculate the first difference between the first system extended failure probability and the second system extended failure probability, and calculate the first ratio between the first difference and the second system extended failure probability; second, calculate the first expected value of the absolute value of the first ratio, and determine whether the updated Kriging surrogate model satisfies the model convergence condition based on the first expected value.

[0100] The following will explain and illustrate steps S510-540. Specifically, in the process of updating the initial Kriging proxy model, it is first necessary to select the second training sample points based on the system state misjudgment probability of the turbine blade system; based on this, it is necessary to calculate the system state misjudgment probability of the turbine blade system. Specifically, the specific calculation process of the system state misjudgment probability corresponding to the input variable samples included in the candidate sample pool can be shown in the following formula (2):

[0101]

[0102] Among them, P e (x) represents the probability of misjudging the system state. and Let each represent the j-th Kriging proxy model. The predicted mean and predicted standard deviation. Φ(·) represents the cumulative distribution function of the standard normally distributed variable; f X(x) The probability density function of the input variable at the candidate sample point (input variable sample) x; at the same time, based on the above formula (2), it can be known that in the actual application process, firstly, it can be determined whether the working mode of the turbine blade system is a series working mode or a parallel working mode; if it is a series working mode, the system state misjudgment probability is calculated based on the first two formulas in formula (2); if it is a parallel working mode, the system state misjudgment probability is calculated based on the last two formulas in formula (2); secondly, the probability of misjudging the system state at the j-th kriging surrogate model of each candidate sample point is calculated. The system calculates the predicted mean and standard deviation. Then, it determines whether the predicted mean is greater than zero. If the predicted mean is greater than or equal to zero and the turbine blade system is in series operation, the system state misjudgment probability is calculated based on the first formula. If the predicted mean is greater than zero and the turbine blade system is in series operation, the system state misjudgment probability is calculated based on the second formula. Furthermore, if the predicted mean is greater than or equal to zero and the turbine blade system is in parallel operation, the system state misjudgment probability is calculated based on the third formula. If the predicted mean is greater than zero and the turbine blade system is in parallel operation, the system state misjudgment probability is calculated based on the fourth formula.

[0103] Furthermore, after obtaining the system state misjudgment probability, the candidate sample pool S can be selected based on the system state misjudgment probability. x The second training sample point is selected; the specific process of determining the second training sample point can be achieved by the following formula (3):

[0104]

[0105] Where, x u This is the second training sample point; The probability that the second training sample point will cause a misjudgment of the state of the turbine blade system. To unify the sampling density function, P e (x) represents the probability of misjudging the system state.

[0106] Furthermore, after obtaining the second training sample point, it is also necessary to determine the initial sample set to which the second training sample point belongs. Specifically, the process for determining the initial sample set can be shown in the following formula (4):

[0107]

[0108] Where, p u The failure mode is defined, and the initial sample set to which it belongs can be obtained based on the failure mode. The learning function for U is the second training sample point; The predicted mean of the second training sample points; Let x be the predicted standard deviation of the second training sample point. Here, the initial sample set to which the second training sample point belongs is determined using x. u The corresponding state is implemented in the least identifiable mode; that is, the corresponding failure mode is selected based on the result corresponding to the minimum value of the U function; in this way, the convergence efficiency of the initial Kriging surrogate model can be further improved.

[0109] Furthermore, after obtaining the second training sample point and its failure mode, the second training sample point can be added to the corresponding initial training sample set to obtain the target training sample set. In, that is Finally, the initial Kriging proxy model is updated based on the target training sample set to obtain a converged Kriging proxy model.

[0110] In one example embodiment, during the update of the initial Kriging agent model, it can be based on Update p u Kriging surrogate model of failure modes Calculate the extended failure probability of the system based on the mean of the current system's Kriging predictions. Once the corresponding convergence conditions are met, a convergent Kriging surrogate model can be obtained. Among them, the Kriging agent model The convergence condition is the system Kriging prediction The estimated first system extended failure probability Compared with the system's Kriging prediction mean The estimated extended failure probability of the second system relative error The upper bound of the expected value E(ε) is less than 0.01. The specific calculation process can be shown in the following formula (5):

[0111]

[0112] in, and These represent predictions made by the updated Kriging agent model. and the updated Kriging agent model predicted mean The estimated system failure domain indication function. E u (ε) represents the system's Kriging prediction. The estimated system extended failure probability Compared with the system's Kriging prediction mean Estimated system extended failure probability The upper bound of the expected relative error; f X (x) is the probability density function.

[0113] In step S140, the failure probability function of the turbine blade system is solved using a convergent Kriging surrogate model.

[0114] Specifically, the failure probability function of the turbine blade system is solved using a convergent Kriging surrogate model, which can be achieved through the following formula (6):

[0115]

[0116] in, Let be the failure probability function. This indicates that the input variable x is predicted by a convergent Kriging surrogate model. i The obtained system failure domain indication function; f X (x i |θ) represents the input variable sample x i The conditional probability density function of when the value is θ. Indicates the input variable sample x i The unified sampling density function.

[0117] Thus, the method for solving the failure probability function of a turbine blade system based on sample information sharing, as described in the exemplary embodiments of this disclosure, has been fully implemented. Below, specific embodiments will be used to further illustrate the method for solving the failure probability function of a turbine blade system provided by this disclosure. Specifically, in practical applications, the distribution parameter of interest is the mean of the maximum rotational speed. Right now in

[0118] For example, the function g for the following two failure modes can be established. j (x)(j=1,2) and the system failure domain F s :

[0119] g1(x)=g1(x1,x2,x3,x4)=σ * -σ max (x1,x2,x3,x4); Formula (7)

[0120] g2(x)=g2(x1,x2,x3,x4)=Δ * -Δ max (x1,x2,x3,x4); Formula (8)

[0121] F s ={g1(x)∪g2(x)}; Formula (9)

[0122] Where σ max (x1,x2,x3,x4) represents the maximum stress of the turbine blade, σ* =1280MPa represents the maximum allowable stress; meanwhile, Δ max (x1,x2,x3,x4) represents the maximum displacement of the turbine blade, Δ * =1.55mm indicates the maximum permissible displacement.

[0123] Furthermore, the size of the sample pool for the distribution parameters can be set to N = 5 × 10. 5 Furthermore, an initial training sample set T for each failure mode is established using 15 initial training sample points (the first training sample points). j (j=1,2), and according to T j Construct the initial Kriging agent model (j = 1, 2) Furthermore, by adding 5 and 6 training sample points (second training sample points) to training sets T1 and T2 respectively, a convergent Kriging surrogate model is obtained. At this time E u (ε) = 0.0022; Finally, a convergent Kriging surrogate model is used. The failure probability function of the turbine blade system is obtained by solving; the obtained failure probability function of the turbine blade system can be referenced. Figure 6 As shown.

[0124] The following are embodiments of the apparatus disclosed herein, which can be used to execute embodiments of the method disclosed herein. For details not disclosed in the apparatus embodiments of this disclosure, please refer to the embodiments of the method disclosed herein.

[0125] This disclosure also provides an example embodiment of a device for solving the failure probability function of a turbine blade system based on sample information sharing. Specifically, refer to... Figure 7 As shown, the turbine blade system failure probability function solving device based on sample information sharing may include a unified sampling density function construction module 710, an initial Kriging surrogate model construction module 720, an initial Kriging surrogate model update module 730, and a failure probability function solving module 740. Wherein:

[0126] The unified sampling density function construction module 710 can be used to construct a unified sampling density function independent of the distribution parameters of the input variables of the turbine blade system, and to construct a candidate sample pool for solving the failure probability function of the turbine blade system based on the distribution parameters.

[0127] The initial Kriging surrogate model construction module 720 can be used to extract the first training sample points from the candidate sample pool according to the uniform sampling density function, and construct the initial Kriging surrogate model under different failure modes according to the first training sample points.

[0128] The initial Kriging surrogate model update module 730 can be used to select a second training sample point based on the system state misjudgment probability of the turbine blade system, and update the initial Kriging surrogate model based on the second training sample point to obtain a converged Kriging surrogate model.

[0129] The failure probability function solver module 740 can be used to solve the failure probability function of a turbine blade system using a convergent Kriging surrogate model.

[0130] In an exemplary embodiment of this disclosure, constructing a unified sampling density function independent of the distribution parameters of the input variables of the turbine blade system includes: acquiring the input variables of the turbine blade system; wherein the input variables include multiple of the following: a first elastic modulus along the tangent of the turbine blade model corresponding to the turbine blade system, a second elastic modulus along the radial direction, a third elastic modulus along the circumferential direction, and the maximum rotational speed of the turbine blade model; calculating the distribution parameters of the input variables; wherein the distribution parameters include the mean and standard deviation of the input variables; determining a threshold interval of the distribution parameters, and determining the conditional probability density function of the input variables and the prior density function of the distribution parameters; and integrating the product of the conditional probability density function and the prior density function over the threshold interval to obtain the unified sampling density function independent of the distribution parameters.

[0131] In one exemplary embodiment of this disclosure, constructing a candidate sample pool for solving the failure probability function of the turbine blade system based on the distribution parameters includes: generating a distribution parameter sample pool based on the prior density function of the distribution parameters, and determining input variable samples from the distribution parameter sample pool based on the conditional probability density function of the input variables; and constructing a candidate sample pool for solving the failure probability function of the turbine blade system based on the input variable samples.

[0132] In an exemplary embodiment of this disclosure, the process of extracting a first training sample point from the candidate sample pool according to the unified sampling density function, and constructing an initial Kriging surrogate model under different failure modes based on the first training sample point, includes: extracting a first training sample point with a first preset number from the candidate sample pool according to the unified sampling density function; constructing an initial training sample set under different failure modes based on the first training sample point and the failure modes of the turbine blade system; wherein the failure modes include a first failure mode, a second failure mode, ..., an m-th failure mode, where m is the number of failure modes of the turbine blade system; the initial training sample set includes a first initial sample set corresponding to the first failure mode, a second initial sample set corresponding to the second failure mode, ..., an m-th initial sample set corresponding to the m-th failure mode; and constructing an initial Kriging surrogate model under different failure modes based on the initial training sample set under different failure modes and the failure modes of the turbine blade system; the initial Kriging surrogate model includes a first initial Kriging surrogate model, a second initial Kriging surrogate model, ..., an m-th initial Kriging surrogate model.

[0133] In one exemplary embodiment of this disclosure, selecting a second training sample point based on the system state misjudgment probability of the turbine blade system, and updating the initial Kriging surrogate model based on the second training sample point to obtain a converged Kriging surrogate model includes: predicting the predicted mean and predicted standard deviation of the input variable samples in the candidate sample pool in the turbine blade system according to the initial Kriging surrogate model; determining the system state misjudgment probability of the input variable samples in the turbine blade system according to the predicted mean and predicted standard deviation, and selecting a second training sample point based on the system state misjudgment probability; determining the failure mode to which the second training sample point belongs based on the predicted mean and predicted standard deviation of the second training sample point, and adding the second training sample point to the initial training sample set corresponding to the failure mode to obtain a target training sample set; and updating the initial Kriging surrogate model based on the target training sample set to obtain a converged Kriging surrogate model.

[0134] In an exemplary embodiment of this disclosure, determining the system state misjudgment probability of the turbine blade system based on the predicted mean and the predicted standard deviation includes: determining the connection mode of the turbine blade system modes; wherein the connection mode of the system modes includes a series model or a parallel model; determining a calculation rule for the system state misjudgment probability based on the connection mode of the turbine blade system modes and the predicted mean; and substituting the predicted mean and the predicted standard deviation into the calculation rule to obtain the system state misjudgment probability of the turbine blade system.

[0135] In one exemplary embodiment of this disclosure, selecting a second training sample point based on the system state misjudgment probability includes: determining the probability that the input variable sample causes the turbine blade system to generate a state misjudgment according to the unified sampling density function and the system state misjudgment probability; sorting the input variable samples based on the probability of generating a state misjudgment, and selecting the second training sample from the input variable samples in the candidate sample pool based on the sorting result.

[0136] In one exemplary embodiment of this disclosure, determining the failure mode to which the second training sample point belongs based on the predicted mean and predicted standard deviation of the second training sample point includes: determining the U learning function value of the second training sample point under different failure modes based on the predicted mean and predicted standard deviation of the second training sample point; and determining the failure mode to which the second training sample point belongs based on the U learning function value.

[0137] In one exemplary embodiment of this disclosure, updating the initial Kriging surrogate model based on the target training sample set to obtain a converged Kriging surrogate model includes: updating the initial Kriging surrogate model based on the target training sample set to obtain an updated Kriging surrogate model; predicting a first system expansion failure probability for target sample points in the target training sample set based on the updated Kriging surrogate model; obtaining the predicted mean of the target sample points and determining a second system expansion failure probability for the target sample points based on the predicted mean; determining whether the updated Kriging surrogate model satisfies the model convergence condition based on the first system expansion failure probability and the second system expansion failure probability; if the updated Kriging surrogate model satisfies the model convergence condition, then the updated Kriging surrogate model is used as the converged Kriging surrogate model; if the updated Kriging surrogate model does not satisfy the model convergence condition, then the model update steps are repeated until the updated Kriging surrogate model satisfies the model convergence condition, so as to obtain a converged Kriging surrogate model.

[0138] In one exemplary embodiment of this disclosure, determining whether the updated Kriging surrogate model satisfies the model convergence condition based on the first system extended failure probability and the second system extended failure probability includes: calculating a first difference between the first system extended failure probability and the second system extended failure probability, and calculating a first ratio between the first difference and the second system extended failure probability; calculating a first expected value of the absolute value of the first ratio, and determining whether the updated Kriging surrogate model satisfies the model convergence condition based on the first expected value.

[0139] The specific details of each module in the above-mentioned turbine blade system failure probability function solving device based on sample information sharing have been described in detail in the corresponding turbine blade system failure probability function solving method based on sample information sharing, so they will not be repeated here.

[0140] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0141] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0142] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0143] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0144] The following reference Figure 8 To describe an electronic device 800 according to such an embodiment of the present disclosure. Figure 8 The electronic device 800 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0145] like Figure 8 As shown, the electronic device 800 is manifested in the form of a general-purpose computing device. The components of the electronic device 800 may include, but are not limited to: at least one processing unit 810, at least one storage unit 820, a bus 830 connecting different system components (including storage unit 820 and processing unit 810), and a display unit 840.

[0146] The storage unit stores program code that can be executed by the processing unit 810, causing the processing unit 810 to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure. For example, the processing unit 810 can perform actions such as... Figure 1 Step S110: Based on the distribution parameters of the input variables of the turbine blade system, construct a unified sampling density function independent of the distribution parameters, and construct a candidate sample pool for solving the failure probability function of the turbine blade system based on the distribution parameters; Step S120: Extract a first training sample point from the candidate sample pool according to the unified sampling density function, and construct an initial Kriging surrogate model under different failure modes based on the first training sample point; Step S130: Select a second training sample point according to the system state misjudgment probability of the turbine blade system, and update the initial Kriging surrogate model based on the second training sample point to obtain a converged Kriging surrogate model; Step S140: Use the converged Kriging surrogate model to solve the failure probability function of the turbine blade system.

[0147] Storage unit 820 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 8201 and / or cache memory 8202, and may further include a read-only memory (ROM) 8203.

[0148] The storage unit 820 may also include a program / utility 8204 having a set (at least one) of program modules 8205, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0149] Bus 830 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0150] Electronic device 800 can also communicate with one or more external devices 900 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 800, and / or with any device that enables electronic device 800 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 850. Furthermore, electronic device 800 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 860. As shown, network adapter 860 communicates with other modules of electronic device 800 via bus 830. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 800, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0151] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0152] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible implementations, various aspects of this disclosure may also be implemented as a program product including program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of this disclosure described in the "Exemplary Methods" section above.

[0153] The program product for implementing the above-described method according to embodiments of the present disclosure may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto. In this document, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0154] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0155] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0156] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0157] Program code for performing the operations of this disclosure can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0158] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of this disclosure and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0159] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention described herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not invented by this disclosure. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A method for solving the failure probability function of a turbine blade system based on sample information sharing, characterized in that, include: Based on the distribution parameters of the input variables of the turbine blade system, a unified sampling density function independent of the distribution parameters is constructed, and based on the distribution parameters, a candidate sample pool for solving the failure probability function of the turbine blade system is constructed. The first training sample points are extracted from the candidate sample pool according to the unified sampling density function, and the initial Kriging proxy model under different failure modes is constructed based on the first training sample points. The second training sample point is selected based on the system state misjudgment probability of the turbine blade system, and the initial Kriging surrogate model is updated based on the second training sample point to obtain a converged Kriging surrogate model. The failure probability function of the turbine blade system is solved using a convergent Kriging surrogate model. The unified sampling density function is obtained as follows: Input variables of the turbine blade system are acquired; distribution parameters of the input variables are calculated, including the mean and standard deviation of the input variables; a threshold interval for the distribution parameters is determined, and the conditional probability density function of the input variables and the prior density function of the distribution parameters are determined; the product of the conditional probability density function and the prior density function is integrated over the threshold interval to obtain a unified sampling density function independent of the distribution parameters.

2. The method according to claim 1, characterized in that, The input variables include multiple of the following: a first elastic modulus in the tangential direction, a second elastic modulus in the radial direction, a third elastic modulus in the circumferential direction, and the maximum rotational speed of the turbine blade model corresponding to the turbine blade system.

3. The method according to claim 1, characterized in that, Based on the distribution parameters, a candidate sample pool is constructed for solving the failure probability function of the turbine blade system, including: A sample pool of distribution parameters is generated based on the prior density function of the distribution parameters, and a sample of the input variable is determined from the sample pool of distribution parameters based on the conditional probability density function of the input variable. Based on the input variable samples, a candidate sample pool is constructed to solve the failure probability function of the turbine blade system.

4. The method according to claim 1, characterized in that, First training sample points are drawn from the candidate sample pool according to the unified sampling density function, and initial Kriging surrogate models for different failure modes are constructed based on the first training sample points, including: According to the unified sampling density function, a first training sample point with a first preset number is drawn from the candidate sample pool; Based on the first training sample points and the failure modes of the turbine blade system, an initial training sample set is constructed under different failure modes; wherein, the failure modes include a first failure mode, a second failure mode, ..., the m-th failure mode, where m is the number of failure modes of the turbine blade system; the initial training sample set includes a first initial sample set corresponding to the first failure mode, a second initial sample set corresponding to the second failure mode, ..., the m-th initial sample set corresponding to the m-th failure mode; Based on the initial training sample sets under different failure modes and the failure modes of the turbine blade system, initial Kriging surrogate models under different failure modes are constructed; the initial Kriging surrogate models include a first initial Kriging surrogate model, a second initial Kriging surrogate model, ..., the m-th initial Kriging surrogate model.

5. The method according to claim 1, characterized in that, The second training sample point is selected based on the system state misjudgment probability of the turbine blade system, and the initial Kriging surrogate model is updated based on the second training sample point to obtain a converged Kriging surrogate model, including: Based on the initial Kriging proxy model, predict the predicted mean and predicted standard deviation of the input variable samples in the candidate sample pool in the turbine blade system; Based on the predicted mean and predicted standard deviation, the probability of misjudging the system state of the input variable sample in the turbine blade system is determined, and a second training sample point is selected based on the probability of misjudging the system state. The failure mode to which the second training sample point belongs is determined based on the predicted mean and predicted standard deviation of the second training sample point, and the second training sample point is added to the initial training sample set corresponding to the failure mode based on the failure mode to obtain the target training sample set. The initial Kriging proxy model is updated based on the target training sample set to obtain a converged Kriging proxy model.

6. The method according to claim 5, characterized in that, Based on the predicted mean and predicted standard deviation, the probability of misjudgment of the turbine blade system state is determined, including: Determine the connection method of the turbine blade system mode; wherein, the connection method of the system mode includes a series model or a parallel model; Based on the connection method of the turbine blade system mode and the predicted mean, the calculation rules for the system state misjudgment probability are determined; Substituting the predicted mean and predicted standard deviation into the calculation rule, the probability of misjudging the state of the turbine blade system is obtained.

7. The method according to claim 5, characterized in that, The selection of a second training sample point based on the system state misjudgment probability includes: Based on the unified sampling density function and the system state misjudgment probability, determine the probability that the input variable sample will cause the turbine blade system to misjudge its state. The input variable samples are sorted based on the probability of generating a state misjudgment, and the second training sample is selected from the input variable samples in the candidate sample pool based on the sorting result.

8. The method according to claim 5, characterized in that, Determining the failure mode of the second training sample point based on the predicted mean and predicted standard deviation of the second training sample point includes: Based on the predicted mean and predicted standard deviation of the second training sample points, the U learning function values ​​of the second training sample points under different failure modes are determined. The failure mode to which the second training sample point belongs is determined based on the value of the U learning function.

9. The method according to claim 5, characterized in that, The initial Kriging proxy model is updated based on the target training sample set to obtain a converged Kriging proxy model, including: The initial Kriging proxy model is updated based on the target training sample set to obtain the updated Kriging proxy model. Based on the updated Kriging proxy model, the first system expansion failure probability of the target sample points in the target training sample set is predicted. Obtain the predicted mean of the target sample points, and determine the second system extended failure probability of the target sample points based on the predicted mean; Based on the first system expansion failure probability and the second system expansion failure probability, determine whether the updated Kriging proxy model satisfies the model convergence condition. If the updated Kriging surrogate model satisfies the model convergence condition, then the updated Kriging surrogate model is taken as the converged Kriging surrogate model; if the updated Kriging surrogate model does not satisfy the model convergence condition, then the model update steps are repeated until the updated Kriging surrogate model satisfies the model convergence condition, so as to obtain the converged Kriging surrogate model.

10. The method according to claim 9, characterized in that, Determining whether the updated Kriging proxy model satisfies the model convergence condition based on the first system expansion failure probability and the second system expansion failure probability includes: Calculate the first difference between the extended failure probability of the first system and the extended failure probability of the second system, and calculate the first ratio between the first difference and the extended failure probability of the second system. Calculate the first expected value of the absolute value of the first ratio, and determine whether the updated Kriging proxy model satisfies the model convergence condition based on the first expected value.

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