Ultra-high speed rotating head life prediction method, system, medium and product

Abstract

The present application relates to the technical field of super-high-speed rotating machinery structure strength and life prediction, and discloses a super-high-speed rotating head life prediction method, system, medium and product.The method comprises a data acquisition and life prediction module, and the life prediction module comprises: inputting the rotating head working condition parameters to be predicted into a gradient-enhanced multi-kernel integrated Kriging model, outputting life prediction values and prediction intervals point by point, and inversely transforming and restoring to output the complete crack propagation curve and fatigue life of the rotating head under the working condition; the gradient-enhanced multi-kernel integrated Kriging model comprises the following steps: obtaining original data, optimal Latin hypercube sampling, gradient-enhanced information construction, gradient-enhanced multi-kernel integrated Kriging sub-model acquisition, and gradient-enhanced multi-kernel integrated Kriging model acquisition.The key lies in the two aspects of gradient enhancement and multi-kernel integration, which can not only enhance the small sample precision at low cost based on the analytical physical structure, but also quantify the uncertainty of the selected kernel function.

Description

Technical Field

[0001] This invention relates to the field of strength and life prediction technology for ultra-high speed rotating machinery structures, and particularly to a method, system, medium, and product for predicting the life of an ultra-high speed rotating head. Background Technology

[0002] The rotor of an ultra-high-speed centrifuge is subjected to very high centrifugal stress during operation, with speeds reaching hundreds of thousands of revolutions per minute. Significant stress concentrations occur in geometrically discontinuous areas such as the journal transition zone. Under these conditions, subcritical fatigue crack propagation is the main form of rotor structural failure. Accurately predicting the crack propagation life of the rotor is crucial for ensuring the safe operation of the ultra-high-speed rotation system.

[0003] Current methods for predicting the crack propagation life of rotary heads primarily rely on stepwise finite element analysis (FEA) in fracture mechanics. Rotary heads have complex geometry, large centrifugal loads, and no analytical solution for the stress intensity factor at the crack tip, requiring iterative, point-by-point calculations along the crack lead and throughout crack propagation. Performing a complete finite element crack propagation calculation for every combination of rotational speed, stress ratio, and material parameters results in a massive computational burden, making it difficult to meet the needs of rapid evaluation under multiple parameters and conditions. To reduce computational burden, surrogate models can be used to replace stepwise finite element calculations; however, existing surrogate model schemes have the following problems.

[0004] First, most existing surrogate models pre-specify a kernel function, which is equivalent to assuming the smoothness of the response surface. Existing surrogate models, such as the standard Kriging model, only utilize the observed function values ​​of crack length and life to construct the correlation matrix. With only a few dozen training samples, the local curvature information of the response surface is insufficient, and the predicted curve is prone to oscillations deviating from physical laws in sparse sample regions. When there are only a few dozen training samples, the validity of this assumption cannot be determined by the data. If the kernel function is inappropriately chosen, the prediction results will be biased, and the error caused by this bias is not included in the prediction interval given by the model, making the reliability assessment overly optimistic.

[0005] Second, while existing gradient enhancement proxy methods can improve accuracy in small samples using gradient information, most gradients are obtained through numerical difference or additional simulation, which introduces truncation error and increases computational load, without utilizing the analytical relationships contained in the crack propagation physical equation itself.

[0006] Third, the stress intensity factor at the leading edge of the crack exhibits a non-uniform distribution, being high at both ends and low in the middle. Using a single average stress intensity factor to represent the driving force along the entire leading edge would underestimate the risk of expansion in the high-driving-force region at the leading edge. Furthermore, the Paris parameter C is much smaller in magnitude than other input variables such as rotational speed, approximately 10 to the power of -14. Directly using C as an input feature would cause an imbalance in feature magnitude and numerical instability.

[0007] Therefore, it is necessary to provide a new method for predicting the lifespan of ultra-high-speed rotors to solve the above-mentioned technical problems. Summary of the Invention

[0008] The main objective of this invention is to provide a method for predicting the lifetime of ultra-high-speed rotary heads, which can both enhance the accuracy of small samples at low cost by analyzing the physical structure and quantify the uncertainty of kernel function selection. The key lies in two aspects: gradient enhancement and multi-kernel integration. The specific technical solution is as follows: A method for predicting the lifespan of an ultra-high-speed rotary head includes the following steps: Step 1, Data Acquisition, specifically includes: obtaining the rotor operating parameters to be predicted, including: rotational speed. Stress ratio and Paris parameters and ; Step 2, Life Prediction Module: Specifically, the rotor working condition parameters to be predicted obtained in Step 1 are input into the gradient-enhanced multi-kernel integrated Kriging model, the life prediction value and prediction interval are output for each feature point and the model is inversely transformed to restore the model, and the complete crack propagation curve and fatigue life of the rotor under this working condition are output. Obtaining a gradient-enhanced multi-kernel ensemble Kriging model includes: Step ①: Acquiring raw data, specifically: conducting fatigue crack propagation tests on compact tensile specimens of the material used in the ultra-high-speed rotor to identify the material parameters in the Paris formula. and Stress ratio obtained based on ultra-high speed rotor working conditions and rotational speed ; Step ②, optimal Latin hypercube sampling, specifically: selecting samples including rotational speed... Stress ratio and Paris parameters and The parameter range, including the range within which the parameters are taken as input features, is used to generate a parameter range containing the range within which the optimal Latin hypercube sampling is applied within the range of values ​​for each input feature. A sample set of 10 samples; obtain the sample set of each sample. curve; Step ③, Gradient Boosting Information Construction, specifically: for the first... Using the analytical structure of the Paris crack propagation lifetime integral, the logarithm of the lifetime was derived from each sample. The precise gradient of the transformation characteristics; the logarithm of life versus the Paris exponent is derived from the existing crack length and stress intensity factor amplitude data of each sample through truncated integration. The semi-analytical gradient is obtained; the length of each characteristic crack checkpoint is obtained based on the exact gradient and the semi-analytical gradient. Dimensional gradient enhancement samples; combining lifetime function values ​​observed in each sample with... The gradient-enhanced sample joint yields a feature crack length checkpoint containing function value correlation blocks, function value and gradient intersection blocks, and gradient correlation blocks. 3D augmented matrix; ; Step 4: Select at least one Gaussian kernel and Multiple candidate kernel functions, including the 5 / 2 kernel, are selected based on the results obtained in step ③. The hyperparameters of the augmented matrix are determined by the maximum likelihood estimation of the augmented marginal likelihood, and the augmented marginal likelihood is calculated. The predictions of each kernel are weighted and integrated using the posterior weights obtained by normalizing the augmented marginal likelihoods of each kernel, and the integrated prediction value is output to obtain the gradient-enhanced multi-kernel integrated Kriging sub-model. Step 5: Determine if... Greater than If yes, proceed to the next step; otherwise, take... Return to step ③; Step 6: Obtain the gradient-enhanced multi-kernel ensemble Kriging sub-model based on all samples.

[0009] Preferably, the acquisition of the gradient-enhanced multi-kernel ensemble Kriging model also includes internal validation, which specifically involves using ten-fold cross-validation to evaluate the generalization performance of each gradient-enhanced multi-kernel ensemble Kriging sub-model.

[0010] Preferably, the acquisition of the gradient-enhanced multi-kernel ensemble Kriging model also includes external validation. External validation involves: using the turning parameters of the original data that were not used in the training to perform error validation. If the error requirements are met, the gradient-enhanced multi-kernel ensemble Kriging model is output; otherwise, the process returns to step ② for resampling.

[0011] Preferably, in step ② Curve acquisition includes: A finite element model with the same geometry and loading conditions as the compact tensile specimen is established for each sample in the sample set. A finite element model of an ultra-high-speed rotor was established, and a centrifugal load corresponding to the rotational speed was applied. Based on the rotor simulation results, the critical section with the most severe stress concentration was determined. At this section, the crack insertion location was identified, and a crack was introduced. The finite element model was used to solve for the non-uniformly distributed stress intensity factor point by point along the crack leading edge and then integrated step by step to obtain the crack length propagation curve of the rotor under a given working condition as a function of the number of cycles, thus obtaining the crack propagation curve for each sample. curve.

[0012] Preferably, the Paris formula is as follows: ; in: The length of the crack. The number of loops. The stress intensity factor amplitude; The method for obtaining crack length is as follows: the average crack propagation rate is calculated from two adjacent data points using the secant method, and the average value of the two adjacent crack lengths is taken as the crack length corresponding to that rate. The fatigue life required for a crack to propagate from its initial length to its target length is determined by... The stress intensity factor amplitude is obtained by integrating along the crack length, and the evolution of the stress intensity factor amplitude with crack length is given stepwise by finite element calculation. The finite element model utilizes the symmetry of the rotor geometry and load to model a portion of the structure and applies normal displacement constraints on the symmetry plane; The critical section is the transition zone of the rotor journal; the stress intensity factor obtained along the crack tip is non-uniformly distributed with high stress intensity factors at both ends and low stress intensity factors in the middle. Crack propagation is calculated for each point at the crack tip using its local stress intensity factor.

[0013] Preferably, in step ③, the accurate gradient acquisition includes: the lifetime required for the rotating head to expand from the initial crack length to the crack length at the feature point is obtained by Paris integral. Give the Paris parameters. It appears as a constant factor in the integrand, moved outside the integral sign; let the logarithm of the lifetime be... , The logarithm of the transformation characteristic, after substitution, the logarithm of the lifetime equals the negative value of the transformation characteristic plus a factor that is only related to the stress intensity factor amplitude and the Paris exponent. The logarithm of the relevant integral terms, therefore the partial derivative of the lifetime logarithm with respect to this transformation characteristic is always equal to -1, and is related to the rotational speed, stress ratio, and Paris exponent. The value is irrelevant; Semi-analytical gradient acquisition includes: obtained by the Paris exponent Located at the exponent of the integrand, it is obtained by taking the partial derivative of the integrator kernel and then integrating. Its upper limit of integration is the crack length of the current feature point, so that the gradient of the sub-model of the feature point corresponds physically with its predicted lifetime. The required data is provided by the existing finite element results of each sample.

[0014] The effect of applying the technical solution of this invention is: 1. This invention is the first to transform the analytical structure of Paris law lifetime integrals into a zero-cost, error-free gradient that can be directly used by the surrogate model.

[0015] 2. The Paris index in this invention The gradient is derived from existing finite element crack length-stress intensity factor amplitude data through a single truncated numerical integration. Mathematically, it is guaranteed that when the feature point reaches the endpoint, the gradient automatically degenerates into the complete gradient of the total lifetime, thus ensuring strict self-consistency of the physical causality of each feature point sub-model. The two gradients expand the information content of each sample from 1 function value to 3 independent observations. Taking 56 samples as an example, it is equivalent to 168 effective observations, while the simulation cost increases by zero, fundamentally breaking the linear dependence of the surrogate model accuracy on the number of samples.

[0016] 3. In this invention, Group function values ​​and Group gradient observations are combined to construct × The augmented correlation matrix comprises function value-function value blocks, function value-gradient cross blocks, and gradient-gradient blocks. Precise gradient constraints are propagated across the entire parameter space via function value-gradient cross blocks and gradient-gradient blocks. This is equivalent to hard-constraining the predicted slope in a specific direction to -1 at each training sample, ensuring that the model's predicted slope along that direction at each training sample aligns with the Paris crack propagation law. In parameter regions where the rotor operating condition combinations are sparse and training samples are few, introducing this gradient observation can suppress prediction fluctuations in the surrogate model that do not conform to the crack propagation law, thereby improving the reliability of rotor crack propagation life prediction.

[0017] 4. In this invention, the smoothness of the crack propagation life response surface of the rotor is uncertain beforehand, and a single kernel function is difficult to verify its rationality using dozens of samples. Therefore, multiple candidate kernel functions are selected, and each kernel is optimized on augmented data, with the augmented marginal likelihood calculated. The posterior weights obtained by normalizing the marginal likelihoods are then used for weighted ensemble calculation. The ensemble prediction interval is based on the weighted sum of the prediction variances of each kernel, with an additional term consisting of the dispersion between the prediction means of each kernel. This term is used to measure the uncertainty introduced by the kernel function selection itself and is not included when using a single kernel function.

[0018] This invention discloses an ultra-high-speed rotor life prediction system, the ultra-high-speed rotor life prediction system comprising: The data acquisition module is used to acquire the rotor operating parameters to be predicted; The life prediction module, based on the embedded gradient-enhanced multi-kernel integrated Kriging model, outputs the life prediction value and prediction interval for each feature point and performs inverse transformation to restore the value, outputting the complete crack propagation curve and fatigue life of the rotor under this working condition.

[0019] This invention also discloses an ultra-high-speed rotor life prediction system, the ultra-high-speed rotor life prediction system comprising: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the ultra-high-speed rotor life prediction method as described above.

[0020] The present invention also discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the ultra-high-speed rotor life prediction method described above.

[0021] The present invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the ultra-high-speed rotor life prediction method as described above. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0023] Figure 1 This describes the gradient-enhanced multi-core integrated Kriging surrogate model acquisition process in the ultra-high-speed rotor life prediction method disclosed in Embodiment 1. Figure 2 for Figure 1 Weight distribution of four kernel functions in a gradient-enhanced multi-kernel ensemble Kriging surrogate model; Figure 3 For the gradient-enhanced multi-kernel ensemble Kriging surrogate model prediction in Example 1 of this embodiment. The curve is compared with the results of the ordinary Kriging model and finite element calculation, where: (a) is the gradient-enhanced multi-kernel ensemble Kriging surrogate model prediction for a certain test sample in the four test sample sets. (a) Comparison of curves with ordinary Kriging model and finite element calculation results; (b) Prediction of gradient-enhanced multi-kernel ensemble Kriging surrogate model for another test sample in the four test sample sets. Comparison of curves with ordinary Kriging model and finite element calculation results.

[0024] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1: A method for predicting the lifespan of an ultra-high-speed rotary head includes the following steps: Step 1, Data Acquisition, specifically includes: obtaining the rotor operating parameters to be predicted, including: rotational speed. Stress ratio and Paris parameters and ; Step 2, Life Prediction Module: Specifically, the rotor working condition parameters to be predicted obtained in Step 1 are input into the gradient-enhanced multi-kernel integrated Kriging model, the life prediction value and prediction interval are output for each feature point and the model is inversely transformed to restore the model, and the complete crack propagation curve and fatigue life of the rotor under this working condition are output. Obtaining a gradient-enhanced multi-kernel ensemble Kriging model includes: Step ①: Acquiring raw data, specifically: conducting fatigue crack propagation tests on compact tensile specimens of the material used in the ultra-high-speed rotor to identify the material parameters in the Paris formula. and Stress ratio obtained based on ultra-high speed rotor working conditions and rotational speed ; Step ②, optimal Latin hypercube sampling, specifically: selecting samples including rotational speed. Stress ratio and Paris parameters and The parameter range, including the range within which the parameters are taken as input features, is used to generate a parameter range containing the range within which the optimal Latin hypercube sampling is applied within the range of values ​​for each input feature. A sample set of 10 samples; obtain the sample set of each sample. curve; Step ③, Gradient Enhancement Information Construction, specifically: for the first... Using the analytical structure of the Paris crack propagation lifetime integral, the logarithm of the lifetime was derived from each sample. The precise gradient of the transformation characteristics; the logarithm of life versus the Paris exponent is derived from the existing crack length and stress intensity factor amplitude data of each sample through truncated integration. The semi-analytical gradient is obtained; the length of each characteristic crack checkpoint is obtained based on the exact gradient and the semi-analytical gradient. Dimensional gradient enhancement samples; combining lifetime function values ​​observed in each sample with... The gradient-enhanced sample joint yields a feature crack length checkpoint containing function value correlation blocks, function value and gradient intersection blocks, and gradient correlation blocks. 3D augmented matrix; ; Step 4: Select at least one Gaussian kernel and Multiple candidate kernel functions, including the 5 / 2 kernel, are selected based on the results obtained in step ③. The hyperparameters of the augmented matrix are determined by the maximum likelihood estimation of the augmented marginal likelihood, and the augmented marginal likelihood is calculated. The predictions of each kernel are weighted and integrated using the posterior weights obtained by normalizing the augmented marginal likelihoods of each kernel, and the integrated prediction value is output to obtain the gradient-enhanced multi-kernel integrated Kriging sub-model. Step 5: Determine if... Greater than If yes, proceed to the next step; otherwise, take... Return to step ③; Step 6: Obtain the gradient-enhanced multi-kernel ensemble Kriging model based on the gradient-enhanced multi-kernel ensemble Kriging sub-models of all samples. In this embodiment, obtaining the gradient-enhanced multi-kernel ensemble Kriging model also includes internal validation, specifically: using 10-fold cross-validation to evaluate the generalization performance of each gradient-enhanced multi-kernel ensemble Kriging sub-model.

[0027] In this embodiment, the acquisition of the gradient-enhanced multi-kernel ensemble Kriging model also includes external verification. The external verification is as follows: the error verification is performed using the turning condition parameters in the original data that were not used in the training. If the error requirements are met, the gradient-enhanced multi-kernel ensemble Kriging model is output; otherwise, the process returns to step ② for resampling.

[0028] In this embodiment, Curve acquisition includes: A finite element model with the same geometry and loading conditions as the compact tensile specimen is established for each sample in the sample set. A finite element model of an ultra-high-speed rotor was established, and a centrifugal load corresponding to the rotational speed was applied. Based on the rotor simulation results, the critical section with the most severe stress concentration was determined. At this section, the crack insertion location was identified, and a crack was introduced. The finite element model was used to solve for the non-uniformly distributed stress intensity factor point by point along the crack leading edge and then integrated step by step to obtain the crack length propagation curve of the rotor under a given working condition as a function of the number of cycles, thus obtaining the crack propagation curve for each sample. curve.

[0029] In this embodiment, the Paris formula is as follows: ; in: The length of the crack. The number of loops. The stress intensity factor amplitude; The method for obtaining crack length is as follows: the average crack propagation rate is calculated from two adjacent data points using the secant method, and the average value of the two adjacent crack lengths is taken as the crack length corresponding to that rate. The fatigue life required for a crack to propagate from its initial length to its target length is determined by... The stress intensity factor amplitude is obtained by integrating along the crack length, and the evolution of the stress intensity factor amplitude with crack length is given stepwise by finite element calculation. The finite element model utilizes the symmetry of the rotor geometry and load to model a portion of the structure and applies normal displacement constraints on the symmetry plane; The critical section is the transition zone of the rotor journal; the stress intensity factor obtained along the crack tip is non-uniformly distributed with high stress intensity factors at both ends and low stress intensity factors in the middle. Crack propagation is calculated for each point at the crack tip using its local stress intensity factor.

[0030] In this embodiment, the precise gradient acquisition in step ③ includes: the lifetime required for the rotating head to expand from the initial crack length to the crack length at the feature point is calculated by the Paris integral. Give the Paris parameters. It appears as a constant factor in the integrand, moved outside the integral sign; let the logarithm of the lifetime be... , The logarithm of the transformation characteristic, after substitution, the logarithm of the lifetime equals the negative value of the transformation characteristic plus a factor that is only related to the stress intensity factor amplitude and the Paris exponent. The logarithm of the relevant integral terms, therefore the partial derivative of the lifetime logarithm with respect to this transformation characteristic is always equal to -1, and is related to the rotational speed, stress ratio, and Paris exponent. The value is irrelevant; Semi-analytical gradient acquisition includes: obtained by the Paris exponent Located at the exponent of the integrand, it is obtained by taking the partial derivative of the integrator kernel and then integrating. Its upper limit of integration is the crack length of the current feature point, so that the gradient of the sub-model of the feature point corresponds physically with its predicted lifetime. The required data is provided by the existing finite element results of each sample.

[0031] The following example uses the TC18 titanium alloy ultra-high-speed centrifuge rotor as an example. The process for obtaining the gradient-enhanced multi-core integrated Kriging surrogate model in the ultra-high-speed rotor life prediction method is as follows: Figure 1 As shown, the kernel function weight distribution is as follows: Figure 2 As shown, the comparison between the prediction method of this invention and the original Kriging and finite element calculation results is as follows: Figure 3 As shown.

[0032] In this embodiment, according to ASTM E647 standard, a type I fatigue crack propagation test was conducted on TC18 titanium alloy using compact tensile specimens. The loading frequency was 10Hz, triangular wave, and stress ratio was 0.1. The crack propagation rate and stress intensity factor amplitude were calculated using the secant method. The material parameters for this embodiment were identified by linear regression after taking the logarithm of both sides of the Paris formula. The impact absorbed energy was determined by Charpy impact testing, and the fracture toughness was obtained through conversion. The average value of 8 sets was taken as the material fracture toughness. The critical crack size was determined by using the stress intensity factor reaching the fracture toughness as the termination criterion. The above calibration process and the calculation of the stress intensity factor of the compact tensile specimens are all mature methods in the field. A three-dimensional finite element model with the same geometry and loading conditions as the compact tensile specimens was established (approximately 39,589 hexahedral elements in this embodiment). The simulated life is obtained by integrating along the crack length, where the stress intensity factor amplitude is derived stepwise from the finite element method based on the evolution of the crack length. In this embodiment, the maximum relative error between the simulated life and the experimental life is 2.02%, verifying the effectiveness of the fracture mechanics finite element method.

[0033] The above method was applied to the TC18 titanium alloy ultra-high-speed rotor. A quarter-structure model was used, taking advantage of geometric and load symmetry. Normal displacement constraints were applied to the symmetry plane, resulting in a local stress deviation of less than 0.5% from the full-size model. This embodiment used approximately 151,574 tetrahedral elements, applied angular velocity boundary conditions, and achieved a maximum speed of 100,000 rpm. Calculations showed that the high-stress area was concentrated in the journal transition region, identifying it as a critical location. A crack was introduced at this location, and the stress intensity factor was calculated point-by-point along the crack leading edge. The results showed a non-uniform distribution, with high stress intensity factors at both ends and low stress intensity factors in the middle. Therefore, the local stress intensity factor was used to progressively expand the calculation at each point along the crack leading edge, obtaining a high-fidelity result under the given operating conditions. curve.

[0034] In this embodiment, the rotational speed is selected. (80,000–100,000 rpm), stress ratio (0.7~0.9), Paris parameters (1.2×10 -14 ~9.5×10 -14 )and (4.35~4.96) are the input features. 60 samples are generated using optimal Latin hypercube sampling. For each sample (i.e., the working condition sample), its corresponding... The curves were divided into a training set of 56 and an independent validation set of 4. The crack propagation curves were discretized into several feature points along the crack length direction, and a gradient-enhanced multi-kernel ensemble Kriging sub-model was established at each feature point. For the... The inputs of 56 training samples and their corresponding logarithms constitute a sample matrix and a lifetime response vector, as follows: ; in: The rotational speeds corresponding to samples 1-56; This represents the stress ratio corresponding to samples 1-56. This is the logarithm of the Paris parameter C corresponding to the 1st to 56th samples; Paris parameters corresponding to samples 1-56 ; For the 1st to 56th samples curve. The logarithm has been used as a transformation feature to eliminate the imbalance of magnitude, and the output is the logarithm of the life when the rotor extends to the crack length at the feature point under this working condition.

[0035] In this embodiment, The logarithm is used as a transformation feature (specifically in this embodiment: The transformation input is the logarithm to base 10, and the output is the logarithm of the rotor life. Using the Paris formula, the rotor life is extended to the th... Lifetime of each feature point as follows: ; in: The initial crack length is... For the first The crack length at each feature point will After extracting the integral sign and taking the logarithm, the logarithm of the lifetime is logarithmic. The partial derivative of the logarithm is always equal to -1, and the error holds true for all 56 training samples and any predicted operating condition, requiring no additional finite element calculations. (Lifetime logarithm versus Paris exponent) The gradient is calculated using the truncated integral formula described in the invention, where the stress intensity factor amplitude is progressively back-calculated from the existing finite element data of each sample, and the upper limit of the integral is taken as the crack length of the current feature point. In this way, each sample is expanded from one lifetime function value to three observations, and a total of 168 effective observations are obtained from 56 samples, without increasing the amount of finite element simulation.

[0036] In this embodiment, the derived Gradient observations are incorporated into the augmentation system to construct... × Augmented correlation matrix It contains three types of sub-blocks: ① Function value—function value related block; ②, Function value-gradient cross blocks, whose elements are standard correlation function pairs and First-order partial derivative; ③ Gradient—gradient block, containing related function pairs , The second-order mixed partial derivative. For the Gaussian kernel and The kernel and each sub-block have explicit analytical expressions, and the computational cost is comparable to the maximum likelihood estimation of standard Kriging.

[0037] Augmented log-marginal likelihood Simultaneous fitting For each observation, the hyperparameters are determined by its maximum likelihood estimate. Precise gradient constraints. through and The sub-block propagates in the full parameter space, which is equivalent to propagating the sub-block at each training sample. The predicted slope for the direction is hard-constrained to -1. This error-free physical constraint allows gradient-enhanced Kriging to still provide physically consistent predictions in parameter regions where the training data is sparse. This embodiment will augment Kriging in... The 24 feature points of the curve are constructed independently, and the gradient of each sub-model is truncated with integrals to form a multi-point gradient enhancement Kriging sub-model group.

[0038] In this embodiment, standard Kriging uses only 56 lifetime function values ​​to construct a 56th-order correlation matrix. This step incorporates the two gradients mentioned above together, for the... Each feature point constitutes a 168-dimensional augmented observation vector. : ; in: The values ​​are the finite element lifetime logarithmic values ​​corresponding to samples 1-56; the middle 56 components are all -1, which is the exact gradient of lifetime with respect to the logarithm of C, given directly by the Paris formula without calculation. The lifespan versus Paris index for samples 1-56 The gradient of the gradient is then calculated. Correspondingly, a 168th-order augmented correlation matrix is ​​constructed. : ; in: For the related blocks between function values; This represents the intersection block between function values ​​and gradients. This represents the intersection block between the gradient and the function value; This represents the correlation blocks between gradients.

[0039] In this embodiment, a kernel containing a Gaussian kernel is selected. 5 / 2 cores Multiple candidate kernel functions, including 3 / 2 kernels and rational quadratic kernels, are used, and the computational cost of solving hyperparameters is comparable to that of standard Kriging. Under this augmented system, arbitrary head operating conditions are addressed. Lifespan prediction This can be written as a weighted combination of the function values ​​and gradients of each sample: ; in: For the first Observation of lifetime function values ​​for each sample; For the first training samples Orientation gradient observation; To ensure precise gradient constraint -1; For the first one sample The contribution weights of the directional gradient observations to the prediction point are obtained by simultaneously solving the augmented correlation matrix and the correlation vector at the prediction point. The gradient used in the second summation term is always -1, which is equivalent to directly writing the Paris crack propagation law into the prediction function with a fixed slope. It is this term that enables the surrogate model to give physically consistent predictions even in the sparse parameter region of the rotating condition.

[0040] In this embodiment, gradient-enhanced multi-kernel integrated Kriging sub-models are independently constructed at each of the 24 feature points of the crack propagation curve. Each sub-model... The upper limit of the directional gradient integral is taken as the crack length of the current feature point, forming a multi-point sub-model group that can cover the entire crack propagation trajectory, thus predicting the cycle number under any crack length.

[0041] In this embodiment, the smoothness of the crack propagation life response surface of the rotor is determined by the Paris integral. , The nonlinear relationship is determined and cannot be predetermined. This embodiment selects a Gaussian kernel... 5 / 2 cores There are four candidate kernels: the 3 / 2 kernel and the rational quadratic kernel. Each kernel independently optimizes its hyperparameters and calculates its augmented marginal likelihood on the same set of 168-dimensional augmented data. The posterior weights are obtained using the following formula: ; in: For the first The posterior weights of the kernel function are obtained by normalizing the augmented marginal likelihood of the kernel; To adopt the first Seed kernel function At that time, the augmented log-marginal likelihood corresponding to the model; For all The sum of the true augmented marginal likelihoods of the candidate kernel functions.

[0042] Since the augmented marginal likelihood simultaneously fits the lifetime function value and two physical gradients, the weights of the kernel function are determined not only by the lifetime data but also by the Paris gradient constraint. For any turning condition to be predicted, each kernel provides a prediction mean and prediction variance, and the ensemble prediction mean is a weighted average of the means of each kernel. : ; in: Based on the Predicted values ​​of a single-kernel PI-GEK surrogate model trained with a variety of kernel functions; Integrated Prediction Variance It consists of two parts: ; in, The vector of parameters for the rotating head's operating condition to be predicted; This represents the prediction variance of the single-kernel PI-GEK model. The first term on the right is the weighted sum of the prediction variances of each kernel, reflecting the interpolation uncertainty caused by the sparsity of the training samples; the second term is the weighted dispersion between the prediction means of each kernel, reflecting the uncertainty caused by the inability to determine the smoothness of the response surface using only a few dozen samples. The prediction interval of a single kernel function only contains the first term, while the ensemble prediction interval of this method contains both terms, making the judgment of the remaining lifetime of the rotor more reliable. The kernel function weight distribution is as follows: Figure 2 As shown.

[0043] To verify the improvement effect of the method of the present invention compared with the existing surrogate model, this embodiment additionally constructs a regular Kriging model as a control: using the same 56 training samples as the gradient-enhanced multi-kernel ensemble Kriging, only the lifetime function value corresponding to the crack length is observed, gradient observation is not introduced, the kernel function is fixed as a Gaussian kernel, and it is trained according to the standard Kriging process. The prediction curves of this control model and the method of the present invention on the same validation samples are plotted together, as shown below. Figure 3 As shown in (a) and (b).

[0044] In this embodiment, ten-fold cross-validation is used to evaluate the generalization performance of each feature point sub-model on the training samples. The mean absolute percentage error (MASE), root mean square error (RMSE), mean absolute error (MASE), and coefficient of determination (COP) are used as indicators. In this embodiment, the MASE for most feature points is between 3.90% and 4.80%, and the COP is between 0.9959 and 0.9980. Four independent samples not involved in training and cross-validation are then used for external validation. After transformation, these samples are input into the multi-point sub-model group, and feature point-by-feature point prediction is integrated and inversely transformed to restore the model, resulting in a complete head crack propagation curve. The maximum relative errors of the four validation examples are 4.47%, 3.19%, 1.18%, and 1.46%, respectively, all below 5%. Two test samples are selected for validation, and their predicted curves match the finite element curves well, outperforming the prediction accuracy of ordinary Kriging.

[0045] In this embodiment, for any combination of rotor operating parameters to be predicted ( , , and By simply transforming the data and inputting it into a pre-trained multi-point sub-model group, the complete crack propagation curve, fatigue life, and prediction range of the rotating head under the working condition can be obtained in a short time, thus achieving efficient and high-precision life prediction under multi-parameter working conditions with low computational cost.

[0046] Example 2: This embodiment provides an ultra-high-speed rotary head life prediction system, including: The data acquisition module is used to acquire the rotor operating parameters to be predicted; The life prediction module, based on the embedded gradient-enhanced multi-kernel integrated Kriging model, outputs the life prediction value and prediction interval for each feature point and performs inverse transformation to restore the value, outputting the complete crack propagation curve and fatigue life of the rotor under this working condition.

[0047] Example 3: This embodiment provides an ultra-high-speed rotor life prediction system, which includes: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the ultra-high-speed rotor life prediction method as described above.

[0048] Example 4: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the ultra-high-speed rotor life prediction method described above.

[0049] Example 5: This embodiment provides a computer program product, including a computer program that, when executed by a processor, implements the ultra-high-speed rotor life prediction method as described above.

[0050] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for predicting the lifespan of an ultra-high-speed rotary head, characterized in that, Includes the following steps: Step 1, Data Acquisition, specifically includes: obtaining the rotor operating parameters to be predicted, including: rotational speed. Stress ratio and Paris parameters and ; Step 2, Life Prediction Module: Specifically, the rotor working condition parameters to be predicted obtained in Step 1 are input into the gradient-enhanced multi-kernel integrated Kriging model, the life prediction value and prediction interval are output for each feature point and the model is inversely transformed to restore the model, and the complete crack propagation curve and fatigue life of the rotor under this working condition are output. Obtaining a gradient-enhanced multi-kernel ensemble Kriging model includes: Step ①: Acquiring raw data, specifically: conducting fatigue crack propagation tests on compact tensile specimens of the material used in the ultra-high-speed rotor to identify the material parameters in the Paris formula. and Stress ratio obtained based on ultra-high speed rotor working conditions and rotational speed ; Step ②, optimal Latin hypercube sampling, specifically: selecting samples including rotational speed... Stress ratio and Paris parameters and The parameter range, including the range within which the parameters are taken as input features, is used to generate a parameter range containing the range within which the optimal Latin hypercube sampling is applied within the range of values ​​for each input feature. A sample set of 10 samples; obtain the sample set of each sample. curve; Step ③, Gradient Boosting Information Construction, specifically: for the first... Using the analytical structure of the Paris crack propagation lifetime integral, the logarithm of the lifetime was derived from each sample. The precise gradient of the transformation characteristics; the logarithm of life versus the Paris exponent is derived from the existing crack length and stress intensity factor amplitude data of each sample through truncated integration. The semi-analytical gradient is obtained; the length of each characteristic crack checkpoint is obtained based on the exact gradient and the semi-analytical gradient. Dimensional gradient enhancement samples; combining lifetime function values ​​observed in each sample with... The gradient-enhanced sample joint yields a feature crack length checkpoint containing function value correlation blocks, function value and gradient intersection blocks, and gradient correlation blocks. 3D augmented matrix; ; Step 4: Select multiple candidate kernel functions, including at least the Gaussian kernel and the Matérn 5 / 2 kernel, based on the results obtained in Step 3. The hyperparameters of the augmented matrix are determined by the maximum likelihood estimation of the augmented marginal likelihood, and the augmented marginal likelihood is calculated. The predictions of each kernel are weighted and integrated using the posterior weights obtained by normalizing the augmented marginal likelihoods of each kernel, and the integrated prediction value is output to obtain the gradient-enhanced multi-kernel integrated Kriging sub-model. Step 5: Determine if... Greater than If yes, proceed to the next step; otherwise, take... Return to step ③; Step 6: Obtain the gradient-enhanced multi-kernel ensemble Kriging sub-model based on all samples.

2. The method for predicting the lifespan of an ultra-high-speed rotary head according to claim 1, characterized in that, The acquisition of the gradient-enhanced multi-kernel ensemble Kriging model also includes internal validation, which specifically involves using ten-fold cross-validation to evaluate the generalization performance of each gradient-enhanced multi-kernel ensemble Kriging sub-model.

3. The method for predicting the lifespan of an ultra-high-speed rotary head according to claim 1, characterized in that, The acquisition of the gradient-enhanced multi-kernel ensemble Kriging model also includes external validation. External validation involves using the turning parameters in the original data that were not used in the training to perform error verification. If the error requirements are met, the gradient-enhanced multi-kernel ensemble Kriging model is output; otherwise, the process returns to step ② for resampling.

4. The method for predicting the lifespan of an ultra-high-speed rotary head according to claim 1, characterized in that, In step ② Curve acquisition includes: A finite element model with the same geometry and loading conditions as the compact tensile specimen is established for each sample in the sample set. A finite element model of an ultra-high-speed rotor was established, and a centrifugal load corresponding to the rotational speed was applied. Based on the rotor simulation results, the critical section with the most severe stress concentration was determined. At this section, the crack insertion location was identified, and a crack was introduced. The finite element model was used to solve for the non-uniformly distributed stress intensity factor point by point along the crack leading edge and then integrated step by step to obtain the crack length propagation curve of the rotor under a given working condition as a function of the number of cycles, thus obtaining the crack propagation curve for each sample. curve.

5. The method for predicting the lifespan of an ultra-high-speed rotary head according to claim 4, characterized in that, The Paris formula is as follows: ； in: The length of the crack. The number of loops. The stress intensity factor amplitude; The method for obtaining crack length is as follows: the average crack propagation rate is calculated from two adjacent data points using the secant method, and the average value of the two adjacent crack lengths is taken as the crack length corresponding to that rate. The fatigue life required for a crack to propagate from its initial length to its target length is determined by The stress intensity factor amplitude is obtained by integrating along the crack length, and the evolution of the stress intensity factor amplitude with crack length is given stepwise by finite element calculation. The finite element model utilizes the symmetry of the rotor geometry and load to model a portion of the structure and applies normal displacement constraints on the symmetry plane; The critical section is the transition zone of the rotor journal; the stress intensity factor obtained along the crack tip is non-uniformly distributed with high stress intensity factors at both ends and low stress intensity factors in the middle. Crack propagation is calculated for each point at the crack tip using its local stress intensity factor.

6. The method for predicting the lifespan of an ultra-high-speed rotary head according to claim 1, characterized in that, Step ③, precise gradient acquisition, includes: the lifetime required for the rotating head to expand from the initial crack length to the crack length at the feature point, calculated by the Paris integral. Give the Paris parameters. It appears as a constant factor in the integrand, moved outside the integral sign; let the logarithm of the lifetime be... , The logarithm of the transformation characteristic, after substitution, the logarithm of the lifetime equals the negative value of the transformation characteristic plus a factor that is only related to the stress intensity factor amplitude and the Paris exponent. The logarithm of the relevant integral terms, therefore the partial derivative of the lifetime logarithm with respect to this transformation characteristic is always equal to -1, and is related to the rotational speed, stress ratio, and Paris exponent. The value is irrelevant; Semi-analytical gradient acquisition includes: obtained by the Paris exponent Located at the exponent of the integrand, it is obtained by taking the partial derivative of the integrator kernel and then integrating. Its upper limit of integration is the crack length of the current feature point, so that the gradient of the sub-model of the feature point corresponds physically with its predicted lifetime. The required data is provided by the existing finite element results of each sample.

7. A life prediction system for ultra-high-speed rotary heads, characterized in that, The prediction is performed using the ultra-high-speed rotor life prediction method as described in any one of claims 1-6, wherein the ultra-high-speed rotor life prediction system comprises: The data acquisition module is used to acquire the rotor operating parameters to be predicted; The life prediction module, based on the embedded gradient-enhanced multi-kernel integrated Kriging model, outputs the life prediction value and prediction interval for each feature point and performs inverse transformation to restore the value, outputting the complete crack propagation curve and fatigue life of the rotor under this working condition.

8. A life prediction system for ultra-high-speed rotary heads, characterized in that, The ultra-high-speed rotor life prediction system includes: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the ultra-high-speed rotor life prediction method as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When executed by the processor, the program implements the ultra-high-speed rotor life prediction method as described in any one of claims 1-6.

10. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the ultra-high-speed rotor life prediction method as described in any one of claims 1-6.

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