A high-speed train gearbox fatigue reliability analysis method fusing deep Gaussian process model and new active learning function

Abstract

The application proposes a high-speed train gearbox reliability analysis method which fuses deep Gaussian process model and new active learning function. The proposed technical path contains the following steps: (1) using SIMPACK software to establish the dynamics model of high-speed train gearbox, and obtaining its stress-time load spectrum; (2) using rain flow counting method to count the obtained load spectrum, and combining Goodman model and Miner criterion to establish the fatigue life prediction model of high-speed train gearbox; (3) identifying and quantifying the uncertainty influencing factors of high-speed train gearbox fatigue life, and establishing the limit state equation and its initial deep Gaussian process surrogate model according to the design life requirement; (4) introducing new active learning function ALF to update and iterate the above initial surrogate model until meeting certain convergence condition, and outputting the fatigue reliability analysis result of high-speed train gearbox. The method constructs a complete fatigue reliability analysis framework according to the level logic progression of "dynamics modeling-fatigue life prediction-uncertainty quantification-reliability analysis", and provides important method support for ensuring the safe and reliable operation of high-speed train gearbox.

Description

Technical Field

[0001] This invention belongs to the technical field of fatigue life prediction and reliability analysis of high-speed train gearboxes, specifically involving a fatigue reliability analysis method for high-speed train gearboxes that integrates a deep Gaussian process model and a novel active learning function. Background Technology

[0002] High-speed trains represent a highly integrated achievement of modern rail transit development, combining multiple disciplines such as aerodynamics, traction transmission, control engineering, communication signals, new materials technology, and intelligent diagnostics. They are a core piece of equipment in modern transportation systems. High-speed trains effectively alleviate transportation capacity constraints caused by uneven regional development, meet the ever-increasing travel quality demands of passengers, and play a crucial role in improving network efficiency, optimizing energy consumption, and enhancing operational safety and comfort. Therefore, they are widely used in intercity commuting, trunk line transportation, and the construction of national comprehensive three-dimensional transportation networks. The reliability of high-speed trains is critical to their long-term stable operation; malfunctions or failures can lead to severe economic losses and other serious consequences.

[0003] As a core component of the high-speed train transmission system, the reliability of the gearbox directly determines whether the train can operate smoothly for extended periods under high-speed, heavy-load conditions. Gearbox failure can lead to operational interruptions, traffic accidents, and consequently, significant socio-economic losses. Currently, reliability analysis of high-speed train gearboxes faces the following main technical challenges:

[0004] 1. Extreme scarcity of full life cycle data: Due to the characteristics of long life and high reliability of gearboxes, and the high cost of full life cycle testing, the amount of failure sample data is severely insufficient.

[0005] 2. Significant individual differences in products: Minor differences in the manufacturing and assembly process, as well as the diversity of operating environments, result in a significant dispersion in the performance degradation trajectory of different gearboxes.

[0006] 3. Wide range of uncertainties: Design parameters, material properties, external loads and internal system states all have wide range of uncertainties, which increases the difficulty of accurately assessing its reliability.

[0007] Existing technologies have proposed several adaptive prediction methods for structural life distribution or remaining service life distribution. However, most of these methods are data-driven, such as using maximum likelihood estimation to estimate the mean and standard deviation of life from real-time collected data. In such methods, the prediction of life distribution parameters is passive, meaning that effective prediction cannot be achieved in the absence of real-time monitoring data. To address these issues, this invention introduces a novel Active Learning Function (ALF) and a deep Gaussian process model, aiming to achieve adaptive prediction of the fatigue reliability of high-speed train gearboxes under uncertain conditions. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a high-precision and highly applicable fatigue reliability analysis method for high-speed train gearboxes.

[0009] The technical solution of the present invention is as follows:

[0010] Step S1: Use SIMPACK to establish a dynamic model of the high-speed train gearbox and obtain its stress-time load spectrum;

[0011] To construct a dynamic model of a high-speed train gearbox, the multibody dynamics simulation software SIMPACK was used to establish its multibody system model. This model fully considers multiple nonlinear factors such as time-varying gear meshing stiffness, tooth flank clearance, and tooth surface friction. In the SIMPACK environment, system modeling was completed by defining rigid bodies, constraint pairs, force elements, and contact parameters. Dynamic solutions were then obtained using the software's built-in efficient numerical integrator, ultimately outputting the dynamic stress history curves of the key meshing pairs of the gearbox under operating conditions.

[0012] Step S2: Statistically analyze the obtained load spectrum using the rainflow counting method, and establish a fatigue life prediction model for high-speed train gearboxes by combining the Goodman model and the Miner criterion.

[0013] Based on the stress-time load spectrum obtained in step S1, the following is carried out:

[0014] The rainflow counting method is used for load statistics. First, peak and valley values ​​are extracted from the stress-time load spectrum to simplify the data. Second, based on the "four-point method" cycle judgment criterion, complete closed stress hysteresis loops are identified and extracted through stack operations, and the amplitude, mean and number of cycles of each cycle are calculated simultaneously. Finally, the remaining data segments that fail to form complete loops are processed as semi-loops.

[0015] Goodman Correction: The Goodman correction method used is based on the classic Goodman line model, and its core formula is as follows: The aim is to represent the actual non-zero average stress. Stress amplitude under Equivalent stress amplitude under symmetrical cyclic (mean stress is zero) conditions. In order to directly utilize materials The curve is used for life assessment.

[0016] Miner's linear cumulative damage theory: Based on Miner's linear cumulative damage theory, for each stress cycle after rainflow counting and Goodman correction, through... The curve is used to calculate the corresponding failure cycle number. And calculate the cumulative damage. When D accumulates to 1, fatigue failure is determined. Finally, the fatigue life of the gearbox under the load spectrum is predicted using the reciprocal of the total damage, thereby achieving a quantitative assessment of fatigue failure under variable amplitude loads.

[0017] Step S3: Identify and quantify the uncertain influencing factors of fatigue life of high-speed train gearboxes, and establish the limit state equation and its initial deep Gaussian process surrogate model according to its design life requirements.

[0018] In uncertainty identification and quantification, the input torque of a high-speed train gearbox is obtained using a normally distributed random variable. and its fatigue limit Characterized as a normal distribution The initial input samples are generated using the Latin hypercube sampling method. Combined with the high-speed train gearbox dynamics model and fatigue life prediction model, the random predicted value of gearbox fatigue life is obtained and quantified.

[0019] The main steps in constructing a Deep Gaussian Process (DGP) model are as follows: First, the model architecture is defined, selecting a 1- to 3-layer DGP structure based on problem complexity. Each layer consists of implicit functions with independent Gaussian process priors, and structural simplification strategies such as conditional independence and isotropic kernels are used to balance expressive power and computational burden. Next, data preprocessing and parameter initialization are performed. Functions such as check inputs and check initialization are used to standardize the input and output data and verify their integrity, while initial values ​​are assigned to hyperparameters and latent variables. The core inference stage employs a complete Bayesian framework based on MCMC: a Gibbs sampling loop is used, where hyperparameters are updated using the Metropolis Hastings algorithm, and latent variables are efficiently traversed using Elliptic Slice Sampling (ESS), specifically designed for Gaussian priors; log-likelihood is continuously calculated during sampling to assess acceptance probability. After completing a specified number of MCMC iterations, the trim function is used for post-processing, removing aging samples and diluting them to reduce autocorrelation. After the model is trained, predictions are made using the predict function. This function is based on the Kriging conditional expectation formula, uses the trained hidden layer representation to calculate the posterior prediction mean and variance of new points, and can optionally output the complete covariance matrix.

[0020] Step S4: Introduce a novel active learning function ALF to update and iterate the initial surrogate model until a certain convergence condition is met, and output the fatigue reliability analysis results of the high-speed train gearbox.

[0021] Using the predicted mean of DGP output with standard deviation Introducing a new learning function By comprehensively evaluating the potential of candidate points to be "close to the failure boundary" and "have high cognitive uncertainty," the system intelligently identifies the sample points with the most informational value for correcting the failure probability and updates and iterates them until certain convergence conditions are met. (error is recommended to be 10) -2 The results of fatigue reliability analysis of high-speed train gearboxes are output.

[0022] Beneficial effects of the present invention

[0023] 1. Overcoming the limitations of non-stationarity: Traditional surrogate models such as Kriging are based on the assumption of stationarity, making it difficult to accurately characterize common local abrupt changes in engineering responses (such as stress concentration). DGP automatically distorts the input space through its hierarchical structure, and is essentially a non-stationary modeling framework that can more flexibly adapt to complex and heterogeneous limit state function forms.

[0024] 2. More Complete Uncertainty Quantification: Unlike deterministic neural networks or approximate Bayesian methods using variational inference, the MCMC inference scheme employed provides DGP with full Bayesian uncertainty quantification. It can simultaneously capture both accidental and cognitive uncertainties, especially in small-sample scenarios, providing more reliable prediction confidence intervals and offering a credible foundation for uncertainty-based decision-making.

[0025] 3. Handling High-Dimensionality and Implicit Limit State Functions: DGP's hierarchical nonlinear mapping capability enables it to better handle problems with multiple design variables. Furthermore, this method does not require explicit expressions for the limit state functions, making it perfectly suitable for "black box" systems where performance function values ​​are obtained through simulation, thus expanding its engineering applicability.

[0026] 4. Provide full-process technical specifications: Provide a complete and operable technical route from dynamic analysis to system comprehensive evaluation.

[0027] 5. Solving the small sample problem: By utilizing the novel learning function ALF and the deep Gaussian process model, the feasibility of evaluation in small sample scenarios is greatly improved. Attached Figure Description

[0028] Figure 1 : Overall implementation flowchart of the present invention;

[0029] Figure 2 : Dynamic model of high-speed train gearbox;

[0030] Figure 3 Stress-time load spectrum curve;

[0031] Figure 4 Rainflow count results;

[0032] Figure 5 Failure probability iterative results based on deep Gaussian process model and ALF learning function; Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and a specific embodiment of a high-speed train gearbox.

[0034] Step S1 Implementation: System dynamics modeling and dynamic load solution (corresponding to) Figure 2 , Figure 3 )

[0035] according to Figure 2 The multibody dynamics model shown is used to establish the dynamic model of the high-speed train gearbox. Input the large number of teeth. Small number of teeth Modulus Pressure angle Tooth width Input torque Based on parameters such as [parameters], a dynamic model of a high-speed train gearbox was constructed using SIMPACK multibody dynamics software. The system dynamic equations were numerically solved using the built-in multibody dynamics solution algorithm (GSTIFF integrator) of SIMPACK, yielding the following results: Figure 3 The stress-time load spectrum at the tooth root of the high-speed train gearbox shown is used as an accurate input for subsequent fatigue life prediction.

[0036] Step S2 Implementation: Construct a fatigue life prediction model based on rainflow counting, Goodman correction, and Minner's rule (corresponding to...) Figure 4 )

[0037] The tooth root stress-time load spectrum output by SIMPACK Statistical analysis was conducted using the rainflow counting method, and the results are as follows: Figure 4 And using Goodman's criterion (tensile strength of materials) The non-zero average stress load is corrected to obtain the equivalent symmetrical cyclic stress amplitude. Based on the corrected stress amplitude and gear contact... The curve model calculates the cumulative damage over a specified task duration based on Miner's linear cumulative damage rule. Finally, by comparing the cumulative damage with a preset failure threshold, a quantitative assessment of the gear contact fatigue state and a life prediction are completed.

[0038] Step S3 Implementation: Identify and quantify the uncertain influencing factors of fatigue life of high-speed train gearboxes, and establish the limit state equation and its initial deep Gaussian process surrogate model based on its design life requirements.

[0039] Uncertainty Characterization: The input torque of the high-speed train gearbox is characterized as... The fatigue limit of gears is characterized as .

[0040] Taking the CRH380 high-speed train as an example, its design life is generally required to be 20 years, and the limit state equation is established based on this. (s is the predicted fatigue life value). The condition is considered a failure state. To address the uncertainties in the gearbox input torque and fatigue limit, a Latin hypercube sampling method was used to select 12 initial samples. Combining the gearbox dynamics model and fatigue life prediction model, 12 corresponding fatigue lives were calculated. This established an initial deep Gaussian surrogate model, and the predict function was used to predict... The predicted mean and standard deviation of the limit state equation of a high-speed train gearbox under candidate samples.

[0041] Step S4 Implementation: Introduce a novel active learning function ALF to update and iterate the initial surrogate model until the convergence condition is met, and output the fatigue reliability analysis results of the high-speed train gearbox (corresponding to...). Figure 5 )

[0042] Based on the current sample set, and combining the predicted mean and standard deviation of the limit state equation output by the deep Gaussian process, a novel active learning function is introduced. The initial proxy model is updated and iterated until the convergence condition is met. The event will end at that time. Figure 5 The results clearly show that the failure probability stabilized at 0.1218 after multiple iterations. This result provides crucial quantitative evidence for maintenance decisions regarding high-speed train gearboxes.

Claims

1. A fatigue reliability analysis method for high-speed train gearboxes that integrates a deep Gaussian process model and a novel active learning function, characterized in that, Includes the following steps: S1. Use SIMPACK software to establish a dynamic model of a high-speed train gearbox and obtain its stress-time load spectrum; S2. The obtained load spectrum is statistically analyzed using the rainflow counting method, and a fatigue life prediction model for high-speed train gearbox is established by combining the Goodman model and the Miner criterion. S3. Identify and quantify the uncertainty factors affecting the fatigue life of high-speed train gearboxes, and establish the limit state equation and its initial deep Gaussian process proxy model according to its design life requirements. S4. Introduce a novel active learning function ALF to update and iterate the initial surrogate model until a certain convergence condition is met, and output the fatigue reliability analysis results of the high-speed train gearbox.

2. The method according to claim 1, characterized in that, In step S1, the dynamic model is a multibody dynamic model of a high-speed train gearbox. The modeling process specifically includes: importing or creating a geometric model and simplifying it into a multibody component, defining its mass attributes and local coordinate system; establishing the system topology connection relationship by defining rotational pair constraints; characterizing gear meshing behavior by setting gear force elements and importing time-varying meshing stiffness data fitted by Fourier series, while integrating nonlinear effects of tooth flank clearance and tooth surface friction; simulating bearing support characteristics using spring-damping force elements; and solving the stress-time load spectrum using the built-in numerical integrator of the software after completing the drive and load settings.

3. The method according to claim 1, characterized in that, In step S2, the core calculation process of the fatigue life prediction model based on linear cumulative damage theory includes: decomposing the stress-time load spectrum into load amplitude, mean, and number of cycles using the rainflow counting method; further correcting the mean stress using the Goodman model to obtain the equivalent stress amplitude; and finally, based on the corrected... Curve calculation of cumulative damage Finally, the damage degree corresponding to each load cycle is calculated according to the Miner criterion, and the total damage is accumulated to obtain the predicted value of the fatigue life of the high-speed train gearbox.

4. The method according to claim 1, characterized in that, In step S3, the uncertainty identification and quantification process utilizes a normal random variable to determine the input torque of the high-speed train gearbox. and its fatigue limit Characterized as a normal distribution The initial samples were generated using the Latin hypercube sampling method. Combined with gearbox dynamics and fatigue life prediction models, random predicted values ​​of fatigue life were obtained and quantified.

5. The method according to claim 1, characterized in that, In step S3, the core steps of establishing the initial deep Gaussian process model specifically include: Step 31. Data Preparation and Preprocessing: Perform dimension, range, and normalization checks on the input and output data. You can choose to scale the input to a unit hypercube and normalize the output to zero mean and unit variance to lay the foundation for model training. Step 32. Model Structure Definition and Initialization: Specify the number of DGP layers (1~3 layers) using modular functions, and use verification to complete initial parameters such as hidden layer states, length scale, noise level, and output scale; if the hidden layers are not specified, initialize them using Kriging interpolation. Step 33. Model Training (MCMC Sampling) adopts a hierarchical Gibbs sampling framework. Within each layer, the Metropolis-Hastings algorithm is used to sample hyperparameters (noise level, length scale), while elliptic slice sampling (ESS) is used to sample hidden layer variables (such as W, Z). Complete Bayesian posterior inference is achieved through iterative loops. Step 34. Post-processing and model optimization: Burnout period removal and trimming are performed on the MCMC sampling results to reduce autocorrelation, optimize storage efficiency, and improve the stability of the posterior distribution; at the same time, the consistency of parameter configuration and sampling order is ensured through built-in validation functions (check settings, etc.). Step 35. Model Prediction and Active Learning Integration: The predict function is used to predict test points and return the posterior mean and variance (the lite mode only outputs the marginal variance). The final predicted distribution is obtained through MCMC chain averaging. Active learning functions such as U, EFF, and H are integrated to select the most likely failure sample points based on prediction uncertainty, thereby achieving efficient reliability analysis.

6. The method according to claim 1, characterized in that, In step S4, the novel active learning function ALF is introduced to update and iterate the initial deep Gaussian surrogate model. Specifically, the predicted mean and standard deviation output by the deep Gaussian process model are used to comprehensively evaluate the degree to which candidate points are close to the failure boundary and the magnitude of cognitive uncertainty through the learning function ALF. The model is updated and iterated on the sample points that are most informative for correcting the failure probability, until the predetermined convergence condition is met, and the fatigue reliability analysis results of the high-speed train gearbox are output.

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