Conditional probability meta-learning rotor model correction method for training non-covered rotating speed

Abstract

The present application relates to the technical field of rotor dynamics model correction, and discloses a conditional probability meta-learning rotor model correction method for training non-covered rotating speed, comprising: constructing a nominal dynamics observation model of a rotor system, dividing a meta training set and a target adaptation set based on a set rotating speed, and generating a cross-rotating speed meta task; performing normalization on a to-be-corrected parameter, a multi-channel time sequence response and a rotating speed working condition, extracting and splicing features, constructing a conditional probability inverse mapping model, and outputting a diagonal Gaussian joint distribution in a normalized space; constructing a compound loss function by using a parameter error and a negative log likelihood, performing offline double-layer meta updating and online target rotating speed adaptation on the model; performing parameter sampling and dynamics forward propagation on the conditional probability distribution output after adaptation, and calculating evaluation indexes of the parameter and the response space. The present application realizes small sample fast migration under non-seen rotating speed working conditions, quantifies prediction uncertainty, and improves the correction reliability of the rotor model.

Description

Technical Field

[0001] This invention relates to the field of rotor dynamics model correction technology, specifically to a method for correcting rotor models using conditional probabilistic element learning for speeds not covered in the training. Background Technology

[0002] Rotor systems are core components of large rotating machinery such as aero-engines and gas turbines. Constructing high-precision dynamic models is fundamental for achieving equipment condition monitoring, fault diagnosis, and digital twin applications. Due to manufacturing errors, assembly tolerances, and variations in the operating environment, theoretically established finite element models often deviate from the actual dynamic characteristics of the equipment. Therefore, it is necessary to use measured vibration response data to inversely correct key equivalent parameters such as support stiffness and damping in the nominal model to eliminate the discrepancies between the theoretical model and the actual physical object.

[0003] Traditional model correction methods often employ deterministic iterative optimization based on sensitivity analysis or heuristic algorithms, which suffer from high computational costs and a tendency to get trapped in local optima. In recent years, data-driven inverse mapping methods based on deep neural networks have been increasingly applied to rotor model correction. However, the operating conditions of real-world engineering equipment are complex and variable, making it difficult to obtain complete labeled data across the entire speed range. Existing deep learning correction networks typically employ a single-layer empirical risk minimization strategy, which is heavily dependent on the data distribution in the training set. When the model faces interpolated or extrapolated speed conditions not included in the training, the shift in system dynamics caused by speed changes often prevents conventional networks from adapting to this data distribution shift, leading to decreased prediction accuracy and failing to meet the generalization correction requirements under cross-condition conditions.

[0004] Furthermore, due to the prevalence of measurement noise and system simplification biases in actual testing, the inverse problem between dynamic response and support parameters is inherently highly ill-conditioned and uncertain. Most current mainstream deep learning correction methods only output deterministic point estimates, failing to characterize the prediction dispersion caused by parameter compensation effects. Simultaneously, in the face of unseen operating conditions, re-collecting large amounts of labeled data on-site for model fine-tuning is extremely impractical in engineering. Existing techniques struggle to rapidly achieve adaptive transfer of network weights under small sample conditions and cannot output parameter probability distribution intervals that include statistical confidence levels.

[0005] Existing verification systems for corrected models are also relatively one-sided, typically relying on a single metric such as the mean square error of the response space to evaluate the correction effect. This evaluation method, which solely depends on the degree of waveform fitting, cannot identify the true deviations in the extraction of underlying parameters of the network model. When dealing with multi-parameter coupling, a single metric can easily mask hidden defects such as extreme dispersion in model parameter estimation or failure of energy amplitude mapping, resulting in verification results lacking sufficient engineering persuasiveness and reliability. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for correcting conditional probabilistic learning rotor models for speeds not covered in the training. This method solves the problems in existing technologies, such as deep learning correction models heavily relying on training data, resulting in poor generalization ability under unseen speed conditions, only outputting deterministic point estimates that cannot quantify prediction uncertainty, difficulty in achieving rapid network transfer under small sample conditions, and the tendency of a single response evaluation index to mask hidden defects in parameter estimation.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for correcting rotor models using conditional probabilistic meta-learning for speeds not covered in the training includes the following steps: The task is constructed by building a nominal dynamic observation model of the rotor system, dividing the meta-training set and the target adaptation set based on the set speed conditions, and generating cross-speed meta-tasks. Probabilistic modeling is performed by normalizing the support parameters to be corrected, the multi-channel time series response, and the speed condition, and then performing feature extraction on the multi-channel time series response and the speed condition. Features of different dimensions are spliced ​​together to construct a conditional probability inverse mapping model for the support parameters to be corrected, and the diagonal Gaussian joint distribution in the normalized space is output as the conditional probability distribution. A two-layer optimization is performed, and a composite loss function is constructed using parameter error and negative log-likelihood. The conditional probability inverse mapping model is then subjected to offline two-layer meta-update and online target rotation speed adaptation. Propagation evaluation is performed by conducting parameter sampling and dynamic forward propagation on the conditional probability distribution output after online adaptation, and calculating quantitative evaluation indicators for the parameter space and response space.

[0008] Preferably, based on a set rotational speed condition, a meta-training set and a target adaptation set are divided to generate a cross-rotational speed meta-task, including: Extract the minimum and maximum values ​​of the meta-training speed set, and establish quantization judgment boundary rules for target speeds that are either interpolated or extrapolated and are not found. The quantization judgment boundary rule is as follows: when the target rotational speed is located within the extreme value range formed by the minimum and maximum values ​​and has not participated in training, it is determined that the interpolation does not show any rotational speed. When the target rotational speed is located outside the boundary of the extreme value range, it is determined that no rotational speed is observed during extrapolation. Based on the quantization judgment boundary rules, the multi-channel timing response and the speed condition are isolated from each other. The single training speed dataset is divided into a support set for task adaptation and a query set for adaptation performance evaluation, and the cross-speed meta-task containing the task support set and the task query set is generated.

[0009] Preferably, normalization is performed on the support parameters to be corrected, the multi-channel timing response, and the speed condition, including: A piecewise nonlinear normalization transformation is performed on the support parameters to be corrected. When the original parameters to be transformed belong to the stiffness parameter set, a logarithmic space mapping is used to smooth the distribution. When the original parameters to be transformed belong to the damping parameter set, a linear mapping is used to obtain the normalized parameters. Global minimum-maximum normalization processing is performed on the multi-channel timing response and the speed condition respectively to obtain the normalized multi-channel timing response and the normalized speed condition. Define an inverse transform operator corresponding to the piecewise nonlinear normalization transform, which is used to restore the predicted value to the real space.

[0010] Preferably, feature extraction is performed on the multi-channel timing response and the speed condition, and features of different dimensions are concatenated, including: A temporal response encoder containing a multi-scale parallel one-dimensional convolutional network is used to extract response features from the normalized multi-channel temporal response and output a temporal feature vector. A working condition encoder composed of a multilayer perceptron network containing hidden layers is used to extract working condition features from the normalized speed working condition and output a working condition feature vector. The time-domain feature vector and the operating condition feature vector are directly merged in the feature dimension using a channel-dimensional vector concatenation operator to generate a fused representation vector.

[0011] Preferably, a conditional probability inverse mapping model is constructed for the support parameters to be corrected, and the diagonal Gaussian joint distribution in the normalized space is output as the conditional probability distribution, including: Based on the fusion representation vector, construct a parallel subparameter independent probability head for multiple equivalent parameters to be corrected, and output the normalized parameter mean and the original logarithmic variance; Numerical stability truncation is performed on the original logarithmic variance, constraining it to the range of -10 to 2, to obtain the truncated logarithmic variance; Based on the conversion relationship between logarithmic variance and standard deviation, the truncated logarithmic variance is multiplied by one-half and then subjected to exponential mapping to obtain the standard deviation; Combining the normalized parameter mean and standard deviation of the independent probability head output, the output of the conditional probability inverse mapping model is defined as the diagonal Gaussian joint distribution in the normalized space as the conditional probability distribution.

[0012] Preferably, a composite loss function is constructed using parameter error and negative log-likelihood, including: Calculate the negative log-likelihood loss between the predicted distribution and the true sample distribution within the normalized feature space; The inverse transform operator is used to inversely transform the mean of the normalized parameters output by the network to the real space, introducing a value range of 10. -8 ~10 -6 The minimum bias constant between the parameters and the preset weighting coefficients used to balance the gradient contribution ratios of different types of parameters are used to calculate the parameter absolute relative error auxiliary loss. The overall composite loss function is constructed by combining the negative log-likelihood loss with the parameter absolute-relative error auxiliary loss.

[0013] Preferably, performing offline bi-level meta-update on the conditional probability inverse mapping model includes: During the task loop phase, the weights of all encoders are frozen, and gradient descent local parameter adaptation updates are performed on the subparameter independent probability head using only the support set data of a single rotation speed task. During the inter-task outer loop phase, the generalization performance of all sampling tasks on their respective query sets is aggregated to calculate the meta-target loss, and second-order gradient updates are performed on all global network weights, including the encoder.

[0014] Preferably, performing online target rotational speed adaptation on the conditional probability inverse mapping model includes: Obtain the speed operating condition data corresponding to the target speed that was not involved in the training, and extract the support set for the target operating condition task; The trained encoder weights are forcibly fixed, and the online adaptation update of the globally initialized subparameter independent probability head is performed using only the support set of the target working condition task, outputting the conditional probability distribution that fits the characteristics of the unseen rotational speed distribution.

[0015] Preferably, parameter sampling and dynamic forward propagation are performed on the conditional probability distribution output after online adaptation, including: Based on the reparameterization technique, multiple independent samples are extracted from the diagonal Gaussian joint distribution to generate a normalized parameter vector. After performing a forced constraint closed interval truncation operation on the normalized parameter vector with a numerical range of 0 to 1, the inverse transformation operator is used to map and restore it to the real support parameter space to form a parameter sampling set. The real parameter vector generated by the single sampling mapping is substituted into the nominal dynamic observation model to perform steady-state solution of the differential equation to obtain the simulated steady-state multi-channel time-domain response matrix. The arithmetic mean of the response set is calculated channel by channel and time step by time as the central predicted response. The empirical quantile operator is used to construct the response boundary envelope containing statistical probability.

[0016] Preferably, the quantitative evaluation indicators for computational parameter space and response space include: Extract the real labels corresponding to the samples in the task query set within the parameter space, and calculate the average relative error of parameters and the coverage rate of parameter marginal intervals for all samples in the task query set. Within the response space, a value of 10 is introduced. -8 The minimum zero constant is used to calculate the mean square error of the response, the time response guarantee criterion, and the relative average absolute error. The point state interval coverage and the average point state interval width are calculated based on the effectiveness of the response boundary envelope.

[0017] This invention provides a method for correcting rotor models using conditional probabilistic element learning for speeds not covered during training. It offers the following advantages: 1. This invention uses both the operating speed condition and the multi-channel time-series response as input conditions, and constructs a conditional probability inverse mapping model to output a diagonal Gaussian joint distribution in the normalized space, thus changing the traditional single deterministic point estimation and correction mode. This probabilistic modeling mechanism can fuse external operating conditions and internal vibration characteristics at a high level, characterizing the nonlinear mapping relationship between dynamic response and system parameters, thereby fully quantifying the prediction uncertainty in the parameter correction process when facing unseen operating speed conditions.

[0018] 2. This invention utilizes negative log-likelihood and parameter error to construct a composite loss function, and employs an optimization strategy combining offline bilayer updates and online few-shot adaptation. By freezing the feature encoder during the local update phase and updating only the parameter probability head, and performing second-order gradient differentiation during the global update phase, the network retains its ability to extract general features while avoiding severe overfitting under few-shot conditions, thus achieving rapid adaptive transfer of model weights to new working condition data that were not involved in the training.

[0019] 3. This invention establishes a quantitative evaluation mechanism encompassing dual-domain propagation assessment in both parameter space and response space. By performing Monte Carlo sampling and forward dynamic integration on the output probability distribution, multi-dimensional indicators such as relative parameter error, interval coverage, and time response guarantee criteria are calculated simultaneously. This method overcomes the limitations of relying solely on the mean square error of the response for verification, and can accurately identify hidden model defects such as amplitude mapping failure or extremely discrete distribution, providing a reliable comprehensive verification basis for the correction results of the rotor digital twin model. Attached Figure Description

[0020] Figure 1 This is a block diagram of the rotor model correction system for conditional probabilistic element learning of speeds not covered in the training according to the present invention. Figure 2 This is a flowchart of the method for correcting a rotor model based on a conditional probabilistic element learning method for speeds not covered in the training, according to the present invention. Figure 3A flowchart illustrating the method for constructing the execution task according to the present invention; Figure 4 This is a flowchart of the probability modeling method of the present invention; Figure 5 This is a flowchart of the method for performing two-layer optimization according to the present invention; Figure 6 This is a flowchart of the method for evaluating the propagation of the present invention. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Example 1: See attached document Figure 1 This invention provides a system for correcting conditional probabilistic element learning rotor models for speeds not covered in the training, comprising: The task construction module is used to build a nominal dynamic observation model of the rotor system, divide the meta-training set and the target adaptation set based on the set speed conditions, and generate cross-speed meta-tasks.

[0023] The probability modeling module receives multi-channel response data and speed signals, performs data normalization, feature extraction, and feature concatenation, constructs a conditional probability inverse mapping model for the support parameters, and outputs a diagonal Gaussian joint distribution in the normalized space as the conditional probability distribution.

[0024] The propagation evaluation module is used to perform Monte Carlo parameter sampling and dynamic forward propagation on the conditional probability distribution output after online adaptation, and to calculate quantitative evaluation indicators.

[0025] The two-layer optimization module is used to calculate the composite loss function and perform offline two-layer meta-updates and online target rotation speed adaptation for the probability modeling module.

[0026] Multi-channel response data and speed condition input task construction module. The task construction module performs isolation processing on the input data based on the speed quantization judgment boundary rules, and generates a speed meta-task containing a support set and a query set.

[0027] The task construction module transmits the speed meta-task to the probabilistic modeling module. The probabilistic modeling module extracts features from the input time-series response and speed conditions respectively. The probabilistic modeling module concatenates the extracted features and generates the conditional probability distribution of the support parameters through network mapping.

[0028] The two-layer optimization module operates on the network weights within the probabilistic modeling module. It constructs a composite loss function by combining parameter error and statistical likelihood. In the offline phase, the two-layer optimization module performs inner and outer loop second-order gradient updates on the probabilistic modeling module; in the online phase, it keeps the feature extraction network of the probabilistic modeling module fixed and only performs local updates on the parameter mapping network.

[0029] The probabilistic modeling module, having completed weight updates, transmits the conditional probability distribution under the target rotational speed to the propagation evaluation module. Based on the received distribution information, the propagation evaluation module performs multiple rounds of random sampling, substituting the sampled parameters into the nominal dynamics operator for forward computation. The propagation evaluation module then solves for the corresponding steady-state time-domain response and outputs the verification results in the parameter space and response space.

[0030] See attached document Figure 2 This invention provides a method for correcting a conditional probabilistic learning rotor model for speeds not covered in the training, comprising the following steps: S1, execute task construction, build a nominal dynamics observation model of the rotor system, divide the meta-training set and target adaptation set based on the set speed conditions, and generate cross-speed meta-tasks; S2. Perform probabilistic modeling, normalize the support parameters to be corrected, the multi-channel time series response and the speed condition respectively, and perform feature extraction on the multi-channel time series response and the speed condition. Concatenate features of different dimensions to construct a conditional probability inverse mapping model for the support parameters to be corrected, and output the diagonal Gaussian joint distribution in the normalized space as the conditional probability distribution. S3 performs two-layer optimization, constructs a composite loss function using parameter error and negative log-likelihood, and performs offline two-layer meta-update and online target rotation speed adaptation on the conditional probability inverse mapping model. S4. Perform propagation evaluation, perform parameter sampling and dynamic forward propagation on the conditional probability distribution output after online adaptation, and calculate the quantitative evaluation index of parameter space and response space.

[0031] During task construction, the multi-channel timing response and speed conditions are isolated according to the set speed quantization judgment boundary rules, and a speed meta-task containing a support set and a query set is generated.

[0032] In probabilistic modeling, normalization is performed on the support parameters to be corrected, the time-series response, and the speed condition, and features are extracted for the time-series response and the speed condition respectively. After feature extraction, the features are concatenated and merged, and then input into the network to generate the conditional probability distribution of the equivalent support parameters.

[0033] During the two-layer optimization process, the composite loss is determined by combining the parameter error of the layer with the likelihood distribution of the statistical layer. In the offline stage, second-order gradient updates, including inner and outer loops, are performed on the network weights. In the online stage, the weights of the feature extraction part are fixed, and the weights of the parameter mapping part are locally adapted and updated.

[0034] During propagation evaluation, the conditional probability distribution at the target rotational speed is obtained and Monte Carlo random sampling is performed. The sampled parameters are substituted into the forward nominal dynamic operator to calculate the steady-state time-domain response, yielding parameter verification results and response verification results.

[0035] See attached document Figure 3 In the process of digital twinning and model correction of rotor systems, due to the complex and variable operating conditions of actual equipment, it is often difficult to obtain complete labeled data across the entire speed range. Based on these technical challenges, the task construction process is completed by establishing a model and partitioning the data space, aiming to provide a structured boundary and data foundation for subsequent meta-learning. In this embodiment, the process specifically includes the following sub-steps: S11. Construct the nominal dynamic equations and observation model of the rotor system with multiple degrees of freedom. As a preferred approach, based on the finite element discretization principle, the continuous rotor structure is equivalent to a multi-degree-of-freedom system consisting of concentrated mass, elastic shaft segments, and supporting components. Based on d'Alembert's principle, its equations of motion are derived, and the dynamic equations of the rotating shaft subsystem are constructed: ; In the formula, Here is the mass matrix of the rotation axis; This is a gyroscope matrix, whose internal terms are related to the rotational speed. Explicit coupling; The damping matrix of the rotating shaft structure; Here is the stiffness matrix of the rotation axis; , , These are the generalized displacement vector of the axis of rotation and its first-order velocity and second-order acceleration vectors, respectively. Let be the external excitation vector of the rotating shaft. The above system matrix must be ensured to be a non-singular positive definite or semi-positive definite matrix to guarantee the well-posedness and numerical stability of the dynamic differential equations during the time-domain integration process.

[0036] Establish the dynamic equations of the rigid turntable: ; In the formula, The mass matrix is ​​the lumped mass matrix of the turntable; For the turntable gyroscope matrix; , These are the first-order velocity vector and the second-order acceleration vector of the generalized displacement of the turntable, respectively. This is an unbalanced excitation, the amplitude of which is synchronously proportional to the operating speed and frequency. This characterizes the synchronous excitation force caused by the eccentric mass of the turntable.

[0037] By combining the equations of the rotating shaft and the turntable, the overall rotor dynamics equations are generated: ; In the formula, The assembly quality matrix for the entire machine; Assemble the gyroscope matrix for the entire machine; Assemble the stiffness matrix for the entire machine; Here is the support damping matrix; Here is the support stiffness matrix; The vector of actual equivalent support parameters to be corrected; , , These are the generalized displacements of all degrees of freedom of the entire machine and their first-order velocities and second-order acceleration vectors, respectively. This represents the overall unbalanced excitation vector. Through this assembly equation, the local parameters to be corrected are organically embedded into the global dynamic transmission path.

[0038] Define the Rayleigh structure damping equation in matrix form: ; To characterize the energy dissipation caused by internal friction of the structure, based on the selected two-order target modal circular frequencies , and corresponding modal damping ratio , Calculate the damping coefficient and : ; ; In practical engineering calculations, to prevent the denominator of the formula from approaching zero and causing calculation overflow, the selected two modes must be constrained to have a frequency interval greater than a preset safety threshold, that is, to avoid selecting dense modes of the same order or with extremely similar frequencies.

[0039] Define the forward operator of the rotor steady-state response. Input support parameter vector With operating speed Output the steady-state unbalanced time-domain response of the entire machine at multiple measurement points. : ; Establish a unified observation model that includes both simulation and measured data: ; ; In the formula, For simulation response; This is the measured response; The measurement operator includes measurement point selection, timing extraction, and channel alignment operations. When processing multi-source heterogeneous data, it is necessary to combine interpolation resampling technology to align the simulation integration step size with the sampling frequency of the field sensors in order to eliminate clock drift errors between the domain and the digital domain. This refers to random noise from the sensor. This refers to the systematic experimental deviation composed of finite element discretization error, boundary simplification error, and excitation deviation.

[0040] For the implementation of the discretization process of the finite element model and the assembly of the overall matrix, those skilled in the art can use standard dynamic finite element programming. The method of constructing the element shape function and superimposing the stiffness and mass matrix is ​​a well-known technology in this field and will not be elaborated here.

[0041] S12 establishes quantitative boundary rules for determining operating conditions where speed interpolation and speed extrapolation are not observed. To quantitatively verify the generalization ability of the modified model on non-training distributed data, strict numerical range isolation is required for the operating conditions to be evaluated. Define the meta-training speed set. The subscript indicates the discrete rotational speed number within the set, and the minimum value of the set is extracted. and maximum value .

[0042] Determine the target rotation speed The condition for interpolation without visible rotational speed is: the target rotational speed is located within the extreme value range of the meta-training set and has not participated in training. The formula is expressed as: ; In the formula, This indicates the logical "AND"; It means "does not belong to".

[0043] Determine the target rotation speed The condition for extrapolating without finding the rotational speed is: the target rotational speed is located outside the boundary of the extreme value interval of the meta-training set. The formula is expressed as: ; In the formula, It represents the logical "OR".

[0044] The above interval division based on extreme values ​​aims to distinguish between two distinct vibration response evolution characteristics: interpolation smooth mapping and extrapolation nonlinear abrupt change, thereby enabling model reliability evaluation under multi-dimensional conditions.

[0045] S13, construct a cross-speed rotation meta-task containing a task support set and a task query set. Extract samples from single training speeds to construct a speed rotation dataset: ; In the formula, For the first Data sets at various rotational speeds; For sample index; This corresponds to the steady-state time-domain response; The corresponding support parameters form a feature-label pair; This represents the total sample size at that rotational speed.

[0046] Following the core principle of "task as the basic data unit" in the meta-learning paradigm, the single training rotation speed dataset is divided into a support set and a query set to generate a meta-training single task: ; In the formula, For a set of tasks; A support set consisting of a small number of labeled samples used for task adaptation; This is a query set consisting of samples that are not overlapping with the support set and are used for performance evaluation. For the support set, the sample size must be strictly controlled within a preset small sample threshold range to force the network model to learn a generalized representation mechanism across operating conditions, avoiding overfitting to a single operating condition.

[0047] For tasks where the target rotational speed is not known, construct a target operating condition with an identical structure: ; In the formula, For the target task; A small number of simulation support samples at the target rotational speed; This is a labeled query sample used for quantitative evaluation.

[0048] Based on the above data partitioning rules, the conditional probability distribution to be solved under the target working condition is established: ; In the formula, It is the probability density function; Let be the equivalent support parameter vector to be corrected. This represents the total number of parameters to be corrected. For the target speed The target multi-channel steady-state time-domain response matrix to be retrieved from the parameters to be executed. The number of measurement point channels, For time steps; The target rotational speed; A small set of labeled support for the target rotational speed task; It is a set of modeling assumptions that cover finite element model settings, parameter upper and lower bound constraints, and data preprocessing rules.

[0049] The calculation process of the conditional probability distribution is as follows: First, according to the meta-training set statistics... and Normalization is performed, and time-domain feature vectors and operating condition feature vectors are extracted separately using a time-response encoder and an operating condition encoder, respectively, and then concatenated to form a fused representation vector; then, using... After completing online adaptation, the parameter-independent probability headers output the first... mean of the normalized parameters and standard deviation Thus, in the normalized parameter space, the following is formed: ; in, It is the probability density function; This is the normalized parameter vector; The first in the normalized parameter vector Item parameters; Index of the parameter to be corrected. ; This represents the total number of parameters to be corrected. This is the normalized target multi-channel steady-state time-domain response matrix; The normalized target rotational speed; A small set of labeled support for the target rotational speed task; It is a set of modeling assumptions that cover finite element model settings, parameter upper and lower bound constraints, and data preprocessing rules; For the first operating condition at the target speed The predicted mean of the normalized parameter; For the first operating condition at the target speed The predicted standard deviation of the normalized parameter; Indicates to Multiply the marginal probability densities corresponding to the parameters to be corrected; This represents a normal distribution, specifically a one-dimensional normal distribution in this equation. Subsequent steps involve using a piecewise nonlinear inverse transform operator. Map the normalized parameter sample values ​​to the real parameter space.

[0050] In this embodiment, the meta-training set, validation set, and target rotation speed dataset are stored independently, and the normalized statistics are calculated separately by the meta-training set to prevent the distribution characteristics of the target operating conditions from being leaked into the training network in advance, thus ensuring the objectivity of the generalization validation process.

[0051] See attached document Figure 4After completing model construction and cross-condition data partitioning, establishing a parameter inverse mapping model is a crucial step in correcting uncertainties in the rotor system. In actual engineering, the numerical ranges of support stiffness and damping differ, and the dynamic response exhibits a nonlinear mapping relationship with system parameters. Directly performing deterministic regression can easily lead to gradient vanishing or numerical ill-conditioned problems during network training. Based on these engineering principles, the probabilistic modeling process aims to construct a conditional distribution mapping mechanism that integrates prior knowledge of rotational speed conditions. In this embodiment, the process specifically includes the following sub-steps: S21, perform piecewise nonlinear normalization and inverse transformation programming on the support parameters to be modified. To balance the influence of parameters of different orders of magnitude on the backpropagation gradient of the neural network and eliminate dimensional differences, the original parameters of the corresponding categories are forward normalized. Since the stiffness parameter often spans several orders of magnitude in the search space, a logarithmic space mapping is used to smooth its distribution; the damping parameter has a smaller span, so a linear mapping is used directly.

[0052] When the original parameters to be transformed belong to the set of stiffness parameters, the forward normalization formula is: ; When the original parameters to be transformed belong to the set of damping parameters, the forward normalization formula is: ; In the formula, These are the normalized parameters that are in the range of 0 to 1 after transformation; For the first Original parameters; and These are the lower and upper bounds for this parameter, respectively. As a preferred parameter setting method, it is necessary to ensure that the upper bound is strictly greater than the lower bound to prevent the denominator of the fractional calculation from being zero. At the same time, for the stiffness parameter, its lower bound must be constrained to be strictly greater than zero to ensure the mathematical validity of the logarithmic operation.

[0053] The inverse transformation operation that restores the normalized space to the parameters is defined as a specific mathematical operator. This operator is used to subsequently restore the normalized prediction values ​​output by the network to the true space. The specific inverse mapping logic is as follows: When the parameter to be restored belongs to the set of stiffness parameters: ; When the parameter to be restored belongs to the set of damping parameters: ; In the formula, The predicted parameters are restored using the inverse transform operator; This represents an exponential function with the natural constant e as its base. The piecewise inverse transforms described above, which employ logarithmic inverse mapping for stiffness parameters and linear inverse mapping for damping parameters, are collectively denoted as the piecewise nonlinear inverse transform operator. ,Right now ; in, This is the normalized parameter vector; This is the true parameter space prediction vector obtained after inverse transformation.

[0054] S22 employs a dual-dimensional speed-conditional input mechanism to perform feature extraction and feature fusion. The steady-state unbalanced response of the rotor system is jointly determined by the external excitation speed and internal system parameters. To address this causal relationship, speed is used as an explicit conditional input and fused with the response features at a high level. This aims to constrain the solution space of the inverse problem and improve the model's generalization ability under different operating conditions.

[0055] A multi-channel time-domain response matrix and a scalar operating speed, comprising multiple measurement point channels and multiple sampling points, are obtained. Global min-max normalization is performed on the extreme values ​​statistically derived from the meta-training set to obtain the normalized multi-channel time-series response and the normalized operating speed. As a specific implementation, the neural network includes an encoder structure to perform independent-dimensional data feature extraction. Execution response feature extraction: ; In the formula, These are time-domain feature vectors; It is a timing response encoder; This is the normalized multi-channel timing response; These are the learnable network weight parameters for the time-response encoder. Considering that time-domain vibration signals contain complex harmonics such as fundamental frequency and harmonics, as well as structural attenuation characteristics, the time-response encoder is constructed as a multi-scale parallel one-dimensional convolutional network. This network contains at least two parallel computational branches with different one-dimensional convolutional kernel sizes (preferably, three parallel branches with kernel sizes of 3, 7, and 15) to simultaneously extract high-frequency local mutations and low-frequency global evolution features. The output feature maps of the parallel branches are activated and converged by rectified linear units, and then subjected to temporal dimension reduction through a global average pooling layer, finally outputting a dimensionality-reduced time-domain feature vector. In this embodiment, the time-domain feature vector is set as a real-number vector with 20 elements; the choice of this dimension is an engineering empirical threshold set to balance information retention rate and computational load.

[0056] Extraction of operating speed characteristics: ; In the formula, This is the feature vector of the working condition; For operating condition encoders; The normalized operating speed condition; These are the learnable network weight parameters for the operating condition encoder. For scalar speed data, the operating condition encoder consists of a multilayer perceptron network containing hidden layers, i.e., stacked fully connected layers. Nonlinear activation functions are used between layers to capture the nonlinear system dynamic migration patterns caused by speed changes. The model ultimately outputs the extracted operating condition feature vector. In this embodiment, this operating condition feature vector is mapped to a real number vector containing 8 elements.

[0057] By using the splicing operation, features from different dimensions are fused into a unified space: ; In the formula, The fusion representation vector; It is a channel-dimensional vector concatenation operator used to directly merge time-domain feature vectors and operating condition feature vectors in the feature dimension to form a joint representation that includes vibration characteristics and operating conditions.

[0058] S23, construct the parameter-independent probability head and output the diagonal Gaussian joint distribution in the normalized space. To describe the uncertainty and break the coupling between different supporting parameters in the high-dimensional statistical representation, a multi-branch prediction network is constructed based on the above fused representation vector.

[0059] For a total of multiple equivalent parameters to be corrected, a parallel, subparameter-independent probability head is constructed to output the mean and variance features: ; In the formula, The model predicts the first The mean of each normalized parameter; This is the raw log-variance output directly from the network; In order to target the Independent fully connected prediction branches constructed from each parameter; The global weight set for the parameter-independent probability head consists of all The learnable weights of the prediction branch are constructed. The above operations enable the entire set of learnable parameters to form a complete forward computation graph.

[0060] To prevent the network from outputting extreme variance values ​​in the early stages of training, which could lead to numerical overflow or distribution degradation in the exponential mapping, a numerical stability truncation operation must be performed before exponential restoration. ; ; In the formula, This is the truncated logarithmic variance; This is the upper and lower bound truncation function; the lower bound is set to -10 to avoid the logarithmic variance after truncation being too small, causing the variance obtained by exponential conversion to approach zero excessively, which would lead to the denominator in the subsequent loss function calculation being too small; the upper bound is set to 2 to limit the logarithmic variance from being too large, which would cause numerical overflow or gradient explosion in the exponential calculation. To be based on the truncated logarithmic variance The converted standard deviation.

[0061] Combining the mean and standard deviation of the outputs of the independent probability heads (i.e., each independent prediction branch), the output of the conditional probability inverse mapping model is defined as a diagonal Gaussian joint distribution in the normalized space: ; In the formula, It is the probability density function; This is the normalized parameter vector; This is the normalized multi-channel time-domain response matrix; The normalized scalar operating speed; This represents the total number of equivalent parameters to be corrected. Index of the parameter to be corrected; Indicates to Multiply the marginal probability densities corresponding to the parameters to be corrected; Represents a normal distribution, in this formula Indicates the first The normalized parameters correspond to a one-dimensional normal distribution. Utilizing the diagonalized product assumption, it is assumed that the prediction errors of each supporting parameter are statistically approximately independent. This reduces the computational cost of inverting the high-dimensional covariance matrix and satisfies the basic requirement of independent correction among engineering parameters. This probabilistic modeling approach provides a complete mathematical foundation for subsequent uncertainty quantification and loss calculation during network training.

[0062] See attached document Figure 5 In conventional deep learning model training, a single-layer empirical risk minimization strategy is commonly used. However, when the model faces unseen speed conditions not included in the training, it often struggles to adapt to data distribution shifts. Based on these engineering challenges, the two-layer optimization process aims to achieve overfitting-resistant updates and rapid transfer of network weights by constructing evaluation criteria with both statistical and structural constraints, and utilizing a meta-learning mechanism. In this embodiment, the process specifically includes the following sub-steps: S31, a composite loss function is constructed using the negative log-likelihood loss in the normalized space and the parameter-weighted absolute / relative auxiliary loss in the physical space. For the Gaussian probability distribution output by the model, to narrow the statistical distance between the predicted distribution and the true sample distribution, the negative log-likelihood loss is calculated in the normalized feature space: ; In the formula, The loss is negative log-likelihood. This represents the total number of equivalent parameters to be corrected. For the first label in the sample The true normalized values ​​of each parameter are derived from the real sample set divided during the task construction phase. The model predicts the first The mean of each normalized parameter; The model predicts the first The standard deviation of the variance is a parameter. The preceding numerical truncation operation enforces a lower bound on the variance, ensuring that the denominator in this calculation is strictly greater than zero, thus avoiding the division-by-zero singularity error during the calculation process.

[0063] In the early stages of network training, relying solely on statistical loss often leads to slow convergence. To accelerate network convergence and introduce scale constraints from the real space, the mean of the network output is inversely transformed to the physical space, and the absolute relative error of the parameters is calculated as an auxiliary loss. ; In the formula, To mitigate losses; For the first The preset weighting coefficients of the term parameters are used to balance the gradient contribution ratio of different types of support parameters in the overall loss; For the first label in the sample The actual values ​​of each parameter; The predicted parameters are obtained by restoring the mean using the inverse transform operator; This is the minimum bias constant. As a preferred approach, the value range of this minimum bias constant is set to 10. -6 ~10 -8 The constant is introduced to prevent numerical explosion caused by an extremely small denominator when the true value of certain damping parameters approaches zero; at the same time, setting this order of magnitude ensures that it will not cause numerical interference to normal relative error calculations. Choosing relative error instead of absolute error can eliminate the problem of skewed loss calculations caused by the huge difference in magnitude between stiffness and damping.

[0064] Combining the two loss metrics mentioned above, we construct the overall composite loss function: ; In the formula, It is a composite loss function; The balancing weight coefficient is set differently in different optimization stages in this embodiment: it is 0.1 in the outer loop stage of meta-training and 0.5 in the inner loop and online target adaptation stages. The basis for determining this stage weight is that the auxiliary loss mainly provides gradient guidance during the local adaptation in the inner loop, but its weight should not be too large during the global update in the outer loop, so as not to disrupt the distribution fitting process dominated by the log-likelihood loss.

[0065] S32 performs offline two-layer second-order meta-updates based on a multi-task set. This process is based on a model-independent meta-learning framework, dividing the training process into an intra-task loop and an inter-task outer loop, aiming to find a set of globally initialized network weights with high generalization sensitivity.

[0066] In the inner loop phase, a specific rotation speed task is extracted from the meta-training task set, and local parameter adaptation is performed on the support set for that task. To prevent severe overfitting on small sample support sets and to preserve the encoder's ability to extract generalized features, all encoder weights are frozen in the inner loop computation, and gradient descent updates are performed only on the subparameter-independent probability heads. ; In the formula, For the first The task-specific sub-parameter independent probability head weights are obtained after the support set of each rotational speed task completes the inner loop update; This is the global weight set of the aforementioned parameter-independent probability heads, and is used as the initial weight when the current speed task executes the inner loop adaptation. The learning rate for the inner loop is set to a range of 0.001 to 0.01, which is used to control the step size of the single-step local adaptation. This indicates that the gradient of the partial derivative is taken only with respect to the independent probability head weights of the subparameters; For the current speed task's support set; For timing response encoders Weight parameters; For working condition encoders The weight parameters; during the task's inner loop phase, and All operations remain frozen. To adapt to local tasks and avoid severe overfitting, the number of local update steps in the inner loop is preferably set to ten. This asymmetric local update mechanism constitutes the core lightweight architecture of this embodiment, reducing the memory footprint of the inner loop computation graph.

[0067] In the outer loop phase, the generalization performance of all sampling tasks on their respective query sets is summarized, the meta-objective loss is calculated, and second-order gradient updates are performed on all global network weights, including the encoder. ; In the formula, It is a global set of network weights that includes the parameter header and all encoders; The outer loop learning rate is used to control the outer loop update step size of all global network weights, and its value is set according to the specific meta-training task. The first one constructed in S13 above The query set for the individual training rotation speed task, i.e., used for performance evaluation and corresponding support set. A non-overlapping set of labeled samples; This represents the summation of losses across all sampling tasks within the current batch; Represents the set of all global network weights Calculating the gradient. The outer loop gradient calculation involves further differentiation of the inner loop gradient, constituting a second-order optimization process that forces the network to learn how to better initialize weights to adapt to future new task conditions.

[0068] S33 performs online target adaptation with a small number of samples for targets whose rotational speeds are not yet known. After offline meta-training converges, the global network weights possess the potential for rapid transfer to new operating conditions.

[0069] Obtain the target rotational speed data corresponding to the operating conditions that were not included in the training, and extract the support set for the target operating condition task. As a preferred engineering implementation parameter, to balance the accuracy of recognition with few samples and the computational cost of finite element simulation, the sample size of the support set for the target rotational speed task is preferably set to 50 samples. Based on the asymmetric local update logic of the inner loop, the weights of the already trained encoder are forcibly fixed, and only a small amount of support set data under the target rotational speed is used to perform a small number of iterative online adaptation updates on the globally initialized subparameter independent probability head: ; In the formula, Independent probability header weights for target sub-parameters after online adaptation is completed; The learning rate is adapted online for the target rotational speed to control the local update step size of the subparameter-independent probability head on the target rotational speed task; This indicates that the gradient is calculated for the independent probability head weights of the subparameters; This serves as the support set for the target rotational speed task. As a preferred approach, the number of iterations for online adaptation is strictly limited to between 5 and 15 steps (preferably 10 steps). This limitation is based on multi-dimensional considerations: too few steps make it difficult to fit the characteristics of the new operating conditions, while too many steps can lead to catastrophic forgetting and overfitting on extremely small samples. After online adaptation is completed, the test data under the target operating conditions is input into the network. Combined with a fixed encoder and an updated independent probability head for the target sub-parameters, a conditional probability distribution that fits the characteristics of the unseen rotational speed distribution can be output, thereby completing the generalization correction of the model under unknown rotational speeds.

[0070] See attached document Figure 6 After completing the online target adaptation of the model weights, in order to fully verify the reliability of the modified model and quantify the prediction uncertainty, it is necessary to map the statistical distribution back to the actual verification space. Due to the nonlinear transmission characteristics of the rotor dynamics system, point estimation in the parameter space alone cannot characterize the ill-conditioned nature of the response-parameter inverse problem and the prediction dispersion caused by the parameter compensation effect. Based on the technical objective of establishing a hierarchical verification logic for the propagation from the parameter space distribution to the dynamic response space, the process of performing propagation evaluation aims to establish a dual-domain quantitative assessment mechanism, constructing a high-confidence vibration response statistical envelope through statistical sampling. In this embodiment, the process specifically includes the following sub-steps: S41, based on the conditional probability distribution (i.e., diagonal Gaussian joint distribution) output after online adaptation, normalized parameters are randomly sampled and mapped to space. After obtaining the mean vector and standard deviation vector of the normalized parameters output by the network under the target speed condition, multiple independent samples are extracted from the diagonal Gaussian joint distribution based on the reparameterization technique. This sampling method decouples deterministic prediction from pure random noise, and its corresponding mathematical operation logic is as follows: ; ; In the formula, For the first The normalized parameter vector generated by the next sampling; This is the normalized parameter mean vector output by the model; This is the standard deviation vector of the parameters output by the model; The element-wise multiplication operator between vectors; This is a random noise vector extracted from a standard multivariate normal distribution; The sign of the aforementioned normal distribution is represented in this formula. Represents a P-dimensional standard multivariate normal distribution; It is a P-dimensional vector with all zero mean; Let P be the unit covariance matrix. As a preferred engineering implementation parameter, to balance the convergence of the Monte Carlo statistical distribution with the computational overhead of subsequent calls to high-fidelity finite element models, the total number of Monte Carlo samplings is fixed. Set to 200 times.

[0071] Since the theoretical range of the normal distribution extends infinitely outward, directly generated sampled values ​​have a probability of exceeding the limit. To prevent the subsequent inverse transformation process from generating meaningless negative stiffness or negative damping that could cause the integral of the differential equation to diverge, the random sampled value is forcibly constrained within a closed interval by performing a truncation operation: ; In the formula, For the first In the nth sampling vector One normalized parameter element; This is a numeric truncation function that forces any element less than 0 to be set to 0 and any element greater than 1 to be set to 1.

[0072] After completing the safety constraints, the piecewise nonlinear inverse transform operator defined in S21 is used. , for the Subnormalized parameter sampling vector Perform inverse transform: ; in, The stiffness parameter components are mapped using the logarithmic inverse mapping described in S21, and the damping parameter components are mapped using the linear inverse mapping described in S21. For the first The true support parameter vector is obtained after the inverse transformation of the sampled data. The above inverse transformation is performed on all normalized parameter sample vectors to form the true support parameter sample set.

[0073] S42, perform dynamic forward propagation on the parameters to calculate the steady-state time-domain response and generate the point-state response quantile interval. Substitute the true parameter vector generated by the single-sample mapping into the aforementioned nominal dynamic observation model to perform steady-state solution of the differential equation and measurement extraction: ; In the formula, For the first The simulation steady-state multi-channel time-domain response matrix corresponding to the next sampling; For the first The parameter vector is generated and mapped back by the next sampling; Verify the rotational speed for the target; The forward operator for the rotor steady-state response, defined in S11, is used to complete the assembly and steady-state solution of the rotor dynamics model. The measurement operator defined in S11 is used to perform measurement point filtering, timing extraction, and channel alignment operations.

[0074] After obtaining the time-domain responses of all random samples, in order to eliminate discrete oscillations and extract central tendency, the arithmetic mean of the response set is calculated channel by channel and time step by time, and used as the central predicted response: ; In the formula, For the first The measuring point channel at the first... Mean of the center predicted response at each time step; For the first The elements at the corresponding positions within the simulation response matrix; For measurement point channel index; For time step index; To maintain a fixed total number of samples, and to filter out outlier waveform distortions caused by extreme parameter combinations, an empirical quantile operator is further employed to construct a response boundary envelope containing 95% statistical probability. ; ; In the formula, and These are the lower and upper bounds of the statistical response interval, respectively. To find the cumulative probability is The empirical quantile operator, using symmetric quantile cutoffs of 2.5% and 97.5%, aims to provide a robust and reliable structural vibration reference frequency band.

[0075] S43, calculate the quantitative evaluation indicators for the parameter space and response space and perform a comprehensive judgment. To avoid biased misjudgments caused by a single indicator, a two-level verification system covering multiple sample sets is established. Within the parameter space, extract the true labels corresponding to the query set samples, and calculate the average relative error of the parameters and the parameter marginal interval coverage rate covering all query samples: ; ; In the formula, The average relative error of the parameters; The parameter is the marginal interval coverage rate; To query the total number of samples; This represents the total number of parameters to be corrected. The model predicts the restoration of the first In the nth sample The estimated center point value of the term parameter; This serves as the actual reference label for the corresponding parameter; To minimize the division-to-zero constant, it is set to 10. -8 Specifically, it blocks the fractional divergence induced when the actual damping parameter approaches zero; This is an indicator function (it takes the value 1 if the condition is met, otherwise it takes the value 0). and These are the upper and lower bounds of the 2.5% and 97.5% quantiles, respectively, calculated using the Monte Carlo sampling set in the parameter space. These metrics quantify the absolute accuracy and probabilistic tolerance of the model in extracting underlying mechanism parameters.

[0076] Within the response propagation space, the waveform fitting shape and prediction uncertainty range are simultaneously evaluated. To cross-validate the energy deviation, phase shift, and relative amplitude difference of the response, the mean square error of the response, the time response guarantee criterion, and the relative mean absolute error are calculated sequentially. ; ; ; In the formula, For the response mean square error; This serves as a time response guarantee criterion for evaluating the consistency between the predicted response and the reference true response waveform. The relative mean absolute error; The total number of samples in the task query set; This represents the total number of measurement point channels. The total number of time steps for each channel; To query the sample index; For measurement point channel index; For time step index; For the first The query sample in the 1st... The first measuring point channel, the first The center predicts the response at each time step; For its corresponding reference truth response; The aforementioned minimum divide-by-zero constant is taken to be 10. -8 .exist The query sample index is omitted in the formula. hour, and These represent the current query sample to be evaluated at the [number]th [position]. The first measuring point channel, the first The center predicted response and reference true response at each time step. Specifically, in calculating... To avoid the denominator approaching zero due to a lack of response at a specific steady-state node, the aforementioned minimal divide-by-zero constant is introduced into the inner term of the square root. Numerical stabilization processing was performed.

[0077] To assess the effectiveness of the response boundary envelope, calculate the point-state interval coverage and the average point-state interval width: ; ; In the formula, This is the point-state interval coverage, used to evaluate the proportion of the reference true value response falling within the response boundary envelope; This represents the average point interval width; The total number of samples in the task query set; This represents the total number of measurement point channels. The total number of time steps for each channel; To query the sample index, ; For the measurement point channel index, ; For time step index, ; This is an indicator function; it takes the value 1 if the condition inside the parentheses is true, and 0 otherwise. For the first The query sample in the 1st... The first measuring point channel, the first The reference truth response at each time step; and The first The query sample in the 1st... The first measuring point channel, the first The lower and upper bounds of the response boundary envelope corresponding to each time step are obtained from the aforementioned 2.5% and 97.5% empirical quantiles, respectively.

[0078] After acquiring evaluation data across all dimensions, the system rejects the traditional strategy of judging model performance solely based on a single mean square error. This embodiment aims to accurately identify two types of hidden model failure modes by cross-comparing the aforementioned dual-domain indicators: when the point-state interval coverage... Extremely high but average point state interval width When the range is abnormally broad, it indicates that the network has degraded and outputs an extremely discrete distribution that offers no guidance; when the time response guarantee criterion... Approaching 100% but relative to the mean absolute error When deviating from the baseline, the serious defect of the model successfully capturing phase patterns but failing in energy amplitude mapping is exposed. Furthermore, if a general under-coverage of the response interval occurs when processing measured data containing model validation biases, the root cause is usually that the diagonal Gaussian approximation used in the pre-modeling stage cannot fully characterize the coupling compensation relationship between multiple support parameters. Only when the prediction ensures response coverage under strict control of the interval width and simultaneously reduces the relative error in the parameter space can the conditional probabilistic element learning generalization correction task for the under-covered speed condition be considered successfully validated.

[0079] Example 2: Based on the above system and method, the network structure parameter settings are modified: In this embodiment, the temporal response encoder is constructed as a multi-scale parallel one-dimensional convolutional network. The specific structural parameters are as follows: Conv1D convolution is used for parallel branches, with kernel sizes of 3, 7, and 15, corresponding stride of 2, padding of 1, 3, and 7, and 24 feature channels for each branch. The multi-scale aggregation layer uses a Conv1D with a kernel size of 5, a stride of 2, a padding of 2, and 64 output channels. The depth coding layer uses a Conv1D kernel with a size of 3, a stride of 2, padding of 1, and outputs 128 channels. Finally, the data is compressed to a length of 64 using adaptive average pooling and mapped to 20-dimensional response features using a fully connected layer without activation functions. The speed encoder uses a single fully connected layer and outputs 8-dimensional features. Dropout layers are not used throughout the network.

[0080] During the offline two-layer second-order training phase of the model, eight cross-rotation training tasks are randomly selected for each meta-batch for synchronous computation. For the extracted single rotation speed task, the size of its meta-training support set sample is strictly set to 10, and the size of the query set sample is set to 25.

[0081] In the inner loop phase, stochastic gradient descent (SGD) is used to perform local updates. The number of inner loop update steps is set to 10, and the inner loop learning rate is set to 0.001. In the outer loop phase, the Adam optimizer is used to perform second-order updates on the entire network, including the encoder, and the outer loop learning rate is set to 0.003. In the target speed adaptation phase, the adaptation iteration steps are set to 10 steps, and the target adaptation learning rate is set to 0.003.

[0082] The total number of training iterations for the APU rotor case is set to 72,000 episodes (each 240 episodes is defined as 1 epoch); the single-disc test rotor case is set to 150 epochs.

[0083] Example 3: Dual-validation carrier case configuration: In specific engineering applications, this invention is adaptable to various rotor scenarios: Scenario 1: APU three-disc aerospace rotor (pure simulation without model - experimental deviation).

[0084] This scenario selects four displacement measurement points, with the unbalanced excitation set to 500 g·mm. 1000 simulation samples are generated for each rotational speed condition, with 800 sampling points extracted per channel and a sampling interval of 0.001 s. The parameters to be corrected are four support stiffness parameters, with their auxiliary loss weights configured as follows: The training speed was set to 3500 to 3800 rpm and 4100 to 4500 rpm (in 100 rpm intervals); the verification speed was set to 3900 rpm; the target speed was tested to verify extrapolation at low speed (3400 rpm), interpolation at 4000 rpm, and extrapolation at high speed (4600 rpm).

[0085] Scenario 2: Single-disc test rotor (including measured correction of model-test deviation).

[0086] This scenario features four eddy current displacement measurement points, with a 23g unbalanced mass added to the disk. The sampling frequency is set to 1000Hz, the sampling duration to 0.8s, and each training rotational speed corresponds to 1000 sets of simulation samples. The training rotational speeds are set to 12 discrete conditions: 1550, 1600, 1650, 1750, 1800, 1850, 1950, 2000, 2050, 2100, 2150, and 2200 rpm. The verification rotational speed is set to 1700 rpm. The target rotational speed was tested and verified for extrapolation at low speed (1500 rpm), interpolation (1900 rpm), and extrapolation at high speed (2300 rpm). This scenario simultaneously corrects eight support stiffness and damping parameters, and the bearing damping search interval is set to 1×10⁻⁶. 3 Up to 5×10 4 N·s / m, stiffness search range is 1×10 6 Up to 1×10 7 N / m is used to provide boundaries for the normalized mapping. The auxiliary loss weights for the damping term are set alternately to 0.8 and 0.5, while the auxiliary loss weights for the stiffness term are uniformly set to 0.2, i.e., the weight vector... The vector corresponds sequentially to the y-direction damping of the left support, the z-direction damping of the left support, the y-direction damping of the right support, the z-direction damping of the right support, the y-direction stiffness of the left support, the z-direction stiffness of the left support, the y-direction stiffness of the right support, and the z-direction stiffness of the right support.

[0087] Example 4: Verification based on comparison between ablation experiments and deterministic baselines: To quantitatively verify the technical gains of each core module of this invention, multiple degradation ablation and baseline comparison models were established. First, a deterministic finite element iterative correction baseline comparison model was established. This baseline model adopts a conventional single-layer empirical risk minimization strategy, and its deterministic objective loss function is defined as: ; In the formula, To iteratively correct the target loss function of the baseline model for deterministic finite element methods; This represents the summation over all measurement points, channels, and time steps, where... For the measurement point channel index, For time step index; This represents the summation of all stiffness parameters to be optimized, where For stiffness parameter index; the first term on the right side of the equation is the mean square error of the response fitting, and the second term on the right side of the equation is the stiffness parameter relative regularization term set to prevent parameter out-of-bounds; For the current iteration process The first measuring point channel, the first Simulated steady-state response at each time step; This is the steady-state response of the corresponding reference target; For the first Regularization penalty weight coefficient for the stiffness parameter; For the first The current estimated value of the term stiffness parameter during the iterative optimization process; For the first The prior nominal stiffness corresponding to the stiffness parameter. Online iterative solution is performed using the Adam optimizer (learning rate 0.05, iteration steps 120, parameter constraints between 0.6 and 1.4 times the nominal stiffness).

[0088] Meanwhile, to verify the effectiveness of the modular design, network ablation models were designed, including: a "no speed input" model that removes the speed condition encoder, and a "no parameter auxiliary loss" model that removes the parameter-weighted absolute and relative errors in the composite loss.

[0089] Multiple ablation and comparative experiments show that the aforementioned deterministic objective function can only output a single parameter point estimate, which cannot characterize the ill-conditioned and discrete nature of the response-parameter inverse problem. In contrast, this invention utilizes a cross-rotational speed conditional probabilistic element learning framework, which not only reduces the average relative error of the parameters under the boundary extrapolation speed compared to the baseline model, but also calculates the parameter and response margin interval with 95% confidence by outputting a diagonal Gaussian conditional distribution, thus making up for the technical shortcoming of traditional deterministic finite element correction in that it cannot quantify the uncertainty of prediction.

[0090] Practical engineering tests demonstrate that, for measured data containing actual test noise and model bias, this method achieves conditional probability distribution mapping under extrapolated speeds, relying only on 50 simulated samples from the target support set. The occasional widespread undercoverage phenomenon in the response interval of this measured operating condition is clearly attributed to the inability of the diagonal Gaussian approximation to fully characterize the coupling compensation relationship between multiple support parameters. This quantitative conclusion further provides a credibility verification criterion for the finite element correction of complex nonlinear rotors.

Claims

1. A method for correcting a rotor model using conditional probabilistic element learning for speeds not covered in the training, characterized in that, Includes the following steps: The task is constructed by building a nominal dynamic observation model of the rotor system, dividing the meta-training set and the target adaptation set based on the set speed conditions, and generating cross-speed meta-tasks. Probabilistic modeling is performed by normalizing the support parameters to be corrected, the multi-channel time series response, and the speed condition, and then performing feature extraction on the multi-channel time series response and the speed condition. Features of different dimensions are spliced ​​together to construct a conditional probability inverse mapping model for the support parameters to be corrected, and the diagonal Gaussian joint distribution in the normalized space is output as the conditional probability distribution. A two-layer optimization is performed, and a composite loss function is constructed using parameter error and negative log-likelihood. The conditional probability inverse mapping model is then subjected to offline two-layer meta-update and online target rotation speed adaptation. Propagation evaluation is performed by conducting parameter sampling and dynamic forward propagation on the conditional probability distribution output after online adaptation, and calculating quantitative evaluation indicators for the parameter space and response space.

2. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 1, is characterized in that... Based on a defined rotational speed condition, a meta-training set and a target adaptation set are divided, generating cross-rotational speed meta-tasks, including: Extract the minimum and maximum values ​​of the meta-training speed set, and establish quantization judgment boundary rules for target speeds that are either interpolated or extrapolated and are not found. The quantization judgment boundary rule is as follows: when the target rotational speed is located within the extreme value range formed by the minimum and maximum values ​​and has not participated in training, it is determined that the interpolation does not show any rotational speed. When the target rotational speed is located outside the boundary of the extreme value range, it is determined that no rotational speed is observed during extrapolation. Based on the quantization judgment boundary rules, the multi-channel timing response and the speed condition are isolated from each other. The single training speed dataset is divided into a support set for task adaptation and a query set for adaptation performance evaluation, and the cross-speed meta-task containing the task support set and the task query set is generated.

3. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 2, is characterized in that... Normalization is performed on the corrected support parameters, multi-channel timing response, and speed conditions, including: A piecewise nonlinear normalization transformation is performed on the support parameters to be corrected. When the original parameters to be transformed belong to the stiffness parameter set, a logarithmic space mapping is used to smooth the distribution. When the original parameters to be transformed belong to the damping parameter set, a linear mapping is used to obtain the normalized parameters. Global minimum-maximum normalization processing is performed on the multi-channel timing response and the speed condition respectively to obtain the normalized multi-channel timing response and the normalized speed condition. Define an inverse transform operator corresponding to the piecewise nonlinear normalization transform, which is used to restore the predicted value to the real space.

4. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 3, is characterized in that... Feature extraction is performed on the multi-channel timing response and the speed condition, and features of different dimensions are concatenated, including: A temporal response encoder containing a multi-scale parallel one-dimensional convolutional network is used to extract response features from the normalized multi-channel temporal response and output a temporal feature vector. A working condition encoder composed of a multilayer perceptron network containing hidden layers is used to extract working condition features from the normalized speed working condition and output a working condition feature vector. The time-domain feature vector and the operating condition feature vector are directly merged in the feature dimension using a channel-dimensional vector concatenation operator to generate a fused representation vector.

5. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 4, is characterized in that... Construct a conditional probability inverse mapping model for the support parameters to be corrected, and output a diagonal Gaussian joint distribution in the normalized space as the conditional probability distribution, including: Based on the fusion representation vector, construct a parallel subparameter independent probability head for multiple equivalent parameters to be corrected, and output the normalized parameter mean and the original logarithmic variance; Numerical stability truncation is performed on the original logarithmic variance, constraining it to the range of -10 to 2, to obtain the truncated logarithmic variance; Based on the conversion relationship between logarithmic variance and standard deviation, the truncated logarithmic variance is multiplied by one-half and then subjected to exponential mapping to obtain the standard deviation; Combining the normalized parameter mean and standard deviation of the independent probability head output, the output of the conditional probability inverse mapping model is defined as the diagonal Gaussian joint distribution in the normalized space as the conditional probability distribution.

6. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 5, is characterized in that... A composite loss function is constructed using parameter error and negative log-likelihood, including: Calculate the negative log-likelihood loss between the predicted distribution and the true sample distribution within the normalized feature space; The inverse transform operator is used to inversely transform the mean of the normalized parameters output by the network to the real space, introducing a value range of 10. -8 ~10 -6 The minimum bias constant between the parameters and the preset weighting coefficients used to balance the gradient contribution ratios of different types of parameters are used to calculate the parameter absolute relative error auxiliary loss. The overall composite loss function is constructed by combining the negative log-likelihood loss with the parameter absolute-relative error auxiliary loss.

7. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 6, is characterized in that... Performing offline bi-level meta-updates on the conditional probability inverse mapping model includes: During the task loop phase, the weights of all encoders are frozen, and gradient descent local parameter adaptation updates are performed on the subparameter independent probability head using only the support set data of a single rotation speed task. During the inter-task outer loop phase, the generalization performance of all sampling tasks on their respective query sets is aggregated to calculate the meta-target loss, and second-order gradient updates are performed on all global network weights, including the encoder.

8. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 7, is characterized in that... Performing online target rotational speed adaptation on the conditional probability inverse mapping model includes: Obtain the speed operating condition data corresponding to the target speed that was not involved in the training, and extract the support set for the target operating condition task; The trained encoder weights are forcibly fixed, and the online adaptation update of the globally initialized subparameter independent probability head is performed using only the support set of the target working condition task, outputting the conditional probability distribution that fits the characteristics of the unseen rotational speed distribution.

9. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 8, is characterized in that... Perform parameter sampling and dynamic forward propagation on the conditional probability distribution output after online adaptation, including: Based on the reparameterization technique, multiple independent samples are extracted from the diagonal Gaussian joint distribution to generate a normalized parameter vector. After performing a forced constraint closed interval truncation operation on the normalized parameter vector with a numerical range of 0 to 1, the inverse transformation operator is used to map and restore it to the real support parameter space to form a parameter sampling set. The real parameter vector generated by the single sampling mapping is substituted into the nominal dynamic observation model to perform steady-state solution of the differential equation to obtain the simulated steady-state multi-channel time-domain response matrix. The arithmetic mean of the response set is calculated channel by channel and time step by time as the central predicted response. The empirical quantile operator is used to construct the response boundary envelope containing statistical probability.

10. The method for correcting a conditional probabilistic element learning rotor model for speeds not covered in the training, as described in claim 9, is characterized in that... Quantitative evaluation metrics for computational parameter space and response space include: Extract the real labels corresponding to the samples in the task query set within the parameter space, and calculate the average relative error of parameters and the coverage rate of parameter marginal intervals for all samples in the task query set. Within the response space, a value of 10 is introduced. -8 The minimum zero constant is used to calculate the mean square error of the response, the time response guarantee criterion, and the relative average absolute error. The point state interval coverage and the average point state interval width are calculated based on the effectiveness of the response boundary envelope.

Images