Inverse pinning method based on multi-domain response fusion

Abstract

The application relates to the technical field of dynamic model correction, and discloses a nonlinear model correction method based on a multi-domain response fusion reverse PINN, which comprises the following steps: reading initial model data to establish a nonlinear dynamic motion equation and convert the nonlinear dynamic motion equation into a first-order state equation, and outputting a model prediction state response; dividing measured response data to obtain a response window, and aggregating to generate global multi-domain features; a reverse parameter identification network receives the global multi-domain features and outputs unconstrained variables, performs an asymmetric bounded mapping, and is converted into to-be-corrected variables; a model prediction state response is compared with a measured response to generate a cross-window robust loss, a regularization term is combined to form a model correction total loss, a numerical disturbance gradient is extracted, network parameters are updated, and a convergence parameter is extracted. Through the construction of a multi-domain feature mapping and a bounded mapping iterative architecture, a reverse propagation calculation path is established across a non-differentiable dynamic operator, time offset interference is weakened, and closed-loop correction of nonlinear model parameters is completed.

Description

Technical Field

[0001] This invention relates to the field of dynamic model correction technology, specifically to a method for correcting inverse PINN nonlinear models based on multi-domain response fusion. Background Technology

[0002] As engineering equipment develops towards higher speeds and lighter weights, its dynamic behavior becomes increasingly complex. The widespread nonlinear factors in engineering equipment structures alter the overall stiffness and energy dissipation mechanisms of the dynamic system. Limited by idealized nonlinear model settings, manufacturing and assembly errors, and the influence of service condition evolution, initial dynamic simulation models based on nominal parameters often fail to accurately reflect the nonlinear characteristics of actual structures. Integrating experimental measurement data to correct the parameters of nonlinear dynamic models is a fundamental approach to improving the reliability and cross-condition predictive capabilities of nonlinear simulation models.

[0003] Existing nonlinear model correction schemes typically execute feature extraction, parameter optimization, and dynamic forward modeling independently in separate stages, relying solely on a single time-domain response data to construct the error target. Under a single time-domain response constraint, different combinations of model parameters will produce similar local time history waveforms, exacerbating the numerical coupling between the parameters to be corrected and leading to ill-conditioned or non-unique solutions in the inverse problem solution process. Simultaneously, the actual measurement process is accompanied by environmental noise interference, unmodeled dynamic biases, and differences in structural transmission paths, directly disrupting the point-to-point correspondence between the measured response data and the theoretical simulation response in the time dimension.

[0004] Some model correction methods based on information neural networks still primarily constrain the original time-domain response, failing to fully extract complementary information from the frequency domain distribution, time-frequency evolution, and statistical feature space. Furthermore, existing model correction networks based on gradient backpropagation require the dynamic equation solver to possess fully differentiable properties, making it difficult to directly handle engineering nonlinear dynamics solutions encompassing gap nonlinearity, contact state switching, and logical judgment conditions. This limits the application scope of information neural networks in the field of complex nonlinear model correction. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for correcting inverse PINN nonlinear models based on multi-domain response fusion. This method solves the problems of parameter coupling caused by insufficient information in a single response domain, and the difficulty in establishing a point-by-point correspondence between measured response data and theoretical response models in the time dimension.

[0006] To achieve the above objectives, this invention provides a method for correcting the inverse PINN nonlinear model based on multi-domain response fusion, comprising the following steps: The tensor computation unit reads the initial model data, establishes the nonlinear dynamic equations of motion, and transforms them into first-order state equations. The independent dynamic solver outputs the model's predicted state response. The computer equipment divides the measured response data to obtain a response window, and the tensor computation unit generates a global multi-domain fusion feature. The inverse parameter identification network receives the global multi-domain fusion feature output of unconstrained variables, and the tensor computation unit performs an asymmetric bounded mapping on the unconstrained variables to transform them into model parameters to be corrected. Tensor computation units compare the model's predicted state response with the measured response data to construct local loss, aggregate to generate cross-window robust loss, combine with parameter regularization terms to form the model corrected total loss and extract numerical perturbation gradient; The computer equipment updates the network parameters based on numerical perturbation gradients until the model corrects the total loss to reach the preset convergence criterion. The tensor computation unit extracts the convergence correction parameters to generate a highly reliable digital twin model.

[0007] This invention performs data throughput and parallel matrix operations in the underlying computing environment, establishes a multi-domain feature mapping mechanism based on the inverse parameter identification network, and completes the numerical closed-loop correction task for nonlinear model parameters under the conditions of response error caused by measurement noise, environmental disturbance, artificial noise interference and unmodeled dynamics through a closed-loop iterative architecture of cross-window robust loss and numerical perturbation gradient.

[0008] Preferably, the tensor computation unit reads the initial model data, establishes the nonlinear dynamic equations of motion, and transforms them into first-order state equations in the following specific way: The tensor computation unit extracts the dynamic mass matrix, dynamic damping matrix, and dynamic stiffness matrix, receives the nonlinear dynamic restoring force and obtains the external excitation, executes matrix equations to establish and output the nonlinear dynamic motion equations; The tensor computation unit performs a state vector reduction definition on the nonlinear dynamic equations of motion, transforming them into first-order state equations.

[0009] By extracting the dynamic mass matrix, dynamic damping matrix, and dynamic stiffness matrix and performing a state vector reduction definition, the basic operational conditions for the dynamic simulation model to perform numerical integration and parameter sensitivity calculations are met.

[0010] Preferably, the independent dynamics solver outputs the model to predict the state response in the following way: The independent dynamics solver performs numerical integration calculations on the state evolution function based on the dynamics numerical solver operator and outputs the model's predicted state response; The tensor computation unit calls the state selection or measurement direction projection matrix to perform spatial dimension projection calculations on the model's predicted state response, and combines the observation operator to generate the model's predicted response.

[0011] An observation operator with a fixed observation transfer function is introduced to address the data alignment bias caused by differences in structural transfer paths, ensuring that the model's predicted response and the actual measured response are in the same parameter dimension and sampling form.

[0012] Preferably, the specific process by which the tensor computation unit generates global multi-domain fusion features is as follows: Temporary response window contains temporal evolution information, spectral distribution information, time-frequency structure information, and statistical characteristic information; The tensor computation unit performs standardization processing on time-domain evolution information, performs discrete Fourier transform on spectral distribution information, and performs short-time Fourier transform on time-frequency structure information; Information from each domain is encoded and concatenated using multiple independent feature encoding operators to form local multi-domain fusion features. The mean, median, and standard deviation of the local multi-domain fusion features are then aggregated to generate global multi-domain fusion features.

[0013] By aggregating the mean, median, and standard deviation, a global multi-domain fusion feature is generated that is not affected by the order of response window division, providing a response representation source covering multiple independent dimensions.

[0014] Preferably, the specific process of performing a short-time Fourier transform on the time-frequency structure information is as follows: The tensor computation unit calls the short-time window operator to perform sliding slicing on the window signal, and receives the short-time window length, frame shift length, and short-time window function. Perform a short-time Fourier transform on the window signal to output short-time Fourier complex coefficients, extract the short-time Fourier complex coefficient amplitude, and output the logarithmic time-frequency amplitude.

[0015] We expand the short-time Fourier complex coefficients in the time frame and frequency dimensions to construct a time-frequency domain representation that includes aggregated parameters in the time dimension to reflect the non-stationary evolution characteristics.

[0016] Preferably, the specific steps of the tensor computation unit performing an asymmetric bounded mapping on unconstrained variables to transform them into parameters of the model to be corrected include: The inverse parameter recognition network is configured to include a data input layer, a fully connected hidden layer, and a data output layer, with the data output layer outputting unconstrained variables. Tensor computation units extract the upper and lower limits of the parameters to be corrected in the model to define the feasible interval of the parameters. Unconstrained variables are substituted into the hyperbolic tangent function to generate mapping variables, which are then transformed into model parameters to be corrected with actual dimensions.

[0017] By combining the hyperbolic tangent function to perform bounded mapping, the numerical differences between different parameter dimensions are eliminated, and the parameters of the model to be corrected are strictly restricted to within the feasible range of the parameters.

[0018] Preferably, the specific steps for correcting the total loss by combining the parametric regularization term with the model include: The tensor computation unit establishes a priori regularization terms based on the parameters of the model to be corrected, and compares the model representation output by the simulation calculation of the parameters of the model to be corrected with the multi-domain response set to generate multi-domain response consistency loss. The network weight regularization term, the first penalty weight, and the second penalty weight are extracted. The multi-domain response consistency loss, the parameter prior regularization term multiplied by the first penalty weight, and the network weight regularization term multiplied by the second penalty weight are added and combined to form the model correction total loss.

[0019] A dual constraint architecture of multi-domain data-driven and dynamic model features is established to constrain the deviation of the parameters of the model to be corrected from the initial prior parameters and suppress the overfitting phenomenon in the inverse parameter recognition network.

[0020] Preferably, the specific process of extracting the numerical perturbation gradient includes: The tensor computation unit loads a numerical perturbation gradient estimation operator for the training objective of the inverse parameter identification network, and applies a small numerical perturbation to the parameters of the model to be corrected to calculate the data partial derivatives and prior partial derivatives respectively. Calculate the Jacobian matrix of the model parameters to be corrected with respect to the network parameters, and perform tensor product calculation with the data partial derivatives, prior partial derivatives and the Jacobian matrix to form the network parameter update direction.

[0021] By applying small numerical perturbations to calculate partial derivatives and Jacobian matrices, a backpropagation computation path is established across non-differentiable dynamic operators, maintaining the coherent operation of the network parameter update iteration loop.

[0022] Preferably, the specific steps for extracting the convergence correction parameters include: The tensor computation unit compares the current iteration number with the maximum iteration threshold and simultaneously calculates the difference between the model correction total loss function outputs of two adjacent iterations. When the current iteration number equals the maximum iteration threshold, or the difference in the model's corrected total loss function is less than the loss convergence tolerance, the convergence state is determined, and the mean of the number of iterations in the convergence phase and the total number of iterations is extracted and the convergence correction parameter is output.

[0023] The mean calculation operation is performed by using the parameters extracted in the multi-step iteration during the convergence phase, which reduces the calculation bias introduced by the numerical fluctuations in a single iteration process.

[0024] Preferably, after generating the highly reliable digital twin model, the tensor computation unit also performs: Receive target prediction data containing external excitation loads and environmental boundary conditions sent by the external communication interface; Load a highly reliable digital twin model, use the target predicted working condition data as input node parameters to perform forward dynamic solution, output cross-working condition predicted response set and transmit it to the downstream engineering application server to perform structural fatigue damage early warning calculation.

[0025] Based on the target predicted working condition data, forward dynamics calculation is performed, and the generalized prediction results of cross-working condition response are output to support the downstream engineering application server in performing equipment operation monitoring and analysis tasks.

[0026] This invention provides a method for correcting the inverse PINN nonlinear model based on multi-domain response fusion. It has the following beneficial effects: 1. This invention forms a local multi-domain fusion feature by encoding and concatenating time-domain evolution information, spectral distribution information, time-frequency structure information, and statistical feature information through multiple independent feature encoding operators. The mean, median, and standard deviation of the local multi-domain fusion feature are aggregated to generate a global multi-domain fusion feature. The multi-domain fusion feature provides a response representation source covering independent dimensions, reducing the parameter coupling at the response feature level. The aggregation calculation of the mean, median, and standard deviation across the response window generates a global multi-domain fusion feature that is not affected by the response window division order, weakening the interference of time offset and measurement noise on the correction process of the nonlinear dynamic model.

[0027] 2. This invention receives unconstrained variables from global multi-domain fusion features via an inverse parameter identification network, calls the hyperbolic tangent function to perform an asymmetric bounded mapping on the unconstrained variables to transform them into parameters of the model to be corrected, and loads a numerical perturbation gradient estimation operator to apply small numerical perturbations to the parameters of the model to be corrected, calculating the partial derivatives and Jacobian matrix. The asymmetric bounded mapping eliminates the numerical differences between different parameter dimensions and restricts the parameters of the model to be corrected to within the feasible interval of the parameters, satisfying the boundary constraints of the nonlinear dynamic system. The numerical perturbation gradient estimation operator establishes a backpropagation calculation path across the nondifferentiable dynamic solution operator, maintaining the coherent operation of the closed loop of network parameter update iteration.

[0028] 3. This invention constructs a local loss by comparing the model's predicted state response with the measured response data, aggregates and generates a cross-window robust loss, and combines it with parameter regularization terms to form a model-corrected total loss. After the model-corrected total loss reaches a preset convergence criterion, convergence correction parameters are extracted to generate a highly reliable digital twin model. The cross-window robust loss and parameter regularization terms constitute a dual constraint architecture of data-driven and dynamic model features, suppressing overfitting within the inverse parameter identification network. Based on the highly reliable digital twin model generated by the convergence correction parameters, forward dynamics calculation is performed in conjunction with the target predicted working condition data, outputting a cross-working condition predicted response set, supporting downstream engineering application servers in performing equipment operation monitoring and structural fatigue damage early warning calculation tasks. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a block diagram of the underlying computing power environment data interaction logic of the present invention; Figure 3 This is a logic diagram of local multi-domain feature extraction and global fusion in this invention; Figure 4 This is a flowchart of the reverse parameter recognition network of the present invention; Figure 5 The flowchart for calculating the total loss and numerical perturbation gradient of the model correction in this invention is shown below; Figure 6 This is a flowchart illustrating the process of generating and expanding the training dataset and performing fault diagnosis in this invention. Detailed Implementation

[0030] 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.

[0031] See attached document Figure 1 and attached Figure 2 This invention provides a method for correcting the inverse PINN nonlinear model based on multi-domain response fusion. This method relies on the underlying computing environment to perform hardware-level data throughput and parallel matrix operations.

[0032] The underlying computing environment includes data acquisition sensor channels deployed on the surface of the engineering equipment. These channels are connected in series with data acquisition terminals. Under single-channel measurement conditions, vibration signals are acquired in real time. The data acquisition terminals perform analog-to-digital conversion on the vibration signals. When acquiring measured response data, a small segment of vibration signal within a very short time is extracted as the baseline data for small-sample fault diagnosis. Gaussian white noise of different signal-to-noise ratio levels is artificially superimposed on the measured response data to simulate extreme working conditions. The output is measured response data containing response errors caused by measurement noise, environmental disturbances, artificial noise interference, and unmodeled dynamics. This provides a hardware data source for subsequent verification of the high accuracy and noise robustness of closed-loop iterative correction of parameters.

[0033] The underlying computing environment also includes computer equipment that establishes a communication connection with the data acquisition terminals. Internally, it integrates a motherboard bus, which connects to a storage module and a processor. The storage module is internally divided into a measured data buffer pool and an initial model parameter storage area. The measured data buffer pool continuously receives and stores measured response data, while the initial model parameter storage area pre-stores initial model data based on nominal parameters, including the nonlinear mass matrix, nonlinear damping matrix, nonlinear stiffness matrix, and initial dimensionless values ​​of the model parameters to be corrected.

[0034] The processor includes a tensor computation unit for handling large-scale tensor operations. It reads measured response data and initial model data from the storage module via the motherboard bus, and sequentially performs time-domain normalization, windowed discrete Fourier transform, and short-time Fourier transform extraction on the measured response data, outputting time-domain, frequency-domain, time-frequency-domain, and statistical feature domain information. Internally, it instantiates an independent dynamics solver and an inverse parameter identification network. The independent dynamics solver receives the initial model data, performs forward modeling of the dynamics model, and outputs the model's predicted response data. The inverse parameter identification network establishes an inverse mapping relationship between the measured response data and the parameters of the model to be corrected based on multi-domain response fusion features. The tensor computation unit calculates the cross-window robust loss between the model's predicted response data and the measured response data, and performs closed-loop iterative calculations on the network parameters of the inverse parameter identification network based on the numerical perturbation gradient.

[0035] After the total loss of the model correction reaches the preset convergence criterion, the tensor computation unit writes the output convergence correction parameters back to the storage module. The computer device calls the updated convergence correction parameters in the storage module to generate samples with dynamic consistency, and outputs virtual vibration sample sets under different loads and speeds to the external display terminal to complete the hardware layer data interaction.

[0036] See attached document Figure 1 The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion provided by this invention specifically includes the following steps: S1. The tensor computation unit reads the initial model data, establishes nonlinear dynamic equations of motion containing unknown model parameters, and internally transforms them into first-order state equations. The independent dynamic solver receives the first-order state equations, solves and outputs the model's predicted state response, and simultaneously establishes the mathematical expression of the parametric deviation between the measured response data and the model's predicted state response in the storage module.

[0037] S2. The computer equipment divides the measured response data into multiple response windows using overlapping window sliding division. The storage module allocates cache space to temporarily store the time-domain evolution information, spectral distribution information, time-frequency structure information, and statistical feature information within the response windows. The tensor computation unit performs standardization processing on the time-domain evolution information, performs Discrete Fourier Transform on the spectral distribution information, and performs Short-Time Fourier Transform on the time-frequency structure information. It then encodes and concatenates the information from each domain using multiple independent feature encoding operators to form local multi-domain fusion features. Finally, it performs mean, median, and standard deviation aggregation calculations on the local multi-domain fusion features to generate global multi-domain fusion features.

[0038] S3. The inverse parameter identification network receives global multi-domain fusion features and outputs unconstrained variables. The tensor computation unit performs an asymmetric bounded mapping on the unconstrained variables to eliminate the difference in parameter dimensions, transforming them into model parameters to be corrected with actual dimensions. The independent dynamic solver extracts the model parameters to be corrected and re-executes the forward modeling solution.

[0039] S4. Tensor computation unit compares the multi-domain differences between the model's predicted state response and the measured response data to construct a local loss. After cross-window aggregation, a cross-window robust loss is generated. Combined with the parameter regularization term of the initial model data, the model correction total loss is formed. The numerical perturbation gradient is extracted based on the model correction total loss and is then backpropagated to the inverse parameter recognition network.

[0040] S5. The computer device invokes the network parameter optimizer to update the network parameters of the inverse parameter identification network based on the numerical perturbation gradient. This allows the iterative loop of calculating the consistency loss constraint between the inverse neural network mapping and the multi-domain response to run continuously until the model's total corrected loss reaches the preset convergence criterion. The tensor computation unit extracts the average parameter value from multiple consecutive iterations during the convergence phase as the convergence correction parameter, substitutes it into the nonlinear dynamic equation of motion, and generates a highly reliable digital twin model for cross-condition prediction.

[0041] For S1, the computer device invokes an independent dynamics solver to handle the fundamental modeling task of nonlinear dynamics. The tensor computation unit reads the initial model data from the initial model parameter storage area and extracts the recorded dynamic mass matrix, dynamic damping matrix, and dynamic stiffness matrix. The independent dynamics solver reads the sampling time and combines the generalized displacement with the model parameters to be corrected to generate the nonlinear restoring force.

[0042] The tensor computation unit receives the nonlinear dynamic restoring force output by the independent dynamic solver, synchronously acquires the external excitation provided by the external environment, establishes calculations on the dynamic mass matrix, dynamic damping matrix, dynamic stiffness matrix, nonlinear dynamic restoring force and external excitation execution matrix equations, and outputs the nonlinear dynamic motion equations in the running memory based on the independent dynamic solver.

[0043] The equations of motion for nonlinear dynamics are expressed as follows: ; In the formula, For dynamic generalized displacement, For generalized acceleration in dynamics, For generalized velocity in dynamics, It is a time variable; The dynamic mass matrix is... Here is the dynamic damping matrix. This is the dynamic stiffness matrix; These are the parameters of the model to be corrected. It is a nonlinear dynamic restoring force; External incentives.

[0044] The tensor computation unit receives the nonlinear dynamic equations of motion, performs a state vector reduction definition on the nonlinear dynamic equations of motion, reads the generalized displacement and generalized velocity of the dynamics, performs matrix concatenation of the generalized displacement and generalized velocity of the dynamics to form the model state vector, and transforms the nonlinear dynamic equations of motion into first-order state equations to meet the requirements of numerical integration and parameter sensitivity calculation.

[0045] The first-order state equation is expressed as: ; In the formula, For dynamic state vectors, For dynamic generalized displacement, For generalized velocity in dynamics, This is the matrix transpose symbol. The first derivative of the dynamic state vector. Let be the state evolution function. For time variables, These are the parameters of the model to be corrected. This represents the value of the dynamic state vector at the initial moment. This represents the initial dynamic state.

[0046] The independent dynamics solver reads the parameters of the dynamic model to be corrected, the external excitation, and the initial state of the model. Based on the dynamics numerical solution operator, it performs numerical integration calculations on the state evolution function and outputs the model's predicted state response. The tensor computation unit calls the state selection or measurement direction projection matrix to perform spatial dimension projection calculations on the model's predicted state response. Combined with the observation operators corresponding to sensor installation, signal transmission, and data acquisition, it generates the model's predicted response. The state selection or measurement direction projection matrix and the observation operators ensure that the dynamic model output has the same direction, parameter dimensions, and sampling form as the actual measured response. The observation operator introduces a fixed observation transfer function to solve the problem of mismatch between measured and theoretical responses caused by differences in structural transfer paths, ensuring that the model's predicted response and the actual measured response are compared within the same transfer characteristic domain.

[0047] The model's predicted response output formula is expressed as: ; In the formula, To predict the state response for the model, For the numerical solution operator of dynamics, Let be the state evolution function. This is the initial state of the dynamics. As an external incentive, These are the parameters of the model to be corrected. To predict the response for the model, For the observation operator, Select the projection matrix for the state or measurement direction.

[0048] After outputting the model-predicted response, the computer device reads the actual measured response stored in the storage module. The actual measured response includes the theoretical output data of the actual device operating state under the observation operator and the projection matrix of the state selection or measurement direction, and is superimposed with the response error formed by measurement noise, environmental disturbances, and unmodeled dynamics. The tensor calculation unit expresses the actual measured response as an equation including the response error.

[0049] The actual measured response is expressed by the following formula: ; In the formula, For the actual measured response, For time variables, For the observation operator, Select the projection matrix for the state or measurement direction. For the actual dynamic state, To measure the response error caused by noise, environmental disturbances, and unmodeled dynamics, To predict the response of a model under real but unknown parameters, These are real but unknown model parameters.

[0050] The computer retrieves the pre-defined initial parameters of the model from the storage module. Since there is a numerical difference between the initial parameters and the actual parameters, the tensor computation unit defines this numerical difference as the unknown parameter deviation and constructs the formulas defining the actual model parameters.

[0051] The formula for defining the true parameters of the model is expressed as follows: ; In the formula, For the model's true parameters, These are the initial parameters for the model. This represents the deviation of unknown parameters.

[0052] The tensor computation unit performs computational tasks based on the existing dynamic model. It identifies parameter corrections based on the actual measured response, sums the initial parameters of the model with the parameter corrections to obtain the correction parameters, substitutes them into the dynamic numerical solution operator to obtain the corresponding output correction model response, and performs iterative calculations to make the correction model response approximate the actual measured response.

[0053] The formula for approximating the predicted response with the corrected parameters is expressed as follows: ; In the formula, To correct the parameters, These are the initial parameters for the model. This is the parameter correction value, which is obtained by subtracting the model parameters to be corrected from the initial model parameters after the asymmetric bounded mapping. To correct the model response, For time variables, This is the actual measured response.

[0054] See attached document Figure 3 For S2, after establishing the approximation target, the tensor computation unit performs segmentation and truncation on the actual measurement response, extracts the measurement response length, window length and movement step size sent by the storage module, calculates the total number of windows using the window length and movement step size, calls the window truncation operator and performs sliding truncation on the sequence of actual measurement responses according to the movement step size, and generates multiple independent overlapping windows containing local signal segments.

[0055] The formula for dividing overlapping windows is expressed as follows: ; In the formula, For the first A response window, For the actual measured response, For the first Capture the operator in a window. For actual measurement response in time The corresponding value, For actual measurement response in time The corresponding value, For actual measurement response in time The corresponding value, For the first The starting sampling point of each window, Number the window. For the movement step size, The total number of windows, To measure the length of the response, For window length, This is the floor symbol.

[0056] After obtaining multiple overlapping windows, the tensor computation unit constructs a response representation for each response window and obtains the first response representation. The local waveform, frequency energy, non-stationary evolution, and statistical distribution data contained within each response window are used to establish the first response window based on the corresponding data dimensions. The time-domain representation, frequency-domain representation, time-frequency domain representation, and statistical feature domain representation of each window are merged into a multi-domain response set within the storage module.

[0057] The formula for representing a multi-domain response set is: ; In the formula, For the first A collection of multi-domain responses for a single window. For the first Temporal representation of a window, For the first Frequency domain representation of a window, For the first Time-frequency domain representation of a window, For the first The statistical feature domain of each window is represented.

[0058] Tensor computation unit extracts the first [value] from the multi-domain response set. The first response window performs normalization and frequency domain transformation, receives the mean vector and standard deviation vector of each channel of the complete measurement response transmitted by the storage module, and then performs normalization and frequency domain transformation on the first response window. Subtract the mean vector from the first response window, then divide the result of the subtraction by the sum of the standard deviation vector and the smallest positive number to generate the second response window. The time-domain representation of each window is used to introduce a very small positive number to avoid the anomaly of a zero denominator.

[0059] The time-domain response normalization formula is expressed as: ; In the formula, For the first Temporal representation of a window, For the first A response window, To fully measure the mean vector of the response for each channel, To fully measure the standard deviation vector of each channel of the response, It is a very small positive number.

[0060] Computer equipment for the first The first window The mean of the window signal for each channel is calculated and a mean-reduction calculation is performed. Then, using a tensor computation unit, the mean-reduced signal is multiplied by a window function and a Discrete Fourier Transform is performed. At the frequency... The output is a complex spectrum.

[0061] The formula for the discrete Fourier transform in the frequency domain is expressed as: ; In the formula, For the first The first window, the Each channel at frequency The complex spectrum at that location, Numbered by discrete frequency The corresponding frequencies obtained, and satisfying , Sampling frequency, For window length, Number the sampling points within the window. For window functions, For window signals, The mean of the window signal. The imaginary unit, Pi Number the discrete frequencies.

[0062] The tensor computation unit extracts the complex spectrum amplitude from the complex spectrum and extracts the complete measurement response provided by the storage module. The root mean square value of each channel is used to divide the complex spectrum amplitude by the sum of the root mean square value and the smallest positive number. The result of the division is incremented by one and then incorporated into the logarithmic transformation calculation to form the normalized frequency domain characteristics.

[0063] The formula for constructing the normalized logarithmic spectrum is expressed as: ; In the formula, The frequency domain features are normalized. For complex spectrum amplitude, To fully measure the response, the first... The root mean square value of each channel, It is a very small positive number.

[0064] After the computer equipment completes the frequency domain feature normalization operation, the tensor computation unit calls the short-time window operator to perform the operation on the first... The first window, the The window signal within each channel is slicing, receiving the short-time window length, frame shift length, and short-time window function sent by the storage module. The window signal is then subjected to a short-time Fourier transform, and the output is the short-time Fourier complex coefficients expanded in the time frame and frequency dimensions.

[0065] The short-time Fourier transform formula is expressed as: ; In the formula, These are the short-time Fourier complex coefficients. For short-time window length, It is a short-time window function. This represents the sampled value of the window signal at the offset position. The mean of the window signal. The frame shift length, Assign time frame numbers, For frequency, Number the sampling points within the window. The imaginary unit, Pi Number the discrete frequencies.

[0066] The tensor computation unit extracts the short-time Fourier complex coefficient amplitude, and divides it by the full measurement response. The sum of the root mean square value of each channel and the smallest positive number is divided, one is added to the result, and the result is substituted into the logarithmic function to output the logarithmic time-frequency amplitude value of the corresponding time frame and frequency point.

[0067] The time-frequency coefficient encoding formula is expressed as: ; In the formula, The time-frequency amplitude is logarithmic. The amplitude of the short-time Fourier complex coefficients. To fully measure the response, the first... The root mean square value of each channel, It is a very small positive number.

[0068] The tensor computation unit aggregates logarithmic time-frequency amplitude values ​​in the time dimension, reads the total number of time frames, performs summation and averaging operations on the logarithmic time-frequency amplitude values ​​containing data corresponding to each time frame number, and extracts the time mean of the logarithmic time-frequency amplitude values.

[0069] The formula for the logarithmic time-frequency amplitude and time mean is expressed as: ; In the formula, The logarithmic time-frequency amplitude over time is the mean value. This represents the total number of time frames. The time-frequency amplitude is logarithmic. This is the time frame number.

[0070] The tensor computation unit further calculates the sum of squares of the deviation of the logarithmic time-frequency amplitude from the logarithmic time-frequency amplitude time mean under each time frame number. The sum of squares is divided by the difference between the total number of time frames minus one. The square root operation is performed on the division result to obtain the time standard deviation of the logarithmic time-frequency amplitude. The time mean of the logarithmic time-frequency amplitude and the time standard deviation of the logarithmic time-frequency amplitude are combined and encoded into a time-frequency domain representation.

[0071] when The formula for the time standard deviation of the logarithmic time-frequency amplitude is as follows: ; when When the logarithmic time-frequency amplitude time standard deviation is taken as 0.

[0072] In the formula, The time standard deviation of the logarithmic time-frequency amplitude. This represents the total number of time frames. The time-frequency amplitude is logarithmic. The logarithmic time-frequency amplitude over time is the mean value. This is the time frame number.

[0073] The tensor computation unit synchronously performs time-domain independent variable calculations on the window signal, extracts the root mean square value, kurtosis value, skewness value, and peak-to-peak value of the window signal, and arranges them into a vertical array in a fixed order to generate a low-dimensional statistical feature vector as a representation of the statistical feature domain in the multi-domain response set.

[0074] The definition formula for low-dimensional statistical eigenvectors is expressed as: ; In the formula, It is a low-dimensional statistical eigenvector. The root mean square value of the window signal. This represents the kurtosis value of the window signal. This represents the window signal skewness value. For the peak-to-peak value of the window signal, This is the matrix transpose symbol.

[0075] After generating feature representations within the multi-domain response set, the tensor computation unit performs deep mapping and aggregation operations, extracting the first feature representation from the storage module. The time-domain representation, frequency-domain representation, time-frequency-domain representation, and statistical feature domain representation of each window are input into the corresponding time-domain feature coding operator, frequency-domain feature coding operator, time-frequency-domain feature coding operator, and statistical feature coding operator to perform nonlinear mapping operations. Multiple independent mapping results are then merged using a matrix concatenation operator to output the first window. Local multi-domain fusion features of individual windows.

[0076] The formula for local multi-domain fusion feature splicing is expressed as: ; In the formula, For the first Local multi-domain fusion features of individual windows For time-domain feature encoding operators, For the first Temporal representation of a window, For frequency domain feature coding operators, For the first Frequency domain representation of a window, For time-frequency domain feature coding operators, For the first Time-frequency domain representation of a window, For statistical feature encoding operators, For the first The statistical feature domain representation of each window, This is a matrix concatenation symbol.

[0077] The tensor computation unit traverses all windows generated by the measurement response partitioning, obtains multiple corresponding local multi-domain fusion features, reads the total number of windows, performs summation and averaging operations on multiple local multi-domain fusion features to output the mean of multi-window local features, and simultaneously calculates the square root of the difference between the sum of squares of the deviations from the mean of multi-window local features and the total number of windows minus one to generate the standard deviation of multi-window local features. The mean of multi-window local features and the standard deviation of multi-window local features are then concatenated in parallel according to their dimensional positions to generate a global multi-domain fusion feature that is not affected by the window order and is stored in the storage module.

[0078] when When the set of mean and standard deviation is aggregated, the formula for global features is expressed as: ; when At that time, the standard deviation of local features in multiple windows Take the zero vector that is consistent with the dimension of the local multi-domain fusion feature.

[0079] In the formula, The mean of local features in a multi-window model. The total number of windows, Number the window. For the first Local multi-domain fusion features of individual windows For the standard deviation of local features in a multi-window environment, For global multi-domain fusion features, This is a matrix concatenation symbol.

[0080] See attached document Figure 4 For S3, the tensor computation unit extracts global multi-domain fusion features from the storage module, loads the inverse parameter recognition network into the running memory, and sets the inverse parameter recognition network to include a data input layer, four fully connected hidden layers, and a data output layer. The global multi-domain fusion features are defined as the input tensor of the inverse parameter recognition network and transmitted to the data input layer. The provided inverse mapping weight matrix is ​​used to perform spatial dimension transformation multiplication calculations on the input tensor layer by layer. The output results of the multiplication calculation are summed to the inverse mapping bias vector, and the summation results of the hidden layers are input into the nonlinear activation function to perform nonlinear mapping processing. Finally, the data output layer outputs unconstrained variables without mathematical upper and lower bound constraints and transmits them to the temporary register.

[0081] The formula for the nonlinear inverse mapping is expressed as: ; In the formula, For unconstrained variables, It is a non-linear activation function. This is the inverse mapping weight matrix. For global multi-domain fusion features, This is the inverse mapping bias vector.

[0082] The tensor calculation unit reads the unconstrained variables stored in the temporary register, extracts the upper and lower limits of the model parameters to be corrected sent by the storage module to define the feasible interval of the parameters, calculates the arithmetic mean of the upper and lower limits of the model parameters to be corrected, and takes half of the difference between the upper and lower limits of the model parameters to be corrected to generate the half-range span.

[0083] The tensor computation unit substitutes unconstrained variables into the hyperbolic tangent function to generate mapped variables, multiplies them by the half-amplitude interval span, and adds them to the arithmetic mean to output the model parameters to be corrected with actual dimensions. Combining the hyperbolic tangent mapping and linear transformation eliminates the numerical differences of different parameter dimensions and restricts the model parameters to be corrected within the feasible interval.

[0084] The asymmetric bounded mapping and the formula for restoring the actual dimensions are expressed as: ; In the formula, These are the parameters of the model to be corrected. This represents the upper limit of the parameters of the model to be corrected. These are the lower limits of the parameters of the model to be corrected. It is the hyperbolic tangent function. These are unconstrained variables.

[0085] See attached document Figure 5 For S4, the tensor computation unit receives the model parameters to be corrected with actual dimensions and executes the target evaluation function operation in the running memory. It establishes parameter prior regularization terms based on the model parameters to be corrected, compares the model representation output by the simulation calculation of the model parameters to be corrected with the multi-domain response set to generate multi-domain response consistency loss, extracts the inverse parameter identification network weight regularization terms, the first penalty weight and the second penalty weight, and adds and merges the multi-domain response consistency loss, the parameter prior regularization terms multiplied by the first penalty weight and the network weight regularization terms multiplied by the second penalty weight, and outputs the overall evaluation constraint target.

[0086] The reverse PINN training objective formula is expressed as: ; In the formula, The goal of reverse PINN training is to... For multi-domain response consistency loss, As the first penalty weight, For the parameter prior regularization term, As the second penalty weight, This is the network weight regularization term.

[0087] The computer device invokes the inverse parameter identification network training target to perform gradient backpropagation calculation. To address the issue of non-differentiability of some dynamic operators, the tensor computation unit loads a numerical perturbation gradient estimation operator to obtain the partial derivative vector for the inverse parameter identification network training target. By applying a small numerical perturbation to the parameters to be corrected in the model, the data partial derivatives of the multi-domain response consistency loss with respect to the parameters to be corrected and the prior partial derivatives of the parameter prior regularization term with respect to the parameters to be corrected are calculated. The Jacobian matrix of the parameters to be corrected with respect to the network parameters is calculated. The data partial derivatives, prior partial derivatives, and Jacobian matrix are multiplied by a tensor, and the product result is added to the weight partial derivatives of the network weight regularization term with respect to the network parameters to form the network parameter update direction.

[0088] The gradient calculation of the training objective with respect to the network parameters and the chain rule formula are expressed as follows: ; In the formula, To inversely train PINN, calculate the loss gradient of the objective with respect to the network parameters. The data partial derivatives of the multi-domain response consistency loss with respect to the parameters of the model to be corrected. As the first penalty weight, Let be the prior partial derivative of the parameter prior regularization term with respect to the parameters of the model to be modified. Let be the Jacobian matrix of the model parameters to be corrected with respect to the network parameters. As the second penalty weight, Let be the weight partial derivative of the network weight regularization term with respect to the network parameters. For network parameters, These are the parameters of the model to be corrected.

[0089] The tensor computation unit calculates the multi-domain local bias within the multi-domain response consistency loss. It inputs the parameters to be corrected into the dynamic simulation model, runs the model, and outputs the simulation multi-domain response set, which is decomposed into the simulation time-domain representation, frequency-domain representation, time-frequency-domain representation, and statistical feature domain representation for each window. It then retrieves the first... The measured time-domain, frequency-domain, time-frequency-domain, and statistical feature domain representations of each window are analyzed. The L2 norm of the difference between the simulated and measured representations in each feature domain is calculated. This L2 norm is divided by the measured representation's L2 norm to generate an independent dimensionless local loss. The dimensionless local loss is then multiplied by the domain weights of the associated feature domains and summed. The result is the output that eliminates the numerical scale differences across different feature dimensions. Multi-domain integrated local loss in a single window.

[0090] The unified formula for calculating multi-domain local loss is expressed as follows: ; In the formula, For the first Multi-domain integrated local loss of a window For the set of feature domains, Number the feature domain. For domain weights, For the first Simulation representation of a window, For the first The measured characterization of each window, This is a 2-norm operator. The feature domain set includes the time domain, frequency domain, time-frequency domain, and statistical feature domain.

[0091] The tensor computation unit reads the multi-domain comprehensive local losses corresponding to all windows, performs arithmetic mean calculation to generate the local loss mean. When the total number of windows is greater than 1, it extracts the sum of squares of deviations from the local loss mean, divides it by the difference between the total number of windows minus one, and performs a square root operation to generate the local loss standard deviation. When the total number of windows is equal to 1, the local loss standard deviation is 0. It calculates the product of the local loss standard deviation and the standard deviation penalty coefficient, and combines it with the local loss mean to form a multi-domain response consistency loss to weaken the interference of local abnormal fluctuations.

[0092] The formula for cross-window robust aggregation loss is expressed as: ; In the formula, For multi-domain response consistency loss, This represents the local mean loss. The standard deviation penalty coefficient is... The standard deviation of the local loss. The total number of windows, Number the window. For the first Multi-domain integrated local loss of a window.

[0093] The tensor computation unit extracts the initial prior parameters sent by the storage module, performs a difference calculation between the model parameter to be corrected and the initial prior parameters to generate a parameter deviation vector, calculates the squared L2 norm of the parameter deviation vector and the squared L2 norm of the initial prior parameters respectively, and performs a division operation to generate a parameter regularization term to constrain the range of deviation of the model parameter to be corrected from the initial prior parameters.

[0094] The formula for the parameter regularization term is expressed as: ; In the formula, For the parameter prior regularization term, These are the parameters of the model to be corrected. These are the initial prior parameters. It is the 2-norm square operator.

[0095] The tensor computation unit extracts the inverse parameters to identify the network parameters contained in the network. These parameters are then substituted into the squared Frobenius norm to calculate the network weight regularization term. This term serves as the core condition for mapping the dual constraints of multi-domain data-driven and dynamic model characteristics in the PINN architecture. The multi-domain response consistency loss is used as a data fidelity metric. The first penalty weight is multiplied into the parameter regularization term representing the prior boundary constraints of the dynamics, and the second penalty weight is multiplied into the network weight regularization term. The multi-domain response consistency loss, the parameter regularization term multiplied with weights, and the network weight regularization term are combined and added together to form a model correction total loss function that fits the inverse PINN computation framework and is used to suppress overfitting.

[0096] The formula for the model-corrected total loss function is expressed as follows: ; In the formula, To adjust the total loss function of the model, For multi-domain response consistency loss, As the first penalty weight, For the parameter prior regularization term, As the second penalty weight, For network parameters, For the square operator of the Frobenius norm.

[0097] For S5, the tensor computation unit reads the model's total loss function and the network parameter update direction, calls the adaptive moment estimation optimizer operator sent by the storage module, and performs multiple iterative update calculations on the network parameters included in the inverse parameter identification network in combination with the initial learning rate. Each iterative update calculation outputs the model parameters to be corrected associated with the current iteration number and synchronously stores them in the storage module.

[0098] To perform the iteration termination determination, the tensor computation unit compares the current iteration number with the maximum iteration threshold, and simultaneously calculates the difference between the model correction total loss function outputs of two adjacent iterations. If the current iteration number is equal to the maximum iteration threshold, or the difference between the model correction total loss function is less than the loss convergence tolerance, the inverse parameter identification network is determined to have reached convergence and the adaptive moment estimation optimizer operator is stopped.

[0099] After the inverse parameter identification network reaches convergence, the tensor computation unit extracts the number of iterations in the convergence phase and the total number of iterations, performs mean calculation, retrieves multiple model parameters to be corrected stored within the backward span of the total number of iterations, performs arithmetic summation on the multiple model parameters to be corrected and divides them by the number of iterations extracted in the convergence phase, and outputs the convergence correction parameters to eliminate the oscillations introduced by a single iteration.

[0100] The final formula for extracting the mean of the corrected parameters is expressed as: ; In the formula, To convergence, the parameters are adjusted. To extract the number of iterations during the convergence phase, To identify the total number of iterations during network training for inverse parameter identification, and It is a positive integer; Not greater than positive integers, For iteration numbering, For the first The model parameters to be corrected in the next iteration.

[0101] The tensor computation unit extracts the initial dynamic model, reads the convergence correction parameters and substitutes them into the parameter variable nodes, updates the stiffness characteristic matrix and damping characteristic matrix to complete the reconstruction calculation of the high-reliability digital twin model and synchronously stores it into the storage module.

[0102] The external communication interface sends target predicted load data, including external excitation loads and environmental boundary conditions, to the tensor computation unit. The tensor computation unit loads a highly reliable digital twin model, uses the target predicted load data as input node parameters to perform forward dynamics calculation, outputs a set of cross-load condition predicted responses to provide generalized prediction results, and transmits them to the downstream engineering application server to perform structural fatigue damage early warning calculations.

[0103] To numerically verify the established method model, the tensor computation unit executed a numerical example of a two-degree-of-freedom Duffing oscillator to verify its ability to correct seven model parameters, including damping, linear stiffness, coupling stiffness, and cubic nonlinear stiffness. The tensor computation unit constructed a two-degree-of-freedom nonlinear initial dynamic model for the two-degree-of-freedom Duffing oscillator in its runtime memory, established a unit mass matrix, extracted the first and second damping coefficients to generate a dynamic damping matrix, extracted the first, coupling, and second linear stiffness coefficients to generate a dynamic stiffness matrix, and multiplied the cubes of the first and second degree-of-freedom displacements into the corresponding first and second cubic nonlinear stiffness parameters, respectively, and then vertically concatenated them to generate a nonlinear restoring force vector. After closed-loop iterative correction, the average parameter error was only 0.136%, and even under 100% noise interference, the error remained below 6.5%, demonstrating the invention's extremely strong noise robustness.

[0104] The formulas for the mass, damping, stiffness, and nonlinear restoring force matrices are expressed as follows: , , , ; In the formula, The dynamic mass matrix is... Here is the dynamic damping matrix. The first damping coefficient, This is the second damping coefficient. Here is the dynamic stiffness matrix. The first linear stiffness coefficient, The second linear stiffness coefficient, This is the coupling stiffness coefficient. It is a nonlinear restoring force vector. Let be the first cubic nonlinear stiffness parameter. For cubic nonlinear stiffness parameters, For the first degree of freedom displacement, This represents the displacement of the second degree of freedom.

[0105] The tensor computation unit substitutes the mass matrix, damping matrix, stiffness matrix, and nonlinear restoring force vector into the initial dynamic model, reads the first and second degree-of-freedom excitations, performs time derivative calculations on the degree-of-freedom displacements to generate velocity and acceleration responses, and decomposes the multidimensional matrix multiplication relationship into one dimension to generate mutually independent scalar motion equations of various orders, which serve as the computational basis for the time-domain integral solution of the dynamic simulation model.

[0106] The scalar equations of motion corresponding to the two degrees of freedom are expressed as follows: ; In the formula, For the first degree of freedom acceleration, The first damping coefficient, For the first degree of freedom, velocity, The first linear stiffness coefficient, For the first degree of freedom displacement, This is the coupling stiffness coefficient. For the second degree of freedom displacement, Let be the first cubic nonlinear stiffness parameter. The excitation amplitude for the first degree of freedom, To excite the angular frequency, For time variables, For the second degree of freedom acceleration, This is the second damping coefficient. For the second degree of freedom, velocity, The second linear stiffness coefficient, This is the second cubic nonlinear stiffness parameter. This represents the excitation amplitude for the second degree of freedom.

[0107] The tensor computation unit extracts the scalar motion equations of each order and performs order reduction transformation calculations. The corresponding displacements and velocities are established as state variables of each order in sequence and combined to generate a four-dimensional state vector. The time derivative of the state vector is calculated to output the two-degree-of-freedom first-order state equations. The second-order differential equations are converted into a system of first-order ordinary differential equations to provide the basic conditions for subsequent numerical solutions.

[0108] The first-order state equation with two degrees of freedom is expressed as: ; In the formula, The time derivative of the state vector. For state vectors, For the first degree of freedom displacement, For the second degree of freedom displacement, For the first degree of freedom, velocity, For the second degree of freedom, velocity, The first damping coefficient, This is the second damping coefficient. The first linear stiffness coefficient, This is the coupling stiffness coefficient. The second linear stiffness coefficient, Let be the first cubic nonlinear stiffness parameter. This is the second cubic nonlinear stiffness parameter. The excitation amplitude for the first degree of freedom, The excitation amplitude for the second degree of freedom. To excite the angular frequency, For time variables, This is the initial state vector.

[0109] The tensor computation unit combines the time step and the initial state vector to call the numerical integration operator to perform discrete time step recursive calculations on the two-degree-of-freedom first-order state equations. It collects the outputs of each discrete time step to generate a complete state sequence. Based on the scalar motion equations corresponding to the two degrees of freedom, it calculates the acceleration of the first degree of freedom and the acceleration of the second degree of freedom respectively. It then arranges and combines the acceleration of the first degree of freedom and the acceleration of the second degree of freedom vertically to generate an acceleration prediction response, which is then transmitted to a temporary storage for storage.

[0110] The complete state sequence and acceleration prediction response formula are expressed as follows: ; ; In the formula, For a complete state sequence, Let be the initial state vector. This is the state vector at the first moment. For the first Time-state vector To predict the acceleration response, For the first degree of freedom acceleration, For the second degree of freedom acceleration, The time derivative of the third state variable. This is the time derivative of the fourth state variable.

[0111] The tensor computation unit establishes an inverse parameter identification network structure for the nonlinear oscillator model in the running memory. It divides the displacement, velocity, and acceleration data into time-domain waveform representation, spectrum representation, and complex time-frequency representation. It establishes three input channels of the inverse parameter identification network to independently receive the representations of each domain, and seven output channels to output the unconstrained variables corresponding to the first damping coefficient, the second damping coefficient, the first linear stiffness coefficient, the coupling stiffness coefficient, the second linear stiffness coefficient, the first cubic nonlinear stiffness parameter, and the second cubic nonlinear stiffness parameter, respectively.

[0112] The tensor computation unit extracts the reference acceleration response sequence and acceleration prediction response superimposed with Gaussian white noise, calculates the corresponding time-domain waveform difference L2 norm, spectral difference L2 norm, and complex time-frequency matrix difference Frobenius norm, divides them by the reference norm to generate the deviation components of each domain, and multiplies them by the corresponding domain weights to perform summation calculation to generate the special loss function for oscillator model correction.

[0113] The formula for the correction of the oscillator model's specific loss function is expressed as follows: ; In the formula, To correct the dedicated loss function for the oscillator model, For time domain weights, To predict the time-domain waveform of the acceleration response, The time-domain waveform of the reference acceleration response sequence. For a norm 2 operator, For frequency domain weights, To predict the spectrum of the acceleration response, The spectrum of the reference acceleration response sequence, For time-frequency domain weights, For the complex time-frequency matrix of the acceleration prediction response, The complex time-frequency matrix of the reference acceleration response sequence, For Frobenius norm operators.

[0114] To verify the established method model through engineering experiments, model correction and diagnostic tests were performed based on bearings with outer ring failures. The tensor calculation unit receives local defect feature parameters and performs equivalent geometric boundary calculations in the running memory. Based on the square root of the difference between the squared difference of the rolling element radius and depth, the critical defect width is output. The relationship between the geometric width of the defect and the critical defect width is compared. If the defect is wider than the critical condition, the maximum depth of the defect is established as the maximum displacement excitation. If the defect is narrower than the critical condition, the numerical difference in geometric depth is used to generate the maximum displacement excitation that limits the fall of the rolling element.

[0115] The formula for determining the maximum displacement excitation condition is expressed as follows: ; In the formula, For the maximum displacement excitation, The maximum depth of the defect The geometric width of the defect. Where is the radius of the rolling element.

[0116] After the maximum displacement excitation is generated, the tensor calculation unit calculates the instantaneous angular position of each rolling element based on the input time series and performs interval determination. If it falls within the interval between the defect entry angle and the departure angle, the angle span ratio is calculated, substituted into the sine function to solve, and multiplied by the maximum excitation to output the time-varying displacement excitation. If it does not fall within the interval, it is assigned a zero value to form a nonlinear displacement input boundary condition.

[0117] when When the rolling element and the defect depth are in the same condition, the geometric relationship between them is expressed as: ; when At that time, the length of the defect angle interval is 0, and the time-varying displacement excitation is taken as 0.

[0118] In the formula, For the first Time-varying displacement excitation of a rolling element For the maximum displacement excitation, For the first The instantaneous angular position of each rolling element For the defect entry angle, This is the defect departure angle.

[0119] The tensor calculation unit receives the outer ring defect parameter, calculates the ratio of the difference between the rolling element position and the entry angle, multiplies it by the constant pi, substitutes it into the sine operator, multiplies the output result by the maximum depth to generate a semi-sine outer ring fault excitation of the quantized discontinuous impact amplitude, and assigns a value of zero in the non-defect angle range.

[0120] When the outer ring defect departure angle is greater than the outer ring defect entry angle, the half-sine form of the outer ring fault excitation formula is expressed as: ; When the outer ring defect departure angle is equal to the outer ring defect entry angle, the length of the outer ring defect angle interval is zero, and the half-sine form outer ring fault excitation is 0.

[0121] In the formula, For a half-sine outer ring fault excitation, The maximum depth of the outer ring defect, For the first The instantaneous angular position of each rolling element The outer ring defect entry angle, This refers to the departure angle of the outer ring defect.

[0122] The tensor calculation unit extracts the cage angular velocity and multiplies it with the time variable, and combines it with the rolling element number distribution to generate the angular offset. It then performs a summation calculation with the initial phase angle to determine the instantaneous angular position of the rolling elements in the internal spatial distribution of the bearing.

[0123] The formula relating the cage angular velocity to the initial phase is expressed as: ; In the formula, For the first The instantaneous angular position of each rolling element To maintain the frame angular velocity, For time variables, Number the rolling element. The total number of rolling elements. This is the initial phase angle.

[0124] The tensor calculation unit extracts the horizontal and vertical displacements of the inner and outer rings to generate anisotropic differences, retrieves the angular position of the rolling element to generate trigonometric function projection factors, multiplies them to synthesize the total radial displacement, and deducts the radial clearance and fault excitation to output the outer ring contact deformation that represents the dynamic extrusion depth.

[0125] The formula for contact deformation considering outer ring failure is expressed as: ; In the formula, This represents the contact deformation of the outer ring. For the inner circle horizontal displacement, For the outer ring horizontal displacement, For the first The instantaneous angular position of each rolling element This represents the vertical displacement of the inner ring. This represents the vertical displacement of the outer ring. For radial clearance, The outer ring fault excitation is a half-sine wave.

[0126] The tensor calculation unit calls the step operator to perform a non-negative judgment condition screening on the outer ring contact deformation. If the non-negative condition is met, the output value is one; otherwise, the output value is zero. The Hertzian contact stiffness, the power of the deformation, and the step result are multiplied together to generate the nonlinear contact force of a single rolling element.

[0127] The tensor calculation unit combines the angle trigonometric function projection factor to calculate the horizontal and vertical contact force components of the nonlinear contact force, and then sums up the components of each rolling element to generate the total horizontal and vertical restoring forces over the entire domain.

[0128] The tensor calculation unit extracts the rotor's equivalent mass and support damping, and generates velocity and acceleration by differentiating the displacement. It then establishes a horizontal equilibrium equation by combining the total horizontal restoring force and external excitation, and a vertical equilibrium equation by combining the total vertical restoring force, gravity constant, and vertical excitation. Finally, it longitudinally splices the two-dimensional dynamic equilibrium equations of the inner ring to form the dynamic control equation of the faulty bearing.

[0129] The dynamic control equation for a bearing with an outer ring failure is expressed as follows: ; ; In the formula, For rotor equivalent mass, For the inner circle horizontal acceleration, To support damping, The inner circle horizontal speed, The total number of rolling elements. Number the rolling element. For Hertzian contact stiffness, This represents the contact deformation of the outer ring. For step operators, For the first The instantaneous angular position of each rolling element For horizontal external excitation force, The vertical acceleration of the inner circle. The vertical velocity of the inner circle. For vertical external excitation force, It is the constant of gravitational acceleration.

[0130] The tensor computation unit establishes the outer ring fault bearing dynamic control equation as the core state deduction kernel of the non-smoothly coupled bearing dynamic model. It extracts the rotor equivalent mass, support damping and Hertz contact stiffness, performs initial assignment to obtain the parameter sequence to be corrected and sends it back to the storage module for storage, thus establishing the benchmark starting point for closed-loop iterative calculation.

[0131] The tensor computation unit extracts the parameter sequence to be corrected, substitutes it into the control equation, performs time-domain integration to solve the predicted vibration response, performs envelope demodulation on the measured and predicted responses to extract low-frequency impact features, generates the absolute value of the analytical signal based on the Hilbert transform, and performs fast Fourier transform to obtain the measured and predicted envelope spectra.

[0132] The tensor computation unit calls statistical functions to extract the discrete points of the measured and predicted responses, respectively, and calculates the root mean square, kurtosis, and peak-to-peak value. These are then combined and spliced ​​to form the corresponding one-dimensional measured and predicted statistical feature vectors.

[0133] The tensor computation unit calculates the envelope spectrum and statistical eigenvector difference L2 norm, divides it by the measured reference to generate the deviation, reads and multiplies it by the corresponding weights, sums and outputs the quantized energy frequency band distance bearing model correction total loss.

[0134] The formula for correcting the total loss of the bearing model, which includes the envelope spectrum and statistical characteristics, is expressed as follows: ; In the formula, To correct the total loss for the bearing model that incorporates envelope spectrum and statistical characteristics, For the envelope spectrum weights, To predict the envelope spectrum, For the actual measured envelope spectrum, For a norm 2 operator, For statistical feature weights, To predict statistical feature vectors, This is the measured statistical feature vector.

[0135] The tensor computation unit adjusts the dynamic parameter values ​​based on the loss gradient, updates the stiffness and damping nodes, and replaces the original nodes inside the control equation to generate a modified non-smoothly coupled bearing dynamic model.

[0136] The tensor computation unit extracts multiple sets of variable working condition parameters, including rotational speed, load, and defect size, and substitutes them into the corrected model as boundary input conditions to perform time-domain integration calculations. The output is summarized and a virtual vibration sample set covering multiple working conditions is constructed.

[0137] See attached document Figure 6 The tensor computation unit vertically concatenates the virtual vibration sample set with the received real bearing vibration small sample dataset to generate an expanded training dataset. A one-dimensional convolutional network is established to receive data from the input layer. Based on the convolutional and pooling layers, feature extraction and downsampling are performed to output a dimensionality-reduced feature matrix. The fully connected layer is used to flatten and map the data, and the weight bias vector is continuously updated based on the backpropagation of the classification layer error.

[0138] The tensor computation unit outputs a trained one-dimensional convolutional network upon convergence. This network receives the vibration signal under test, performs local feature extraction, downsampling, and flattening mapping, and combines this with the classification layer's output to reflect the fault category and state prediction labels, which are then stored in the storage module. By using the modified high-fidelity dynamic model as a dynamic model-driven sample generator, small virtual samples of outer ring faults under various operating conditions such as different loads and speeds are generated, effectively expanding the training set and improving the diagnostic accuracy of small outer ring fault samples from 82.8% to 97.9%.

Claims

1. A method for correcting the inverse PINN nonlinear model based on multi-domain response fusion, characterized in that, Includes the following steps: Acquire initial model data and measured response data, read the initial model data to establish nonlinear dynamic motion equations and transform them into first-order state equations, and output the model's predicted state response. The measured response data is divided into response windows, and features are extracted to generate global multi-domain fusion features; The global multi-domain fusion features are input into the inverse parameter recognition network, and the inverse parameter recognition network outputs unconstrained variables. The unconstrained variables are then transformed into model parameters to be corrected by performing an asymmetric bounded mapping. Based on the parameters of the model to be corrected, a parameter regularization term is established. The multi-domain response set corresponding to the model representation output by the simulation calculation is compared with the measured response data to generate a multi-domain response consistency loss. The cross-window robust loss is aggregated and generated. The parameter regularization term is combined to form the model correction total loss and extract the numerical perturbation gradient. The network parameters of the inverse parameter identification network are updated based on the numerical perturbation gradient until the model corrects the total loss to reach the preset convergence criterion. The convergence correction parameters are then extracted to generate a highly reliable digital twin model.

2. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The process of reading the initial model data, establishing the nonlinear dynamic equations of motion, and transforming them into the first-order state equations includes: Extract the dynamic mass matrix, dynamic damping matrix, and dynamic stiffness matrix; calculate the nonlinear dynamic restoring force and obtain the external excitation; execute matrix equations to establish and output the nonlinear dynamic motion equations. The nonlinear dynamic equations of motion are transformed into first-order state equations by performing a state vector reduction definition.

3. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The process of outputting the model's predicted state response includes: The state evolution function is extracted based on the first-order state equation, and numerical integration is performed on the state evolution function based on the dynamic numerical solution operator to output the model's predicted state response. The system invokes the state selection or measurement direction projection matrix to perform spatial dimension projection calculations on the model's predicted state response, and generates the model's predicted response by combining it with preset observation operators.

4. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The process of generating the global multi-domain fusion feature includes: Extract the window signal within the response window, and obtain the corresponding time-domain evolution information, spectral distribution information, time-frequency structure information, and statistical feature information respectively; The time-domain evolution information is subjected to standardization processing, the spectral distribution information is subjected to discrete Fourier transform, and the time-frequency structure information is subjected to short-time Fourier transform. The time-domain evolution information output by the standardized processing, the spectral distribution information output by the discrete Fourier transform, the time-frequency structure information output by the short-time Fourier transform, and the statistical feature information are encoded and concatenated with each other by multiple independent feature encoding operators to form a local multi-domain fusion feature. The mean, median, and standard deviation of the local multi-domain fusion feature are aggregated and calculated to generate the global multi-domain fusion feature.

5. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 4, characterized in that, The process of performing a short-time Fourier transform on the time-frequency structure information includes: The short-time window operator is invoked to perform a sliding slice on the window signal to obtain the short-time window length, frame shift length, and short-time window function; Perform a short-time Fourier transform on the window signal to output short-time Fourier complex coefficients, and extract the short-time Fourier complex coefficient amplitude to output the logarithmic time-frequency amplitude.

6. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The steps of performing an asymmetric bounded mapping on the unconstrained variables to transform them into the parameters of the model to be corrected include: The inverse parameter recognition network is configured to include a data input layer, a fully connected hidden layer, and a data output layer, with the unconstrained variable output by the data output layer. Extract the preset upper and lower limits of the model parameters to be corrected to define the feasible interval of the parameters, and substitute the unconstrained variables into the hyperbolic tangent function to generate mapping variables, which are then transformed into the model parameters to be corrected with actual dimensions.

7. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The steps for forming the corrected total loss of the model include: Extract the network weight regularization term, the first penalty weight, and the second penalty weight. Add the multi-domain response consistency loss, the parameter regularization term multiplied by the first penalty weight, and the network weight regularization term multiplied by the second penalty weight to form the model correction total loss.

8. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The process of extracting the numerical perturbation gradient includes: For the model correction total loss, a numerical perturbation gradient estimation operator is applied, and small numerical perturbations are applied to the parameters of the model to be corrected to calculate the data partial derivatives and prior partial derivatives respectively; Calculate the Jacobian matrix of the model parameters to be corrected with respect to the network parameters of the inverse parameter recognition network, and perform tensor product calculation on the data partial derivatives, the prior partial derivatives, and the Jacobian matrix to form the network parameter update direction.

9. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, The step of extracting the convergence correction parameter includes: Compare the current iteration number with the preset maximum iteration threshold, and simultaneously calculate the difference between the model correction total loss function outputs of two adjacent iteration updates; When the current iteration number is equal to the maximum iteration threshold, or when the difference in the model's corrected total loss function is less than the preset loss convergence tolerance, the convergence state is determined, and the mean of the number of iterations in the convergence phase and the total number of iterations is extracted and the convergence correction parameter is output.

10. The method for correcting the inverse PINN nonlinear model based on multi-domain response fusion according to claim 1, characterized in that, After generating the highly reliable digital twin model, the process also includes: Receive target prediction working condition data that includes external excitation loads and environmental boundary conditions; The highly reliable digital twin model is loaded, and the target predicted working condition data is used as input node parameters to perform forward dynamic calculation and output a set of cross-working condition predicted responses, which is used to instruct the downstream engineering application server to perform structural fatigue damage early warning calculation.

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