A method and system for real-time monitoring of process forces in a concentric shaft

Abstract

The application relates to the technical field of industrial precision machining and intelligent manufacturing, and discloses a process force real-time monitoring method and system of a concentric shaft, which comprises the following steps: acquiring an original synchronous signal stream and decomposing and extracting a pure strain sequence, so as to construct a composite data set; performing covariance characteristic decomposition and component separation on the data set to obtain interference distribution characteristics; obtaining a preliminary axial force estimation value through spatial mapping analysis and nonlinear domain projection reduction; obtaining accurate axial force data through multidimensional error iterative correction and numerical compensation; simulating a stress transmission path, performing signal stripping, extracting a corrected axial force component signal; extracting a timing fluctuation characteristic and performing dynamic reverse compensation to obtain an independent axial force value; and finally outputting an accurately separated axial force component through consistency distribution detection. The method can realize reliable and real-time monitoring of process force of the concentric shaft.

Description

Technical Field

[0001] This invention relates to the field of industrial precision machining and intelligent manufacturing technology, and in particular to a method and system for real-time monitoring of process force of a concentric shaft. Background Technology

[0002] In modern precision mechanical equipment and intelligent manufacturing systems, concentric shaft structures, as core components for transmitting multidimensional loads, are widely used in high-precision fields such as robot joints, multi-axis machine tool spindles, and aero-engine rotors. To ensure the safe operation of these complex equipment under extreme dynamic conditions and optimize their performance, achieving highly reliable and accurate real-time monitoring of force loads has become a key aspect of equipment intelligence. With the continuous evolution of intelligent sensor technology, integrating sensing elements into key components to obtain real-time stress states has become a core means of improving the self-diagnosis and self-adaptation capabilities of mechanical systems.

[0003] In a current technology, strain sensors are typically arranged on the inner and outer surfaces of a concentric shaft. By acquiring strain signals along a single axis and combining them with static calibration coefficients, the electrical signals are directly converted into corresponding axial force values, thereby monitoring the load on each shaft. However, the inner and outer shafts of the concentric shaft are physically tightly nested, and the strain fields generated under stress are highly coupled and interpenetrating. The deformation of the outer shaft under stress directly transmits and interferes with the measurement points on the inner shaft. This results in each sensor capturing a composite response of the combined effects of the inner and outer forces, rather than a true reflection of the independent axial force. Under dynamic operating conditions, due to the asynchronous changes and significant differences in amplitude of the loads on the inner and outer shafts, traditional one-to-one calibration and compensation methods are insufficient to effectively remove complex parasitic interference signals, leading to severely distorted measurement results.

[0004] In summary, existing technologies suffer from axial force monitoring distortion due to strong coupling between the inner and outer shaft strain fields. Summary of the Invention

[0005] This invention provides a method and system for real-time monitoring of process forces on concentric shafts to solve the problem of axial force monitoring distortion caused by strong coupling of strain fields between inner and outer shafts.

[0006] In a first aspect, to solve the above-mentioned technical problems, the present invention provides a method for real-time monitoring of process force on a concentric shaft, comprising:

[0007] The original synchronization signal stream in the concentric shaft structure is obtained, and the original synchronization signal stream is decomposed into a pure strain sequence by multi-scale decomposition. Coupled feature extraction is performed based on the pure strain sequence to obtain a composite dataset.

[0008] Based on the composite dataset, covariance feature decomposition is performed to obtain the projected feature vector, and the feature components with low contribution rate are separated from the projected feature vector to obtain the interference distribution features.

[0009] Based on the interference distribution characteristics, spatial mapping analysis is performed to obtain the interaction intensity characteristics. If the interaction intensity characteristics exceed the preset deviation probability threshold, nonlinear domain projection restoration is performed on the composite dataset to obtain a preliminary axial force estimate.

[0010] Based on the preliminary axial force estimate, multidimensional error iterative correction is performed to obtain the corrected residual data, and intermediate state numerical compensation is performed based on the corrected residual data to obtain accurate axial force data.

[0011] The coupling interference component is obtained by simulating the stress transmission path based on the precise axial force data, and the corrected axial force component signal is obtained by signal stripping and extraction based on the coupling interference component.

[0012] The dynamic working condition range is obtained by extracting the time-series fluctuation features based on the corrected axial force component signal, and the independent axial force value is obtained by performing dynamic inverse compensation based on the dynamic working condition range.

[0013] The residual distribution result is obtained by performing consistency distribution detection on the independent axial force value and the original synchronization signal stream. If the residual distribution result is within the preset confidence interval, the accurately separated axial force component is output.

[0014] Secondly, the present invention provides a real-time process force monitoring system for concentric shafts, comprising:

[0015] The data acquisition module is used to acquire the original synchronization signal stream in the concentric shaft structure, perform multi-scale decomposition on the original synchronization signal stream to obtain a pure strain sequence, and perform coupling feature extraction based on the pure strain sequence to obtain a composite dataset.

[0016] The interference analysis module is used to perform covariance feature decomposition on the composite dataset to obtain the projected feature vector, and to separate the feature components with low contribution rate based on the projected feature vector to obtain the interference distribution characteristics.

[0017] The preliminary grouping module is used to perform spatial mapping analysis based on the interference distribution characteristics to obtain the interaction intensity characteristics. If the interaction intensity characteristics exceed the preset deviation probability threshold, the composite dataset is then subjected to nonlinear domain projection restoration to obtain a preliminary axial force estimate.

[0018] The iterative correction module is used to perform multidimensional error iterative correction based on the preliminary axial force estimate to obtain the corrected residual data, and to perform intermediate state numerical compensation based on the corrected residual data to obtain accurate axial force data.

[0019] The transmission correction module is used to simulate the stress transmission path based on the accurate axial force data to obtain the coupling interference component, and to extract the signal by stripping the coupling interference component to obtain the corrected axial force component signal.

[0020] The dynamic compensation module is used to extract the time-series fluctuation characteristics based on the corrected axial force component signal to obtain the dynamic working condition range, and to perform dynamic reverse compensation based on the dynamic working condition range to obtain the independent axial force value.

[0021] The consistency verification module is used to perform consistency distribution detection based on the independent axial force value and the original synchronization signal stream to obtain the residual distribution result. If the residual distribution result is within a preset confidence interval, the module outputs the accurately separated axial force components.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] (1) This invention can accurately extract pure strain time series at the millivolt level by deploying multiple strain sensors in a concentric shaft structure and introducing wavelet packet decomposition technology. The scheme performs multi-channel synchronous decomposition of the original signal at a depth of 5 layers using the db4 wavelet basis, effectively stripping complex environmental noise and high-frequency electromagnetic interference to the detail layer, thereby improving the signal-to-noise ratio of the reconstructed signal by about 12-18dB. This eliminates the contamination of the underlying signal by the external environment and lays a solid foundation of original data for the high-precision identification of subsequent loads.

[0024] (2) This invention quantifies the distribution of parasitic interference using principal component analysis and combines it with support vector machine to perform feature grouping in high-dimensional space, thereby achieving deep separation of the inner and outer axis coupled loads. This scheme uses radial basis kernel function to map the strongly coupled nonlinear strain characteristics to a high-dimensional feature space to construct the optimal decision hyperplane, which significantly reduces the proportion of interference energy from the original 31% to within 11%, thus solving the problem of measurement distortion caused by the mutual penetration of inner and outer axis strain fields and significantly enhancing the system's signal identification capability under complex load conditions.

[0025] (3) This invention simulates the interaction between the inner and outer shafts by constructing a deformation transmission mechanism model and calls the inverse model of shaft dynamics to correct the inertial additional load under dynamic working conditions in real time. Based on the spatial distribution characteristic vector of the transmission path determined by finite element calibration, this scheme eliminates the interference of rotor mass eccentricity and gyro effect on the force signal while deducting the parasitic influence of the structure, so that the deviation between the final force value and the calibration true value is controlled at about 1%, thereby ensuring the monitoring consistency of the equipment in transient processes such as high-speed lifting and lowering loads, and greatly improving the robustness and engineering application value of real-time monitoring of process force. Attached Figure Description

[0026] Figure 1 This is a schematic flowchart of the real-time process force monitoring method for concentric shafts provided in the first embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of the process force real-time monitoring system for concentric shafts provided in the second embodiment of the present invention. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only 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.

[0029] Reference Figure 1 The first embodiment of the present invention provides a method for real-time monitoring of process forces on a concentric shaft, comprising the following steps:

[0030] S11, Obtain the original synchronization signal stream in the concentric shaft structure, perform multi-scale decomposition on the original synchronization signal stream to obtain a pure strain sequence, and extract coupled features based on the pure strain sequence to obtain a composite dataset;

[0031] S12, perform covariance feature decomposition on the composite dataset to obtain the projected feature vector, and separate the feature components with low contribution rate based on the projected feature vector to obtain the interference distribution features;

[0032] S13, based on the interference distribution characteristics, perform spatial mapping analysis to obtain interaction intensity characteristics. If the interaction intensity characteristics exceed a preset deviation probability threshold, perform nonlinear domain projection restoration on the composite dataset to obtain a preliminary axial force estimate.

[0033] S14. Perform multidimensional error iterative correction based on the preliminary axial force estimate to obtain the corrected residual data, and perform intermediate state numerical compensation based on the corrected residual data to obtain accurate axial force data.

[0034] S15, based on the precise axial force data, stress transmission path simulation is performed to obtain the coupling interference component, and based on the coupling interference component, signal stripping and extraction are performed to obtain the corrected axial force component signal.

[0035] S16, extract the time-series fluctuation features based on the corrected axial force component signal to obtain the dynamic working condition range, and perform dynamic reverse compensation based on the dynamic working condition range to obtain the independent axial force value.

[0036] S17. Based on the consistency distribution detection of the independent axial force value and the original synchronization signal stream, the residual distribution result is obtained. If the residual distribution result is within the preset confidence interval, the accurately separated axial force component is output.

[0037] In step S11, the original synchronization signal stream in the concentric shaft structure is obtained, and the original synchronization signal stream is decomposed into a pure strain sequence through multi-scale decomposition. Coupled feature extraction is then performed based on the pure strain sequence to obtain a composite dataset, including:

[0038] The original synchronization signal stream is decomposed into coefficients at each level using the db4 wavelet basis, and the coefficients at each level are reconstructed by thresholding to obtain a pure strain sequence.

[0039] The distribution positions of corresponding measurement points on the inner and outer axes of the concentric shaft structure are obtained. Based on the distribution positions, the measurement point signal pairs in the pure strain sequence are extracted, and cross-correlation analysis is performed on the measurement point signal pairs to obtain the peak value of the correlation function.

[0040] The preset concentric shaft operating condition parameters are converted into load condition labels, and the correlation metric is quantified based on the peak value of the correlation function to obtain the feature correlation degree value.

[0041] If the value of the feature correlation degree exceeds the preset coupling benchmark, the peak value of the correlation function is mapped and encapsulated with the load condition label to obtain a composite dataset.

[0042] First, raw strain signal data of the inner and outer shafts under various loads are collected by multiple intelligent sensors arranged in the concentric shaft structure. For example, analog voltage values ​​transmitted by multiple sets of strain sensors mounted on the inner and outer shafts are acquired, and the analog voltage values ​​are time-aligned according to a high-precision sampling clock to generate a multi-channel synchronous signal stream. To ensure the accuracy of signal processing, the sampling frequency is set to 10kHz to ensure that the time deviation between channels is controlled within microseconds.

[0043] Subsequently, the multi-channel synchronous signal stream is subjected to five-layer wavelet packet decomposition using the db4 wavelet basis to obtain the coefficients of each layer. During this process, the decomposed subbands are divided into a low-frequency approximation layer and a high-frequency detail layer according to the frequency from low to high. Specifically, the low-frequency portion within the main frequency range of the signal is defined as the low-frequency approximation layer, while the component exceeding the upper limit of the process force change frequency is defined as the high-frequency detail layer. Threshold reconstruction is performed on the coefficients of each layer. Specifically, the absolute value of each coefficient is calculated and compared with a preset noise suppression gain threshold. If the absolute value of the coefficient is less than or equal to the noise suppression gain threshold, the coefficient is set to zero; if the absolute value of the coefficient is greater than the noise suppression gain threshold, the coefficient is retained. The noise suppression gain threshold is set based on the root mean square error of the noise in the no-load state. A general setting method is used to calculate the standard deviation estimate of the noise segment of the no-load signal, and then multiply this standard deviation estimate by the square root of the logarithm of twice the signal length. The signal length refers to the total number of sampling points contained in the data segment undergoing wavelet decomposition. This reconstruction process can concentrate noise and environmental interference in the high-frequency detail layer for removal, retaining the pure strain time sequence that directly reflects the process force, thereby improving the signal-to-noise ratio by about 12 to 18 dB.

[0044] Next, the distribution positions of corresponding measurement points on the inner and outer axes of the concentric shaft structure are obtained. Based on these distribution positions, measurement point signal pairs are extracted from the pure strain sequence, and cross-correlation analysis is performed on these signal pairs to obtain the peak value of the correlation function. Specifically, the inner axis signal sequence is used as a reference sequence, and the outer axis signal sequence is time-shifted to obtain a shifted sequence. The cumulative sum of the products of the reference sequence and the shifted sequence at corresponding time points is calculated to obtain the cross-correlation function that varies with the shift time. The maximum value of the cross-correlation function is found among all shift time points, which is the peak value of the correlation function.

[0045] Subsequently, the current operating parameters of the concentric shaft system, such as rotational speed, torque, and load level, are obtained, and these parameters are converted into load condition labels according to a preset encoding rule. The preset encoding rule is a mapping rule based on the range of operating parameters, and its setting is based on equally dividing the rated parameter range of the shaft system design; for example, the rotational speed range is segmented into 5,000 revolutions per minute, and the feature values ​​of different segments are combined into unique binary or hexadecimal strings as operating condition labels. Correlation quantification is performed based on the peak value of the correlation function. Specifically, the autocorrelation function of the inner shaft signal sequence in the measurement point signal pair is obtained, and the maximum value of the autocorrelation function is extracted as the inner shaft signal autocorrelation peak value. Then, the peak value of the correlation function is used as the numerator, and the peak value of the inner shaft signal autocorrelation is used as the denominator; the ratio of the two is calculated, and the quotient is the characteristic correlation degree value representing the load transfer intensity and linear correlation degree between the inner and outer shafts.

[0046] Finally, if the feature correlation value exceeds the preset coupling benchmark, the peak value of the correlation function is mapped and encapsulated with the load condition label to obtain a composite dataset. Specifically, using the timestamp as an index, the peak value of the correlation function, the lag time feature, and the corresponding load condition label are filled into a preset feature matrix template to form a composite feature matrix where each row represents a sampling condition and each column represents a feature attribute. The composite dataset is stored in a local cache in the form of a structured table, containing timestamps, hexadecimal condition codes, strain amplitude vectors, and cross-correlation features. Whenever the system identifies a new typical load (such as a step load during acceleration), it automatically updates the feature library of the dataset, retaining the most recent 10,000 valid samples using a first-in-first-out principle. It should be noted that the preset coupling benchmark is determined based on the historical operating data of the concentric shaft system of the aero-engine under healthy conditions. Its general setting method is to collect no less than one hundred hours of stable operating condition data and calculate the 85th percentile of its correlation distribution as the threshold.

[0047] It should be noted that the initial mapping table of the load condition labels involved in this embodiment is stored in the system's non-volatile memory. This mapping table is pre-calibrated based on the typical acceleration and deceleration test curves of aero-engines. The parameters of the pre-trained iterative correction model are initialized by conducting single-axis and dual-axis joint loading tests on a laboratory bench, and the initial value of the response matrix is ​​initially determined using the least squares method.

[0048] In step S12, covariance feature decomposition is performed on the composite dataset to obtain a projected feature vector, and low contribution rate feature components are separated from the projected feature vector to obtain interference distribution features, including:

[0049] The composite dataset is normalized to zero mean to obtain a normalized matrix, and covariance operation is performed on the normalized matrix to obtain a covariance matrix. The covariance matrix is ​​then decomposed into eigenvalue sequences and orthogonal eigenvector matrices.

[0050] The cumulative contribution rate is obtained by summing the feature value sequence, and parasitic interference basis vectors below a preset contribution threshold are separated from the orthogonal feature vector matrix based on the cumulative contribution rate.

[0051] The normalized matrix is ​​projected onto the parasitic interference basis vectors for reconstruction to obtain the parasitic interference signal sequence. The spatial spectrum of the parasitic interference signal sequence is then estimated to obtain the projection weights of each channel.

[0052] The interference distribution characteristics are obtained by normalizing the projection weights of each channel.

[0053] First, a composite strain dataset containing coupling effects is acquired, and zero-mean standardization is performed on each channel of the composite dataset. Specifically, the arithmetic mean and standard deviation of each channel within the sampling time period are calculated. The original sampled data is subtracted from the arithmetic mean and then divided by the standard deviation to unify the data of each channel into a standard distribution with a mean of zero and a variance of unit scale, thus obtaining a standardization matrix. Covariance is then calculated based on the standardization matrix to obtain a covariance matrix. Specifically, the standardization matrix is ​​multiplied by its transpose to obtain the covariance values ​​between each channel. These covariance values ​​are then normalized by dividing the difference between the total number of sampling points and one, thereby constructing a covariance matrix reflecting the statistical characteristics of the coupling between the inner and outer axis strain signals.

[0054] Next, the covariance matrix is ​​decomposed into eigenvalues ​​to obtain a sequence of eigenvalues ​​arranged in descending order and the corresponding orthogonal eigenvector matrix. Then, the eigenvalue sequence is summed from largest to smallest to obtain a cumulative eigenvalue sum, which is then divided by the sum of all eigenvalues ​​to obtain a cumulative contribution rate. Based on the cumulative contribution rate, low-contribution-rate eigencomponents are separated from the orthogonal eigenvector matrix; that is, the remaining eigenvectors whose cumulative contribution rate exceeds a preset interference identification cumulative threshold are selected and identified as parasitic interference basis vectors. The interference identification cumulative threshold is set based on the proportion of principal characteristic energy of the system under standard operating conditions. Specifically, it is determined by collecting no less than fifty sets of standard load experimental data for principal component analysis to statistically analyze the minimum cumulative contribution rate that can cover the main frequency energy distribution of the signal; for example, 92% is selected as the threshold.

[0055] After determining the parasitic interference basis vectors, the normalized matrix is ​​projected onto the subspace spanned by the parasitic interference basis vectors for reconstruction. Specifically, the normalized matrix is ​​multiplied by the parasitic interference basis vector matrix to obtain projection coefficients, which are then multiplied by the transpose of the parasitic interference basis vector matrix to reconstruct the parasitic interference signal sequence in the original space. This sequence represents the non-process force interference components in the original signal caused by environmental vibration, electromagnetic interference, or local thermal strain. Furthermore, spatial spectrum estimation is performed on the parasitic interference signal sequence. By calculating the squared modulus of the reconstructed sequence corresponding to each sensor channel, the energy proportion of each channel in the interference subspace is quantified, and the projection weight of each channel is obtained.

[0056] Finally, normalization is performed based on the projection weights of each channel. The projection weight of each channel is divided by the sum of the weights of all channels to obtain the interference distribution characteristics. It should be noted that these interference distribution characteristics are used to identify sensor installation locations sensitive to parasitic interference. For example, if the weight of a sensor near the bearing housing is significantly higher than other locations, it is determined that this location is severely affected by mechanical vibration or oil film disturbance. Exemplarily, through this interference separation process, the proportion of interference energy in the subsequent load identification model can be reduced from approximately 31% to less than 11%. The matrix transpose, multiplication, and other conventional mathematical operations and covariance definitions involved in this embodiment can be implemented with reference to existing data processing techniques, and will not be elaborated upon here.

[0057] In step S13, spatial mapping analysis is performed based on the interference distribution characteristics to obtain interaction intensity characteristics. If the interaction intensity characteristics exceed a preset deviation probability threshold, nonlinear domain projection reconstruction is performed on the composite dataset to obtain a preliminary axial force estimate, including:

[0058] The interaction intensity value is obtained by analyzing the interference distribution characteristics. If the interaction intensity value exceeds the preset deviation probability threshold, the feature vector to be classified is extracted from the composite dataset, and the radial basis kernel function is used to map the feature vector to be classified to a high-dimensional feature space.

[0059] An optimal decision hyperplane is constructed in the high-dimensional feature space, and probabilistic classification is performed based on the feature vector to be classified to obtain a classification label;

[0060] Based on the classification labels, a target feature subset is extracted, and the target feature subset is subjected to spatial inverse mapping to obtain a preliminary axial force estimate.

[0061] In this invention, principal component analysis (PCA) is used in S12 to obtain the interference distribution characteristics. The purpose is to identify the feature subspace sensitive to parasitic interference and its contribution weights in each sensor channel from a global statistical perspective. The necessity of introducing Support Vector Machine (SVM) in S13 lies in the fact that the process force coupling of the concentric axis system is not a simple linear superposition, but rather a strongly nonlinear mapping relationship. The interference distribution characteristics identified in S12 serve as prior knowledge to guide the selection of the SVM kernel function and the construction of the classification hyperplane. Specifically, the SVM classification is based on distinguishing between feature subsets containing real process forces and feature subsets containing parasitic interference. The reason for not directly removing interference in S12 is that PCA is a linear dimensionality reduction technique; directly removing low-contribution components would lead to the accidental deletion of some linearly coupled real load features, causing signal distortion. However, by using the radial basis function (RBF) kernel function of SVM to map the feature vectors to a high-dimensional space, nonlinear and accurate separation of axial force components and interference components can be achieved, thereby preserving the details of the real load to the maximum extent in complex backgrounds and obtaining a preliminary axial force estimate.

[0062] First, the interference distribution features obtained in the previous step are acquired and spatial mapping analysis is performed. Specifically, the distribution vector of the projection weights of each channel is obtained, and the distribution vector is multiplied by the preset inner and outer axis sensor topology matrix to obtain a mapping matrix reflecting the distribution of interference energy of each channel in physical space. The interaction strength feature characterizing the mechanical coupling degree between the inner and outer axes is calculated based on the mapping matrix. Specifically, the off-diagonal elements corresponding to the intersection positions of the inner and outer axes in the mapping matrix are extracted, the sum of squares of these off-diagonal elements is calculated, and the arithmetic square root is taken to obtain the interaction strength value representing the coupling degree between the inner and outer axes. If the interaction strength value exceeds the preset deviation probability threshold, it is determined that the interaction effect between the inner and outer axes is significant, and it is necessary to extract the feature vector to be classified from the composite dataset and use the radial basis function to map the feature vector to be classified to a high-dimensional feature space. The deviation probability threshold is set based on the interaction feature distribution of the concentric shaft system of the aero-engine under standard installation conditions. Specifically, it is determined by collecting no less than one hundred sets of experimental data under known load conditions, statistically analyzing the interaction strength values ​​and calculating the probability density distribution, and selecting the value corresponding to a cumulative probability distribution of 90% as the deviation probability threshold.

[0063] Subsequently, a radial basis function kernel is used to calculate the nonlinear similarity between feature vectors. Specifically, the Euclidean distance between the feature vector to be classified and the preset center vector is calculated. The square of the Euclidean distance is negatively processed and then divided by twice the square of the preset kernel function width parameter. The quotient is then used as the exponent of the natural logarithm base and raised to the power of the result to obtain the nonlinear similarity value. The preset center vector is determined based on the cluster centers of the training sample set in the feature space. By performing mean clustering on the historical payload feature data, the calculated cluster centers are used as the preset center vectors. The preset kernel function width parameter is determined based on the sparsity of the sample points in the feature space. It is calculated by averaging the distances between all training sample pairs and set as the preset kernel function width parameter. Through this mapping, the nonlinearly distributed feature data in the original low-dimensional space is transformed into a linearly separable form in the high-dimensional feature space. An optimal decision hyperplane is then constructed in the high-dimensional feature space. Under the constraints of maximizing the classification margin and minimizing the classification error, a set of feature vectors satisfying the Kuhn-Tucker condition is found as support vectors by solving a quadratic programming problem with Lagrange multipliers. The optimal decision hyperplane is then constructed from the normal vector and bias term determined by the support vectors. For example, an offline training set containing known loads on the inner and outer axes and interference labels is obtained. Cross-validation is used to find the optimal combination of the penalty factor and kernel parameters until the model achieves a classification accuracy of over 95% on the validation set.

[0064] Next, probabilistic classification is performed based on the spatial geometric position of the feature vector to be classified relative to the optimal decision hyperplane. Specifically, the feature vector to be classified is input into a support vector machine model containing the optimal decision hyperplane, and the signed distance from the feature vector to the optimal decision hyperplane is calculated. If the signed distance is greater than a preset zero-point threshold, a positive classification label is assigned; if the signed distance is less than or equal to the preset zero-point threshold, a negative classification label is assigned. The preset zero-point threshold is determined based on the decision robustness of the classifier. Specifically, during the model training phase, the center offset is selected as zero based on the distance between the support vectors on both sides of the classification surface, i.e., the origin of the coordinate system is used as the preset zero-point threshold. Based on the classification label, a target feature subset is extracted. This target feature subset contains the axial strain amplitude component and strain rate component directly related to the axial force, after removing the interference components corresponding to the negative classification label.

[0065] The support vector machine model adopts a radial basis function kernel support vector machine. The input is a feature vector extracted from a composite dataset, and the output is a binary label that distinguishes between axial force-related components and interference components. The model is trained by collecting a sample set of known loads and interferences offline, with the goal of maximizing the classification margin. The loss function is hinge loss, and the kernel parameters and penalty factor are optimized by cross-validation until the accuracy of the validation set reaches more than 95%.

[0066] Finally, spatial inverse mapping is performed on the target feature subset. Specifically, the feature matrix after classification and filtering in the high-dimensional space is multiplied by the inverse matrix of the radial basis kernel function mapping matrix, thereby restoring the feature data from the high-dimensional feature space back to the original physical strain space. A preliminary axial force estimate is calculated based on the inverse-mapped data. Specifically, the material parameters and structural dimensions of the concentric shaft are obtained, the elastic modulus of the material is extracted from the material parameters, and the corresponding stress-bearing cross-sectional area is calculated based on the structural dimensions. For example, the elastic modulus of the material is obtained by consulting the technical specifications of high-temperature alloy materials for aero-engines (e.g., GH4169 alloy, approximately 210 GPa at room temperature), and the stress-bearing cross-sectional area is obtained by measuring the diameter of each segment of the concentric shaft and using the formula for calculating the area of ​​a circle. The uniaxial strain component obtained after inverse mapping is multiplied by the elastic modulus and the corresponding stress-bearing cross-sectional area to obtain independent preliminary axial force estimates for the inner and outer shafts.

[0067] In step S14, multidimensional error iterative correction is performed based on the preliminary axial force estimate to obtain corrected residual data, and intermediate state numerical compensation is performed based on the corrected residual data to obtain accurate axial force data, including:

[0068] The preliminary axial force estimate is analyzed by feature component analysis to obtain the nonlinear cross-coupling error component, and the nonlinear cross-coupling error component is input into the pre-trained iterative correction model to calculate the dynamic compensation coefficient vector.

[0069] The preliminary axial force estimate is weighted and corrected using the dynamic compensation coefficient vector to obtain an intermediate axial force value. The sum of squared deviations is then calculated based on the intermediate axial force value to obtain the corrected residual data.

[0070] If the corrected residual data is lower than the preset convergence threshold, the intermediate axial force value is confirmed as the accurate axial force data.

[0071] First, a multidimensional coupled response matrix constructed from multi-channel strain, torque, and vibration signals is obtained. The preliminary axial force estimate obtained in the previous step is then input into the multidimensional coupled response matrix for eigencomponent analysis. Specifically, off-diagonal components caused by material nonlinearity and geometric eccentricity are extracted from the multidimensional coupled response matrix to obtain nonlinear cross-coupling error components. The multidimensional coupled response matrix is ​​a real-time observation matrix composed of multi-channel strain, rotational speed, torque, and vibration signals. This matrix is ​​constructed using the original eigenvalues ​​of each synchronously acquired sensor as column vectors and is used to characterize the overall mechanical response state of the concentric shaft system under complex dynamic conditions. The diagonal elements of the matrix represent the sensitivity response of each sensor channel to the axial load, reflecting the sensor's conversion gain in its main measurement dimension. The off-diagonal components represent the cross-axis interference weights caused by material nonlinear deformation, shaft geometric eccentricity, and poor dynamic balance. Extracting the off-diagonal components aims to quantify the error contribution of each interference source to the target axial force measurement channel.

[0072] Subsequently, the nonlinear cross-coupling error components are input into a pre-trained iterative correction model to calculate a dynamic compensation coefficient vector for the current estimate. The iterative correction model calculates the dynamic compensation coefficient vector round by round based on the input error components, obtains the gradient direction of the error components in the current iteration step, multiplies the preset learning rate step by the gradient direction to obtain the step increment, and subtracts the step increment from the compensation coefficient of the current round to update the compensation coefficient, thereby obtaining the dynamic compensation coefficient vector of the current round. The preset learning rate step is determined based on the balance between the convergence speed and stability of the iterative algorithm. During the offline calibration phase of the system, trial-and-error analysis is conducted through multiple sets of load experiments with different amplitudes, and the maximum value that allows the residual to decrease smoothly within ten iterations without oscillation is selected as the learning rate step. For example, for this concentric shaft monitoring system, the learning rate step is typically set between 0.01 and 0.1.

[0073] It should be noted that the pre-trained iterative correction model employs a multi-layer feedforward neural network. The network's input is a vector of preliminary axial force estimates, with dimensions including the number of sensor channels and synchronously acquired auxiliary operating parameters such as rotational speed and temperature. The output is a vector of dynamic compensation coefficients, with the same dimensions as the input. The network structure contains two hidden layers, with 64 and 32 neurons per layer, respectively. The activation function is ReLU, and the output layer uses linear activation to ensure that the compensation coefficients can be positive or negative. The model's training data can be obtained on a laboratory bench by applying known multi-dimensional loads to the concentric shaft structure, including combinations of individual loading of the inner shaft, individual loading of the outer shaft, and combined loading of the inner and outer shafts. Simultaneously, the strain sensor signals from each channel are recorded, and the data is obtained through high-precision external force sensing. The instrument acquires the true axial force value as a label. After processing the collected raw strain signal, a preliminary axial force estimate is obtained, which forms a training sample pair with the true axial force value. The model training uses mean squared error (MSE) as the loss function, which minimizes the error between the corrected force value after the compensation coefficient of the network output and the true force value. At the same time, an L2 regularization term is introduced to prevent overfitting. The Adam optimizer is used, with an initial learning rate of 0.001, a batch size of 32, and 200 training epochs. Early stopping (patience=20) is used to avoid overfitting. The training set, validation set, and test set are divided in a 6:2:2 ratio. After the model training is completed, the network weights are saved for online inference in real-time monitoring.

[0074] Next, the preliminary axial force estimate is weighted and corrected using the dynamic compensation coefficient vector to obtain an intermediate axial force value. Specifically, the preliminary axial force estimate of the inner shaft is multiplied by the first principal term coefficient in the dynamic compensation coefficient vector, then added to the product of the preliminary axial force estimate of the outer shaft and the second cross term coefficient in the dynamic compensation coefficient vector. Finally, the bias product calculated from the environmental interference characteristics and the third compensation coefficient is added to obtain the corrected intermediate axial force value of the inner shaft. The weights are set based on the sensitivity matrix of each channel response to the real load during the offline calibration phase. Multiple calibration samples are fitted using the least squares method, and the normalized partial derivatives of each channel response are calculated as initial weights, which are adjusted in real time according to the operating conditions. Subsequently, the sum of squared deviations of the intermediate axial force value is calculated to obtain the corrected residual data. Specifically, the combined force deviation between the intermediate axial force value and the original synchronization signal stream of the sensor at the corresponding time is calculated, and the deviations are squared and summed to obtain the corrected residual data characterizing the correction accuracy.

[0075] Finally, it is determined whether the corrected residual data is lower than a preset convergence threshold. If the corrected residual data is lower than the preset convergence threshold, the intermediate axial force value is confirmed as the final accurate axial force data after eliminating the cross-coupling effect. The preset convergence threshold is set based on the proportion of the initial residual of the system. It is calculated by taking 5% of the total residual in the initial uncorrected state as the convergence threshold for stopping the iteration. If the corrected residual data is greater than or equal to the preset convergence threshold, the currently calculated intermediate value is compensated as the corrected initial input, and the process returns to the step of calculating the dynamic compensation coefficient vector for re-iteration until the residual meets the convergence requirement, thus forming a complete error correction closed loop. For example, in a joint loading test, after three iterations, the residual decreased to 4.2% of the initial value, and the deviation between the finally determined accurate axial force data and the static calibration value was less than 1.5%. It is worth noting that the iterative correction model provides a technical means to suppress nonlinear interference through dynamic compensation in complex mechanical environments. Those skilled in the art will understand that in scenarios with higher real-time requirements, a more complex residual regression model based on deep learning training can be used to replace the iterative process in order to improve the accuracy of capturing transient high-load conditions.

[0076] In step S15, the coupling interference component is obtained by simulating the stress transmission path based on the accurate axial force data, and the signal is stripped and extracted based on the coupling interference component to obtain the corrected axial force component signal, including:

[0077] The precise axial force data is parsed into spatial distribution feature vectors, and the spatial distribution feature vectors are input into a pre-trained deformation transfer mechanism model to calculate the stress transfer function matrix.

[0078] The nonlinear coupling interference component is obtained by quantization based on the stress transfer function matrix, and the nonlinear coupling interference component is stripped to obtain the uniaxial strain response sequence.

[0079] The uniaxial strain response sequence is dimensionally transformed using a preset material elastic modulus to obtain the corrected axial force component signal.

[0080] It should be noted that, in this embodiment of the invention, the input data used for stress transmission path simulation is actually the corrected residual data obtained in step S14; this data reflects the residual deviation between the accurate axial force data and the true value, and can extract the coupling interference component more accurately; those skilled in the art should understand that the corrected residual data is closely related to the accurate axial force data, and the stress transmission path simulation based on the accurate axial force data described in the claims should be understood to include the use of the corrected residual data.

[0081] First, the residual data after iterative correction is obtained, and spatial analysis is performed on the residual data to obtain a spatial distribution feature vector. Specifically, multi-point strain deviation sequences along the axial and circumferential directions of the concentric axis are extracted, and the deviation sequences are mapped into low-dimensional spatial distribution feature vectors using principal component analysis. Specifically, the multi-point strain deviation sequences are constructed as an input matrix, the autocorrelation matrix of this matrix is ​​calculated, and eigenvalues ​​are extracted. Based on the magnitude of the eigenvalues, the top three principal component vectors are selected as the basis, and the original deviation sequences are projected onto the basis space to obtain a low-dimensional numerical combination that represents the spatial distribution law of the residuals, i.e., the spatial distribution feature vector. Subsequently, the spatial distribution feature vector is input into a pre-trained deformation transfer mechanism model to calculate the stress transfer function matrix. The deformation transfer mechanism model is a mathematical model constructed based on the pre-calibrated stress transfer path of the finite element method. It is based on the convolution operation pre-calibrated by the finite element simulation. By applying a unit pulse load on the inner axis, the strain response curves of each measuring point on the outer axis are obtained and discretized into a sequence of transfer coefficients. The model input is a spatially distributed feature vector, which is obtained by analyzing the accurate axial force data. The output is a stress transfer function matrix. The model parameters are directly determined by physical simulation, without the need for training data and learning process.

[0082] The process of calculating the stress transfer function matrix involves obtaining the weight distribution of each dimension in the spatially distributed feature vector and performing a convolution operation with the pre-stored transfer coefficients in the model. The spatially distributed feature vector is used as the input excitation sequence, and the pre-stored transfer coefficient sequence is used as the system's unit impulse response function. When calculating each item in the stress transfer function matrix, one sequence is fixed, and the other sequence is reversed and translated. Subsequently, within each translation step, the corresponding elements of the overlapping portions of the two sequences are multiplied, and the resulting product is summed to obtain the response value at that translation position. By sliding the translation step across the entire signal length, traversing all overlapping positions, and repeating the above product summation process, a stress transfer function matrix characterizing the coupling propagation law of internal and external axial deformation is finally generated.

[0083] The pre-stored transfer coefficients are discretized Green's function response sequences, determined based on the Green's function response of the concentric shaft structure under a unit load. Each coefficient is a one-dimensional row vector, its length depending on the attenuation period of the stress wave propagating from the inner axis to the observation point on the outer axis in the finite element simulation. A three-dimensional mechanical model of the concentric shaft is established using finite element simulation software. A unit pulse load is applied to the inner axis, and the strain response curves at the corresponding measurement points on the outer axis are recorded. The numerical sequence obtained by discretizing this response curve according to the sampling interval is used as the pre-stored transfer coefficients. For example, for a typical nickel-based alloy concentric shaft, the initial term of this coefficient sequence is usually between 0.05 and 0.12, and it decays exponentially with increasing spatial distance.

[0084] Next, the nonlinear coupling interference component is obtained by quantization based on the stress transfer function matrix. Specifically, the stress transfer function matrix is ​​multiplied by the estimated load vector of the current cycle, and the principal contribution of each channel is subtracted from the result to obtain the nonlinear coupling interference component reflecting the penetration of internal and external axial deformation. The quantization basis of the nonlinear coupling interference component is determined based on the local contact stiffness change of the concentric structure under load. Subsequently, signal stripping and extraction are performed based on the nonlinear coupling interference component to obtain the uniaxial strain response sequence. Specifically, the nonlinear coupling interference component is directly subtracted from the original multi-channel sensor strain data to eliminate parasitic strain fluctuations and extract a relatively pure uniaxial strain response sequence.

[0085] Finally, the uniaxial strain response sequence is dimensionally transformed using a preset material elastic modulus to obtain the corrected axial force component signal. Specifically, the elastic modulus value of the material used in the concentric shaft is obtained, and the value of each sampling point in the uniaxial strain response sequence is multiplied by the elastic modulus, and then multiplied by the corresponding force-bearing cross-sectional area of ​​the concentric shaft, thus completing the dimensional transformation from strain to force. The preset material elastic modulus and material parameters are set with reference to AMS5662 (nickel-based alloy standard) and the original equipment manufacturer's specifications; for example, for high-temperature alloy materials commonly used in aero-engines, this value is typically set to 210 gigapascals, and the force-bearing cross-sectional area is predetermined by measuring the shaft system cross-sectional diameter and applying the circular area calculation method. Through the above stripping and transformation process, the continuous contamination of force value estimation by cross-coupling can be effectively cut off.

[0086] It is important to clarify that the accurate axial force data obtained in S14 of this embodiment focuses on numerical domain correction. It eliminates numerical calculation errors caused by nonlinearity of the sensor measurement matrix, temperature fluctuations in material modulus, and geometric eccentricity of the shaft system through an iterative algorithm, ensuring that numerical aliasing caused by off-diagonal terms in the multidimensional coupled response matrix is ​​suppressed. The corrected axial force component signal obtained in S15 focuses on compensation in the physical path domain. It is based on stress transmission path simulation, subtracting physical penetration interference caused by the nested inner and outer shaft structures during stress deformation. In other words, S14 solves the problem of how to calculate the data accurately, while S15 solves the problem of how to remove physical force path interference. These two approaches, progressing step by step, ultimately ensure the purity of the output force value.

[0087] In step S16, the dynamic operating condition range is obtained by extracting the time-series fluctuation features based on the corrected axial force component signal, and dynamic inverse compensation is performed based on the dynamic operating condition range to obtain independent axial force values, including:

[0088] The real-time volatility value is obtained by performing multi-scale variance analysis based on the corrected axial force component signal. If the real-time volatility value exceeds the preset volatility threshold, the current dynamic operating condition range is identified.

[0089] Within the dynamic operating condition range, the preset shaft dynamics inverse model is invoked to perform inertial force analysis to obtain the inertial additional load, and the inertial additional load is subtracted from the corrected axial force component signal to obtain the net load sequence.

[0090] An adaptive low-pass filter is applied to the net load sequence to obtain a smooth load trajectory, and endpoint values ​​are extracted based on the smooth load trajectory to obtain independent axial force values.

[0091] First, the corrected axial force component signal obtained in the previous step is acquired, and time-series feature analysis is performed on it. Specifically, multi-scale variance analysis is performed on the corrected axial force component signal to obtain the real-time volatility value. A set of sliding window lengths, ranging from small to large, is set, and the sample variance of the corrected axial force component signal within each sliding window is calculated. The variances at each scale are then weighted and averaged to obtain the real-time volatility value. If the real-time volatility value exceeds a preset volatility threshold, the current sampling time is identified as being in a dynamic operating condition range. The preset volatility threshold is determined based on the signal standard deviation of the system under steady-state cruise conditions. Specifically, at least thirty minutes of stable operating data are collected, the maximum variance of the signal fluctuation is calculated, and 2.5 times the maximum variance is set as the preset volatility threshold. For example, for a concentric shaft system, when the energy fluctuation of the signal exceeds a specific multiple of the steady-state background noise, it can be determined that a dynamic process of start-up, acceleration, or load change has begun.

[0092] Next, within the determined dynamic operating condition range, a preset inverse shaft dynamics model is invoked to analyze the inertial force. Specifically, the real-time angular acceleration, mass distribution, and moment of inertia parameters of the concentric shaft system are acquired, and these parameters are input into the preset inverse shaft dynamics model to calculate the inertial additional load. Specifically, the moment of inertia of the shaft system is multiplied by the real-time angular acceleration to obtain the inertial torque component. Then, according to the axial force balance equation, the inertial force components generated by each rotating component in the axial direction are accumulated to obtain the inertial additional load. Subsequently, the inertial additional load is subtracted from the corrected axial force component signal to obtain the net load sequence. This subtraction process is achieved by performing a subtraction operation on the corresponding time sequence, thereby eliminating the dynamic interference caused by the change in the acceleration of the rotating shaft system to the actual load.

[0093] Finally, the net load sequence is subjected to adaptive low-pass filtering to obtain a smooth load trajectory. Specifically, the cutoff frequency of the filter is dynamically adjusted according to the real-time volatility value. When the volatility increases, the cutoff frequency is reduced to enhance the smoothing effect, thereby obtaining a smooth load trajectory. Endpoint values ​​are extracted from the smooth load trajectory to obtain independent axial force values. Specifically, the start and end points of the smooth load trajectory within the current operating cycle are identified, and the steady-state force value at the end point or the average value within the calculation interval is extracted as the independent axial force value. It should be noted that the parameter settings of the preset shaft dynamics inverse model are determined based on the mechanical design specifications of the concentric shaft structure, where the mass and moment of inertia are obtained by consulting the CAD model properties; for example, for a specific model of hollow outer shaft, its moment of inertia is set to 0.45 kg / m². Through the above-mentioned dynamic compensation, spurious load fluctuations caused by shaft acceleration can be eliminated. Specifically, the shaft dynamic inverse model is an analytical model based on Newtonian mechanics. The real-time angular acceleration, mass distribution, and moment of inertia parameters of the shaft system are given by the mechanical design specifications. The inertial additional load is calculated according to Newton's second law. The model structure is a physical formula, such as the moment of inertia multiplied by the angular acceleration, without the need for training data and a learning process.

[0094] In step S17, a residual distribution result is obtained by performing a consistency distribution detection on the independent axial force value and the original synchronization signal stream. If the residual distribution result is within a preset confidence interval, the accurately separated axial force components are output, including:

[0095] Obtain the original sampling sequence from the original synchronization signal stream, calculate the cross-correlation between the independent axial force value and the original sampling sequence, and generate a similarity mapping matrix containing peak values;

[0096] If the peak value of the similarity mapping matrix satisfies a preset matching degree threshold, a joint observation matrix is ​​constructed, and sequence reconstruction is performed based on the joint observation matrix to obtain a reconstructed signal sequence.

[0097] Calculate the reconstructed residual sequence between the reconstructed signal sequence and the original sampling sequence, and perform statistical testing on the reconstructed residual sequence to obtain a consistency label. If the consistency label is within a preset confidence interval, then output the accurately separated axial force component.

[0098] First, the original sampling sequence in the original synchronization signal stream is acquired, and the cross-correlation between the independent axial force value and the original sampling sequence is calculated. Specifically, the calculated independent axial force value is mapped back to the time axis according to the sampling frequency to construct a reference force value sequence, and the product summation of the reference force value sequence and the original sampling sequence under different time lags is calculated to generate a similarity mapping matrix containing peak values. If the peak value in the similarity mapping matrix meets a preset matching threshold, it is determined that the currently separated independent axial force value is highly consistent with the original sensing signal in terms of trend. The preset matching threshold is set based on the linear correlation benchmark of the system within the full load range. Specifically, through offline calibration experiments, the response data of the sensor under standard single-axis loading is acquired, the cross-correlation coefficient between the excitation force and the response signal is calculated, and 90% of the average value is taken as the matching threshold. For example, for this concentric axis monitoring system, this threshold is usually set to 0.85%.

[0099] Next, after the similarity verification is passed, a joint observation matrix is ​​constructed. Specifically, the time-domain sequence of the independent axial force values, the corrected axial force component signal, and the original sampling sequence are horizontally concatenated as column vectors to form a multidimensional joint observation matrix. Sequence reconstruction is then performed based on the joint observation matrix. Specifically, singular value decomposition is performed on the joint observation matrix to extract orthogonal basis vectors that can characterize the main feature components of the signal. The process of projecting the joint observation matrix onto the feature space spanned by the orthogonal basis vectors and then performing inverse transformation involves performing matrix multiplication on the joint observation matrix and the orthogonal basis vector matrix to obtain a projection coefficient matrix reflecting the distribution of the signal in the principal component space. Subsequently, matrix multiplication is performed on the projection coefficient matrix and the transpose of the orthogonal basis vector matrix, thereby eliminating random interference components and restoring a reconstructed signal sequence with the same dimension as the original sensing space.

[0100] Subsequently, the reconstructed residual sequence of the reconstructed signal sequence and the original sampling sequence is calculated. Under the same timestamp index, the value of each sampling point in the original sampling sequence is subtracted from the corresponding value in the reconstructed signal sequence to obtain the reconstructed residual sequence. Statistical distribution detection is performed on the reconstructed residual sequence. Specifically, the mean and variance of the reconstructed residual sequence are calculated, and the chi-square test is used to determine whether the reconstructed residual sequence conforms to the zero-mean normal distribution characteristic, thereby obtaining a consistency discrimination label. If the consistency discrimination label is located within a preset confidence interval, it is determined that the load separation process has effectively stripped away all nonlinear interference and parasitic components, outputting an accurately separated axial force component. The preset confidence interval is set based on the statistical significance level of the normal distribution. According to the three sigma principle in probability and statistics theory, an interval containing 95% to 99% probability distribution is selected as the confidence interval; for example, in this embodiment, the quantile corresponding to the 0.95% confidence level is selected as the boundary. It should be noted that the above-mentioned consistency distribution detection provides a closed-loop verification method, ensuring that the output axial force component is both free from interference and does not lose the core mechanical characteristics of the original signal.

[0101] It is worth noting that if the detection result of the consistency discrimination label fails to fall within the preset confidence interval (such as 0.95 confidence level) for three consecutive times, the system will determine that the current sensor probe is physically loose or the environmental noise exceeds the system decoupling limit. At this time, the system will switch to the safety fallback logic, output the protective predictive force value based on historical trend extrapolation and trigger the equipment shutdown inspection signal.

[0102] It should be noted that this system adheres to the principle of safety first. When the original synchronization signal stream experiences amplitude saturation (exceeding 120% of the sensor's range) or when the inertial load calculated by the inverse dynamic model exhibits a non-physical step, the system will automatically cut off the output of the independent axial force value, trigger a safety warning alarm, and use the sensor's last valid monitoring value as the protection benchmark to ensure the controllability of the monitoring logic under extreme operating conditions. Furthermore, all textual descriptions of computational logic used in this invention (such as deviation sum of squares calculation, convolution operations, etc.) are intended to describe the physical process of the technical implementation. Those skilled in the art will understand that in actual algorithm implementation, if the denominator term approaches zero (e.g., under no-load static conditions), a very small positive bias term (e.g., ...) should be pre-added. This is to prevent errors in division by zero calculations.

[0103] In summary, this invention achieves high-precision real-time separation and independent monitoring of strongly coupled axial forces in concentric shaft structures by combining multi-channel synchronous signal acquisition, principal component analysis and support vector machine for feature separation, as well as iterative correction and dynamic compensation of the inverse dynamic model.

[0104] Reference Figure 2 The second embodiment of the present invention provides a real-time process force monitoring system for concentric shafts, comprising:

[0105] The data acquisition module is used to acquire the original synchronization signal stream in the concentric shaft structure, perform multi-scale decomposition on the original synchronization signal stream to obtain a pure strain sequence, and perform coupling feature extraction based on the pure strain sequence to obtain a composite dataset.

[0106] The interference analysis module is used to perform covariance feature decomposition on the composite dataset to obtain the projected feature vector, and to separate the feature components with low contribution rate based on the projected feature vector to obtain the interference distribution characteristics.

[0107] The preliminary grouping module is used to perform spatial mapping analysis based on the interference distribution characteristics to obtain the interaction intensity characteristics. If the interaction intensity characteristics exceed the preset deviation probability threshold, the composite dataset is then subjected to nonlinear domain projection restoration to obtain a preliminary axial force estimate.

[0108] The iterative correction module is used to perform multidimensional error iterative correction based on the preliminary axial force estimate to obtain the corrected residual data, and to perform intermediate state numerical compensation based on the corrected residual data to obtain accurate axial force data.

[0109] The transmission correction module is used to simulate the stress transmission path based on the accurate axial force data to obtain the coupling interference component, and to extract the signal by stripping the coupling interference component to obtain the corrected axial force component signal.

[0110] The dynamic compensation module is used to extract the time-series fluctuation characteristics based on the corrected axial force component signal to obtain the dynamic working condition range, and to perform dynamic reverse compensation based on the dynamic working condition range to obtain the independent axial force value.

[0111] The consistency verification module is used to perform consistency distribution detection based on the independent axial force value and the original synchronization signal stream to obtain the residual distribution result. If the residual distribution result is within a preset confidence interval, the module outputs the accurately separated axial force components.

[0112] It should be noted that the real-time process force monitoring system for a concentric shaft provided in this embodiment of the invention is used to execute all the process steps of the real-time process force monitoring method for a concentric shaft in the above embodiment. The working principles and beneficial effects of the two are one-to-one, so they will not be described again.

[0113] It should be noted that the system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the system embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0114] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A method for real-time monitoring of process forces on a concentric shaft, characterized in that, include: The original synchronization signal stream in the concentric shaft structure is obtained, and the original synchronization signal stream is decomposed into a pure strain sequence by multi-scale decomposition. Coupled feature extraction is performed based on the pure strain sequence to obtain a composite dataset. Based on the composite dataset, covariance feature decomposition is performed to obtain the projected feature vector, and the feature components with low contribution rate are separated from the projected feature vector to obtain the interference distribution features. Based on the interference distribution characteristics, spatial mapping analysis is performed to obtain the interaction intensity characteristics. If the interaction intensity characteristics exceed the preset deviation probability threshold, nonlinear domain projection restoration is performed on the composite dataset to obtain a preliminary axial force estimate. Based on the preliminary axial force estimate, multidimensional error iterative correction is performed to obtain the corrected residual data, and intermediate state numerical compensation is performed based on the corrected residual data to obtain accurate axial force data. The coupling interference component is obtained by simulating the stress transmission path based on the precise axial force data, and the corrected axial force component signal is obtained by signal stripping and extraction based on the coupling interference component. The dynamic working condition range is obtained by extracting the time-series fluctuation characteristics based on the corrected axial force component signal, and the independent axial force value is obtained by performing dynamic inverse compensation based on the dynamic working condition range. The residual distribution result is obtained by performing consistency distribution detection on the independent axial force value and the original synchronization signal stream. If the residual distribution result is within the preset confidence interval, the accurately separated axial force component is output.

2. The method for real-time monitoring of process force on a concentric shaft according to claim 1, characterized in that, The process involves obtaining the original synchronization signal stream from the concentric shaft structure, performing multi-scale decomposition on the original synchronization signal stream to obtain a pure strain sequence, and extracting coupled features based on the pure strain sequence to obtain a composite dataset, including: The original synchronization signal stream is decomposed into coefficients at each level using the db4 wavelet basis, and the coefficients at each level are reconstructed by thresholding to obtain a pure strain sequence. Obtain the distribution positions of the corresponding measuring points on the inner and outer axes in the concentric shaft structure, extract the measuring point signal pairs in the pure strain sequence based on the distribution positions, and perform cross-correlation analysis on the measuring point signal pairs to obtain the peak value of the correlation function; The preset concentric shaft operating condition parameters are converted into load condition labels, and the correlation metric is quantified based on the peak value of the correlation function to obtain the feature correlation degree value. If the value of the feature correlation degree exceeds the preset coupling benchmark, the peak value of the correlation function is mapped and encapsulated with the load condition label to obtain a composite dataset.

3. The method for real-time monitoring of process force on a concentric shaft according to claim 1, characterized in that, The step of performing covariance feature decomposition on the composite dataset to obtain a projected feature vector, and separating the low contribution rate feature components based on the projected feature vector to obtain the interference distribution features, includes: The composite dataset is normalized to zero mean to obtain a normalized matrix, and covariance operation is performed on the normalized matrix to obtain a covariance matrix. The covariance matrix is ​​then decomposed into eigenvalue sequences and orthogonal eigenvector matrices. The cumulative contribution rate is obtained by summing the feature value sequence, and parasitic interference basis vectors below a preset contribution threshold are separated from the orthogonal feature vector matrix based on the cumulative contribution rate. The normalized matrix is ​​projected onto the parasitic interference basis vectors for reconstruction to obtain the parasitic interference signal sequence. The spatial spectrum of the parasitic interference signal sequence is then estimated to obtain the projection weights of each channel. The interference distribution characteristics are obtained by normalizing the projection weights of each channel.

4. The method for real-time monitoring of process force on a concentric shaft according to claim 1, characterized in that, The interaction intensity features are obtained by spatial mapping analysis based on the interference distribution characteristics. If the interaction intensity features exceed a preset deviation probability threshold, the composite dataset is then subjected to nonlinear domain projection reconstruction to obtain a preliminary axial force estimate, including: The interaction intensity value is obtained by analyzing the interference distribution characteristics. If the interaction intensity value exceeds the preset deviation probability threshold, the feature vector to be classified is extracted from the composite dataset, and the radial basis kernel function is used to map the feature vector to be classified to a high-dimensional feature space. An optimal decision hyperplane is constructed in the high-dimensional feature space, and probabilistic classification is performed based on the feature vector to be classified to obtain a classification label; Based on the classification labels, a target feature subset is extracted, and the target feature subset is subjected to spatial inverse mapping to obtain a preliminary axial force estimate.

5. The method for real-time monitoring of process force on a concentric shaft according to claim 1, characterized in that, The step of performing multidimensional error iterative correction based on the preliminary axial force estimate to obtain corrected residual data, and then performing intermediate state numerical compensation based on the corrected residual data to obtain accurate axial force data, includes: The preliminary axial force estimate is analyzed by feature component analysis to obtain the nonlinear cross-coupling error component, and the nonlinear cross-coupling error component is input into the pre-trained iterative correction model to calculate the dynamic compensation coefficient vector. The preliminary axial force estimate is weighted and corrected using the dynamic compensation coefficient vector to obtain an intermediate axial force value. The sum of squared deviations is then calculated based on the intermediate axial force value to obtain the corrected residual data. If the corrected residual data is lower than the preset convergence threshold, then the intermediate axial force value is confirmed as the accurate axial force data.

6. The method for real-time monitoring of process force on a concentric shaft according to claim 5, characterized in that, The process of simulating the stress transmission path based on the precise axial force data to obtain the coupling interference component, and then extracting the signal based on the coupling interference component to obtain the corrected axial force component signal, includes: The precise axial force data is parsed into spatial distribution feature vectors, and the spatial distribution feature vectors are input into a pre-trained deformation transfer mechanism model to calculate the stress transfer function matrix. The nonlinear coupling interference component is obtained by quantization based on the stress transfer function matrix, and the nonlinear coupling interference component is stripped to obtain the uniaxial strain response sequence. The uniaxial strain response sequence is dimensionally transformed using a preset material elastic modulus to obtain the corrected axial force component signal.

7. The method for real-time monitoring of process force on a concentric shaft according to claim 1, characterized in that, The step of extracting the time-series fluctuation features based on the corrected axial force component signal to obtain the dynamic operating condition range, and performing dynamic inverse compensation based on the dynamic operating condition range to obtain independent axial force values, includes: The real-time volatility value is obtained by performing multi-scale variance analysis based on the corrected axial force component signal. If the real-time volatility value exceeds the preset volatility threshold, the current dynamic operating condition range is identified. Within the dynamic operating condition range, the preset shaft dynamics inverse model is invoked to perform inertial force analysis to obtain the inertial additional load, and the inertial additional load is subtracted from the corrected axial force component signal to obtain the net load sequence. An adaptive low-pass filter is applied to the net load sequence to obtain a smooth load trajectory, and endpoint values ​​are extracted based on the smooth load trajectory to obtain independent axial force values.

8. The method for real-time monitoring of process force on a concentric shaft according to claim 1, characterized in that, The process of obtaining a residual distribution result by performing consistency distribution detection based on the independent axial force value and the original synchronization signal stream, and outputting accurately separated axial force components if the residual distribution result is within a preset confidence interval, includes: Obtain the original sampling sequence from the original synchronization signal stream, calculate the cross-correlation between the independent axial force value and the original sampling sequence, and generate a similarity mapping matrix containing peak values; If the peak value of the similarity mapping matrix meets the preset matching degree threshold, then a joint observation matrix is ​​constructed, and sequence reconstruction is performed based on the joint observation matrix to obtain the reconstructed signal sequence. Calculate the reconstructed residual sequence between the reconstructed signal sequence and the original sampling sequence, and perform statistical testing on the reconstructed residual sequence to obtain a consistency label. If the consistency label is within a preset confidence interval, then output the accurately separated axial force component.

9. The method for real-time monitoring of process force on a concentric shaft according to claim 2, characterized in that, The concentric shaft structure includes an inner shaft, an outer shaft, and a plurality of strain sensor groups arranged on the surfaces of the inner shaft and the outer shaft.

10. A real-time process force monitoring system for concentric shafts, characterized in that, include: The data acquisition module is used to acquire the original synchronization signal stream in the concentric shaft structure, perform multi-scale decomposition on the original synchronization signal stream to obtain a pure strain sequence, and perform coupling feature extraction based on the pure strain sequence to obtain a composite dataset. The interference analysis module is used to perform covariance feature decomposition on the composite dataset to obtain the projected feature vector, and to separate the feature components with low contribution rate based on the projected feature vector to obtain the interference distribution characteristics. The preliminary grouping module is used to perform spatial mapping analysis based on the interference distribution characteristics to obtain the interaction intensity characteristics. If the interaction intensity characteristics exceed the preset deviation probability threshold, the composite dataset is then subjected to nonlinear domain projection restoration to obtain a preliminary axial force estimate. The iterative correction module is used to perform multidimensional error iterative correction based on the preliminary axial force estimate to obtain the corrected residual data, and to perform intermediate state numerical compensation based on the corrected residual data to obtain accurate axial force data. The transmission correction module is used to simulate the stress transmission path based on the accurate axial force data to obtain the coupling interference component, and to extract the signal by stripping the coupling interference component to obtain the corrected axial force component signal. The dynamic compensation module is used to extract the time-series fluctuation characteristics based on the corrected axial force component signal to obtain the dynamic working condition range, and to perform dynamic reverse compensation based on the dynamic working condition range to obtain the independent axial force value. The consistency verification module is used to perform consistency distribution detection based on the independent axial force value and the original synchronization signal stream to obtain the residual distribution result. If the residual distribution result is within a preset confidence interval, the module outputs the accurately separated axial force components.

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