A method for detecting micro-ripple distortion of a flexspline of a harmonic reducer

Abstract

The application provides a method for detecting harmonic reducer flexspline micro waveform distortion, and belongs to the technical field of detecting harmonic reducer flexspline micro waveform distortion. The application acquires a flexspline radial profile sampling sequence through multi-sensor superposition average based on encoder synchronous triggering, uses a high-precision reference model with adaptive reference updating to calculate a theoretical elastic deformation reference in real time and output a residual signal, adopts a physical information sparse decomposition algorithm to expand the residual signal under the mode shape of the Donnell thin shell theory to obtain mode coefficients of each order, uses an artificial intelligence cross-condition migration detection model to classify and identify the mode coefficients of each order and output a waveform distortion type and severity, and finally reconstructs a flexspline micro waveform distortion three-dimensional space distribution matrix based on a Bayesian compressed sensing framework, so that the technical problem that micro waveform distortion features cannot be effectively separated and accurately reconstructed under the background of strong elastic deformation in multiple conditions is solved.

Description

Technical Field

[0001] This invention belongs to the technical field of detecting micro-waveform distortion of the flex wheel in a harmonic reducer, and more specifically, relates to a method for detecting micro-waveform distortion of the flex wheel in a harmonic reducer. Background Technology

[0002] Harmonic reducers are widely used in industrial robot joints, precision instruments, and aerospace transmission systems due to their high transmission ratio, high precision, and compact structure. The flexspline, as the core elastic component of the harmonic reducer, undergoes periodic elliptical elastic deformation on its outer wall under wave generator drive. Under long-term alternating loads, it is prone to micro-waveform distortion. Existing detection methods mainly rely on contact roundness testers or general vibration signal analysis methods to measure the flexspline profile under static or low-speed conditions and identify abnormal components through spectral analysis. Some studies apply wavelet transform or empirical mode decomposition to sensor signal denoising and combine it with threshold judgment methods to achieve fault early warning. However, in actual working conditions with high-speed rotation of the flexspline, frequent load fluctuations, and dynamic changes in the temperature field, the theoretical elastic deformation benchmark is difficult to update in real time with the working conditions. The weak micro-waveform distortion signal is often masked by the elliptical elastic deformation with an amplitude much larger than its own. Conventional spectral analysis and threshold judgment methods cannot effectively extract the modal distortion features of each order in strong background deformation interference, resulting in a persistently high false negative rate. In other words, existing technologies have the technical problem of being unable to effectively separate and accurately reconstruct the micro-waveform distortion features under the background of strong elastic deformation under multiple working conditions. Summary of the Invention

[0003] In view of this, the present invention provides a method for detecting micro-waveform distortion of the flexure wheel of a harmonic reducer, which can solve the technical problem in the prior art that the micro-waveform distortion features cannot be effectively separated and accurately reconstructed from the radial displacement signal due to the background noise of strong elastic elliptical deformation and multi-condition coupling interference during the rotation detection of the flexure wheel of the harmonic reducer.

[0004] This invention is implemented as follows: This invention provides a method for detecting micro-waveform distortion of the flexspline in a harmonic reducer, comprising the following steps:

[0005] Based on multiple displacement sensors evenly arranged along the circumference on the outer wall of the flexible wheel, and with the encoder signal as the synchronous trigger source, the radial displacement data of the flexible wheel in multiple rotation cycles are synchronously superimposed and averaged to obtain the noise-reduced radial contour sampling sequence of the flexible wheel.

[0006] The radial profile sampling sequence of the flexible wheel is input into a high-precision reference model. The theoretical elastic deformation benchmark is calculated online by combining the measured speed, measured load and measured temperature data. The adaptive benchmark update mechanism is used to dynamically compensate for changes in working conditions and outputs the residual signal.

[0007] The vibration equation of the flexure is established based on Donnell thin shell theory. The residual signal is expanded into a linear combination of the basis functions of the flexure's natural mode shape using the modal superposition principle. The residual signal is sparsely decomposed using the physical information sparse decomposition algorithm to obtain the modal coefficients of each order.

[0008] The modal coefficients of each order are input into the cross-condition migration detection model. The cross-condition migration detection model classifies and identifies the modal coefficients of each order, outputs the waveform distortion type and the severity of waveform distortion, and converts the severity of waveform distortion into the maximum distortion amplitude of the dynamic distortion variability function.

[0009] Based on the Bayesian compressed sensing framework, the sparsity of modal coefficients under the modal basis is utilized. The full-field waveform is reconstructed using a sparse reconstruction algorithm with finite discrete measurement points. The modal coefficients are mapped back to the spatial domain to obtain the three-dimensional spatial distribution matrix of the flex wheel micro-waveform distortion, which is used as the output of the flex wheel micro-waveform distortion detection result of the harmonic reducer.

[0010] Specifically, the displacement sensor is a laser triangular displacement sensor or a focused capacitive displacement sensor, which is uniformly arranged along the circumference. The number of sensors is determined by simulation experiments on the change of spatial interpolation reconstruction error with the number of sensors.

[0011] Specifically, the synchronous superposition averaging process is based on the encoder trigger pulse, and the average value is calculated by accumulating the sampled values ​​corresponding to the same angular position in multiple rotation cycles. The number of superposition cycles is determined by the number of cycles corresponding to the minimum sum of the missed detection rate and the false alarm rate.

[0012] The high-precision reference model is specifically a multibody dynamics simulation model established with the stiffness, damping, tooth profile parameters and assembly parameters of each component of the harmonic reducer as inputs. The model parameters are iteratively corrected by least-squares fitting with the measured deformation data until the simulation error converges.

[0013] Specifically, the adaptive reference update mechanism involves periodically collecting measured rotational speed, measured load, and measured temperature values. When the operating condition deviation exceeds a preset operating condition deviation threshold, the high-precision reference model is triggered to recalculate and replace the current theoretical elastic deformation reference.

[0014] Specifically, the residual signal is a difference sequence obtained by subtracting the radial profile sampling sequence of the flexible wheel from the theoretical elastic deformation benchmark point by point, which contains information on the micro-waveform distortion of the flexible wheel.

[0015] Specifically, the physical information sparse decomposition algorithm adopts a grouped orthogonal matching pursuit strategy, which groups the flexural mode basis functions according to the number of nodal diameters, and subtracts the modal contributions of each order from the residual signal in turn. In each iteration, the modal basis most relevant to the current residual is selected by the inner product maximization criterion, and a physical constraint pruning mechanism is introduced to verify the energy bounded condition.

[0016] Specifically, the energy bounded condition is that the weighted sum of squares of the modal coefficients does not exceed the theoretical upper limit of elastic strain energy determined by the material's elastic modulus, wall thickness, and working load. The theoretical upper limit of elastic strain energy is determined by performing finite element simulation on a standard flexible wheel and taking the physical constraint pruning coefficient multiple of the maximum value of each modal strain energy under rated load.

[0017] Specifically, the cross-condition migration detection model employs a convolutional neural network with a collaborative mechanism of adversarial domain adaptation and meta-learning, comprising a feature encoder, a domain encoder, a gradient inversion layer, a domain classifier, a distortion classifier, and a prototype memory.

[0018] Wherein, the gradient reversal coefficient of the gradient reversal layer Adaptive adjustment based on training progress, the adjustment formula is as follows: ,in This represents the ratio of current training steps to total training steps. This is the scaling factor.

[0019] Specifically, the prototype memory stores the prototype feature vectors for each type of waveform distortion mode. During inference, it uses cosine similarity to retrieve the nearest neighbor prototype for classification decisions and supports online unsupervised updates to adapt to operating condition drift.

[0020] Specifically, the dynamic distortion scaling function takes the maximum distortion amplitude, distortion spatial coverage, and inference confidence as inputs to calculate the comprehensive evaluation value. The memory allocation and inference thread priority of the cross-condition migration detection model are adjusted according to the range of the comprehensive evaluation value.

[0021] Specifically, the memory allocation is as follows: when the comprehensive evaluation value is not less than the high memory allocation threshold, the memory allocation ratio of the CUDA stream of the feature encoder is increased to the high memory allocation ratio; when the comprehensive evaluation value is in the middle range, the memory is evenly distributed among the four CUDA streams; when the comprehensive evaluation value is less than the low memory allocation threshold, the memory allocation ratio of the CUDA stream of the prototype memory is reduced to the low memory allocation ratio.

[0022] Specifically, the three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion is a two-dimensional discrete matrix composed of discrete angular positions along the circumferential direction of the flexible wheel's outer wall as row indices, discrete axial positions as column indices, and radial distortion displacement as matrix elements.

[0023] The typical range for the number of superimposed cycles is 32–256; the number of displacement sensors is 8–32; the preset operating condition deviation threshold is the operating condition deviation corresponding to an influence exceeding 1 μm; the physical constraint pruning coefficient is 1.2–1.5 times; and the scaling factor... The value range is 8 to 12; refer to the distortion amplitude benchmark. The value range is 5–20 μm; weighting coefficient , , The initial values ​​are 0.5, 0.3, and 0.2 respectively; the high threshold for video memory allocation is 0.8, the low threshold for video memory allocation is 0.5, the high percentage of video memory allocation is 60%, and the low percentage of video memory allocation is 5%.

[0024] This invention constructs a high-precision reference model with adaptive benchmark updates, subtracting the real-time calculated theoretical elastic deformation benchmark from the radial profile sampling sequence of the flexible wheel, fundamentally eliminating the masking effect of strong elastic deformation background on weak distortion features. Based on this, a physical information sparse decomposition algorithm embeds the prior physical constraints of Donnell thin-shell theory into the sparse reconstruction iteration process. This allows for the elimination of spurious solutions through energy-bounded constraint pruning, even under underdetermined conditions where the number of sensors is far less than the number of unknown modal parameters, significantly improving the distinguishability of weak distortion modes in strong elastic deformation backgrounds. The cross-condition migration detection model decouples distortion discrimination features from condition domain distribution information through a collaborative mechanism of adversarial domain adaptation and meta-learning, ensuring robustness of classification and recognition under different conditions. In summary, this invention solves the technical problem mentioned in the background art of the inability to effectively separate and accurately reconstruct micro-waveform distortion features in multi-condition strong elastic deformation backgrounds. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method of the present invention.

[0026] Figure 2 This is a comparison chart of the distortion type identification results of the cross-condition migration detection model under different conditions and the reference annotation.

[0027] Figure 3 This is a diagram showing the circumferential distribution pattern of the three-dimensional spatial distribution matrix of the micro-waveform distortion of the flexible wheel.

[0028] Figure 4 The graph shows the relationship between the full-field waveform reconstruction error of the Bayesian compressed sensing framework and the number of measurement points. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0030] like Figure 1The diagram shown is a flowchart of a method for detecting micro-waveform distortion of a harmonic reducer flexspline provided by the present invention. This method includes the following steps:

[0031] S01. Based on multiple laser triangular displacement sensors or focused capacitive displacement sensors uniformly arranged along the circumferential direction on the outer wall of the flexible wheel, and using the encoder signal as the synchronous trigger source, the radial displacement data of the flexible wheel in multiple rotation cycles are synchronously superimposed and averaged to obtain the denoised radial contour sampling sequence of the flexible wheel.

[0032] S02. Input the radial profile sampling sequence of the flexible wheel into the high-precision reference model, combine the measured speed, measured load and measured temperature data to calculate the theoretical elastic deformation benchmark online, and dynamically compensate for changes in working conditions through the adaptive benchmark update mechanism, and output the residual signal.

[0033] S03. The vibration equation of the flexure is established based on Donnell's thin shell theory. The residual signal is expanded into a linear combination of the basis functions of the flexure's natural mode shape using the modal superposition principle. The residual signal is sparsely decomposed using the physical information sparse decomposition algorithm to obtain the modal coefficients of each order.

[0034] S04. Input the modal coefficients of each order into the cross-condition migration detection model. The cross-condition migration detection model classifies and identifies the modal coefficients of each order, outputs the waveform distortion type and the severity of waveform distortion, and converts the severity of waveform distortion into the maximum distortion amplitude of the dynamic distortion transformation function.

[0035] S05. Based on the Bayesian compressed sensing framework, the sparsity of the modal coefficients of each order under the modal basis is utilized. The full-field waveform is reconstructed using a sparse reconstruction algorithm with finite discrete measurement points. The modal coefficients of each order are mapped back to the spatial domain to obtain the three-dimensional spatial distribution matrix of the flex wheel micro-waveform distortion, which is used as the output of the flex wheel micro-waveform distortion detection result of the harmonic reducer.

[0036] S06, optionally, also includes: calculating a comprehensive evaluation value based on the dynamic distortion function, using the maximum distortion amplitude, distortion space coverage, and inference confidence as inputs, and adjusting the memory allocation and inference thread priority of the cross-condition migration detection model according to the interval to which the comprehensive evaluation value belongs.

[0037] The synchronous superposition averaging process refers to averaging the sampled values ​​corresponding to the same angular position within multiple rotation cycles based on the encoder trigger pulse. This causes random noise to attenuate with increasing superposition cycle number due to statistical independence, while the effective signal is linearly enhanced due to phase alignment, thereby improving the signal-to-noise ratio without sacrificing weak distortion characteristics. The number of superposition cycles is determined by conducting multiple rounds of comparative tests with different cycle numbers on a standard test bench, statistically analyzing the curves of the missed detection rate and false alarm rate as a function of the number of cycles, and taking the cycle number corresponding to the minimum sum of the missed detection rate and false alarm rate as the final parameter. The typical range is 32 to 256 cycles.

[0038] The laser triangular displacement sensor refers to a sensor that uses a laser beam to illuminate the surface being measured at a fixed angle. The distance between the surface and the sensor is calculated by receiving the displacement of the reflected light spot on a position-sensitive detector, achieving dynamic displacement measurement with zero contact force. The sampling bandwidth is no less than 100... The measurement range covers submicron to hundreds of micrometers; the number of sensors is usually 8 to 32, and the specific number is determined by simulation experiments on the change of spatial interpolation reconstruction error with the number of sensors. The minimum number of sensors corresponding to the point where the reconstruction error no longer decreases significantly is taken.

[0039] The focused capacitive displacement sensor refers to a non-contact displacement sensor that uses the principle that the capacitance between the electrode and the conductive surface being measured changes with the distance to perform non-contact displacement measurement. It is suitable for low-speed or medium-speed rotation scenarios, with zero measurement force and a resolution at the nanometer level.

[0040] The radial profile sampling sequence of the flexible wheel refers to the discrete numerical sequence of radial displacement corresponding to each measurement point along the circumferential direction of the outer wall of the flexible wheel after synchronous superposition and averaging. The sequence length is equal to the product of the number of sensors and the number of sampling points per sensor.

[0041] The high-precision reference model refers to a multi-body dynamics simulation model of the flexure under wave generator excitation, established using the stiffness, damping, tooth profile parameters, and assembly parameters of each component of the harmonic reducer as input. It utilizes measured speed, load, and temperature data to drive the simulation calculation of the theoretical elastic deformation benchmark in real time. The model parameters are iteratively corrected by collecting measured deformation data of a standard flexure under multiple speed and load conditions and performing least-squares fitting with the simulation results until the simulation error converges to 1. Up to this point.

[0042] The theoretical elastic deformation benchmark refers to the sequence of theoretical radial displacement values ​​of the elastic elliptical deformation of the flexural body calculated by the high-precision reference model under the current measured rotational speed, measured load, and measured temperature conditions.

[0043] The residual signal refers to the difference sequence obtained by subtracting the radial profile sampling sequence of the flexible wheel from the theoretical elastic deformation benchmark point by point, which contains the micro-waveform distortion information of the flexible wheel.

[0044] The adaptive reference update mechanism refers to periodically collecting the current measured rotational speed, measured load, and measured temperature values ​​during the detection process and comparing them with the corresponding values ​​at the previous update time. When the operating condition deviation exceeds a preset operating condition deviation threshold, the high-precision reference model is triggered to recalculate and replace the current theoretical elastic deformation reference. The preset operating condition deviation threshold is determined by statistically analyzing the impact of the theoretical elastic deformation reference deviation on the residual signal under different operating condition combinations, taking the value where the impact exceeds 1. The corresponding working condition deviation is used as the preset working condition deviation threshold, and the specific value is obtained through experimental data analysis.

[0045] The flexure's inherent mode shape basis functions refer to the analytical eigenfunctions of the flexure vibration equation established based on Donnell's thin shell theory. They are grouped according to the number of pitch diameters, and each group contains mode shape components in the radial, circumferential, and axial directions for the corresponding number of pitch diameters.

[0046] The modal coefficients of each order refer to the linear combination coefficients of the residual signal under the basis function expansion of the flexural mode, reflecting the contribution amplitude of each mode to the residual signal.

[0047] The physical information sparse decomposition algorithm establishes the partial differential vibration equation of the flexible wheel under wave generator excitation based on Donnell thin shell theory. It expands the residual signal into a linear combination of the flexible wheel's natural mode shape basis functions using the modal superposition principle, and establishes a sparse linear equation system between the residual signal and the modal coefficients of each order. The algorithm adopts a grouped orthogonal matching pursuit strategy, grouping the flexible wheel's natural mode shape basis functions according to the number of nodal diameters, and subtracting the modal contributions of each order from the residual signal in turn. In each iteration, the modal basis most relevant to the current residual is selected by the inner product maximization criterion. A physical constraint pruning mechanism is introduced to verify whether the current combination of modal coefficients of each order satisfies the energy bounded condition after each iteration, and to eliminate physically infeasible decomposition results. Finally, the reconstructed modal coefficients of each order are mapped back to the spatial domain to obtain the three-dimensional spatial distribution matrix of the flexible wheel's micro-waveform distortion.

[0048] The technical effects of the physical information sparse decomposition algorithm are as follows: It embeds prior physical knowledge of the partial differential vibration equations into the sparse reconstruction iteration process, ensuring the physical feasibility of the reconstruction results even under underdetermined conditions where the number of sensors is far less than the number of unknown modal parameters, by eliminating spurious solutions that do not meet the energy bounded condition through physical constraint pruning. The grouped orthogonal matching pursuit strategy utilizes the orthogonality of the flexural wheel's inherent mode shape basis functions grouped by the number of nodal diameters, ensuring that each iteration selects only the maximum product between the current residual and each group's basis. This significantly reduces the sensitivity of the underdetermined equation solution to noise, improves the distinguishability of weakly distorted modes under strong elastic deformation, and ultimately achieves high-precision reconstruction of the flexural wheel's micro-waveform distortion three-dimensional spatial distribution matrix with a small number of discrete measurement points.

[0049] The Donnell thin-shell theory refers to a simplified elasticity partial differential equation system established for thin-walled cylindrical shells. By neglecting the influence of the curvature of the shell surface on the membrane force and retaining the bending stiffness term, a fourth-order partial differential equation for radial displacement is obtained, which is applicable to thin-walled flexible wheels with a wall thickness to radius ratio of less than 1 / 20.

[0050] The grouped orthogonal matching pursuit refers to selecting and projecting the candidate basis functions in groups according to the number of nodal diameters based on the orthogonal matching pursuit algorithm. In each iteration, the coefficients of all flexure natural mode basis functions corresponding to the same number of nodal diameters are determined simultaneously, which improves the convergence speed and reconstruction accuracy of sparse reconstruction in structured sparse scenarios. The inner product maximization criterion refers to calculating the inner product between the residual signal and each group of flexure natural mode basis functions in each iteration, and selecting the basis function group with the largest absolute value of the inner product as the support set expansion direction of the current step.

[0051] The energy bounded condition refers to the fact that, within the normal elastic deformation range of the flexible wheel, the weighted sum of the squares of the modal coefficients of each order does not exceed the theoretical upper limit of elastic strain energy determined by the material's elastic modulus, wall thickness, and working load. The theoretical upper limit of elastic strain energy is obtained by performing finite element simulation on a standard flexible wheel under rated load, extracting the maximum value of the modal strain energy of each order, and taking 1.2 to 1.5 times it as the physical constraint pruning threshold. The specific multiple is determined through experimental verification under multiple working conditions.

[0052] The Bayesian compressed sensing framework refers to introducing a Bayesian prior probability model into the compressed sensing signal reconstruction problem. It uses a sparse prior to constrain the sparsity of the mode coefficients of each order, solves the underdetermined equation system through maximum a posteriori estimation or variational inference, and outputs the point estimates and confidence intervals of the mode coefficients of each order. Compared with deterministic regularization methods, the Bayesian compressed sensing framework automatically determines the regularization strength without manual parameter tuning, and provides quantitative information on reconstruction uncertainty.

[0053] The cross-condition migration detection model is a convolutional neural network that employs an adversarial domain adaptive and meta-learning collaborative mechanism. It is used to robustly classify and identify the modal coefficients of each order of the flexible wheel micro-waveform distortion under different operating conditions, and output the waveform distortion type and the severity of the waveform distortion.

[0054] The specific structure of the cross-condition migration detection model is as follows: The main body of the model adopts a dual encoder architecture. The feature encoder consists of 5 stacked one-dimensional convolutional layers, with the number of kernels in each layer being 32, 64, 128, 128, and 64 respectively, and the kernel size being 3. Each convolutional layer is followed by a batch normalization layer and a ReLU activation function. Finally, a global average pooling layer outputs a 128-dimensional condition-independent distortion discrimination feature vector. The domain encoder consists of 3 fully connected layers with dimensions of 128, 64, and 32 respectively, outputting a 32-dimensional domain distribution embedding vector. A gradient inversion layer is inserted between the feature encoder output and the domain classifier, and the gradient inversion coefficients are... The adjustment is adaptive and follows the training progress. The adjustment formula is as follows: ;in This is the ratio of the current number of training steps to the total number of training steps (dimensionless). The scaling factor (dimensionless) ranges from 8 to 12 and is determined by grid search on the validation set. The domain classifier consists of two fully connected layers with dimensions 32 and 2, outputting the discrimination probability between the source and target domains. The distortion classifier consists of three fully connected layers with dimensions 128, 64, and the number of waveform distortion categories, determined based on the actual fault mode library, typically ranging from 6 to 12. The prototype memory stores 128-dimensional prototype feature vectors for each waveform distortion mode. During inference, the nearest neighbor prototype is retrieved using cosine similarity for classification decisions, supporting online unsupervised updates to adapt to operating condition drift. The skip connection is designed as a conditional activation type, activating the cross-layer feature fusion path between layers 2 and 4 of the feature encoder only during the meta-testing stage and remaining closed during the meta-training stage. The contrastive learning loss uses a supervised contrastive loss function, applying the same waveform distortion pattern. The feature representations under different operating conditions are brought closer together, while the feature representations of different types of waveform distortion are pushed further apart. An improved model-independent meta-learning framework is wrapped around this framework, and meta-training is performed on multiple simulated operating conditions. The number of meta-training tasks ranges from 16 to 64, with 5 to 15 samples in both the support set and query set. The specific number is determined through multi-round meta-training convergence speed experiments. Regarding resource allocation, the 5-layer convolution operation of the feature encoder is distributed to two independent CUDA streams for parallel execution, the domain encoder and distortion classifier are distributed to a third CUDA stream, and the prototype memory retrieval operation is distributed to a fourth CUDA stream. The memory allocation of the four CUDA streams is hierarchically based on the comprehensive evaluation value output by the dynamic distortion function: when the comprehensive evaluation value is not less than 0.8, the memory allocation of the feature encoder stream increases to 60%, and the other three streams each account for approximately 13%; when the comprehensive evaluation value falls within the range... When the overall evaluation value is less than 0.5, the proportion of video memory in the prototype memory stream is reduced to 5%, releasing video memory resources for the feature encoder.

[0055] The steps for establishing the training dataset for the cross-condition migration detection model specifically include: collecting multi-sensor fusion feature data of a flexible wheel with artificially pre-fabricated micro-waveform distortion defects under standard laboratory conditions, labeling the waveform distortion type and maximum distortion amplitude, and constructing a source domain labeled dataset, with the maximum distortion amplitude range covering 1 to 50. For each type of waveform distortion, at least 500 samples are collected. Finite element simulation is used to parameterize and generate modal coefficient samples of different nodal diameters and amplitude combinations to form a simulation domain augmented dataset. Unlabeled flexible wheel operation data is collected under various variable operating conditions in the field to form a target domain unlabeled dataset. The source domain labeled dataset, simulation domain augmented dataset, and target domain unlabeled dataset are divided into a meta-training set, a meta-validation set, and a meta-test set in a 7:1:2 ratio. The division ratio is determined by comparing the accuracy of the meta-test under different ratios using cross-validation on small-scale pre-experiment data.

[0056] The specific steps for training the cross-condition migration detection model include: initializing outer-layer meta-parameters using an improved model-independent meta-learning framework on a meta-training task that mixes labeled datasets from the source domain and augmented datasets from the simulation domain. The inner-layer task adaptation learning rate ranges from 0.001 to 0.01, and the outer-layer meta-learning rate ranges from 0.0001 to 0.001. Specific values ​​are determined by searching on the meta-validation set using a Bayesian hyperparameter optimization method. In each meta-training task, the weighted sum of waveform distortion classification cross-entropy loss, adversarial domain adaptation loss, and supervised contrastive loss is simultaneously minimized. The initial weight ratios of these three factors are set as follows: The ratio of prototype features to data is set to 1:0.5:0.3 and dynamically adjusted during training based on the domain adaptation error on the meta-validation set. The initial prototype feature vectors in the prototype memory are obtained by averaging the waveform distortion feature vectors of various types in the labeled dataset of the source domain. An unsupervised online update strategy is adopted on the unlabeled dataset of the target domain, updating various prototype feature vectors with an exponential moving average. The update coefficient ranges from 0.9 to 0.99, and is determined by observing the classification stability on the validation data of the target domain. The total number of training epochs is determined by monitoring the change in the loss of the meta-validation set, and training is terminated when the loss no longer decreases for 20 consecutive meta-cycles.

[0057] The technical effects of the cross-condition migration detection model are as follows: The dual encoder architecture decouples the distortion discrimination features from the condition domain distribution information, allowing the feature encoder to focus on learning the essential waveform distortion features that are independent of the condition, thus avoiding the degradation of classification performance caused by feature distribution shifts under different conditions; the gradient inversion layer-driven adversarial training forces the condition-independent distortion discrimination feature vectors output by the feature encoder to be indistinguishable from the domain classifier, thereby achieving adaptive migration from the source domain to the target domain; the improved model-independent meta-learning framework gives the model the ability to quickly adapt to new conditions with a small number of target domain samples, reducing the dependence of field deployment on labeled data; the online unsupervised update mechanism of the prototype memory enables the model to track the slow changes in feature distribution caused by condition drift, maintaining long-term detection stability.

[0058] The dynamic distortion function is used to adjust the memory allocation and inference thread priority of the cross-condition migration detection model to maximize the distortion amplitude. (unit ), Distortion space coverage (Dimensionless, values ​​0-1) and inference confidence (Dimensionless, value 0-1) is the input, and the comprehensive evaluation value is... The formula for calculating (dimensionless) is as follows: ;in For reference distortion amplitude benchmark (unit) The value ranges from 5 to 20. The mean of the maximum distortion amplitude under normal operating conditions was obtained by statistically analyzing multiple batches of flexible wheel samples. , , The dimensionless weighting coefficients were initially set to 0.5, 0.3, and 0.2, and were determined iteratively by minimizing the weighted sum of resource waste rate and false negative rate on the validation dataset; the maximum distortion amplitude... The distortion spatial coverage is calculated from the waveform distortion severity output by the cross-condition migration detection model in step S04. The inference confidence level is calculated by the ratio of the number of spatial points in the three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion exceeding a preset amplitude threshold to the total number of spatial points. The maximum classification probability value is directly obtained from the distortion classifier output by the cross-condition migration detection model; when the comprehensive evaluation value When the value is not less than 0.8, the CUDA stream memory allocation ratio of the feature encoder is increased to 60%, the remaining memory is evenly distributed among the other three streams, and the inference thread priority is increased to the highest level; when the comprehensive evaluation value Belongs to the interval At that time, the four CUDA streams share the GPU memory equally, and the inference thread priority is set to medium; when the overall evaluation value When the value is less than 0.5, the proportion of CUDA stream video memory in the prototype memory library is reduced to 5%, and video memory resources are released for use by the feature encoder. The priority of the inference thread is set to low level. The preset amplitude threshold is obtained by taking the maximum value of the distortion amplitude in the three-dimensional spatial distribution matrix of the normal flexible wheel as the preset amplitude threshold in the comparative test of multiple batches of normal flexible wheels and defective flexible wheels. The specific value is obtained through experimental data analysis.

[0059] The severity of waveform distortion refers to the amplitude estimation results of various waveform distortions output by the distortion classifier of the cross-condition migration detection model. The maximum distortion amplitude is obtained by mapping the category labels output by the classifier to a pre-defined amplitude range. The amplitude range is determined by statistically analyzing the maximum distortion amplitude distribution of various waveform distortion samples in the labeled dataset of the source domain, and taking the mean ± 1 standard deviation of each category as the amplitude range of the corresponding category. The specific values ​​are obtained through experimental data analysis.

[0060] The three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion refers to a two-dimensional discrete matrix formed by mapping the modal coefficients of each order back to the spatial domain, with the discrete angular position of the outer wall of the flexible wheel in the circumferential direction as the row index, the discrete position in the axial direction as the column index, and the radial distortion displacement as the matrix element. It reflects the spatial distribution of the flexible wheel micro-waveform distortion in the circumferential and axial directions.

[0061] Optionally, the present invention also provides a system for detecting micro-waveform distortion of a harmonic reducer flexspline by means of a computer, wherein the computer is provided with a readable storage medium storing program instructions, and the program instructions execute the above-described method when the computer is run.

[0062] The specific implementation of step S01 is as follows: 8 to 32 laser triangular displacement sensors or focused capacitive displacement sensors are uniformly arranged along the circumferential direction on the outer wall of the flexible wheel. The laser triangular displacement sensor uses a laser beam to illuminate the outer wall of the flexible wheel at a fixed angle, and calculates the radial distance by receiving the displacement of the reflected light spot on the position-sensitive detector. The sampling bandwidth is not less than 100. Suitable for high-speed rotation scenarios; the focused capacitive displacement sensor utilizes the principle of capacitance change between the electrode and the conductive surface with distance for non-contact measurement, achieving nanometer-level resolution, suitable for low-speed or medium-speed scenarios. The number of sensors is determined through simulation experiments of spatial interpolation reconstruction error varying with the number of sensors, taking the minimum number corresponding to when the reconstruction error no longer significantly decreases. Using the encoder output pulse as the synchronous trigger source, the sampled values ​​at the same angular position are accumulated and averaged over multiple cycles of flexspline rotation, i.e., synchronous superposition averaging. This processing utilizes the statistical independence of random noise, causing the noise amplitude to attenuate with increasing superposition cycles, while the periodic signal aligned with the encoder phase is linearly enhanced, thereby improving the signal-to-noise ratio without sacrificing weak distortion characteristics. The number of superposition cycles is determined by statistically minimizing the sum of the false alarm rate and the missed detection rate on a standard test bench, typically ranging from 32 to 256 cycles. The final output length of the flexspline radial profile sampling sequence is equal to the product of the number of sensors and the number of sampling points per sensor.

[0063] The specific implementation of step S02 is as follows: A high-precision reference model is established using the stiffness, damping, tooth profile parameters, and assembly parameters of each component of the harmonic reducer as input. A multi-body dynamics simulation model of the flexure under wave generator excitation is established. The simulation is driven in real-time using measured speed, load, and temperature data. The theoretical radial displacement sequence of the flexure's main body elastic elliptical deformation under the current operating condition is calculated, i.e., the theoretical elastic deformation benchmark. Model parameters are iteratively corrected by collecting measured deformation data of the standard flexure under multiple speed and load conditions and performing least-squares fitting with the simulation results until the simulation error converges to within 1 μm. An adaptive benchmark update mechanism periodically collects the current measured speed, load, and temperature values ​​and compares them with the corresponding values ​​at the previous update time. When the operating condition deviation exceeds a preset operating condition deviation threshold, the model is triggered to recalculate and replace the current theoretical elastic deformation benchmark. The preset operating condition deviation threshold is the operating condition deviation amount corresponding to the influence of the theoretical elastic deformation benchmark deviation on the residual signal exceeding 1 μm, obtained through experimental data analysis. The radial profile sampling sequence of the flexible wheel is subtracted point by point from the theoretical elastic deformation benchmark to obtain the residual signal, which contains information on the micro-waveform distortion of the flexible wheel.

[0064] The specific implementation of step S03 is as follows: The vibration equation of the flexible wheel is established using Donnell's thin-shell theory. This theory, for thin-walled flexible wheels with a wall thickness-to-radius ratio less than 1 / 20, obtains a fourth-order partial differential equation regarding radial displacement by neglecting the influence of the shell's mid-surface curvature on the membrane force and retaining the bending stiffness term. Using the modal superposition principle, the residual signal is expanded into a linear combination of the flexible wheel's inherent mode shape basis functions. These basis functions are grouped according to the number of nodal diameters, with each group containing mode shape components in the radial, circumferential, and axial directions. The physical information sparse decomposition algorithm employs a grouped orthogonal matching pursuit strategy, selecting the flexible wheel's inherent mode shape basis functions in groups according to the number of nodal diameters. In each iteration, the inner product maximization criterion is used to select the mode basis set most relevant to the current residual, while simultaneously determining all basis function coefficients corresponding to the same nodal diameter. After each iteration, a physical constraint pruning mechanism is introduced to verify whether the weighted sum of squares of the current modal coefficients satisfies the energy bounded condition, that is, it does not exceed the theoretical upper limit of elastic strain energy determined by the material elastic modulus, wall thickness and working load. The theoretical upper limit of elastic strain energy is taken as 1.2 to 1.5 times the maximum value of modal strain energy of each order under rated load in finite element simulation. Physically infeasible decomposition results are eliminated, and finally the modal coefficients of each order are obtained.

[0065] The specific implementation of step S04 is as follows: The cross-condition migration detection model adopts a dual-encoder architecture. The feature encoder consists of five stacked one-dimensional convolutional layers. Each convolutional layer is followed by a batch normalization layer and a ReLU activation function. Finally, a global average pooling layer outputs a 128-dimensional condition-independent distortion discrimination feature vector. The domain encoder outputs a 32-dimensional domain distribution embedding vector. A gradient inversion layer is inserted between the feature encoder output and the domain classifier, and the gradient inversion coefficients... According to the formula Adaptive adjustment as training progresses. The value range is 8–12. Adversarial training forces the feature vector output by the feature encoder to be indistinguishable from the domain classifier, achieving adaptive transfer from the source domain to the target domain. The prototype memory stores 128-dimensional prototype feature vectors for each waveform distortion mode. During inference, the nearest neighbor prototype is retrieved using cosine similarity for classification decisions, and the model is updated online in unsupervised using an exponential moving average, with update coefficients ranging from 0.9 to 0.99. An improved model-independent meta-learning framework is wrapped around the model, and meta-training is performed on multiple simulated tasks, giving the model the ability to quickly adapt to new conditions with a small number of target domain samples. The model outputs the waveform distortion type and the severity of the waveform distortion, the latter being converted into the maximum distortion amplitude by mapping the category label to a pre-defined amplitude range. Input the dynamic distortion function.

[0066] The specific implementation of step S05 is as follows: Based on the Bayesian compressed sensing framework, a sparse prior constraint is introduced to constrain the sparsity of each order of modal coefficients. Underdetermined equations are solved through maximum a posteriori estimation or variational inference, outputting point estimates and confidence intervals for each order of modal coefficients without requiring manual adjustment of regularization parameters. Each order of modal coefficients is mapped back to the spatial domain. Using the discrete angular positions along the circumference of the flexible wheel's outer wall as row indices, the discrete axial positions as column indices, and the radial distortion displacement as matrix elements, a three-dimensional spatial distribution matrix of the flexible wheel's micro-waveform distortion is constructed. This matrix reflects the spatial distribution of micro-waveform distortion in the circumferential and axial directions, and serves as the output of the micro-waveform distortion detection result for the harmonic reducer's flexible wheel.

[0067] The specific implementation of step S06 is as follows: the dynamic distortion function uses the maximum distortion amplitude. Distortion space coverage and inference confidence For input, according to the formula Calculate the comprehensive evaluation value ,in As a reference for distortion amplitude, the value ranges from 5 to 20 μm, with a weighting factor... , , The initial values ​​were 0.5, 0.3, and 0.2. When the comprehensive evaluation value... When the value is not less than 0.8, the CUDA stream memory ratio of the feature encoder is increased to 60%, and the inference thread priority is set to the highest level; when the comprehensive evaluation value is... When the memory usage falls within the range [0.5, 0.8), all four streams share the memory equally, and the priority is set to medium. When the comprehensive evaluation value... When the value is less than 0.5, the proportion of CUDA stream memory in the prototype memory library is reduced to 5%, releasing memory resources for use by the feature encoder, and the priority is set to low.

[0068] It should be noted that the key technologies of this invention include: the high-precision reference model for adaptive benchmark updating precisely removes the strongly elastic deformation benchmark from the radial contour sampling sequence through multibody dynamics simulation and real-time driving of working conditions, so that only the real micro-waveform distortion information is retained in the residual signal, overcoming the problem of pseudo-distortion mixing caused by fixed benchmark in traditional methods; the physical information sparse decomposition algorithm embeds the prior physical constraints of Donnell thin shell theory into the grouped orthogonal matching pursuit iteration process, and eliminates false solutions through energy bounded condition pruning, solving the problem of reliable estimation of modal coefficients of each order under underdetermined measurement conditions, and improving the distinguishability of weak distortion modes under strong background deformation; the cross-working condition migration detection model decouples the distortion discrimination features from the working condition domain distribution information through adversarial domain adaptation and meta-learning collaboration, ensuring the robustness of classification and recognition under different working conditions. The synergistic effect of the three is as follows: the benchmark separation provides a clean residual input for modal decomposition, the physical constraint sparse decomposition provides high-quality modal features for cross-condition identification, and the cross-condition identification results adjust the allocation of computing resources through the feedback of the dynamic distortion function, forming a self-consistent closed loop from signal acquisition to three-dimensional reconstruction. Overall, it realizes the effective separation and accurate reconstruction of micro-waveform distortion features under the background of strong elastic deformation in multiple conditions.

[0069] It should be noted that during the long-term service of the flexure in a harmonic reducer, the micro-waveform distortion mode of the flexure's outer wall will slowly drift as the operating time increases. This means that the spatial distribution of distortion, the number of dominant pitch diameters, and the amplitude distribution will gradually deviate from the initial calibration state. This phenomenon is particularly pronounced under harsh service conditions such as high-frequency start-stop cycles and wide-temperature-range alternating loads. This leads to the technical problem of long-term model stability degradation. Specifically, after the detection model is trained under initial conditions, its classification accuracy continuously decreases over time, eventually resulting in missed or misjudged micro-waveform distortions. The cause of this technical problem is that distortion mode drift is essentially the result of the combined effects of fatigue accumulation and residual stress redistribution in the flexure material. This causes a slow shift in the statistical distribution of modal coefficients in the feature space, gradually reducing the cosine similarity between the class prototype feature vectors stored in the prototype memory and the current actual distortion features, thus invalidating the classification decision boundary. Common solutions to this technical problem include periodically re-collecting labeled data and retraining the model, or using a fixed-window incremental learning strategy to replace old samples. However, full retraining requires a large amount of newly labeled data, which is extremely costly in actual service scenarios due to the limited data acquisition window. Fixed-window incremental learning strategies are prone to catastrophic forgetting when faced with slow drift, meaning that adaptation to new operating conditions leads to a decrease in the ability to distinguish old operating conditions, and neither method can autonomously track the drift process under unlabeled conditions. This invention effectively solves this technical problem. The prototype memory uses an exponential moving average to perform online unsupervised updates on various prototype feature vectors, enabling the prototype feature vectors to continuously track the slow drift of the current actual distortion feature distribution in a smooth manner without the intervention of any new labeled data. The update coefficient of the exponential moving average ranges from 0.9 to 0.99, determined by observing classification stability on target domain validation data. A larger update coefficient ensures sufficient preservation of historical information, suppresses prototype jitter caused by noise disturbances, and allows slow drift components to be gradually integrated into the prototype representation. At the same time, the improved model-independent meta-learning framework gives the model the ability to quickly adapt to new operating conditions with a small number of target domain samples. Even when the drift amplitude is large, prototype correction can be completed quickly through inner layer adaptation with a very small number of new operating condition samples without retraining the entire network. The synergy of the two mechanisms enables the model to complement unsupervised drift tracking and supervised fast correction, fundamentally ensuring the stability and reliability of the detection model under long-term service conditions.

[0070] Specifically, the principle of this invention is as follows: The logical chain by which the technical solution of this invention solves the aforementioned core technical problems is as follows. First, random noise and periodic elastic deformation during the rotation of the flexible wheel superimpose in the signal space, and a single measurement cannot distinguish between the two. Synchronous superposition averaging processing utilizes the statistical independence of random noise, causing the noise to attenuate as the number of superposition cycles increases, while the periodic elastic deformation signal aligned with the encoder phase is linearly enhanced, thereby improving the signal-to-noise ratio without losing weak distortion characteristics, providing a high-quality radial profile sampling sequence for subsequent processing. Second, the theoretical elastic deformation benchmark of the flexible wheel differs significantly under different speeds, loads, and temperatures. If the benchmark cannot be dynamically updated with the operating conditions, a large amount of pseudo-distortion components caused by changes in operating conditions will be mixed into the residual signal. The high-precision reference model is based on multibody dynamics simulation, using measured speed, measured load, and measured temperature to drive the simulation calculation in real time, and triggers benchmark recalculation when the operating condition deviation exceeds a preset threshold through an adaptive benchmark update mechanism, thereby retaining only the true micro-waveform distortion information in the residual signal. Secondly, the residual signal is a complex waveform in the spatial domain, consisting of low amplitude and multiple superimposed modes, making it difficult to decompose the modal contributions directly using general signal processing methods. The physical information sparse decomposition algorithm uses the flexure's natural mode shape basis functions established by Donnell's thin-shell theory as a dictionary. Leveraging the orthogonality of the flexure modes under grouping by pitch diameter, it sequentially subtracts the modal contributions from the residual signal using a grouped orthogonal matching pursuit strategy. Simultaneously, it introduces energy bounded conditions to prune physically infeasible decomposition results, ensuring the physical feasibility of the reconstruction. This mechanism allows for reliable estimation of modal coefficients even under underdetermined measurement conditions. Furthermore, the statistical distribution of modal coefficients under different operating conditions exhibits domain shift, causing classifiers trained under a single operating condition to degrade in cross-operating-condition scenarios. The cross-operating-condition migration detection model employs a dual-encoder architecture, with a gradient inversion layer driving adversarial training. This makes the distortion discrimination features output by the feature encoder indistinguishable from those of the domain classifier, achieving operating-condition-independent distortion type recognition. The meta-learning framework endows the model with the ability to quickly adapt to new operating conditions using a small number of target domain samples, while the online unsupervised update mechanism of the prototype memory ensures long-term detection stability. Finally, the Bayesian compressed sensing framework utilizes the sparsity of modal coefficients under the modal modal basis to reconstruct the full-field waveform using a sparse reconstruction algorithm with a finite number of discrete measurement points, mapping the modal coefficients back to the spatial domain to obtain the three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion. The entire scheme forms a complete closed loop from signal acquisition, reference separation, modal decomposition, cross-operating condition identification to full-field reconstruction. Each step is based on physical constraints, ensuring effective separation and accurate reconstruction of micro-waveform distortion features under strong elastic deformation background and multi-operating condition interference.

[0071] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0072] The specific implementation of step S01 is as follows: Based on 8 to 32 laser triangular displacement sensors or focused capacitive displacement sensors uniformly arranged along the circumference of the outer wall of the flexible wheel, and using the encoder signal as the synchronous trigger source, the radial displacement data within multiple cycles of the flexible wheel rotation are synchronously superimposed and averaged to obtain a noise-reduced radial contour sampling sequence of the flexible wheel. The sampling bandwidth of the laser triangular displacement sensor is not less than 100. The measurement range covers submicron to hundreds of micrometers. The number of sensors was determined through simulation experiments showing the spatial interpolation reconstruction error as a function of the number of sensors. The minimum number of sensors was chosen when the reconstruction error no longer decreased significantly. Synchronous superposition and averaging processing was performed based on the encoder trigger pulse. The average value is calculated by summing the sampled values ​​corresponding to the same angular position within each rotation cycle. Let the th rotation cycle be... The sensor at the first The first rotation cycle, the first The radial displacement sampled values ​​at each sampling angle position are (unit Then the denoised flex wheel radial profile sampling sequence (unit The calculation formula for ) is expressed as follows:

[0073] ;

[0074] In the formula, Number the sensor. Number the sampling angle position. Number the rotation period. To determine the number of cycles, the curves showing the changes in false alarm rate and false alarm rate with the number of cycles are statistically analyzed on a standard test bench. The number of cycles corresponding to the minimum sum of the two is then determined, typically ranging from 32 to 256 cycles. Random noise varies with statistical independence. As the signal increases, it decreases, and the effective signal is linearly enhanced due to phase alignment.

[0075] The specific implementation of step S02 is as follows: sampling the radial profile sequence of the flexible wheel. Input a high-precision reference model, combined with actual measured rotational speed (unit ), measured load (unit ) and measured temperature (unit The theoretical elastic deformation benchmark is calculated online, and an adaptive benchmark update mechanism is used to dynamically compensate for changes in working conditions, outputting residual signals. A high-precision reference model is established using the stiffness, damping, tooth profile parameters, and assembly parameters of each component of the harmonic reducer as input. A multibody dynamics simulation model of the flexible wheel is established. The model parameters are iteratively corrected by least-squares fitting of measured deformation data and simulation results under multiple working conditions until the simulation error converges to 1. Within. The theoretical elastic deformation reference sequence is denoted as... (unit ), residual signal (unit The calculation formula for ) is expressed as follows:

[0076] ;

[0077] In the formula, For the first The sensor at the first Residual values ​​at each angular position (units) ), The corresponding theoretical elastic deformation reference value (unit) The adaptive benchmark update mechanism periodically collects the current measured rotational speed. Actual load and measured temperature The value is compared with the corresponding value at the previous update time. When the operating condition deviation exceeds the preset operating condition deviation threshold, the high-precision reference model is triggered to recalculate and replace the current value. The preset working condition deviation threshold is determined by statistically analyzing the influence of the elastic deformation benchmark deviation on the residual signal, taking the value of the influence exceeding 1. The corresponding operating condition deviation is determined.

[0078] The specific implementation of step S03 is as follows: The vibration equation of the flexible wheel is established based on Donnell's thin-shell theory. The residual signal is expanded into a linear combination of the natural mode shape basis functions of the flexible wheel using the modal superposition principle. A physical information sparse decomposition algorithm is then used to sparsely decompose the residual signal to obtain the modal coefficients of each order. For thin-walled flexible wheels with a wall thickness-to-radius ratio less than 1 / 20, Donnell's thin-shell theory establishes a fourth-order partial differential vibration equation regarding radial displacement, and the natural mode shape basis functions of the flexible wheel are... (Dimensionless) By number of nodes The components are arranged in groups, each group containing mode shape components in the radial, circumferential, and axial directions. Angular coordinates in the circumferential direction (units) ), Axial coordinates (units) The modal superposition expansion formula for the residual signal under the modal basis functions is expressed as follows:

[0079] ;

[0080] In the formula, For continuous domain residual signals (units) ), The maximum number of nodes, The mode order for each section diameter. For the first No. 1 Modal coefficients of order (units) ), These are the corresponding dimensionless normalized mode shape basis functions. To reconstruct the error term (unit) The physical information sparse decomposition algorithm employs a grouped orthogonal matching pursuit strategy, dividing the flexural gear's natural mode basis functions according to the number of pitch diameters. Grouping, defining the initial residual vector The residual signal output in step S02 The vector (unit) formed by arranging the measurement points in order. In each iteration, the mode basis set most relevant to the current residual is selected using the inner product maximization criterion. The formula for calculating the inner product maximization criterion is as follows:

[0081] ;

[0082] In the formula, For the first The current residual vector (in units) of the next iteration ), For the first The dimensionless matrix of the mode shape basis functions corresponding to the number of nodal diameters. The number of sections selected in the current step. This represents the inner product operation, and the unit of the inner product result is 1. After selecting the number of section diameters, the current support set... The update is performed, and the update formula is expressed as follows:

[0083] ;

[0084] In the formula, For the first The support set after one iteration, This is the support set from the previous iteration. This is a set union operation. After the support set is updated, the least squares update formulas for the modal coefficients of each order are expressed as follows:

[0085] ;

[0086] In the formula, For the first Modal coefficient estimation vector after one iteration (unit) ), This is the dimensionless submatrix of the mode shape basis function corresponding to the current support set. The vector of modal coefficients to be determined (units) ), For vector L2 norm, both terms within the parentheses on the right side of the equals sign have units of 1. After squaring, the dimensions are consistent. The update formula for the residual vector is expressed as follows:

[0087] ;

[0088] In the formula, For the first The residual vector after one iteration (units) The meanings of the variables are the same as above, and the units of the two terms on the right side of the equal sign are all... After each iteration, a physical constraint pruning mechanism is introduced to verify whether the modal coefficients of each order satisfy the energy boundedness condition. The formula for the energy boundedness condition is as follows:

[0089] ;

[0090] In the formula, For the first No. 1 Modal strain energy weighting coefficients corresponding to mode shapes (units) ), Units are Therefore Units are Right now , The maximum modal strain energy (in units) extracted from the finite element simulation of a standard flexible wheel under rated load. ), The physical constraint pruning threshold coefficient (dimensionless) is typically set to 1.2–1.5 and determined through multiple sets of experimental verification. Decomposition results that do not meet the energy boundedness condition are discarded to ensure the physical feasibility of the reconstruction results.

[0091] The specific implementation of step S04 is as follows: The modal coefficients of each order are... Input the cross-condition migration detection model, which classifies and identifies the modal coefficients of each order, outputs the waveform distortion type and the severity of waveform distortion, and converts the severity of waveform distortion into the maximum distortion amplitude. (unit The input to the dynamic distortion normalization function is used as the feature encoder. The cross-condition migration detection model adopts a dual encoder architecture. The feature encoder consists of 5 stacked one-dimensional convolutional layers, with the number of convolutional kernels in each layer being 32, 64, 128, 128, and 64 respectively. The kernel size is 3 for each layer. Each convolutional layer is followed by a batch normalization layer and a linear rectified activation function. A global average pooling layer outputs a 128-dimensional condition-independent distortion discrimination feature vector. (Dimensionless). Gradient reversal coefficient (Dimensionless) Adaptively adjusts with training progress; the adjustment formula is as follows:

[0092] ;

[0093] In the formula, This is the ratio of the current number of training steps to the total number of training steps (dimensionless). This is a scaling factor (dimensionless), typically ranging from 8 to 12, determined through a grid search on the validation set. This is a natural exponential function, and the entire right side of the equation is dimensionless. The prototype memory stores a 128-dimensional prototype feature vector for each waveform distortion mode. (Dimensionless), during reasoning, the nearest neighbor prototype is retrieved using cosine similarity to make classification decisions. The formula for calculating cosine similarity is as follows:

[0094] ;

[0095] In the formula, This is the current input 128-dimensional distortion discrimination feature vector (dimensionless). For the first The prototype feature vector (dimensionless) of waveform distortion. The waveform distortion category number is assigned. It is the dot product of vectors (dimensionless). and These are the L2 norms (dimensionless) of the corresponding vectors. The entire right side of the equation is dimensionless. The classification decision takes the class with the highest cosine similarity as the output. The severity of waveform distortion is calculated by mapping the class label output by the classifier to a pre-defined amplitude range. The amplitude range is determined by statistically analyzing the maximum distortion amplitude distribution of various waveform distortion samples in the labeled dataset of the source domain, taking the mean of each category ± 1 standard deviation.

[0096] The specific implementation of step S05 is as follows: Based on the Bayesian compressed sensing framework, utilizing the sparsity of modal coefficients under the modal modal basis, a sparse reconstruction algorithm is used to reconstruct the full-field waveform with a finite number of discrete measurement points, mapping the modal coefficients back to the spatial domain to obtain the three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion. The Bayesian compressed sensing framework introduces sparse prior constraints to constrain the sparsity of the modal coefficients, solves the underdetermined equations through maximum a posteriori estimation, and simultaneously outputs the point estimates and confidence intervals of the modal coefficients. The three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion is then obtained. The matrix is ​​constructed using discrete angular positions along the circumference of the flexible wheel's outer wall as row indices, discrete axial positions as column indices, and radial distortion displacements as matrix elements. The formula is as follows:

[0097] ;

[0098] In the formula, For the first The discrete positions of the circumferential angles, the first Radial distortion displacement at discrete axial positions (units) ), The number of discrete angle points along the circumference. The number of discrete position points along the axis. After mapping the modal coefficients of each order back to the spatial domain, according to The result is obtained through conversion.

[0099] The specific implementation of step S06 is as follows: based on the dynamic distortion function, with the maximum distortion amplitude... Distortion space coverage and inference confidence To input the comprehensive evaluation value Comprehensive evaluation value The formula for calculating (dimensionless) is as follows:

[0100] ;

[0101] In the formula, Maximum distortion amplitude (unit) ), For reference distortion amplitude benchmark (unit) ), It is a dimensionless quantity. The distortion space coverage (dimensionless, value 0-1) is given by the matrix. The ratio of the number of spatial points with distortion exceeding the preset amplitude threshold to the total number of spatial points is calculated. The inference confidence level (dimensionless, ranging from 0 to 1) is directly obtained from the maximum classification probability value output by the distortion classifier. , , The weighting coefficients are dimensionless, initially set to 0.5, 0.3, and 0.2. They are determined through iterative optimization by minimizing the weighted sum of resource waste rate and false negative rate on the validation dataset. All three terms in the numerator and denominator are dimensionless. The whole is a dimensionless quantity. The value is obtained by statistically analyzing the average maximum distortion amplitude under normal operating conditions on multiple batches of flexible wheel samples, typically ranging from 5 to 20. Based on the comprehensive evaluation value Memory allocation and inference thread priority for the cross-condition migration detection model within the specified range: when When the memory usage is not less than 0.8, the feature encoder stream's memory usage increases to 60%, while the other three streams each account for approximately 13%, and the inference thread's priority is increased to the highest level; when Belongs to the interval At that time, the four streams share the video memory equally, and the inference thread priority is set to medium. When the value is less than 0.5, the proportion of prototype memory stream memory is reduced to 5%, and memory resources are released for use by the feature encoder. The priority of the inference thread is set to low level.

[0102] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: To verify the effect of the invention, technicians set up a test environment and completed the full-process verification from sensor arrangement to micro-waveform distortion three-dimensional spatial distribution matrix output in the detection task of a certain type of harmonic reducer flexure according to the method described in this invention.

[0103] The flexible wheel has an outer diameter of 80 mm and a wall thickness of 1.8 mm, with a wall thickness-to-radius ratio of approximately 0.045, satisfying the applicability conditions of Donnell's thin-shell theory. Sixteen laser triangular displacement sensors are uniformly arranged along the circumference of the flexible wheel's outer wall, with a sampling bandwidth set to 200 kHz. The measurement range covers 0–500 μm. The number of sensors was determined through simulation experiments. With 16 sensors, the spatial interpolation reconstruction error no longer significantly decreases with increasing sensor count. The encoder resolution is 4096 lines / revolution, using encoder pulses as the synchronous trigger source, and the flexspline operates at 300... Data was collected under rotating conditions, with the number of superimposed cycles set to 128. By comparing the sum of the missed detection rate and false alarm rate under different number of cycles on a standard test bench, the comprehensive error rate corresponding to 128 cycles was the smallest. After the data collection was completed, the radial profile sampling sequence of the flexible wheel was output, with a sequence length of 16×256=4096 sampling points.

[0104] A high-precision reference model was established using the stiffness matrix, damping coefficient, tooth profile modification, and assembly preload of this type of harmonic reducer as inputs to create a multibody dynamics simulation model. The model parameters were iteratively corrected through least-squares fitting with measured deformation data of a standard flexspline under eight sets of speed and load conditions, resulting in a simulation error convergence to within 0.6 μm. Under the current operating condition, the measured speed is 300 rpm. The measured load was 60% of the rated load, and the measured temperature was 42℃. The theoretical elastic deformation benchmark was calculated in real time by the model. The radial profile sampling sequence of the flexible wheel was subtracted point by point from the theoretical elastic deformation benchmark to output the residual signal. The amplitude range of the residual signal was approximately 0 to 18 μm. The preset operating condition deviation threshold of the adaptive benchmark update mechanism was set as follows: the speed deviation exceeds 10 μm. When the load deviation exceeds 5% of the rated load or the temperature deviation exceeds 3℃, a recalculation is triggered. In this test, the baseline recalculation was triggered twice, which effectively suppressed the spurious distortion caused by the slow drift of the operating conditions.

[0105] The physical information sparse decomposition algorithm is based on the dictionary of natural mode basis functions of the flexible wheel established by Donnell thin shell theory. The basis functions are arranged in groups from 0 to 12 according to the number of nodal diameters, for a total of 13 groups. The grouped orthogonal matched pursuit strategy subtracts the modal contributions of each order from the residual signal in turn. The upper limit of the theoretical elastic strain energy under the energy bounded condition is taken as 1.35 times the finite element simulation result. The decomposition satisfies the convergence condition after 7 iterations. The main contributions come from the 2nd, 3rd and 4th order nodal diameter modes. The modal coefficients of each order are shown in Table 1.

[0106] Table 1. Statistical table of main modal coefficients for each order of nodal diameter.

[0107]

[0108] The modal coefficients of each order are input into the cross-condition migration detection model, and the feature encoder outputs a 128-dimensional condition-independent distortion discrimination feature vector. By searching the prototype memory through cosine similarity, it is identified that the current flexible wheel has ellipticity distortion dominated by the second-order pitch diameter, and the maximum distortion amplitude corresponds to the severity of waveform distortion. Converted to 11.3 μm, inference confidence level It is 0.91. For example... Figure 2 As shown, the comparison between the distortion type identification results of the cross-condition migration detection model under different conditions and the reference annotation intuitively reflects the model's cross-condition robustness.

[0109] Dynamic distortion function with μm, μm, , , , , Using the input as input, a comprehensive evaluation value is calculated. The memory is within the range [0.5, 0.8). The four CUDA streams share the video memory equally. The inference thread priority is set to medium. The system resources are allocated reasonably, and there is no video memory overflow or inference delay abnormality.

[0110] Based on a Bayesian compressed sensing framework, this study utilizes the sparsity of modal coefficients under modal modal bases. Using 16 discrete measurement points, a sparse reconstruction algorithm reconstructs the entire waveform, mapping the modal coefficients back to the spatial domain. The output is a three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion. The matrix row indices correspond to 360 discrete angular positions in the circumferential direction, and the column indices correspond to 8 discrete positions in the axial direction. The matrix elements represent radial distortion displacements in μm. Figure 3 As shown, the circumferential distribution pattern of the three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion intuitively demonstrates the spatial distribution characteristics of ellipticity distortion dominated by the second-order nodal diameter. The distortion amplitude exhibits two symmetrical extreme value regions in the circumferential direction, which highly matches the decomposition results of grouped orthogonal matching pursuit. Distortion spatial coverage The amplitude was calculated as the ratio of the number of spatial points in the matrix whose distortion exceeded a preset amplitude threshold to the total number of spatial points. The preset amplitude threshold was set to the maximum value of the distortion amplitude of the normal flexible wheel three-dimensional spatial distribution matrix, 6.2 μm. This indicates that approximately 34% of the circumferential axial spatial locations exhibit over-threshold distortion.

[0111] The sensor setup and data acquisition parameters for this testing process are summarized in Table 2.

[0112] Table 2 Sensor Layout and Data Acquisition Parameters

[0113]

[0114] like Figure 4 As shown, the relationship between the full-field waveform reconstruction error of the Bayesian compressed sensing framework under different sparsity conditions and the number of measurement points intuitively reflects the mechanism by which sparse prior constraints improve the underdetermined reconstruction accuracy. When the number of measurement points increases from 8 to 16, the reconstruction error decreases significantly, while when it increases from 16 to 32, the error decrease becomes gradual, verifying the rationality of selecting 16 sensors in this invention.

[0115] Compared to traditional contact roundness meters or general vibration spectrum analysis methods, this invention represents a fundamental advancement in its technical principles. Traditional methods, based on single measurements under static or low-speed conditions, cannot separate weak distortion components in a highly elastic deformation background. Furthermore, the fixed theoretical benchmark does not change with the operating conditions, leading to a large amount of spurious distortion mixed into the residual signal in multi-condition scenarios. This invention dynamically compensates for changes in operating conditions through an adaptive benchmark update mechanism, fundamentally eliminating spurious distortion interference. The physical information sparse decomposition algorithm embeds the prior physical constraints of Donnell's thin-shell theory into the sparse iterative process, ensuring the physical feasibility of modal coefficient estimation under underdetermined conditions and overcoming the spurious solution problem of general sparse decomposition methods in the absence of physical constraints. The cross-condition migration detection model, through adversarial domain adaptation and meta-learning collaboration, achieves robust recognition without a large amount of cross-condition labeled data, fundamentally solving the inherent performance degradation defect of traditional classifiers in cross-condition migration scenarios.

[0116] It should be noted that the variables involved in this invention are explained in detail in Table 3.

[0117] Table 3. Variable Explanation Table

[0118]

[0119] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for detecting micro-waveform distortion of the flexspline in a harmonic reducer, characterized in that, Includes the following steps: Based on multiple displacement sensors evenly arranged along the circumference on the outer wall of the flexible wheel, and with the encoder signal as the synchronous trigger source, the radial displacement data of the flexible wheel in multiple rotation cycles are synchronously superimposed and averaged to obtain the noise-reduced radial contour sampling sequence of the flexible wheel. The radial profile sampling sequence of the flexible wheel is input into a high-precision reference model. The theoretical elastic deformation benchmark is calculated online by combining the measured speed, measured load and measured temperature data. The working condition changes are dynamically compensated by an adaptive benchmark update mechanism, and the residual signal is output. The vibration equation of the flexure is established based on Donnell thin shell theory. The residual signal is expanded into a linear combination of the basis functions of the flexure's natural mode shape using the modal superposition principle. The residual signal is sparsely decomposed using the physical information sparse decomposition algorithm to obtain the modal coefficients of each order. The modal coefficients of each order are input into the cross-condition migration detection model, which classifies and identifies the modal coefficients of each order and outputs the waveform distortion type and the severity of waveform distortion. Based on the Bayesian compressed sensing framework, the sparsity of modal coefficients under the modal modal basis is utilized. The full-field waveform is reconstructed using a sparse reconstruction algorithm with finite discrete measurement points. The modal coefficients are then mapped back to the spatial domain to obtain the three-dimensional spatial distribution matrix of the flex wheel micro-waveform distortion, which is used as the output of the flex wheel micro-waveform distortion detection result of the harmonic reducer. Specifically, the physical information sparse decomposition algorithm adopts a grouped orthogonal matching pursuit strategy, which groups the flexural mode basis functions according to the number of nodal diameters, and subtracts the modal contributions of each order from the residual signal in turn. In each iteration, the modal basis most relevant to the current residual is selected by the inner product maximization criterion, and a physical constraint pruning mechanism is introduced to verify the energy bounded condition. Specifically, the energy bounded condition is that the weighted sum of squares of the modal coefficients of each order does not exceed the theoretical upper limit of elastic strain energy determined by the material's elastic modulus, wall thickness, and working load. The theoretical upper limit of elastic strain energy is determined by performing finite element simulation on a standard flexible wheel and taking the physical constraint pruning coefficient multiple of the maximum value of each modal strain energy under rated load. Specifically, the cross-condition migration detection model employs a convolutional neural network with a collaborative mechanism of adversarial domain adaptation and meta-learning, comprising a feature encoder, a domain encoder, a gradient inversion layer, a domain classifier, a distortion classifier, and a prototype memory.

2. The method for detecting micro-waveform distortion of the flexspline in a harmonic reducer according to claim 1, characterized in that, The displacement sensors, specifically laser triangular displacement sensors or focused capacitive displacement sensors, are uniformly arranged along the circumference, and their number is determined through simulation experiments on the variation of spatial interpolation reconstruction error with the number of sensors.

3. The method for detecting micro-waveform distortion of the flexspline in a harmonic reducer according to claim 2, characterized in that, The synchronous superposition averaging process specifically uses the encoder trigger pulse as a reference, accumulates the sampled values ​​corresponding to the same angular position within multiple rotation cycles, and then calculates the average value. The number of superposition cycles is determined by the number of cycles corresponding to the minimum sum of the missed detection rate and the false alarm rate.

4. The method for detecting micro-waveform distortion of the flexspline in a harmonic reducer according to claim 3, characterized in that, The high-precision reference model is specifically a multibody dynamics simulation model established with the stiffness, damping, tooth profile parameters and assembly parameters of each component of the harmonic reducer as inputs. The model parameters are iteratively corrected by least-squares fitting with the measured deformation data until the simulation error converges.

5. The method for detecting micro-waveform distortion of the flexspline in a harmonic reducer according to claim 4, characterized in that, The adaptive reference update mechanism specifically involves periodically collecting measured rotational speed, measured load, and measured temperature values. When the operating condition deviation exceeds a preset operating condition deviation threshold, the high-precision reference model is triggered to recalculate and replace the current theoretical elastic deformation reference.

6. The method for detecting micro-waveform distortion of the flexspline in a harmonic reducer according to claim 5, characterized in that, The residual signal is specifically a difference sequence obtained by subtracting the radial profile sampling sequence of the flexible wheel from the theoretical elastic deformation benchmark point by point, which contains information on the micro-waveform distortion of the flexible wheel.

7. The method for detecting micro-waveform distortion of the flexspline in a harmonic reducer according to claim 6, characterized in that, The three-dimensional spatial distribution matrix of the flexible wheel micro-waveform distortion is specifically a two-dimensional discrete matrix composed of discrete angular positions along the circumference of the flexible wheel's outer wall as row indices, discrete axial positions as column indices, and radial distortion displacement as matrix elements.

Images