Error prediction method for multistage transmission system

Abstract

The invention discloses a multi-stage transmission system error prediction method, which comprises the steps of performing first-stage time sequence feature joint extraction on an assembly error parameter and a planetary reducer short-time output error curve based on a first time-varying feature fusion layer to obtain a first prediction error sequence of a multi-stage transmission system; based on a second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, performing second-stage time sequence feature joint extraction on the first prediction error sequence and the harmonic reducer input end short-term error data to obtain a second prediction error sequence of the multi-stage transmission system; and based on a third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer, performing third-stage time sequence feature extraction on the second prediction error sequence to obtain a third prediction error sequence of the multi-stage transmission system, and taking the third prediction error sequence as a final error of the multi-stage transmission system, thereby accurately depicting the error based on cascading.

Description

Technical Field

[0001] The present application relates to the field of artificial intelligence technology, and in particular to a method for predicting errors in a multi-stage transmission system. Background Art

[0002] Multi-stage reduction mechanisms, with their high transmission ratios, compact structure, and high precision, have gained a significant presence in high-end equipment such as robotics, aerospace, and medical devices. In particular, tandem multi-stage reduction systems have become the mainstream choice for complex assembly scenarios with stringent requirements for motion accuracy and operational stability. These systems consist of multiple sub-stage reducers with varying structures, functions, and precision requirements. Each sub-stage has a distinct division of labor, such as some responsible for high-torque output and others for high-precision transmission.

[0003] In actual operation, because the transmission path is formed by the specific connection between the sub-stage reducers, the assembly errors of each sub-stage will propagate and accumulate along the path in a coupled manner. This multi-stage coupled error propagation exhibits nonlinear characteristics and the presence of an error feedback loop, causing errors at different stages to be interconnected and amplified step by step. Ultimately, this leads to significant dynamic errors at the system output, seriously affecting the equipment's operational performance.

[0004] Currently, modeling and prediction techniques for multi-stage transmission error propagation mechanisms are still imperfect. Traditional methods, such as polynomial regression, BP neural networks, and support vector machines (SVMs), primarily model static input-output relationships or single-stage errors, and are only applicable to scenarios with simple structures and clear characteristic relationships. Faced with the complex nonlinear coupling, error feedback, and dynamic inter-stage correlations in multi-stage transmission systems, these methods struggle to accurately characterize error propagation patterns, and their prediction accuracy and generalization capabilities fall short of practical requirements. Summary of the Invention

[0005] An embodiment of the present application provides a technical solution for a multi-stage transmission system error prediction method.

[0006] A multi-stage transmission system error prediction method, comprising:

[0007] Based on the first time-varying feature fusion layer, the first-level time series features of the assembly error parameters and the short-term output error curve of the planetary reducer are jointly extracted to obtain the first prediction error sequence of the multi-stage transmission system;

[0008] Based on the second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, the second-level time series feature is jointly extracted from the first prediction error sequence and the short-term error data at the input end of the harmonic reducer to obtain the second prediction error sequence of the multi-stage transmission system;

[0009] Based on the third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer, the third-level temporal feature extraction is performed on the second prediction error sequence to obtain a third prediction error sequence of the multi-stage transmission system, and the third prediction error sequence is used as the final error of the multi-stage transmission system.

[0010] A multi-stage transmission system error prediction method, comprising:

[0011] Based on the first time-varying feature fusion layer, the first-level temporal features are jointly extracted from the previous-stage static assembly parameters and the previous-stage short-term output error curve to obtain the first prediction error sequence of the multi-stage transmission system;

[0012] Based on a second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, second-level time series features are jointly extracted from the first prediction error sequence and the short-term error data at the input end of this level to obtain a second prediction error sequence for the multi-stage transmission system; based on a third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer, third-level time series features are extracted from the second prediction error sequence to obtain a third prediction error sequence for the multi-stage transmission system, and the third prediction error sequence is used as the final error of the multi-stage transmission system;

[0013] The multi-stage transmission system includes at least two-stage transmission structures, and each stage transmission structure has independent assembly parameters and error output characteristics.

[0014] A multi-stage transmission system error prediction method, comprising:

[0015] Based on the first time-varying feature fusion layer, the first-level temporal features are jointly extracted from the previous-stage static assembly parameters and the previous-stage short-term output error curve to obtain the first prediction error sequence of the multi-stage transmission system;

[0016] Based on the next time-varying feature fusion layer cascaded with the previous time-varying feature fusion layer, the previous level prediction error sequence and the short-term error data at the input end of this level are input to jointly extract the next level of time series features to obtain the prediction error sequence of the corresponding level;

[0017] Repeat the above steps until multi-level temporal feature extraction is completed through at least two layers of time-varying feature fusion layers, and use the prediction error sequence output by the last level of time-varying feature fusion layer as the final error of the multi-level transmission system;

[0018] The multi-stage transmission system comprises at least two transmission structures, each of which has independent assembly parameters and error output characteristics. The technical solution provided by the embodiment of the present application has at least the following beneficial effects:

[0019] This solution constructs a three-level cascade structure of time-varying feature fusion layers, which strictly corresponds to the actual error transmission path of the multi-stage transmission system. The first time-varying feature fusion layer jointly extracts the assembly error parameters and the short-term output error curve for the planetary reducer to accurately capture the primary error source; the second time-varying feature fusion layer is based on the prediction results of the previous level, combined with the short-term error data at the input end of the harmonic reducer, to model the process of error transmission from the planetary reducer to the harmonic reducer; the third time-varying feature fusion layer completes the final error prediction. This cascade architecture transforms the complex characteristics of error coupling, feedback, and step-by-step amplification in the multi-stage system into a clear stage-by-stage prediction task. Compared with traditional methods, it can fully characterize the dynamic evolution of the entire process from error generation to final output, making the error propagation path analyzable and predictable.

[0020] This solution achieves deep interaction between static and dynamic data through a time-varying feature fusion layer. In the first-level joint extraction of temporal features, a cross-attention mechanism uses static assembly parameters as queries and calculates similarity with the keys of dynamic error sequences. Subsequent cascaded time-varying feature fusion layers continuously utilize the previous prediction results as auxiliary information, strengthening the interaction between static and dynamic information. Compared to traditional methods that only process a single data type, this solution improves prediction accuracy by an average of over 30% across various operating conditions and assembly states.

[0021] This solution integrates a temporal convolutional network (TCN), a bidirectional long short-term memory network (BiLSTM), and a multi-head attention mechanism (MHA) within the time-varying feature fusion layer to achieve multi-scale temporal feature extraction. TCN's causal convolution ensures that feature extraction conforms to temporal causal logic, while dilated convolution expands the receptive field, capturing local mutations in error sequences, such as sudden errors caused by shock and vibration at the moment of device startup. BiLSTM explores long-range dependencies in sequences from both forward and reverse directions, accurately modeling periodic error fluctuations, such as those caused by gear meshing. The multi-head attention mechanism adaptively focuses on key time steps, such as when the load suddenly changes, to enhance the extraction of error features at that moment. Working together, these three improve the accuracy of modeling nonlinear error changes by 40% compared to traditional single-network structures, enabling more accurate prediction of the complex evolution of errors in multi-level systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Flowchart of the multi-stage transmission system error prediction method provided for the implementation of this application.

[0023] Figure 2 Schematic diagram of the system framework provided for the implementation of this application. DETAILED DESCRIPTION

[0024] like Figure 1 Shown and Figure 2As shown, a multi-stage transmission system error prediction method includes:

[0025] Based on the first time-varying feature fusion layer, the first-level time series features of the assembly error parameters and the short-term output error curve of the planetary reducer are jointly extracted to obtain the first prediction error sequence of the multi-stage transmission system;

[0026] Based on the second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, the second-level time series feature is jointly extracted from the first prediction error sequence and the short-term error data at the input end of the harmonic reducer to obtain the second prediction error sequence of the multi-stage transmission system;

[0027] Based on the third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer, the third-level temporal feature extraction is performed on the second prediction error sequence to obtain a third prediction error sequence of the multi-stage transmission system, and the third prediction error sequence is used as the final error of the multi-stage transmission system.

[0028] Optionally, at least one of the first time-varying feature fusion layer, the second time-varying feature fusion layer, and the third time-varying feature fusion layer includes: a cascaded time feature extraction layer, a dependency extraction layer, and an attention layer, the time feature extraction layer performs time series feature extraction on the assembly error parameter and the planetary reducer short-time output error curve, or at least one of the second prediction error sequence to obtain a corresponding output, the dependency extraction layer performs dependency feature relationship extraction on the output of the time feature extraction layer to obtain a corresponding output, and the attention layer performs attention calculation on the output of the dependency extraction layer to obtain a corresponding output.

[0029] Optionally, the temporal feature extraction layer is constructed based on a TCN network or a Transformer Encoder layer; the dependency extraction layer is constructed based on a BiLSTM, GRU, or Unidirectional LSTM; and the attention layer is constructed based on a multi-head attention layer.

[0030] Preferably, in a specific scenario, from an optional or alternative perspective, the specific technical details of the above solution are as follows:

[0031] 1. Mathematical model of the time-varying feature fusion layer

[0032] 1.1 Temporal Feature Extraction Layer

[0033] According to the timing characteristics of the assembly error parameters and the output error curve of the planetary reducer, the improved TCN network adopts a causal dilated convolution structure, and its mathematical model is:

[0034]

[0035] in: represents the input feature vector at time t, which includes assembly error parameters (such as sun gear eccentricity, wave generator tilt angle, etc.) and error curve sampling values ​​(such as vibration acceleration, angular displacement, etc.), D in The total dimension of the input features, including the sum of the dimensions of static parameters and dynamic time series data. d : represents the dilated convolution operation with a dilation factor of d, which expands the receptive field of the convolution kernel by interval sampling, enabling the network to capture longer-distance temporal dependencies.

[0036] is the convolution kernel weight, K is the convolution kernel size (i.e. the number of time steps involved in the convolution operation), D in is the input feature dimension, D out It is the output feature dimension, which is used to convert the input features into a higher-level representation. is a bias term that introduces a learnable offset to the result of the convolution operation to increase the model's fitting ability. σ: is a sigmoid activation function that maps the input to the (0,1) interval and is used to generate a gating signal. g: is a GLU (Gated Linear Unit) activation function that controls the flow of information through a gating mechanism. The formula is Represents element-wise multiplication, used to fuse corresponding elements of two vectors. Expansion factor d = 2 l , l is the number of network layers, ensuring that as the number of network layers increases, the receptive field grows exponentially and can capture longer-term temporal dependencies.

[0037] For the processing of assembly error parameters, a cross-modal attention mechanism is introduced:

[0038]

[0039] in: is the assembly error parameter matrix, M is the number of samples (such as different assembly batches or test instances), D param It is the dimension of the assembly error parameter (such as the number of parameters such as eccentricity and tilt angle). and is the projection matrix used to map the assembly error parameters and input feature vectors to the feature space of attention calculation, D attn is the dimension of the attention mechanism. is the parameter attention weight, which indicates the degree of attention of the assembly error parameter to the input features at time t. It is normalized by the softmax function and used to weightedly fuse the input features.

[0040] 1.2 Dependency Extraction Layer

[0041] To capture the bidirectional dependency of the error sequence, the improved BiLSTM adopts a gated residual connection structure:

[0042]

[0043] in:

[0044] and Represent the forward and backward LSTM units, respectively, which are used to extract the temporal dependencies of the error sequences from two directions.

[0045] [;]: represents the vector concatenation operation, which concatenates the outputs of the forward and backward LSTMs in the dimension.

[0046] α t : It is an adaptive gating parameter that controls the strength of the residual connection and determines the relationship between the forward and backward LSTM outputs and the original input. fusion ratio.

[0047] and is the gating parameter, used to calculate the gating signal, D hidden is the dimension of the LSTM hidden layer.

[0048] In order to deal with nonlinear mutations in the error sequence, a dynamic forget gate mechanism is introduced:

[0049]

[0050] in:

[0051] is a dynamic gain term used to adjust the sensitivity of the forget gate to error mutations.

[0052] γ: A learnable parameter that is adjusted through training to control the intensity of the dynamic gain.

[0053] and To calculate the parameters of the forget gate, where D out is the TCN output dimension, D hidden is the LSTM hidden layer dimension.

[0054] 1.3 Attention Layer

[0055] To meet the need for identifying the key time steps of the error sequence, the improved multi-head attention mechanism introduces time-aware weights:

[0056] MultiHead(Q,K,V)=Concat(head1,...,head h )W O

[0057] in:

[0058] head i =Attention(QW i Q ,KW i K ,VW i V )

[0059]

[0060] Time-aware matrix A t Defined as:

[0061] A t =β·sin(ωt+φ)·I n×n

[0062] in:

[0063] Q, K, V: query, key, and value matrices, respectively, used to calculate attention weights. Their dimensions are usually related to the model input features.

[0064] is the projection matrix, d model is the feature dimension of the model, d k and d v are the dimensions of keys and values ​​respectively.

[0065] To output the projection matrix, the results of the multi-head attention are mapped back to the feature dimension of the model, where h is the number of attention heads.

[0066] β, ω, φ: are learnable time modulation parameters, β controls the strength of the time perception signal, ω controls the cycle frequency, and φ controls the phase offset.

[0067] I n×n : is the unit matrix, ensuring that the time perception signal can be correctly integrated into the attention calculation, and n is the dimension of the attention matrix.

[0068] 2. Mathematical Expression of Cascade Prediction Framework

[0069] 2.1 Output of the First Time-Varying Feature Fusion Layer

[0070]

[0071] in:

[0072] is the assembly error parameter matrix, with the same meaning as above.

[0073] is the short-time output error curve of the planetary reducer, M is the number of samples, T1 is the time step (such as the number of sampling points), D err It is the dimension of the error characteristic (such as vibration amplitude, speed, etc.).

[0074] is the first prediction error sequence, D pred It is the characteristic dimension of the prediction error, which contains the prediction results of the planetary reducer error.

[0075] 2.2 Output of the Second Time-Varying Feature Fusion Layer

[0076]

[0077] in:

[0078] is the short-term error data of the harmonic reducer input, T2 is the time step of the harmonic reducer data, D in is the input feature dimension.

[0079] The timing map for the static assembly error parameters is generated as follows: Repeat(·,T2) means that the static parameters are replicated T2 times along the time dimension. and is a learnable parameter; Convert static assembly errors into temporal representations aligned with dynamic sequences to resolve the problem of mismatch in spatiotemporal dimensions;

[0080] is the second prediction error sequence, which includes the error prediction results of the harmonic reducer after considering the static assembly error and the error transmission of the planetary reducer.

[0081] 2.3 Output of the Third Time-Varying Feature Fusion Layer

[0082]

[0083] in:

[0084] is the final prediction error sequence, which represents the error prediction result of the final output of the multi-stage transmission system when the static assembly error is considered, and T3 is the time step of the final prediction.

[0085] is a nonlinear mapping of static assembly errors, generated as follows:

[0086] σ is the sigmoid function, W p2 ,W p3 ,b p2,b p3 is the learnable parameter Gate(E2)=σ g (W g E2+b g ) is a gating mechanism that controls the influence of static parameters on different time steps. ⊙ represents element-by-element multiplication to achieve adaptive fusion of static and dynamic features.

[0087] Introducing nonlinear transformation in the third layer Capture the complex nonlinear relationship between static parameters and dynamic errors; dynamically adjust the influence weights of static parameters at different time steps through Gate (E2) to enhance the model's adaptability to changes in working conditions. Feature cascade: retain E2 and the fused static information simultaneously in the third-layer input to form a complete error propagation chain representation.

[0088] 3. Dynamic Weighted Loss Function

[0089] In order to optimize the training process of the cascade model, a dynamic weighted loss function is designed:

[0090]

[0091] in:

[0092] α i : is the learnable weight of the i-th level, which is adjusted through back propagation to balance the contribution of prediction results of different levels to the total loss.

[0093] Y i : is the target error sequence of level i, which is the real error data obtained by actual measurement.

[0094] It is the mean square error, which measures the square mean of the error between the predicted value and the true value and is used to penalize larger errors.

[0095] The mean absolute error measures the mean absolute value of the error between the predicted value and the true value, and is relatively robust to outliers.

[0096] It is the symmetric mean absolute percentage error, which measures the prediction error as a percentage and is suitable for comparing the prediction accuracy of data of different magnitudes.

[0097] λ1,λ2,λ3: To balance the hyperparameters of different loss functions, by adjusting their proportions, we can control the weights of different types of losses in the total loss.

[0098] Dynamic weight update mechanism:

[0099]

[0100] in:

[0101] η: is the learning rate, which controls the step size of weight update and determines the convergence speed of the model during training.

[0102] 4. Mathematical modeling of error propagation paths

[0103] In order to quantify the propagation characteristics of errors in multi-level systems, the error propagation coefficient matrix Γ is introduced:

[0104]

[0105] in:

[0106] γ ij : It represents the influence coefficient of the i-th level error on the j-th level error and is calculated by the following formula:

[0107]

[0108] This formula quantifies the degree of amplification or attenuation of the error transferred from the i-th level to the j-th level by calculating the partial derivative of the j-th level error with respect to the i-th level error and combining the norms of the two-level errors.

[0109] The final error prediction can be expressed as:

[0110] E3=Γ 31 ·E1+Γ 32 E2+∈

[0111] in:

[0112] ∈: is the unmodeled error term, which obeys Gaussian distribution It indicates random errors that cannot be captured by the model or complex factors that are not considered.

[0113] The meanings of other parameters in the above formula are as follows:

[0114] Q m : The query vector of the mth sample, after the static assembly error parameters are embedded in the spatiotemporal tensor and transformed, is mapped to the attention query space, which is used to calculate the similarity with the dynamic feature sequence in the cross-attention layer. The dimension is

[0115] K mt : The key vector of the mth sample at time t is generated by multi-scale convolution and maximum pooling operations on the feature sequence containing long-term span information, with a dimension of Serves as the key input for calculating similarity with the query vector in the cross-attention layer.

[0116] Score mt: The similarity score between the assembly error parameter and the feature sequence containing long-span information at time t and the mth sample. The score is calculated based on the hyperbolic space. The smaller the value, the higher the degree of correlation between the two. It is used to generate the attention weight later.

[0117] α mt : The attention weight of the mth sample at time t is obtained by processing the similarity score through the Gaussian mixture model. The value range is [0,1]. It is used to measure the correlation between static parameters and dynamic features and guide the feature fusion process.

[0118] In the second time-varying feature fusion layer, the complex bidirectional LSTM network forward propagates the hidden state at time t to capture the information dependency from the past to the current moment.

[0119] The complex bidirectional LSTM network backpropagates the hidden state at time t to capture the information dependency from the future to the present moment.

[0120] h t : The bidirectional dependency feature representation obtained by fusing the forward and reverse hidden states through the gating mechanism integrates the forward and backward information and serves as the basic feature for subsequent calculations.

[0121] β t : The attention weight distribution generated by the tensor decomposition attention mechanism at time t is used to measure the importance of features at different time steps and then perform weighted fusion of features.

[0122] E 2t : The value of the second prediction error sequence output by the second time-varying feature fusion layer at time t integrates the bidirectional dependency characteristics of the first prediction error sequence and the short-term error data at the input of the harmonic reducer.

[0123] In the third time-varying feature fusion layer, the second prediction error sequence E 2t The results after nonlinear perturbation by Lie group transformation are used for subsequent mutation feature detection.

[0124] ΔE 2t : Measure the error sequence after nonlinear perturbation With the original sequence E 2t The difference index takes into account the sequence amplitude change and gradient change, and is used to detect mutation characteristics in the system.

[0125] Alert t : The mutation alarm signal at time t is a binary variable. 2t Exceeding the adaptive threshold (μ t +k·σ t) t A value of 1 indicates that a mutation is detected; otherwise, a value of 0 indicates that no mutation is detected. It is used to indicate whether the system has experienced abnormal changes.

[0126] E 3t : The value of the third prediction error sequence output by the third time-varying feature fusion layer at time t, which is fused with the second prediction error sequence E 2t , mutation characteristic index ΔE 2t And mutation alert signal Alert t The related information is the further prediction result of the multi-stage transmission system error.

[0127] E final :The prediction result of the final output of the complete system architecture is obtained by the attention mechanism on the output of the three-level time-varying feature fusion layer (E 1t 、E 2t 、E 3t ) is obtained by adaptive weighted integration, which integrates the feature information of different levels and is the final conclusion of the error prediction of the multi-stage transmission system.

[0128] In this application, considering that in a multi-stage transmission system, the error sources are complex and the propagation paths are intertwined, it is difficult for traditional methods to accurately model them. Therefore, the above-mentioned specific algorithm is designed to solve the problems of dynamic timing and static parameter fusion, long-term and short-term dependency capture, and error propagation quantification. For ease of understanding, its core principles and technical advantages are explained as follows.

[0129] 1. Time-varying feature fusion layer:

[0130] 1.1 Improved TCN: Multi-scale Capture of Temporal Features and Parameter Fusion

[0131] During the operation of the planetary reducer, the error curve contains multi-scale features such as transient mutations of the starting impact and periodic vibrations of the gear meshing. At the same time, assembly parameters (such as the eccentricity of the sun gear) will cause nonlinear changes in the error. In the example, the expansion factor d = 2 l This exponentially increases the network's receptive field, enabling it to capture features over longer time spans with fewer layers than traditional TCNs. For example, when analyzing 1,000 time steps of gearbox vibration data, this architecture can capture the first 64 time steps in just the third layer, while a traditional TCN would require six layers to achieve a similar effect, significantly reducing computational complexity.

[0132] Cross-modal attention mechanism and For the first time, static assembly parameters are linked to dynamic error sequences. For example, in an industrial robot joint, when the sun gear is 0.05mm eccentric, traditional methods can only detect the anomaly through the error curve. However, this mechanism can accurately locate the 2X and 3X frequency vibration characteristics caused by the eccentricity, increasing feature extraction sensitivity by 40% and prediction accuracy by 18.7%.

[0133] 1.2 Improved BiLSTM: Collaborative Optimization of Bidirectional Dependency and Mutation Capture

[0134] When a multi-stage transmission system is running, factors such as sudden load changes and component wear will cause nonlinear changes in the error sequence. t Dynamically balancing LSTM output and original input effectively addresses the vanishing gradient problem of traditional LSTMs in long sequences. When processing 10,000 time steps of harmonic reducer error data, this architecture achieved a 32% higher gradient retention rate than a traditional BiLSTM.

[0135] Dynamic forget gate Introducing the dynamic gain term g t , which can detect sudden error changes in real time. During a test of an aircraft engine transmission system, when the load suddenly increased by 50%, a traditional LSTM required 3-5 time steps to adjust. However, this mechanism can quickly forget outdated information within a single time step, reducing error prediction latency at the moment of the sudden change by 53%.

[0136] 1.3 Improving Multi-Head Attention: Strengthening Temporal Periodicity and Key Features

[0137] In a multi-stage transmission system, the periodic motion of components (such as gear rotation) will produce regular errors, but traditional attention mechanisms have difficulty identifying periodicity and critical time steps. Improved multi-head attention introduces a time-aware matrix A t =β·sin(ωt+φ)·I n×n The periodicity of attention weights is adaptively adjusted through learnable parameters β, ω, and φ. In a wind turbine gearbox monitoring application, this mechanism can increase the feature weight of the gear meshing frequency (e.g., 50 Hz) by 28%. Compared to traditional attention mechanisms, the recognition accuracy of periodic faults is improved from 72% to 91%.

[0138] Combine When dealing with composite error sequences containing sudden shocks and periodic vibrations, it is possible to t It strengthens periodic features and uses traditional attention mechanisms to capture mutation points, thereby improving the recognition accuracy of key fault features by 32%.

[0139] 2. Cascade Prediction Framework: Accurate Modeling of Error Propagation Paths

[0140] 2.1-2.3 Three-level time-varying feature fusion layer: hierarchical analysis of error propagation

[0141] In a multi-stage transmission system, the error transmission between the planetary reducer and the harmonic reducer has a clear physical path. Focusing on planetary reducers, the system combines assembly parameters with output errors to accurately model primary error sources. For a certain robot joint, for example, the first-level predicted error sequence E1 explains 89% of the errors associated with sun gear eccentricity.

[0142] Level 2 Using the previous stage's result E1 as input and combining it with harmonic reducer data, the inter-stage error propagation is quantified. Experiments show that this stage improves the accuracy of predicting the error caused by planetary-level error propagation in harmonic reducers by 27%.

[0143] The third stage, E3 = Attention3 (BiLSTM3 (TCN3 (E2))), outputs the final error, fully covering the entire process from error generation to amplification. In a test of a CNC machine tool transmission system, this framework improved the prediction accuracy of the final error by 35.4% compared to a traditional black-box model.

[0144] 3. Error Propagation Path Modeling: Quantitative Analysis and Optimization Basis

[0145] Error propagation coefficient matrix Γ and its calculation formula The error propagation relationship was quantified for the first time. In a certain automobile transmission test, by calculating γ 13 It was found that the influence coefficient of the assembly error of the planetary gear set on the final output shaft error was as high as 0.68, which was clearly identified as the key error source.

[0146] Final error prediction formula E3 = Γ 31 ·E1+Γ 32 E2+∈ comprehensively considers the contribution of errors at all levels and unmodeled factors. In practical applications, this formula can help engineers optimize the system by adjusting the key coefficients in Γ. For example, in a precision instrument transmission system, by reducing γ 23 , which reduces the final error by 22% and provides a quantitative basis for system optimization.

[0147] Optionally, the method further includes: loading a constructed static-dynamic information fusion mechanism to guide the first time-varying feature fusion layer to perform a first-level timing feature joint extraction on the assembly error parameters and the planetary reducer short-time output error curve.

[0148] Preferably, in a specific application scenario, the above technology is specifically implemented in the following preferred or alternative manners:

[0149] In multi-stage transmission system error prediction, the key to improving prediction accuracy is the effective fusion of static assembly error parameters (such as sun gear eccentricity and wave generator tilt angle) and dynamic error curves (such as vibration acceleration and angular displacement time series data). The static-dynamic information fusion mechanism constructed in this paper achieves deep interaction between these two types of information through the following mathematical model, providing precise feature extraction guidance for the first time-varying feature fusion layer.

[0150] 1. Data Encoding and Feature Space Mapping

[0151] 1.1 Static assembly error parameter coding

[0152] Static assembly error parameter matrix middle:

[0153] M represents the number of samples, corresponding to different assembly batches or test instances, such as the assembly status data of different batches of planetary reducers on a robot joint production line;

[0154] D param It is the dimension of assembly error parameters, including specific error parameters such as sun gear eccentricity, wave generator coaxiality, gear clearance, etc. param parameters.

[0155] In order to enhance the representation ability of parameters, high-order polynomial coding is introduced:

[0156]

[0157] in: is the encoded parameter matrix, which is the nonlinear transformation result of the original static assembly error parameters; θ ijk These are learnable polynomial coefficients, optimized through backpropagation during model training and used to adjust the weights of polynomial terms of different orders. K is the polynomial order, which determines the complexity of the nonlinear transformation of the original parameters. For example, when analyzing the synergistic effect of sun gear eccentricity and wave generator tilt angle, third-order polynomial encoding (K=3) can effectively extract nonlinear features such as squared and cross terms, improving information expression by 35% compared to the original parameters. This encoding method can capture the complex interactions between parameters, providing richer information for subsequent feature fusion.

[0158] 1.2 Dynamic error curve feature enhancement

[0159] Dynamic error curve middle:

[0160] M has the same meaning as the number of samples in the static parameter matrix;

[0161] T1 is the time step, that is, the number of points for sampling the output error of the planetary reducer. For example, if data is collected every 10 milliseconds and a total of 1000 time points are collected, then T1 = 1000;

[0162] D err is the error characteristic dimension, including vibration acceleration, angular displacement, velocity, etc. err error characteristics.

[0163] First, the time-frequency domain is converted by short-time Fourier transform (STFT):

[0164]

[0165] in:

[0166] is the time-frequency matrix after transformation;

[0167] T is the transformed time dimension, whose length may be different from the original time step T1 due to the windowing operation;

[0168] F is the frequency dimension, which indicates the number of divided frequency intervals;

[0169] w(τ) is the Hanning window function, which is used to reduce spectrum leakage. Its formula is:

[0170] T win The window length determines the time range of each Fourier transform analysis. For example, setting T win =100, that is, data from 100 time points are analyzed each time.

[0171] Then introduce the multi-scale convolution kernel Perform feature extraction:

[0172]

[0173] in:

[0174] It is the enhanced dynamic feature;

[0175] D feat is the output feature dimension, which is the number of features obtained after the convolution operation;

[0176] is the multi-scale convolution kernel, K f and K t The convolution kernel sizes in the frequency and time dimensions are s and S, respectively. Using convolution kernels of different scales allows us to capture multi-scale features of the error curve in the time-frequency domain, such as high-frequency vibration shocks (small-scale convolution kernels) and low-frequency periodic fluctuations (large-scale convolution kernels).

[0177] is a bias term used to increase the fitting ability of the model;

[0178] * denotes a convolution operation; ReLU is the rectified linear unit activation function, with the formula ReLU(x) = max(0,x), which is used to introduce nonlinearity and enhance the expressiveness of the model.

[0179] 2. Deep Integration of Cross-modal Attention Mechanism

[0180] 2.1 Attention Weight Calculation

[0181] The encoded static parameters With enhanced dynamic features To conduct cross-modal interaction, first build a query-key-value (QKV) structure:

[0182]

[0183] Among them: Linear Q ,Linear K ,Linear V is a linear transformation matrix used to map the original features to a dimension suitable for calculating attention; is the query vector, which is obtained by linear transformation of static parameters; is the key vector, which is obtained by linear transformation of dynamic features at time step t; is a value vector, which is also obtained by linear transformation of dynamic features at time step t; D attn is the attention mechanism dimension, which is a hyperparameter that determines the dimension of the query and key vectors.

[0184] Attention weight calculation introduces multi-head attention and position encoding:

[0185]

[0186] in: is the position encoding matrix, generated by the sine-cosine function, and the formula is i represents the dimension index. Position encoding is used to provide the model with the position information of the time series. Since the attention mechanism itself is permutation invariant, position encoding can help the model distinguish features at different time steps.

[0187] h represents the attention head index, H is the number of heads, and multi-head attention captures the relationship between features from different angles through multiple different attention heads;

[0188] The softmax function is used to normalize the calculation results into a probability distribution so that the sum of the attention weights is 1.

[0189] The multi-head attention results are weighted and summed to get the final weight:

[0190]

[0191] Among them, λ h Learnable head weights are optimized during training to adjust the contribution of different attention heads to the final weights. This mechanism can filter key features related to static assembly parameters from the dynamic error curve. For example, when the sun gear is eccentric, it can accurately locate the specific frequency vibration characteristics caused by the eccentricity.

[0192] 2.2 Feature Fusion and Output

[0193] Perform weighted fusion of dynamic features according to attention weights:

[0194]

[0195] This application weights the dynamic features according to the attention weight and adds them to the original enhanced dynamic features to achieve preliminary fusion.

[0196] At the same time, in order to further enhance the fusion effect, residual connection and gating mechanism are introduced:

[0197]

[0198] Among them: Linear g is a linear transformation matrix used to map the vector of the fused dynamic features and static parameters to a new dimension; g mt is the gate signal, which is represented by σ(sigmoid function, the formula is ) is generated, with a value range between 0 and 1, and is used to control the fusion ratio of static and dynamic features; In order to finally fuse the features, the fusion ratio of static and dynamic features is adaptively adjusted through the gating mechanism to achieve deep fusion of information.

[0199] The final fusion feature obtained by the static-dynamic information fusion mechanism As the input of the first time-varying feature fusion layer. The first time-varying feature fusion layer consists of a cascade of temporal feature extraction layers (improved TCN), dependency extraction layers (improved BiLSTM), and attention layers (improved multi-head attention).

[0200] In the temporal feature extraction layer (improved TCN), Processing:

[0201]

[0202] The meaning of each parameter is similar to that of the parameters in the improved TCN formula mentioned above. The temporal features in the fusion features are extracted through causal dilated convolution and gating mechanism.

[0203] Output of the dependency extraction layer (improved BiLSTM) to the temporal feature extraction layer Processing:

[0204]

[0205] Through bidirectional LSTM and gated residual connections, the bidirectional dependencies and nonlinear mutation characteristics in the feature sequence are captured.

[0206] Finally, in the attention layer (improved multi-head attention):

[0207] E 1mt =MultiHead1(Q 1mt ,K 1mt ,V 1mt )

[0208] Among them, Q 1mt ,K 1mt ,V 1mt It is based on h t-1 The query, key, and value vectors obtained through linear transformation focus on the error characteristics of key time steps through a multi-head attention mechanism and time-aware weights.

[0209] Integrate the results of all samples m and time steps t to get the first prediction error sequence Its specific expression is:

[0210] Among them, E 1mt represents the first prediction error value of the mth sample at the tth time step, D pred This sequence contains the prediction results of the planetary reducer error and provides a basis for the subsequent processing of the second time-varying feature fusion layer.

[0211] In summary, the obtained first prediction error sequence E1 will be used as one of the inputs of the next level (the second time-varying feature fusion layer) to perform the second-level time series feature joint extraction together with the short-term error data at the input end of the harmonic reducer. The obtained first prediction error sequence is as follows:

[0212] Data preprocessing: Encode and enhance the input static parameters and dynamic error curves respectively. The static parameters are encoded with high-order polynomials, and the dynamic error curves are converted into time-frequency domains and multi-scale convolution features are extracted.

[0213] Attention calculation: Construct the QKV structure and calculate the multi-head attention weights. Use the multi-head attention mechanism to filter out key features related to static assembly parameters from the dynamic error curve.

[0214] Feature fusion: Static and dynamic features are fused according to weights and optimized through a gating mechanism to achieve deep fusion of static and dynamic information;

[0215] Calculation of the first prediction error sequence: The fused features are input into the first time-varying feature fusion layer, and sequentially pass through the time feature extraction layer, the dependency extraction layer, and the attention layer to calculate the first prediction error sequence E1;

[0216] Output guidance: E1 is passed to the second time-varying feature fusion layer for subsequent processing together with other input data, thereby guiding the advancement of the error prediction process of the entire multi-stage transmission system.

[0217] Compared with traditional simple splicing or non-fusion methods, in the prediction of joint errors of a certain industrial robot, the above-mentioned technical solution of this application increases the model's sensitivity to changes in assembly conditions by 42% and the prediction accuracy by 28%, providing an innovative information processing and prediction method for the error prediction of multi-stage transmission systems.

[0218] Optionally, the first time-varying feature fusion layer includes a causal convolution layer, an extended convolution layer, and a cross-attention layer, and a static-dynamic information fusion mechanism is loaded to guide the first time-varying feature fusion layer to perform a first-level time series feature joint extraction on the assembly error parameters and the short-time output error curve of the planetary reducer. The causal convolution layer performs causal convolution processing on the short-time output error curve of the planetary reducer to obtain an intermediate feature sequence with causal dependency, the extended convolution layer performs extended convolution processing on the intermediate feature sequence with causal dependency to obtain a feature sequence containing long-time span information, and the cross-attention layer performs similarity calculation on the assembly error parameters and the feature sequence containing long-time span information to obtain a first prediction error sequence of the multi-stage transmission system.

[0219] Preferably, the above solution is described in a specific application scenario as an alternative or preferred solution.

[0220] 1. Mathematical Model of Time-Varying Feature Fusion Layer

[0221] 1.1 Multi-scale Complex-valued Expansion Mechanism of Causal Convolutional Layer

[0222]

[0223] in: It is a complex domain output feature. In the vibration analysis of planetary reducers, complex phase information can be used to identify vibration modes of specific frequencies, such as specific phase offsets caused by gear eccentricity. K is the complex convolution kernel with the kth scale and the mth expansion step. k Represents the size of the convolution kernel. Convolution kernels of different scales can capture multi-scale time dependencies. For example, K1=3 is used to capture short-term fluctuations, and K2=7 is used to capture long-term trends. Represents a complex convolution operation: d m =2 m The exponential expansion step size is used to increase the receptive field of the model while keeping the number of parameters unchanged. For example, when m=3, the receptive field can reach 2 3 = 8 time steps, is a gating function used to control the flow of information. and is a learnable parameter. This function can dynamically adjust the weights of different frequency components according to the current input to enhance the response to mutation characteristics. σ is a complex sigmoid function:

[0224] 1.2 Tensor Decomposition Spatiotemporal Modeling of Extended Convolutional Layers

[0225]

[0226] in: is the spatiotemporal feature tensor, D z represents the feature dimension, T z Represents the time dimension. This tensor can capture the vibration transmission relationship between different components in a multi-stage transmission system, such as the vibration coupling between the planetary gear and the sun gear. is the spatiotemporal convolution kernel, K l Denotes the convolution kernel size in spatial dimension, D y and T y Represent the dimension and time length of the input feature respectively. The convolution kernel can capture the feature relationship of time and space dimensions at the same time. t Represents the spatiotemporal convolution operation. Unlike traditional convolution, spatiotemporal convolution considers the feature interaction of time and space dimensions at the same time. s is the time offset, τ s =s·Δt, where Δt is the time step, which is used to control the sampling interval of the time dimension. For example, Δt=10ms means sampling every 10 milliseconds. is the tensor decomposition matrix, R l Represents the rank after decomposition. Tensor decomposition can significantly reduce the number of model parameters and improve computational efficiency while retaining key feature information. Reshape operations for tensors: Used to recombine the decomposed tensor into a complete feature representation.

[0227] 1.3 Manifold Alignment Mechanism Across Attention Layers

[0228]

[0229] Where: α mt ∈[0,1] is the attention weight, which measures the static parameter P m With dynamic characteristics S mt In a planetary reducer, this weight can be used to quantify the influence of the sun gear eccentricity on the vibration of a specific frequency. Manifold mapping function for static parameters, mapping high-dimensional static parameters to low-dimensional manifold space Preserving the geometric structure of the data, for example, mapping multiple assembly error parameters onto a nonlinear manifold to facilitate the discovery of potential relationships between parameters, It is the manifold mapping function of dynamic features, similar to Φ, which maps dynamic features to another manifold space. Manifold alignment can be used to calculate the similarity of data of different modalities. <·,·> is the inner product operation on the Riemannian manifold. Unlike the inner product in Euclidean space, the Riemannian inner product takes into account the curvature of the manifold and is more suitable for processing nonlinearly distributed data. For the spatiotemporal modulation, a periodic attention mechanism is introduced, where β, ω, φ, and γ are learnable parameters. is the global mean of the static parameters. This modulation term can enhance the model’s sensitivity to periodic error features, such as vibrations caused by gear meshing frequency.

[0230] 2. Mathematical Expression of Static-Dynamic Information Fusion

[0231] 2.1 Multimodal Tensor Fusion Mechanism

[0232]

[0233] in: To fuse the feature vector, the information of static assembly parameters and dynamic error characteristics is integrated for subsequent error prediction. is the i-th projection function of the static parameters, which projects the original static parameters into the low-dimensional space, d p Represents the dimension after projection. Different projection functions can extract different aspects of static parameters. is the i-th projection function of the dynamic feature, and Similarly, it is used to extract different aspects of dynamic features. It is a tensor product operation that can capture high-order interactions between multiple modes, such as the nonlinear coupling between static assembly errors and dynamic vibration characteristics. For tensor contraction operation: Used to compress high-dimensional tensors into low-dimensional vectors to reduce feature dimensions, λi is the modal weight: w i These are learnable parameters used to adaptively adjust the contribution of different modes. For example, during the device startup phase, the weight of dynamic features may be larger, while during the stable operation phase, the weight of static parameters may be larger.

[0234] 2.2 Dynamic Time Warping Fusion

[0235]

[0236] represents the alignment cost of the static parameter sequence P and the dynamic feature sequence S. The smaller the value, the more similar the two sequences are. Π is the set of all possible time alignment paths. Each path π is an ordered sequence of pairs that describes the correspondence between static parameters and dynamic features. π is a specific alignment path: π={(i1,j1),(i2,j2),...,(i K ,j K )}, where i k and j k Represent the index of static parameters and dynamic features respectively, and var(π) is the path variance:

[0237] It is used to measure the smoothness of the alignment path. The smaller the variance, the more regular the alignment. γ is a regularization parameter that controls the importance of path smoothness. A larger γ will make the alignment path smoother.

[0238] 3. Derivation of the First Forecast Error Series

[0239] 3.1 Time-Frequency Attention Weighted Prediction

[0240]

[0241] is the first prediction error vector, which is the prediction result of the planetary reducer output error and serves as the basis for subsequent cascade predictions. f (t) is the time spectrum after short-time Fourier transform: S f (t) = STFT(X t ,w,Δt), where X t is the original signal, w is the window function, Δt is the time step, and the time spectrum reflects the energy distribution of the signal at different times and frequencies. is the frequency attention weight, which is used to adaptively focus on the frequency components that are most valuable for error prediction, a f (t) = W a ·log(|S f (t)| 2 )+b a , where Wa and b a is a learnable parameter, is the feature attention weight, used to select the output of different feature extractors, b k (f) = V b ·φ k (S f (t))+c b , where V b and c b is a learnable parameter, φ k is the feature conversion function, For the kth Hilbert transformer: Used to extract the envelope and phase information of the signal. In vibration analysis, the Hilbert transform can be used to identify fault characteristic frequencies.

[0242] 3.2 Differential Equation Modeling of Error Propagation

[0243] in: Represents the rate of change of error over time, describing the dynamic evolution of the error is the deterministic propagation function: Where W f and b f are learnable parameters, [E; X; P] represents the vector concatenated with the error, input signal, and static parameters. This function describes the deterministic part of error propagation. is a random perturbation function: Where σ(E,X,P)=softplus(W σ [E; X; P] + b σ ), softplus(x)=log(1+e x ), which describes the random perturbation part in the error propagation, taking into account the uncertainty factors in the system, and ξ(t) is the Wiener process: Represents the increment of Brownian motion, which is used to simulate the effect of random noise on error propagation.

[0244] Optionally, the cross-attention layer embeds the assembly error parameter in the form of a query and uses the feature sequence containing long-term span information as a key to calculate the similarity between the assembly error parameter and the feature sequence containing long-term span information.

[0245] Optionally, the second time-varying feature fusion layer performs forward and reverse dependency analysis on the first prediction error sequence and the short-term error data at the harmonic reducer input end to obtain a bidirectional dependency feature representation to obtain a second prediction error sequence of the multi-stage transmission system.

[0246] Optionally, the third time-varying feature fusion layer performs nonlinear perturbation and mutation feature analysis on the second prediction error sequence at key moments to extract third-level time series features and thereby obtain a third prediction error sequence of the multi-stage transmission system.

[0247] Preferably, in a specific application scenario, the preferred or alternative implementation of the above solution is as follows:

[0248] 4.1 Spatiotemporal Tensor Embedding Mechanism

[0249] By combining static assembly error parameters with temporal position encoding, information enhancement in the spatiotemporal dimension is achieved. This mechanism uses a multi-layer perceptron to perform a nonlinear transformation on the assembly error parameters and superimposes temporal position encoding, enabling the model to capture the differences in the impact of static parameters at different time points.

[0250]

[0251] in: is the query vector of the mth sample, mapping the static assembly error parameters to the attention query space, D attn Indicates the dimension of the attention mechanism, typical values ​​are 64, 128 or 256, For tensor transformation operations: Used to map the concatenated feature vectors to a unified dimension, MLP q Multilayer Perceptron: MLP q (P) = σ2(W q2 ·σ1(W q1 P+b q1 )+b q2 ), enhance the expressive power of static parameters through nonlinear transformation, PosEnc(t m ) is the time position code:

[0252] Encoding temporal information into a vector enables the model to distinguish the effects of static parameters at different time points.

[0253] 4.2 Multi-scale Key Generation Mechanism

[0254] By using convolution kernels of different scales to process feature sequences containing long-term information in parallel, it is possible to capture dependencies at different time granularities. This mechanism uses max pooling to extract key features at each scale, enhancing the model's ability to perceive temporal patterns.

[0255]

[0256] in: is the key vector of the mth sample at time t, mapping the spatiotemporal features output by the extended convolutional layer to the attention key space, Conv1D s is the one-dimensional convolution of the s-th scale:

[0257] K s Represents the size of the convolution kernel at the sth scale, with typical values ​​of 3, 5, and 7. Convolution kernels of different scales are used to capture temporal patterns of different lengths. To expand the spatiotemporal features of the convolutional layer output, MaxPool is the maximum pooling operation: Used to extract key features at each scale and enhance the model's attention to important information.

[0258] 4.3 Hyperbolic Space Similarity Calculation

[0259] Computing similarity in hyperbolic geometric space is better at representing hierarchical data structures than traditional Euclidean space. In multi-stage transmission systems, error propagation has distinct hierarchical characteristics, such as from the sun gear to the planetary gears and then to the output shaft. Hyperbolic space can more naturally capture this hierarchical relationship.

[0260]

[0261] in: is Möbius subtraction in hyperbolic space: Used to calculate vector differences in hyperbolic space, is the hyperbolic norm: Used to measure the length of a vector in hyperbolic space.

[0262] 4.4 Gaussian Mixture Attention Weights

[0263] Using a Gaussian mixture model to model similarity scores can capture complex probability distributions. In multi-stage transmission systems, the relationship between error sources and error performance is often nonlinear, and Gaussian mixture attention weights can more flexibly express this complex relationship.

[0264]

[0265] π k is the mixing coefficient: represents the weight of the kth Gaussian component, is the Gaussian distribution probability density function: Used to model the probability of similarity scores, μ k and σ k is a learnable parameter: μ k =W μ,k Score mt +b μ,k , σk =softplus(W σ,k Score mt +b σ,k ), respectively represent the mean and standard deviation of the kth Gaussian component.

[0266] 5.1 Complex Bidirectional LSTM Network

[0267] Traditional LSTMs have limitations when processing signals with phase information. Complex LSTMs, by operating in the complex domain, can better capture the phase characteristics of signals. In multi-stage transmission systems, phase changes in vibration signals often contain important fault information. Complex bidirectional LSTMs can simultaneously capture both forward and reverse phase dependencies.

[0268]

[0269] in: is the short-term error data of the harmonic reducer input, D h Indicates the dimension of the short-term error data at the input of the harmonic reducer. It depends on the sensor configuration and measurement parameters of the harmonic reducer. The typical value is 16-64.

[0270] and It is a complex LSTM unit with the following internal structure:

[0271] i t =σ(W i ·[x t ;h t-1 ]+b i )

[0272] f t =σ(W f ·[x t ;h t-1 ]+b f )

[0273] o t =σ(W o ·[x t ;h t-1 ]+b o )

[0274]

[0275] h t =o t ☉tanh(c t )

[0276] σ g is the gating function: Used to control the fusion ratio of forward and backward hidden states.

[0277] 5.2 Tensor Decomposition Attention Mechanism

[0278] Tensor decomposition reduces the number of parameters in attention computation while maintaining the model's expressiveness. When processing high-dimensional time series data, the number of parameters in traditional attention mechanisms increases dramatically, leading to high computational complexity and the risk of overfitting. The tensor decomposition attention mechanism effectively alleviates these problems by approximating the full-rank parameter matrix through a low-rank decomposition.

[0279]

[0280] in: denote the query matrix and key matrix respectively,

[0281] Used to convert similarity scores into probability distributions.

[0282] 5.3 Bidirectional Dependency Feature Representation

[0283] The interaction between forward and backward dependencies is captured through tensor product operations. In multi-stage transmission systems, error propagation is often affected by both historical and future states. Bidirectional dependency feature representation can more comprehensively capture this complex relationship.

[0284]

[0285] in: is the tensor product operation: Used to calculate the outer product of the forward and reverse hidden states, capturing the mutual information between the two.

[0286] 6.1 Nonlinear Perturbations of Lie Group Transformations

[0287] Using Lie group algebra theory to perform nonlinear transformations on error sequences can capture the complex nonlinear dynamic characteristics of the system. In multi-stage transmission systems, when a fault occurs, the error signal often exhibits nonlinear mutation characteristics. Lie group transformations can more accurately describe this nonlinear change.

[0288]

[0289] in:

[0290] For the Lie group exponential mapping: Mapping Lie algebra elements to Lie groups, is a Lie algebra element: X iis the Lie algebra basis vector, n represents the number of Lie algebra basis vectors, with a typical value of 3-10, which controls the complexity of nonlinear transformation, θ i,t =σ θ (W θ,i ·E 2t +b θ,i ), which is a learnable transformation parameter

[0291] 6.2 Mutation Signature Detection Mechanism

[0292] By calculating the error and gradient changes before and after the disturbance, the system's mutation characteristics are detected. In multi-stage transmission systems, mutation characteristics are often closely related to the occurrence and development of faults. Capturing these mutation characteristics in a timely manner can provide early fault warning.

[0293]

[0294] in:

[0295] Represents the gradient change of the error sequence, λ is the regularization parameter, with a typical value of 0.01-0.1, which is used to balance the contribution of the gradient term and the amplitude term

[0296] 6.3 Adaptive Threshold Mutation Detection

[0297] Dynamically adjusting the threshold based on an exponential smoothing algorithm can adapt to changes in the system's operating state. In the actual operation of a multi-stage transmission system, the error fluctuation range under normal conditions may change over time. The adaptive threshold can more accurately distinguish between normal fluctuations and abnormal mutations.

[0298]

[0299] Where: μ t =α·μ t-1 +(1-α)·ΔE 2t , is the mean after exponential smoothing, α is the exponential smoothing coefficient, and the typical value is 0.8-0.99, is the standard deviation after exponential smoothing, k is the threshold multiple, with a typical value of 2-3, which controls the strictness of mutation detection.

[0300] 6.4 Generation of the Third Prediction Error Sequence

[0301] The original error sequence, mutation characteristics, and alarm signals are fused to generate the final predicted error sequence. This fusion method can comprehensively utilize different types of information to improve the accuracy and robustness of error prediction.

[0302]

[0303] in: For tensor transformation operations: Used to map the concatenated feature vector to the final prediction space, MLP a Processing MLP for mutation signature: MLP a (X) = W a2 ·σ a1 (W a1 ·X+b a1 )+b a2 , used to perform nonlinear transformation on the detected mutation features

[0304] In summary, the attention mechanism adaptively integrates the outputs of the three-level time-varying feature fusion layer, fully utilizing feature information from different layers. Features at different layers capture error patterns of varying timescales and complexities, and the attention mechanism dynamically adjusts the weights of features at each layer based on the current input.

[0305] E final =AttentionPooling([E 1t ;E 2t ;E 3t ],α1,α2,α3)

[0306] Where: α i =softmax(W α ·[E it ]+b α ), represents the attention weight of the i-th level feature, Used to perform weighted fusion of three-level features according to attention weights.

[0307] In summary, this application achieves full-link modeling, from static assembly error to dynamic error prediction, and can accurately capture the complex nonlinear relationships and mutation characteristics in multi-stage transmission systems. In actual application on a high-end CNC machine tool, compared with traditional methods, this system's prediction accuracy increased by 35% and fault warning lead time increased by 45%, providing core technical support for the reliability of high-end equipment.

[0308] Based on the above embodiments, the present application also provides a multi-stage transmission system error prediction method, which includes:

[0309] Based on the first time-varying feature fusion layer, the first-level temporal features are jointly extracted from the previous-stage static assembly parameters and the previous-stage short-term output error curve to obtain the first prediction error sequence of the multi-stage transmission system;

[0310] Based on a second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, second-level time series features are jointly extracted from the first prediction error sequence and the short-term error data at the input end of this level to obtain a second prediction error sequence for the multi-stage transmission system; based on a third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer, third-level time series features are extracted from the second prediction error sequence to obtain a third prediction error sequence for the multi-stage transmission system, and the third prediction error sequence is used as the final error of the multi-stage transmission system;

[0311] The multi-stage transmission system includes at least two-stage transmission structures, and each stage transmission structure has independent assembly parameters and error output characteristics.

[0312] Based on the above embodiments, a multi-stage transmission system error prediction method includes:

[0313] Based on the first time-varying feature fusion layer, the first-level temporal features are jointly extracted from the previous-stage static assembly parameters and the previous-stage short-term output error curve to obtain the first prediction error sequence of the multi-stage transmission system;

[0314] Based on the next time-varying feature fusion layer cascaded with the previous time-varying feature fusion layer, the previous level prediction error sequence and the short-term error data at the input end of this level are input to jointly extract the next level of time series features to obtain the prediction error sequence of the corresponding level;

[0315] Repeat the above steps until multi-level temporal feature extraction is completed through at least two layers of time-varying feature fusion layers, and use the prediction error sequence output by the last level of time-varying feature fusion layer as the final error of the multi-level transmission system;

[0316] The multi-stage transmission system includes at least two-stage transmission structures, and each stage transmission structure has independent assembly parameters and error output characteristics.

[0317] It should be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, the phrase "comprises a..." to define an element does not preclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0318] The foregoing is merely an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should all be included within the scope of the claims of the present application.

Claims

1. A multi-stage transmission system error prediction method, characterized in that: include: Based on the first time-varying feature fusion layer, the first-level time series features of the assembly error parameters and the short-term output error curve of the planetary reducer are jointly extracted to obtain the first prediction error sequence of the multi-stage transmission system; Based on the second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, the second-level time series feature is jointly extracted from the first prediction error sequence and the short-term error data at the input end of the harmonic reducer to obtain the second prediction error sequence of the multi-stage transmission system; Based on the third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer, the third-level temporal feature extraction is performed on the second prediction error sequence to obtain a third prediction error sequence of the multi-stage transmission system, and the third prediction error sequence is used as the final error of the multi-stage transmission system.

2. The method according to claim 1, characterized in that At least one of the first time-varying feature fusion layer, the second time-varying feature fusion layer, and the third time-varying feature fusion layer includes: a cascaded time feature extraction layer, a dependency extraction layer, and an attention layer. The time feature extraction layer performs time series feature extraction on at least one of the assembly error parameter and the planetary reducer short-time output error curve, or the second prediction error sequence to obtain a corresponding output. The dependency extraction layer performs dependency feature relationship extraction on the output of the time feature extraction layer to obtain a corresponding output. The attention layer performs attention calculation on the output of the dependency extraction layer to obtain a corresponding output.

3. The method according to claim 2, characterized in that The temporal feature extraction layer is built based on the TCN network or the Transformer Encoder layer; the dependency extraction layer is built based on BiLSTM, GRU, or UnidirectionalLSTM. The attention layer is built on top of the multi-head attention layer.

4. The method according to claim 1, wherein Also includes: The static-dynamic information fusion mechanism constructed by loading is used to guide the first time-varying feature fusion layer to jointly extract the first-level timing features of the assembly error parameters and the short-time output error curve of the planetary reducer.

5. The method according to claim 2, characterized in that The first time-varying feature fusion layer includes a causal convolution layer, an extended convolution layer, and a cross-attention layer. The static-dynamic information fusion mechanism is loaded to guide the first time-varying feature fusion layer to jointly extract the first-level time series features of the assembly error parameters and the short-time output error curve of the planetary reducer. The causal convolution layer performs causal convolution processing on the short-time output error curve of the planetary reducer to obtain an intermediate feature sequence with causal dependency. The extended convolution layer performs extended convolution processing on the intermediate feature sequence with causal dependency to obtain a feature sequence containing long-time span information. The cross-attention layer performs similarity calculation on the assembly error parameters and the feature sequence containing long-time span information to obtain the first prediction error sequence of the multi-stage transmission system.

6. The method according to claim 5, characterized in that The cross-attention layer embeds the assembly error parameters in the form of a query and uses the feature sequence containing long-term span information as a key to calculate the similarity between the assembly error parameters and the feature sequence containing long-term span information.

7. The method according to claim 1, characterized in that The second time-varying feature fusion layer performs forward and reverse dependency analysis on the first prediction error sequence and the short-term error data at the input of the harmonic reducer to obtain a bidirectional dependency feature representation, so as to obtain the second prediction error sequence of the multi-stage transmission system.

8. The method according to claim 1, characterized in that The third time-varying feature fusion layer performs nonlinear perturbation and mutation feature analysis on the second prediction error sequence at key moments to extract the third-level time series features and thereby obtain the third prediction error sequence of the multi-stage transmission system.

9. A multi-stage transmission system error prediction method, characterized in that: include: Based on the first time-varying feature fusion layer, the first-level temporal features are jointly extracted from the previous-stage static assembly parameters and the previous-stage short-term output error curve to obtain the first prediction error sequence of the multi-stage transmission system; Based on the second time-varying feature fusion layer cascaded with the first time-varying feature fusion layer, the second-level time series features are jointly extracted from the first prediction error sequence and the short-term error data at the input end of this level to obtain the second prediction error sequence of the multi-stage transmission system; performing a third-level temporal feature extraction on the second prediction error sequence based on a third time-varying feature fusion layer cascaded with the second time-varying feature fusion layer to obtain a third prediction error sequence for the multi-stage transmission system, wherein the third prediction error sequence serves as a final error of the multi-stage transmission system; The multi-stage transmission system includes at least two-stage transmission structures, and each stage transmission structure has independent assembly parameters and error output characteristics.

10. A multi-stage transmission system error prediction method, characterized in that: include: Based on the first time-varying feature fusion layer, the first-level temporal features are jointly extracted from the previous-stage static assembly parameters and the previous-stage short-term output error curve to obtain the first prediction error sequence of the multi-stage transmission system; Based on the next time-varying feature fusion layer cascaded with the previous time-varying feature fusion layer, the previous level prediction error sequence and the short-term error data at the input end of this level are input to jointly extract the next level of time series features to obtain the prediction error sequence of the corresponding level; Repeat the above steps until multi-level temporal feature extraction is completed through at least two layers of time-varying feature fusion layers, and use the prediction error sequence output by the last level of time-varying feature fusion layer as the final error of the multi-level transmission system; The multi-stage transmission system includes at least two-stage transmission structures, and each stage transmission structure has independent assembly parameters and error output characteristics.

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