An abnormal detection method for a multi-axis motion control system based on digital-analog linkage

Abstract

A method for detecting anomalies in a multi-axis motion control system based on digital-analog linkage, first, collects the working condition information of the multi-axis motion control system and extracts the time-frequency features in the working condition information; second, constructs a composite index that characterizes the health status of the multi-axis motion control system; then, uses a random process model to model the time-varying evolution trend of the composite index, and solves the composite index boundary threshold to achieve anomaly detection; further, based on the deviation between the label prediction value and the actual value of the system, constructs an optimization objective function that characterizes the anomaly detection effect; finally, reversely optimizes and adjusts the threshold set in the multi-source sensor fusion function and the random process model to form a closed-loop feedback control between the composite index extraction and the random process modeling, thereby achieving effective cross-linkage between the composite index extraction and the random process modeling. The present invention can accurately detect anomalies in a multi-axis motion control system without the need for prior knowledge of the system model, and can perform anomaly detection when the system model is completely unknown.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence technology, and in particular relates to an abnormality detection method for a multi-axis motion control system based on digital-analog linkage. Background Art

[0002] With the rapid development of modern industrial information technology, multi-axis motion control systems are becoming increasingly intelligent and complex, leading to an increase in equipment R&D, manufacturing, and especially maintenance costs. In real-world industrial scenarios, the performance of key system components can degrade due to factors such as changing environments, multiple operating conditions, and strong disturbances. This can lead to equipment anomalies, disrupting system stability and, in severe cases, causing significant casualties and economic losses. Therefore, studying anomaly detection in multi-axis motion control systems is crucial for ensuring their safety, reliability, and cost-effectiveness.

[0003] Existing anomaly detection methods for multi-axis motion control systems mainly include knowledge-based methods, model-based methods, and data-driven methods. Knowledge-based methods require process knowledge or expert experience of the known system. However, with the increasing complexity of multi-axis motion control systems, the redundancy of rules and the contradictions between rules have become urgent problems that need to be solved by knowledge-based anomaly detection methods. Model-based methods require a more rigorous mathematical modeling process, but most motion control systems are nonlinear and complex, and it is usually difficult to establish their accurate mathematical models. Data-driven anomaly detection methods do not require mechanism models, process knowledge, and expert experience, but this method has the disadvantages of over-reliance on training data, high computational complexity, and poor interpretability. Summary of the Invention

[0004] In order to overcome the shortcomings of existing abnormality detection methods for multi-axis motion control systems, the present invention provides an abnormality detection method for a multi-axis motion control system based on digital-analog linkage.

[0005] First, the present invention collects the working condition information of the multi-axis motion control system and uses the fast Fourier transform method to extract the time-frequency features in the working condition information; secondly, based on the obtained time-frequency feature information, a composite index is constructed by weighted fusion of multi-source sensor information to characterize the health status of the multi-axis motion control system; then, a random process model is used to model the time-varying evolution trend of the composite index, and the boundary threshold of the composite index is solved to realize anomaly detection; further, based on the deviation between the label prediction value and the actual value of the system, an optimization objective function characterizing the anomaly detection effect is constructed; finally, by minimizing the objective function, the thresholds set in the multi-source sensor fusion function and the random process model are reversely optimized and adjusted to form a closed-loop feedback control between the composite index extraction and the random process modeling, thereby realizing effective cross-linkage between the composite index extraction and the random process modeling.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A method for detecting anomalies in a multi-axis motion control system based on digital-analog linkage, the method comprising the following steps:

[0008] 1) Get the dataset of C cycles of a sensor as {U α (j)|0≤α≤a,0≤j≤C×L}; where L is the data length of each cycle, C cycles include K normal cycles and R abnormal cycles, R=CK;

[0009] 2) For the time domain information obtained in step 1), the corresponding N-dimensional frequency domain information is obtained by fast Fourier transform; compared with the normal working condition, the information with greater difference in the abnormal condition is selected as the feature, which can be expressed as x i (t'), where 1≤i≤N,0≤t'≤C;

[0010] 3) Use weighted method to process feature x i (t'), and the composite index Z(t') of the multi-axis motion control system is obtained:

[0011]

[0012] Among them, x i (t') is the i-th feature at time t', w i is the fusion coefficient of the i-th feature;

[0013] Furthermore, under normal working conditions, the system corresponding monitoring time t={t1,t2,...,t k ,...,t K}, then the observation data corresponding to the composite index is Z(t)={z(t1),z(t2),...,z(t k ),...,z(t K )}, where k = 1, 2, ..., K;

[0014] 4) Using stationary processes to characterize the time-varying evolution trend of composite indicators of multi-axis motion control systems:

[0015] Z(t)=z(t1)+σ×B(Λ(t)) (2)

[0016] where z(t1) is the composite index at the initial moment, σ is the diffusion coefficient, B(·) represents the standard Brownian motion, Λ(t) is a monotonically increasing function of time t, and Z(t) has an independent increment, whose increment Δz(t) = z(t+Δt)-z(t) has a mean of 0 and a variance of σ 2 ×(Λ(t+Δt)-Λ(t)) normal distribution;

[0017] Furthermore, the incremental data set of the observation data set Z(t) corresponding to the composite index constructed based on multi-source sensor data can be expressed as ΔZ(t)={Δz(t2),Δz(t3),...,Δz(t k ),...,Δz(t K )}; where Δz(t k )=z(t k )-z(t k-1 ); take Λ(t+Δt)-Λ(t)=Δt, Δz(t) obeys the mean of 0 and the variance of σ 2 ×Δt is normally distributed, then the probability density function of Δz(t) can be expressed as:

[0018]

[0019] 5) For the probability density function of Δz(t) obtained in step 4), further solve the logarithmic form of its likelihood function:

[0020]

[0021] 6) According to the maximum likelihood estimation method, ln(L(σ 2 )) Take the partial derivative and set it to zero, and we can get σ 2 The maximum likelihood estimate of :

[0022]

[0023] 7) After the random stationary process modeling under normal working conditions is completed, anomaly detection is achieved by setting the threshold v. For two different situations, the piecewise function S(t') is set:

[0024]

[0025] Where y(t') is the actual value label. When y(t') = 1, the system is in normal working condition; when y(t') = -1, the system is abnormal. If s(t') ≥ 0, the multi-axis motion control system is predicted to be normal; if s(t') < 0, the multi-axis motion control system is predicted to be abnormal.

[0026] 8) Construct an optimization objective function based on the improved Huber loss function to characterize the prediction effect, perform reverse optimization adjustment on the fusion coefficient and failure threshold, and construct the following optimization objective function according to step 7):

[0027]

[0028]

[0029] 9) Using the quasi-Newton algorithm to minimize J(W,v) to obtain the optimal solution {W* ,v *}, iteratively optimize and adjust the multi-source data fusion coefficient and the failure threshold in random modeling to achieve interactive linkage and cross-fusion of feature extraction and random process modeling.

[0030] The advantages of the present invention are: 1) Different from the traditional residual threshold anomaly detection perspective, by drawing on the idea of digital-analog linkage, a new idea of anomaly detection in a multi-axis motion control system is proposed from the time-frequency domain information level; 2) By constructing a minimization loss function, the composite indicator fusion coefficient and the anomaly threshold in the random stationary process modeling are reversely optimized to ensure the effectiveness of feature extraction and the accuracy of anomaly detection, and closed-loop feedback can also effectively suppress uncertain interference; 3) This method does not require prior knowledge of the system model, and can perform anomaly detection when the system model is completely unknown, which facilitates the promotion of this method in practical applications; 4) The theoretical framework of the detection method is simple, easy to implement and has good generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A closed-loop feedback diagram between digital-analog linkage for modeling random stationary processes and constructing thresholds for anomaly detection;

[0032] Figure 2 This is the experimental setup diagram for the multi-axis engraving machine system;

[0033] Figure 3 This is a diagram of the collected data of the multi-axis engraving machine system experimental device;

[0034] Figure 4 Frequency domain diagram of dual-axis speed, position and torque under normal working conditions;

[0035] Figure 5 Frequency domain diagrams of dual-axis velocity, position, and torque under abnormal conditions;

[0036] Figure 6 The following is a graph showing the accuracy and F1 score of the two algorithms under different numbers of iterations. DETAILED DESCRIPTION

[0037] In order to make the technical solutions and design ideas of the present invention clearer, a detailed description is given below with reference to the accompanying drawings.

[0038] Reference Figures 1-6 A method for detecting abnormalities in a multi-axis motion control system based on digital-analog linkage, comprising the following steps:

[0039] 1) For the multi-axis engraving machine system experimental device, a circular trajectory tracking task is set, where the reference trajectory signal of the X axis is x(j) = 10sin(2πj / 1600), and the reference trajectory signal of the Y axis is y(j) = 10cos(2πj / 1600). At the same time, a type of fault signal with periodic regularity is considered:

[0040] g(j)=sin(0.01j),j≤3200 (1)

[0041] Consider that the fault occurs on the X axis and the fault time starts from the third cycle (3200 points); the number of sensors a is 6, the cycle C is 100, and the length of each cycle L is 1600; the position, speed and torque signals of the X and Y axes of the device are collected to form a sample set {U α (j)|0≤α≤a,0≤j≤C×L}; wherein, the 100 cycles include K (K=46) normal data cycles and R (R=44) abnormal data cycles;

[0042] 2) For the time domain information obtained in step 1), use fast Fourier transform to obtain its corresponding N-dimensional frequency domain information, and select the maximum amplitude and corresponding frequency as the feature x i (t'), where 1≤i≤N, 0≤t'≤K, N=12;

[0043] 3) Use weighted method to process feature x i (t'), and the composite index Z(t') of the multi-axis motion control system is obtained:

[0044]

[0045] Among them, x i (t') is the i-th feature at time t', w i is the fusion coefficient of the i-th feature;

[0046] Furthermore, under normal working conditions, the system corresponding monitoring time t={t1,t2,...,t k ,...,t K}, then the observation data corresponding to the composite index is Z(t)={z(t1),z(t2),...,z(t k ),...,z(t K )}, where k = 1, 2, ..., K;

[0047] 4) Using stationary processes to characterize the time-varying evolution trend of composite indicators of multi-axis motion control systems:

[0048] Z(t)=z(t1)+σ×B(Λ(t)) (3)

[0049] where z(t1) is the composite index at the initial moment, σ is the diffusion coefficient, B(·) represents the standard Brownian motion, Λ(t) is a monotonically increasing function of time t, and Z(t) has an independent increment, whose increment Δz(t) = z(t+Δt)-z(t) has a mean of 0 and a variance of σ 2 ×(Λ(t+Δt)-Λ(t)) normal distribution;

[0050] Furthermore, the incremental data set of the observation data set Z(t) corresponding to the composite index constructed based on multi-source sensor data can be expressed as ΔZ(t)={Δz(t2),Δz(t3),...,Δz(t k ),...,Δz(t K )}; where Δz(t k )=z(t k )-z(t k-1 ): Take Λ(t+Δt)-Λ(t)=Δt, then Δz(t) obeys the mean of 0 and the variance of σ 2 ×Δt is normally distributed, then the probability density function of Δz(t) can be expressed as:

[0051]

[0052] 5) For the probability density function of Δz(t) obtained in step 4), further solve the logarithmic form of its likelihood function:

[0053]

[0054] 6) According to the maximum likelihood estimation method, ln(L(σ 2 )) Take the partial derivative and set it to zero, and we can get σ 2 The maximum likelihood estimate of :

[0055]

[0056] 7) After the random stationary process modeling under normal working conditions is completed, anomaly detection is achieved by setting the threshold v. For two different situations, the piecewise function S(t') is set:

[0057]

[0058] Where y(t') is the actual value label. When y(t') = 1, the system is in normal working condition; when y(t') = -1, the system is abnormal. If s(t') ≥ 0, the multi-axis motion control system is predicted to be normal; if s(t') < 0, the multi-axis motion control system is predicted to be abnormal.

[0059] 8) Construct an optimization objective function based on the improved Huber loss function to characterize the prediction effect, perform reverse optimization adjustment on the fusion coefficient and failure threshold, and construct the following optimization objective function according to step 7):

[0060]

[0061]

[0062] 9) Use the constrained quasi-Newton method to minimize J(W,v) to solve equation (9), where the constraint is Get the optimal fusion coefficient and threshold {W * ,v *}, expressed as:

[0063] {W * ,v *}=argminJ(W,v) (10)

[0064] Iteratively optimize and adjust the multi-source data fusion coefficient and the failure threshold in random modeling to achieve interactive linkage and cross-fusion of feature extraction and random process modeling;

[0065] 10) Based on the above fusion coefficient and threshold, the data on the test set is discriminated, and finally the test results are analyzed through the confusion matrix.

[0066] In order to verify the effectiveness and superiority of the proposed method, the present invention was tested on an engraving machine system. The digital-analog linkage method was used to obtain the fusion coefficient {W *}={6.499615,-5.040356,3.036640,-3.291961,-1.720807,0.644562,0.278718,0.078718,0.078718,0.078718,0.278718,0.078718}, threshold v * =0.703785. Then the data on the test set are distinguished between normal and abnormal conditions, and finally the test results are analyzed by confusion matrix. The support vector machine (SVM) method is selected for comparison with the method proposed in this invention. The experimental results are shown in Figure 2. Figure 6 As shown in the figure, as the number of iterations increases, the accuracy and F1 scores of the two algorithms increase until they stabilize. However, compared with the SVM method, the digital-analog linkage method proposed in the present invention maintains obvious advantages in accuracy and F1 score.

Claims

1. A method for detecting abnormalities in a multi-axis motion control system based on digital-analog linkage, characterized in that: The following steps are involved: 1) Get the dataset of C cycles of a sensor as {U α (j)|0≤α≤a,0≤j≤C×L}; where L is the data length of each cycle, C cycles include K normal cycles and R abnormal cycles, R=CK; 2) For the time domain information obtained in step 1), use fast Fourier transform to obtain its corresponding N-dimensional frequency domain information; compared with the normal working condition, the information with greater difference in abnormal conditions is selected as the feature, which is expressed as x i (t'), where 1≤i≤N,0≤t'≤C; 3) Use weighted method to process feature x i (t'), and the composite index Z(t') of the multi-axis motion control system is obtained: Among them, x i (t') is the i-th feature at time t', w i is the fusion coefficient of the i-th feature; 4) Using the stationary process to characterize the composite indicators of the multi-axis motion control system: Where z(t1) is the composite index at the initial moment, σ is the diffusion coefficient, B(·) represents the standard Brownian motion, Λ(t) is a monotonically increasing function of time t, and Z has an independent increment, whose increment △z(t)=z(t+△t)-z(t) obeys the mean of 0 and the variance of σ 2 ×(Λ(t+△t)-Λ(t)); the incremental data set of the observation data set Z corresponding to the composite indicator constructed based on multi-source sensor data is expressed as Y={△z(t2),△z(t3),...,△z(t k ),...,△z(t K )}; where △z(t k )=z(t k )-z(t k-1 ); take Λ(t+△t)-Λ(t)=△t, △z(t) obeys the mean of 0 and the variance of σ 2 ×△t's normal distribution, the probability density function of△z(t) is expressed as: 5) For the probability density function of △z(t) obtained in step 4), further solve the logarithmic form of its likelihood function: 6) According to the maximum likelihood estimation method, ln(L(σ 2 ))Find the partial derivative and set it to zero, and we get σ 2 The maximum likelihood estimate of : 7) After the random stationary process modeling under normal working conditions is completed, anomaly detection is achieved by setting the failure threshold v. For two different situations, the piecewise function S(t') is set: Where y(t') is the actual value label. When y(t') = 1, the system is in normal working condition; when y(t') = -1, the system is abnormal. If s(t') ≥ 0, the multi-axis motion control system is predicted to be normal; if s(t') < 0, the multi-axis motion control system is predicted to be abnormal. 8) Construct an optimization objective function based on the improved Huber loss function to characterize the prediction effect, perform reverse optimization adjustment on the fusion coefficient and failure threshold, and construct the following optimization objective function according to step 7): 9) Using the quasi-Newton algorithm to minimize J(W,v) to obtain the optimal solution {W * ,v * }, iteratively optimize and adjust the multi-source data fusion coefficient and the failure threshold in random modeling to achieve interactive linkage and cross-fusion of feature extraction and random process modeling.

2. The method for detecting anomalies in a multi-axis motion control system based on digital-analog linkage according to claim 1, characterized in that: In step 3), under normal working conditions, set the system corresponding monitoring time T = {t1, t2, ..., t k ,...,t K }, then the observation data set corresponding to the composite index is Z={z(t1),z(t2),...,z(t k ),...,z(t K )}, where k = 1, 2, ..., K.

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