CN113792610A - Harmonic reducer health assessment method and device - Google Patents

Harmonic reducer health assessment method and device Download PDF

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CN113792610A
CN113792610A CN202110959720.0A CN202110959720A CN113792610A CN 113792610 A CN113792610 A CN 113792610A CN 202110959720 A CN202110959720 A CN 202110959720A CN 113792610 A CN113792610 A CN 113792610A
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刘成良
丁浩伦
余宏淦
陶建峰
李彬
徐孜
孙浩
毛帅
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Shanghai Jiaotong University
Shanghai Platform For Smart Manufacturing Co Ltd
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Abstract

The invention discloses a harmonic reducer health assessment method and device, wherein the health assessment method comprises the following steps: collecting the rotating speed and torque data of the harmonic reducer; extracting time domain characteristics of the rotating speed and torque data, and converting the time domain characteristics into high-dimensional characteristic vectors; converting the high-dimensional feature vector into a low-dimensional feature by using a dimension reduction algorithm; obtaining a distance set by measuring the low-dimensional features through the Mahalanobis distance; converting the distance set into a health index; and comparing the health index with a health threshold, and judging that the health is achieved when the health index is higher than the health threshold. The invention provides a data-driven-based method, which is used for collecting signals in the actual operation process, conveniently and quickly analyzing the health performance and relieving the technical problem that a model-based method depends on more physical assumptions.

Description

Harmonic reducer health assessment method and device
Technical Field
The invention relates to the technical field of system health assessment, in particular to a harmonic reducer health assessment method and device.
Background
The harmonic reducer has the advantages of small volume, high transmission efficiency, light weight, strong bearing capacity and the like, and is increasingly widely applied to the field of machinery. In an industrial robot, a harmonic reducer is an important transmission part, mainly plays a role in reducing speed and increasing torque, determines the positioning precision, the bearing capacity, the service life and other performances of the robot, and in long-time high-strength work, the performance of the harmonic reducer is degraded, the reliability is reduced, and the overall safety and production of the robot are directly influenced. Therefore, the health state and the evaluation method of the harmonic reducer need to be researched, and the overall health and the accuracy of the robot are improved.
At present, the research aiming at the health performance of the harmonic reducer is mainly based on a model driving method. The harmonic reducer is analyzed by using model driving methods such as dynamics, tribology and finite elements, and a failure physical model or a mathematical model of the harmonic reducer is established. The traditional model driving method depends on more physical assumptions and has certain limitations, so that the evaluation effect is limited.
Disclosure of Invention
Objects of the invention
In view of the above, the present invention provides a method and an apparatus for evaluating health of a harmonic reducer based on data driving, which directly utilize data of an actual machining process to analyze, collect operation data of the harmonic reducer, and efficiently and quickly evaluate the health performance of the harmonic reducer.
(II) technical scheme
According to some embodiments, in a first aspect of the invention there is provided a harmonic reducer health assessment method comprising: collecting the rotating speed and torque data of the harmonic reducer; extracting time domain characteristics of the rotating speed and torque data, and converting the time domain characteristics into high-dimensional characteristic vectors; converting the high-dimensional feature vector into a low-dimensional feature by using a dimension reduction algorithm; obtaining a distance set by measuring the low-dimensional features through the Mahalanobis distance; converting the distance set into a health index; and comparing the health index with a health threshold, and judging that the health is achieved when the health index is higher than the health threshold.
Optionally, the time domain features are mean, peak-to-peak, standard deviation and kurtosis values of the rotational speed and torque within 2min of the time window.
Optionally, the dimension reduction algorithm is one of locally preserving projection mapping, laplacian feature mapping, t-distribution random neighbor embedding, and LargeVis.
Optionally, the LargeVis algorithm parameter settings are as follows: the low-dimensional dimensionality is 2, the neighbor propagation times are 3, the gradient descent learning rate is 1.0, the number of negative samples is 3, the number of neighbors of the k neighbor graph is 30, the negative edge weight is 5, and the value determining the edge weight in the k neighbor graph is 10.
Optionally, the formula for the mahalanobis distance metric is:
Figure BDA0003221781290000021
d (x, y) is the mahalanobis distance; x and y are any two samples in n-dimensional space; sigmaxyRepresenting the covariance matrix between two data samples.
Optionally, the distance set is converted into a health index formula as follows: HV (═ exp (-k × d (x, y)), and HV is a health index; k is 0.02.
Optionally, the acquiring of the health threshold includes: carrying out accelerated degradation test on the similar harmonic reducers; calculating health indexes of similar harmonic reducers in a preset time interval before failure in an accelerated degradation test; the health indicator within the predetermined time interval is a health threshold.
Optionally, the health threshold is 0.9.
According to some embodiments, in a second aspect of the present invention, there is provided a harmonic reducer health assessment apparatus comprising: the acquisition module is used for acquiring the rotating speed and torque data of the harmonic reducer; the preprocessing module is used for extracting time domain characteristics of the rotating speed and torque data and converting the time domain characteristics into high-dimensional characteristic vectors; the dimensionality reduction module is used for converting the high-dimensional feature vector into a low-dimensional feature by using a dimensionality reduction algorithm; the distance module is used for obtaining a distance set from the low-dimensional features through Mahalanobis distance measurement; the conversion module is used for converting the distance set into a health index; and the output module is used for comparing the health index with the health threshold value, and the health index is healthy when the health index is higher than the health threshold value.
(III) advantageous effects
The technical scheme of the invention has the following beneficial technical effects:
in order to relieve the limitation of a model driving method on evaluation of the harmonic reducer, a data driving-based method is provided, signals in the operation process of the harmonic reducer are collected, feature extraction and feature dimension reduction are carried out, a health index of the harmonic reducer is established through data, and the health performance is conveniently and quickly analyzed.
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FIG. 1 is a schematic flow chart of a harmonic reducer health assessment method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the LargeVis algorithm according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the feature distribution after dimension reduction of LargeVis according to the embodiment of the present invention;
FIG. 4 is a diagram illustrating the distribution of low-dimensional features of different dimension reduction algorithms according to an embodiment of the present invention;
fig. 4(a) is a schematic diagram of the feature distribution of the local preserving projection mapping algorithm, fig. 4(b) is a schematic diagram of the feature distribution of the laplacian feature mapping algorithm, and fig. 4(c) is a schematic diagram of the feature distribution of the t-distribution random neighbor embedding algorithm.
FIG. 5 is a comparison diagram of a low-dimensional spatial distance metric according to an embodiment of the present invention;
fig. 5(a) is a mahalanobis spatial distance measurement diagram, and fig. 5(b) is a euclidean spatial distance measurement diagram.
FIG. 6 is a graph of a health indicator according to an embodiment of the present invention;
fig. 7 is a schematic structural diagram of a harmonic reducer health assessment apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In addition, the technical features involved in the different embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 1 is a schematic flow chart of a harmonic reducer health assessment method according to an embodiment of the present invention.
As shown in fig. 1, a method for evaluating the health of a harmonic reducer provided by an embodiment of the present application mainly includes 6 steps, and the 6 steps are described in detail below.
And step S1, acquiring the rotation speed and torque data of the harmonic reducer.
For example, in one embodiment the load is set to an acceleration stress. The rated torque of the harmonic reducer is 32Nm, and as shown in Table 1, the state data of 2h of operation under the rated torque are tested, and the state data under the rated torque of 3.5 times are continuously collected. The data acquisition is divided into 5 stages, wherein the P1 stage harmonic reducer works at rated torque for 2 hours, the P2, P3, P4 and F stage harmonic reducer works at 3.5 times of rated torque, the working time is shown in the table 1, and the rotating speed and torque data are acquired during the working time.
TABLE 1 data acquisition List
Figure BDA0003221781290000041
And step S2, extracting time domain characteristics of the rotating speed and torque data, and converting the time domain characteristics into high-dimensional characteristic vectors.
In an alternative embodiment, the time domain features are the mean, peak to peak, standard deviation, and kurtosis values of the speed and torque over a time window of 2 min.
Extracting the signals of the rotating speed and the torque for analysis. Taking torque as an example, as the data acquisition amount is large, window interception analysis is carried out on the data, the size of a time window is 2min, and time domain features of the data in the time window, including a mean value, a peak-to-peak value, a standard deviation and a kurtosis value, are extracted to form a feature vector of the time window. Exemplarily, the data collected at 2min is x1，x2…xnMean value of
Figure BDA0003221781290000056
Peak to peak value xppStandard deviation xstdThe specific calculation formula of the kurtosis value K is as follows.
Mean value
Figure BDA0003221781290000051
Peak to peak value
xpp＝xmax-xmin
Standard deviation of
Figure BDA0003221781290000052
Kurtosis value
Figure BDA0003221781290000053
Illustratively, set the sample vector to
Figure BDA0003221781290000054
And aiming at five working conditions P1-P4 and F in the table 1, 50 groups of sample vectors are selected to form a high-dimensional feature vector.
Figure BDA0003221781290000055
Step S3: and converting the high-dimensional feature vector into the low-dimensional feature by using a dimension reduction algorithm.
In some embodiments, the dimension reduction algorithm is one of a local preserving projection mapping, a laplacian eigenmapping, a t-distribution random neighbor embedding, a LargeVis.
FIG. 2 is a schematic diagram of a LargeVis algorithm according to an embodiment of the present invention.
In an alternative embodiment, the dimension reduction algorithm is LargeVis.
The LargeVis algorithm as shown in fig. 2 is to first construct a high-dimensional feature vector k neighbor map and then project the map to a low-dimensional space. The method comprises the following specific steps:
(1) a k-neighbor graph is constructed. Distance similarity of high-dimensional spatial sample points is essentially the process of constructing a k-nearest neighbor map. In a large number of high-dimensional feature vectors, data points in the normal state generally converge together, while outlier points are far from the normal data point cluster. The LargeVis obtains the k neighbor graph efficiently and accurately by means of a random projection tree algorithm and a neighbor search algorithm.
(2) High dimensional spatial conditional probability distribution
Figure BDA0003221781290000061
pj|iRepresents a sample point xjAs xiProbability of neighbor σiIs represented by xiIs the variance of the gaussian distribution of the center point. Joint probability in high dimensional space
Figure BDA0003221781290000062
(3) Low dimensional spatial conditional probability distribution
p(eij＝1)＝f(||yi-yj||)
yiAnd yjRepresenting two points in a low-dimensional space, wherein the two points have a weight e in a k-neighbor graphijA binary edge of 1. Wherein
Figure BDA0003221781290000063
Figure BDA0003221781290000064
(4) Objective function
Figure BDA0003221781290000065
Where E is the set of edges of the graph i.e. the positive sample set,
Figure BDA0003221781290000066
for the negative sample set, γ is a weight value set uniformly for the negative sample edge. In the process of solving the maximum objective function, the LargeVis also utilizes negative sampling and side sampling optimization, and an asynchronous random gradient descent method is adopted for training, so that the iteration efficiency is improved.
In a preferred embodiment, the LargeVis algorithm parameter settings are as follows: the low-dimensional dimensionality is 2, the neighbor propagation times are 3, the gradient descent learning rate is 1.0, the number of negative samples is 3, the number of neighbors of the k neighbor graph is 30, the negative edge weight is 5, and the value determining the edge weight in the k neighbor graph is 10.
FIG. 3 is a schematic diagram of feature distribution after dimension reduction of LargeVis according to the embodiment of the present invention.
As shown in fig. 3, the distribution rule and the development trend of the harmonic reducer data can be observed. The data under different load conditions have certain similarity and are gathered together in a low-dimensional space. The data samples under different working conditions are effectively distinguished by the manifold learning algorithm based on the LargeVis, so that the low-dimensional manifold embedded in the high-dimensional feature vector set is well characterized. Table 2 shows algorithm parameters set according to the actual data set size.
TABLE 2 LargeVis parameter settings
Figure BDA0003221781290000071
FIG. 4 is a diagram illustrating the distribution of low-dimensional features of different dimension reduction algorithms according to an embodiment of the present invention;
fig. 4(a) is a schematic diagram of the feature distribution of the local preserving projection mapping algorithm, fig. 4(b) is a schematic diagram of the feature distribution of the laplacian feature mapping algorithm, and fig. 4(c) is a schematic diagram of the feature distribution of the t-distribution random neighbor embedding algorithm.
In some embodiments, the dimension reduction algorithm is one of a local preserving projection mapping, a laplacian eigenmapping, a t-distribution random neighbor embedding.
As shown in fig. 4, respectively: the feature distribution map is realized by three dimensionality reduction algorithms, namely local preserving projection mapping (LPP), Laplace feature mapping (LE), t-distributed random neighbor embedding (t-SNE) reduced low-dimensional features. The three algorithms can better classify the data of the harmonic reducers in different health states, but the precision is slightly different. In order to evaluate the classification effect of different dimensionality reduction algorithms, a K-nearest neighbor graph method is selected to verify the classification precision of the model, and the result is shown in Table 3. The LargeVis has the highest classification precision of 98.2 percent, and the evaluation is most accurate. In addition, the different algorithm runtimes were compared, and the LargeVis runtime was about 2.6s after 300 iterations. The LargeVis is improved based on a t-SNE algorithm, and the operation efficiency is higher due to the utilization of optimization algorithms such as negative sampling and edge sampling.
TABLE 3 comparison of results of different dimensionality reduction algorithms
Figure BDA0003221781290000081
Step S4: and obtaining a distance set by the low-dimensional features through the Mahalanobis distance measurement.
In some embodiments, the formula for the mahalanobis distance metric is:
Figure BDA0003221781290000082
d (x, y) is the mahalanobis distance, and x and y are any two samples in the n-dimensional space; sigmaxyRepresenting the covariance matrix between two data samples.
The distance set is obtained by measuring the covariance distance of data, is an algorithm for effectively calculating the similarity of two position sample sets, and can be used as a correction of Euclidean distance. Let any two samples x and y in the n-dimensional space be denoted as x ═ x (x), respectively1，x2…xn) And y ═ y1，y2…yn)，∑xyRepresenting the covariance matrix between two data samples, the mahalanobis distance d (x, y) between samples x and y is defined as:
Figure BDA0003221781290000083
FIG. 5 is a comparison diagram of a low-dimensional spatial distance metric according to an embodiment of the present invention;
fig. 5(a) is a mahalanobis spatial distance measurement diagram, and fig. 5(b) is a euclidean spatial distance measurement diagram.
And selecting the dimensionality reduction characteristics in the healthy state of the harmonic reducer as baseline data, and comparing the Mahalanobis distance between the sample data and the baseline data in different states. The change curve shown in FIG. 5(a) was obtained. Compare the Euclidean distance metric spaces, as in FIG. 5 (b).
Comparing fig. 5(a) and 5(b), after dimension reduction by LargeVis, P2 and P3, P4 and failure data in the euclidean space metric have little difference, and the evaluation effect is not ideal. The Mahalanobis distance is increased along with performance decay, and the fluctuation of the Mahalanobis distance of the failure data is larger, so that the method is more suitable for the actual situation. In conclusion, the result is more reliable by using the mahalanobis distance for health assessment.
Step S5: and converting the distance set into a health index.
In some embodiments, the distance set is converted to a health indicator formula as follows: HV (═ exp (-k × d (x, y)), HV is a health index, and k is 0.02.
And quantifying the health state of the equipment by using the Mahalanobis distance to obtain a health evaluation value. The mapping rule is as follows: the smaller the mahalanobis distance from the baseline, the higher the similarity to the health state data, and the health index is close to 1; otherwise, the performance of the harmonic reducer is declined and the health index is reduced to 0. The health index is defined as follows:
HV＝exp(-k*d(x，y))
FIG. 6 is a graph of a health indicator according to an embodiment of the present invention.
k is 0.02, and a health index change curve shown in FIG. 6 is obtained.
Step S6: and comparing the health index with a health threshold, and judging that the health is achieved when the health index is higher than the health threshold.
In some embodiments, the obtaining of the health threshold comprises: carrying out accelerated degradation test on the similar harmonic reducers; calculating health indexes of similar harmonic reducers in a preset time interval before failure in an accelerated degradation test; the health indicator within the predetermined time interval is a health threshold. Illustratively, the similar harmonic reducers are subjected to an accelerated degradation test shown in table 1, the mean values of the health indexes of the working conditions P1-P4 and F are respectively 0.982, 0.928, 0.926, 0.907 and 0.869, and the whole harmonic reducers are in a descending trend, wherein after the accelerated degradation test is continuously carried out for about 40 hours, the amplitude of a vibration signal of the harmonic reducers is increased, the harmonic reducers have noise to be transmitted out, and the performance degradation is obvious. After continuously testing for a few hours, the harmonic reducer is taken down, and the flexible gear is found to be broken and completely fails. And the F stage is a failure stage of the accelerated degradation test of the harmonic reducer. Illustratively, the predetermined time intervals are selected from F and P4, and the health indicator at the time intervals of F and P4 is the health threshold.
In a preferred embodiment, the health threshold is 0.9. Illustratively, an accelerated degradation test was performed on a harmonic reducer of the same type, and the health threshold was determined to be 0.9.
The health threshold value is set to be 0.9, and the performance of the harmonic reducer is considered to be declined to some extent when the health index is lower than 0.9, so that the harmonic reducer influences the work and needs to be shut down for inspection and maintenance in time.
Fig. 7 is a schematic structural diagram of a harmonic reducer health assessment apparatus according to an embodiment of the present invention.
As shown in fig. 7, the harmonic reducer health evaluation device 200 includes:
the acquisition module 201 is used for acquiring the rotating speed and torque data of the harmonic reducer;
the preprocessing module 202 is used for extracting time domain features of the rotating speed and torque data and converting the time domain features into high-dimensional feature vectors;
a dimension reduction module 203 for converting the high-dimensional feature vector into a low-dimensional feature using a dimension reduction algorithm;
a distance module 204, configured to obtain a distance set from the low-dimensional features through mahalanobis distance measurement;
a conversion module 205 for converting the distance set into a health indicator;
an output module 206 for comparing the health indicator with a health threshold, above which it is healthy.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.

Claims (9)

1. A harmonic reducer health assessment method, comprising:
collecting the rotating speed and torque data of the harmonic reducer;
extracting time domain characteristics of the rotating speed and torque data, and converting the time domain characteristics into high-dimensional characteristic vectors;
converting the high-dimensional feature vector into a low-dimensional feature by using a dimension reduction algorithm;
obtaining a distance set by measuring the low-dimensional features through the Mahalanobis distance;
converting the distance set into a health index;
comparing the health indicator to a health threshold above which health is indicated.
2. The method of claim 1, wherein the time domain features are mean, peak-to-peak, standard deviation, and kurtosis values of rotational speed and torque over a time window of 2 min.
3. The method of claim 1, wherein the dimensionality reduction algorithm is one of a local preserving projection mapping, a laplacian eigenmapping, a t-distributed random neighbor embedding, and a LargeVis.
4. The method of claim 3, wherein the LargeVis algorithm parameter settings are as follows: the low-dimensional dimensionality is 2, the neighbor propagation times are 3, the gradient descent learning rate is 1.0, the number of negative samples is 3, the number of neighbors of the k neighbor graph is 30, the negative edge weight is 5, and the value determining the edge weight in the k neighbor graph is 10.
5. The method of claim 1, wherein the mahalanobis distance metric is formulated as:
Figure FDA0003221781280000011
d (x, y) is the mahalanobis distance, and x and y are any two samples in the n-dimensional space; sigmaxyRepresenting the covariance matrix between two data samples.
6. The method of claim 1, wherein the converting the distance set into a health indicator formula is as follows: HV (═ exp (-k × d (x, y)), HV is a health index, and k is 0.02.
7. The method of claim 1, wherein the obtaining of the health threshold comprises:
carrying out accelerated degradation test on the similar harmonic reducers;
calculating the health index of the similar harmonic speed reducer in a preset time interval before failure in an accelerated degradation test;
the health index in the preset time interval is a health threshold value.
8. The method of claim 7, wherein the health threshold is 0.9.
9. A harmonic reducer health assessment device, comprising:
the acquisition module is used for acquiring the rotating speed and torque data of the harmonic reducer;
the preprocessing module is used for extracting time domain characteristics of the rotating speed and torque data and converting the time domain characteristics into high-dimensional characteristic vectors;
a dimension reduction module for converting the high-dimensional feature vector into a low-dimensional feature using a dimension reduction algorithm;
a distance module, configured to obtain a distance set from the low-dimensional features through mahalanobis distance measurement;
a conversion module for converting the distance set into a health indicator;
and the output module is used for comparing the health index with a health threshold value, and the health index is healthy when the health index is higher than the health threshold value.
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