Gear wear state prediction method based on time sequence ARIMA model

Abstract

The invention relates to the technical field of mechanical equipment fault diagnosis, in particular to a gear wear state prediction method based on a time sequence ARIMA (autoregressive integrated moving average) model, which is characterized by comprising the following steps: step S10, constructing a prediction model based on ARIMA (p, d, q): step S11, constructing an abrasive particle group characteristic time sequence; step S12, carrying out stability inspection; step S13, determining the order of the model; step S14, estimating parameters; step S15, carrying out model inspection; and step S20, analysis and verification of a prediction result based on the ARIMA model. According to the method, the wear state is predicted by establishing the time sequence ARIMA prediction model for the constructed abrasive particle group feature time sequence, the wear severity can be analyzed and judged in advance, and the failure rate of mechanical equipment is effectively reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical equipment fault diagnosis, and particularly relates to a gear wear state prediction method based on a time series ARIMA model. BACKGROUND

[0002] Gears present different states at different wear periods and have stage regularity. Abnormities and faults of gears caused by wear are not sudden, but have trend and analyzability due to the comprehensive factors of wear accumulation and load increase. An online wear time series model is established based on historical data to predict and analyze future trends, and effective prediction of future values is realized under long time series, which can provide an important means for condition-based maintenance. At present, there are corresponding researches on the prediction of wear based on the characteristics of abrasive particles by using online ferrography analysis technology. For example, a multi-model concentration trend prediction method is proposed based on the time series of abrasive particle concentration. However, this method is a multi-model prediction of a single feature, which has high complexity. Or, the early faults of a marine engine are reflected by the value sensitivity based on the monitoring of the marine engine. However, this method does not establish an effective prediction model. In actual application, pure empirical analysis is not accurate, and some prediction models only analyze a small amount of data and cannot effectively express the trend of parameter changes under time series, so the prediction of wear state cannot be effectively realized, the severity of wear cannot be analyzed and judged in advance, and the mechanical equipment failure rate cannot be effectively reduced. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a gear wear state prediction method based on a time series ARIMA model, which can realize the prediction of wear state by establishing a time series ARIMA prediction model for the constructed abrasive particle group feature time series, analyze and judge the severity of wear in advance, and effectively reduce the mechanical equipment failure rate.

[0004] To solve the above technical problems, the technical scheme adopted by the present application is as follows: a gear wear state prediction method based on a time series ARIMA model, characterized by comprising the following steps: Step S10, constructing a prediction model based on ARIMA( p , d , q ), and the specific steps are as follows: Step S11, constructing an abrasive particle group feature time series; Step S12, stationary test: the stationary of the feature time series is comprehensively judged by the trend of the feature time series itself and the tailing and truncation principles of the autocorrelation function and the partial autocorrelation function. When the stationary test result of the feature time series is non-stationary, the stationary is processed by using a difference processing method, and the difference order is determined according to the processing effectd ; Step S13, model order determination: determine the autocorrelation order of the prediction model by using the order determination method p and the moving average order q ; Step S14, parameter estimation: predict the characteristic time series data The estimated value needs to calculate the autoregressive coefficient in the prediction model and the moving average coefficient , and determine the final prediction model; Step S15, model test: I. Model adaptability test: the model adaptability test is white noise test, which is verified by residual sequence, to judge whether the obtained residual sequence is white noise; II. Model parameter significance test: test the estimated parameter value in the prediction model to determine whether it is significantly non-zero; Step S20, analysis and verification of ARIMA model prediction results: Select the stable wear period and severe wear period of the three characteristic parameters of the grinding grain coverage area index , the number of grinding grains , the maximum grinding grain chain width Two different time series of model establishment and prediction are carried out, and the prediction effect of the prediction model is analyzed by comparing the experimental value and the predicted value, and then the wear severity of the gear is judged.

[0005] Further, the expression of the prediction model based on ARIMA( p , d , q ) is: In the formula: Non-stationary time series; Autoregressive coefficient; Moving average coefficient; White noise; Autoregressive order; Moving average order; Difference factor. Respectively, the error of the model at different times.

[0006] Further, in step S12, the stationary judgment criterion of the characteristic time series is as follows: ​1. The horizontal axis of the autocorrelation function (ACF) and partial autocorrelation function (PACF) graphs represents the lag term k, the vertical axis represents the correlation coefficient, and the upper and lower horizontal lines represent the standard deviation range of the coefficients. Tailing refers to the autocorrelation function and partial autocorrelation function values ​​​​over the entire order being greater than 2 times the standard deviation range, showing a very weak trend of change or suddenly decreasing to zero at the initial order, and then oscillating alternately within and outside 2 times the standard deviation. Truncation refers to the sudden decrease to zero at the initial order, and the correlation coefficient values ​​​​at subsequent orders all fall within the range of 2 times the standard deviation; 2. The characteristic time series showing a monotonic trend is a non-stationary time series; the characteristic time series showing a periodic change is a stationary time series. For the establishment of the prediction model, starting from the initial order, if the autocorrelation function and the partial autocorrelation function are always controlled within the range of two standard deviations and fluctuate around the zero axis, the characteristic time series is a stationary time series with very strong randomness.

[0007] Furthermore, in step S12, the differential processing method is to d The ARMA( p , q ) model is converted to ARIMA( p , d , q ) model, its difference form is: .

[0008] Furthermore, in step S13, the order determination method is the Bayesian Information Criterion. When the sample sequence length is When , the model order determined by the Bayesian Information Criterion can converge to the true value according to probability, and the smaller the BIC value in the regression model, the better the fitting effect. The judgment criteria are: Where: —The number of independent parameters of the model; — sample size; —likelihood function; —Penalty term, to avoid the dimensionality disaster when the dimension is too large.

[0009] Furthermore, in step S14, the parameter estimation method is Yule-Walker estimation, and the autocovariance function, autocorrelation function, and sample partial correlation function of the sample under the characteristic time series are calculated using Yule-Walker estimation, and then the autoregressive coefficient is solved. and the sliding average coefficient .

[0010] Furthermore, the autocorrelation function is the degree of autocorrelation between variables, and is expressed as Indicates that for the extracted feature time series , after differential processing, a stationary characteristic time series with a mean of zero is obtained Solving the delay with sample autocovariance function Autocorrelation function of order p The formula for solving the sample autocorrelation function is: Wherein: is the sample autocovariance function of time series; is the mean of the sample points of the sequence; The purpose of the partial correlation function is to eliminate the influence of the lag period on the characteristic time series, and the PACF is calculated by the partial correlation coefficient According to the autocorrelation function The partial correlation function can be obtained by the Yule-Walker equation The expression is as follows: Through the above matrix operation, we can get It is also calculated by the Levinson recursive formula, and the specific derivation formula is as follows: Wherein: When the partial correlation function is taken , we can get Therefore, the autoregressive coefficient of the prediction model based on ARIMA( p , d , q ) is actually the value of selected in the partial correlation function ; The autoregressive coefficient is represented by in the autocorrelation function, and its expression is as follows: According to the above calculation results, the moving average coefficient and the variance of the error sequence are calculated, and Wherein: is the model of MA( q ), and its autocovariance function can be expressed as: Substitute in the formula into the following formula, and solve the nonlinear equation set to get the moving average coefficient and : .

[0011] Further, in step S20, the following three conditions are set for the establishment of the prediction model: 1. Abrasive grain coverage area index 2. Abrasive grain number 3. Maximum abrasive grain chain width ​The three characteristic parameters select the same time sequence point, the first time period selects initial wear-stable wear period (48 hours before); the second time period selects initial wear-severe wear (78 hours before); II. Based on the historical data prediction, the prediction of the future 100 feature points is realized; III. Selecting 30 feature points under the initial condition to compare and analyze the experimental value and the predicted value.

[0012] Further, in step S15, if the prediction model fails the test, the order of the prediction model needs to be re-set p And q The model fitting is performed again.

[0013] Further, in step S15, the Box-Ljung statistical quantity is used to test whether the autocorrelation coefficient is statistically significant.

[0014] From the above description, the gear wear state prediction method based on the time sequence ARIMA model provided by the application has the following beneficial effects: I. For the constructed wear particle group characteristic time sequence, the wear state prediction is realized by establishing the time sequence ARIMA prediction model, the wear severity can be analyzed and judged in advance, and the mechanical equipment failure rate is effectively reduced; II. According to the model establishment steps, the initial wear-stable wear period (48 hours before) and the initial wear-severe wear (78 hours before) of the three characteristic time sequences of the wear particle coverage area index, the wear particle number and the maximum wear particle chain width are selected, six different prediction models are established, and the comparison between the predicted value and the experimental value further illustrates that the established prediction model can be applied to the prediction of the characteristic time sequence; III. The ARIMA prediction model based on the characteristic time sequence realizes the prediction of the future value by using the historical data change information, provides necessary analysis conditions for the diagnosis and monitoring of the mechanical equipment, and the three selected wear particle group characteristics can be used as wear information, and the prediction model can be used for the analysis and judgment of the gear wear severity. DETAILED DESCRIPTION

[0015] Figure 1 The (a) part of the wear particle coverage area index time sequence.

[0016] Figure 2 The (a) part of the wear particle coverage area index time sequence.

[0017] Figure 2 The (b) part of the wear particle coverage area index time sequence.

[0018] Figure 3 The (a) part of the wear particle coverage area index time sequence.

[0019] Figure 3 The (b) part in FIG. 14 is the first-order difference partial autocorrelation function plot.

[0020] Figure 4 The is the first-order difference abrasive grain coverage area index time series.

[0021] Figure 5 The is the residual ACF and PACF after first-order difference.

[0022] Figure 6 The is the ARIMA (1, 1, 11) prediction curve of the abrasive grain coverage area index.

[0023] Figure 7 The (a) part in FIG. 16 is the ARIMA (1, 1, 8) prediction curve of the abrasive grain number.

[0024] Figure 7 The (b) part in FIG. 16 is the ARIMA (1, 1, 12) prediction curve of the maximum abrasive grain chain width.

[0025] Figure 8 The (a) part in FIG. 18 is the comparison between the characteristic model prediction value and the experimental value of the abrasive grain coverage area index in the first time period.

[0026] Figure 8 The (b) part in FIG. 18 is the comparison between the characteristic model prediction value and the experimental value of the abrasive grain number in the first time period.

[0027] Figure 8 The (c) part in FIG. 18 is the comparison between the characteristic model prediction value and the experimental value of the maximum abrasive grain chain width in the first time period.

[0028] Figure 9 The is the ARIMA (1, 1, 14) prediction curve of the abrasive grain coverage area index.

[0029] Figure 10 The (a) part in FIG. 20 is the ARIMA (1, 1, 10) prediction curve of the abrasive grain number.

[0030] Figure 10 The (b) part in FIG. 20 is the ARIMA (3, 1, 11) prediction curve of the maximum abrasive grain chain width.

[0031] Figure 11 The (a) part in FIG. 22 is the comparison between the characteristic model prediction value and the experimental value of the abrasive grain coverage area index in the second time period.

[0032] Figure 11 The (b) part in FIG. 22 is the comparison between the characteristic model prediction value and the experimental value of the abrasive grain number in the second time period.

[0033] Figure 11Part (c) is a comparison chart of the maximum abrasive chain width characteristic model predicted value and experimental value in the second time period. DETAILED DESCRIPTION

[0034] The present invention is further described below through specific embodiments.

[0035] This invention is based on the research and development results of the Fujian Provincial Natural Science Foundation General Project, project number 2024J011544, and the project name is "Research on wear monitoring and remaining life of gear transmission system based on group wear particle microscopic image information".

[0036] A time series prediction model describes the patterns of changes in the components of a system over time, and expresses the relationship between features and time in a mathematical modeling way.

[0037] ARMA( p , q ) is an autoregressive moving average model, which is a modeling method that uses historical data to predict future values ​​by combining the regression (Auto Regression, AR) model and the moving average (Moving Average, MA) model. This model has strong state description and prediction analysis capabilities, can realize the state prediction of single variable time series, and accurately reflect the dynamic relationship and development law of the entire time series data. For a data time series Building ARMA( p , q ) model, which is expressed in the form of linear difference: Where: —Stationary time series; —autoregressive coefficient; — sliding mean coefficient; —white noise; —autoregressive order; — sliding average order; (1) When the sliding average order When The model predicts the current point by adding white noise to the linear combination of the past points in the time series. Model expression: Where: is the observation value of the time series at the moment; , ,… For time series lagged series; (2) when the autoregressive order When, it is MA( q ) model, which is a linear combination prediction of time white noise, MA( q )Model expression: In the formula: Respectively, the model in Error at different times; (3) Establish a time series prediction model, first determine the type of model, as shown in Table 1, gives the basic principles of model selection: ARIMA( p , d , q ) model to the partial autocorrelation function (PACF) tail, to the autocorrelation function (ACF) tail; MA(q) model to the autocorrelation function (ACF) tail, to the partial autocorrelation function (PACF) tail; When the autocorrelation function and the partial autocorrelation function are trailing, select ARMA( p , q ) model.

[0038] Table 1 Basic principles of model category determination .

[0039] ARIMA( p , d , q ) model full name difference autoregressive moving average model, difference autoregressive moving average model as a kind of prediction model based on time series can analyze the randomness and stationarity of characteristic time series, the ARIMA( p , d , q ) model contains AR, MA, ARMA and difference components, is the extension of ARMA( p , q ) model, mainly to solve the non-stationary problem of sequence, through one or several times difference will non-stationary time series into stationary time series, and then model analysis on stationary time series, can be used to analyze complex time series with long-term trend, through ARIMA( p , d , q ) model can realize the prediction of future characteristic value, the expression of the prediction model based on ARIMA( p , d , q ) is: In the formula: Non-stationary time series; Autoregressive coefficient; Moving average coefficient; White noise; Autoregressive order; Moving average order; Difference factor. Respectively, the model in Error at different times.

[0040] The present invention provides a method for predicting gear wear state based on a time series ARIMA model, comprising the following steps: Step S10, constructing ARIMA ( p , d , q ) prediction model, the specific steps are as follows: Step S11, constructing a wear particle group characteristic time series; Step S12, stationarity test: The stationarity of the characteristic time series is comprehensively judged by analyzing the trend of the characteristic time series itself and the truncation and tailing principles of the autocorrelation function and the partial autocorrelation function. When the stationarity test result of the characteristic time series is non-stationary, the stationarity processing method is used to process it, and the difference order is determined according to the processing effect. d ; Step S13: Determine the order of the model: Use the order determination method to determine the autocorrelation order of the prediction model. p With the sliding average order q ; Step S14, parameter estimation: predict the characteristic time series to obtain data To estimate the value of , we need to calculate the autoregressive coefficient in the prediction model and the sliding average coefficient , and determine the final prediction model; Step S15: Model verification: 1. Model adaptability test: The model adaptability test is a white noise test, which is verified by the residual sequence to determine whether the obtained residual sequence is white noise; 2. Model parameter significance test: Test the estimated parameter values ​​in the prediction model to determine whether they are significantly non-zero; Step S20: Analysis and verification of the prediction results based on the ARIMA model: Select the wear coverage index , number of abrasive particles , Maximum abrasive chain width The model is established and predicted for two different time series: the stable wear period and the severe wear period under three characteristic parameters. The prediction effect of the prediction model is explained by comparing the experimental values ​​with the predicted values, and then the severity of gear wear is judged.

[0041] The gear full-life wear experiment lasted a total of 91 hours from startup to complete failure. The equipment parameters were adjusted, and oil sampling was performed every two minutes. Online wear particle images were obtained using online ferrography technology, where each online wear particle image corresponds to a time point. Therefore, characteristic parameters of multiple wear particle groups in the online wear particle image were extracted to construct a characteristic time series based on full-life wear.

[0042] Wear particle group characteristics include wear particle coverage index , number of abrasive particles , Maximum abrasive chain width After the wear particle image is segmented online, the ratio of the total area of ​​the wear particle group in the pixel sense to the total area of ​​the spectrum is the wear particle coverage area index. The number of wear particles in a single wear particle image is different. The number of rectangles marked in the image is automatically calculated according to the program. The number of rectangles in the image is the number of wear particles. The minimum rectangle width marked for the wear particle is equivalent to the chain width of the connected area of ​​a single wear particle. The maximum width of the marked rectangle is automatically screened out, which is equivalent to the maximum wear particle width.

[0043] Correspondingly, the truncation and tailing principles of the autocorrelation function and partial autocorrelation function in SPSS statistical analysis software can be used to comprehensively judge the stationarity of the characteristic time series.

[0044] The criteria for judging the stationarity of characteristic time series are as follows: 1. In the autocorrelation function (ACF) and partial autocorrelation function (PACF) graphs, the horizontal axis represents the lag term k, the vertical axis represents the correlation coefficient, and the upper and lower horizontal lines represent the standard deviation range of the coefficients. The "tailing" refers to the autocorrelation function and partial autocorrelation function values ​​​​over the entire order being greater than 2 times the standard deviation range, showing a very weak trend of change or suddenly decreasing to zero at the initial order, and then oscillating alternately within and outside 2 times the standard deviation. The "tailing" refers to the sudden decrease to zero at the initial order, and the correlation coefficient values ​​​​at subsequent orders all fall within the range of 2 times the standard deviation; 2. The characteristic time series showing a monotonic trend is a non-stationary time series; the characteristic time series showing a periodic change is a stationary time series. For the establishment of the prediction model, starting from the initial order, if the autocorrelation function and the partial autocorrelation function are always controlled within the range of two standard deviations and fluctuate around the zero axis, the characteristic time series is a stationary time series with very strong randomness.

[0045] In this embodiment, the wear particle coverage area index time series is selected as the analysis object, and an ARIMA prediction model is established for the wear particle coverage area index time series to clarify the specific steps of model establishment and parameter determination method, such as Figure 1 As shown, the time series of the wear coverage index during the entire wear process is given.

[0046] SPSS statistical analysis software was used to solve the autocorrelation function diagram and partial autocorrelation function diagram of the wear particle coverage area index time series, as shown in the following figure: Figure 2 Part (a) and Figure 2 As shown in part (b), according to the above judgment criteria, the ACF is much larger than the 2-fold range and shows a slightly weakening trend. After decreasing to zero, the PACF does not always remain within the 2-fold range, proving that the wear coverage area index time series is a non-stationary time series.

[0047] For non-stationary sequence, data conversion and difference processing can be performed when the interval of the data before and after the observation sequence is inconsistent. For non-stationary sequence containing trend, difference processing is used to make it stationary, and the difference processing is to convert the ARMA( d ) model into the ARIMA( p , q ) model through p first-order difference, and the difference form is as follows: d . q . .

[0048] The autocorrelation function graph and the partial autocorrelation function graph after solving the first-order difference are shown in (a) and (b) of FIG. 6, respectively. The values of the two functions are within two standard deviations and gradually tend to 0. The time sequence after the first-order difference is stationary, as shown in FIG. 7, which is the stationary time sequence. Figure 3 Figure 3 After the characteristic time sequence is stationary, the model order needs to be determined. Commonly used order determination methods include autocorrelation function and partial correlation function order determination method, Akaike information criterion (AIC), Bayesian information criterion (BIC), and best criterion function order determination method. Figure 4 The Bayesian information criterion is similar to the Akaike information criterion and is used for model order determination. Increasing the number of model parameters increases the complexity of the model, which is prone to overfitting. The introduction of a penalty term related to the number of model parameters can solve the problem of overfitting. Since the BIC penalty term is larger than the AIC penalty term, and when the data sample is too large, the BIC can eliminate the information dispersion problem in a long time sequence, and can effectively prevent the model from being too complex due to the high precision of the model.

[0049] In this embodiment, the order determination method is the Bayesian information criterion. When the length of the sample sequence is

[0050] , the model order determined by the Bayesian information criterion can converge to the true value according to the probability, and the smaller the BIC value in the regression model, the better the fitting effect. The judgment criterion is as follows:

[0051] In the formula, p is the number of independent parameters of the model, n is the number of samples, L is the likelihood function, and λ is the penalty term, which can avoid the dimension disaster phenomenon in the case of too large dimension. As shown in (a) and (b) of FIG. 8, respectively.

[0052] As shown in (a) and (b) of FIG. 8, respectively. Figure 3 Figure 3 ​​​​​​​As shown in part (b) of FIG. 1, the first-order difference autocorrelation function and the first-order difference partial autocorrelation function are respectively and truncated at the order of 9, an ARIMA(3, 1, 9) prediction model can be established for the sequence, and according to the Bayesian information criterion, from the fitting statistics of the established model in Table 2, the standard BIC value is 9.281, which is the minimum value, indicating that the fitting effect is optimal.

[0053] Table 2 ARIMA(3, 1, 9) prediction model fitting statistics .

[0054] The parameter estimation method includes Yule-Walker estimation, least squares estimation, maximum likelihood estimation, and point estimation. In this embodiment, the parameter estimation method is Yule-Walker estimation, the sample autocovariance function, the autocorrelation function, and the sample partial correlation function of the sample under the characteristic time sequence are calculated by using Yule-Walker estimation, and then the autoregressive coefficient and the moving average coefficient .

[0055] The autocorrelation function is the degree of autocorrelation between variables, which is represented by For the extracted characteristic time sequence , after difference processing, a stationary characteristic time sequence with a mean of zero is obtained , the autocorrelation function of the delay order is solved by using the sample autocovariance function , and the sample data autocorrelation function formula is solved In the formula: is the time sequence sample autocovariance function; is the sequence sample point mean.

[0056] The purpose of the partial correlation function is to eliminate the lag period influence on the characteristic time sequence, the PACF is calculated, the partial correlation coefficient , the partial correlation function can be solved by the Yule-Walker equation, and the expression is as follows: Through the above matrix operation, the can be obtained, and the Levinson recursive formula is also used for calculation, and the specific derivation formula is as follows: In the formula: , when is taken in the partial correlation function, the can be obtained, and therefore, based on the ARIMA( p , d ,​q ) is the autoregressive coefficient of the prediction model In fact, the partial correlation function Select The value of .

[0057] Calculate autoregressive coefficients Only the autocorrelation function It is expressed as follows: According to the above calculation results, the sliding average coefficient is calculated and error sequence Variance ,make Where: is MA( q ) model, its autocovariance function It can be expressed as: In the formula Substituting the following formula, solving the nonlinear equations can obtain the sliding average coefficient and : .

[0058] Table 3 Parameter estimates under the ARIMA (3,1,9) forecasting model .

[0059] As shown in Table 3, the model autoregressive parameters and sliding average parameters are determined, AR( p ) has three lag terms, representing the autoregressive model parameters, MA(q) has nine lag terms, whose values ​​are the sliding average model parameters, and the constant term is white noise, with a value of 0.722.

[0060] If the residual sequence obtained is not white noise, it means that the information extracted from the sequence is insufficient. At this time, the model needs to be reset. If there is no autocorrelation in the residual sequence, it proves to be white noise and the model is appropriate.

[0061] like Figure 5 As shown in the figure, the ACF and PACF of the residual series after the first-order difference calculated by SPSS statistical analysis software are both within 2 times the standard deviation and rapidly decrease to zero. There is no significant autocorrelation and bias relationship between the changes in the lag order of the residuals. The residuals are judged to be white noise, indicating that the model can fully provide the correlation information in the sample data.

[0062] Individual insignificant parameters should be deleted and re-modeled to make the model more streamlined.

[0063] If the prediction model fails the test, the order of the prediction model needs to be reset. p and qModel fitting was performed again.

[0064] The Box-Ljung statistics was used to test whether the autocorrelation coefficient was statistically significant. Table 4 shows the statistics data, and the Sig. column shows the significance value of the Ljung-Box statistics. The Sig. value is 0.062, which is greater than 0.05, indicating that the two sequences are random. The estimated value of the total variation proportion of the sequence value is represented by the stationary R-square. The higher the value, the better the model fitting. The value is 0.875, which has good fitting degree.

[0065] Table 4 ARIMA(3,1,9) model statistics .

[0066] After the above test analysis, the model successfully passed the parameter significance test and white noise test, indicating that the model can be used for time series prediction.

[0067] For the abrasive grain coverage area index time series, after the stationary test, parameter determination, and model test step analysis, the ARIMA(3,1,9) prediction model was finally determined. Through data analysis of previous characteristic historical data, effective prediction of future characteristic values was realized. The ARIMA(3,1,9) model was established, and its expression is: .

[0068] Therefore, taking the abrasive grain coverage area index (IPCA) time series as the analysis object, the specific analysis method of model establishment was determined from the four steps of stationary test, model order determination, parameter estimation, and model test.

[0069] The abrasive grain population characteristic time series conforms to the overall distribution of the "bathtub curve" of wear, and presents different states at different wear stages.

[0070] To facilitate data analysis, the following three conditions are set for the establishment of the prediction model: one, the abrasive grain coverage area index , the number of abrasive grains , and the maximum abrasive grain chain width The time series points of the three characteristic parameters are selected in the first time period, which is the initial wear-stable wear period (the first 48 hours); the second time period is selected as the initial wear-severe wear (the first 78 hours); Two, based on historical data prediction, realize the prediction of the future 100 characteristic points; Three, select 30 characteristic points under the initial conditions for experimental and predictive value comparison analysis.

[0071] First time period model prediction: According to the model establishment steps of time series stationarity test, model order determination, parameter estimation and parameter test, the prediction models of three characteristic time series are established. The models established under different characteristic time series are different. For example, the prediction graphs of the first section of time series of the abrasive grain coverage area index, the abrasive grain number and the maximum abrasive grain chain width in (a) of Figure 6 , Figure 7 and (b) of Figure 7 are respectively, and the corresponding models are ARIMA(1, 1, 11), ARIMA(1, 1, 8) and ARIMA(1, 1, 12) respectively.

[0072] The comparison graphs of the prediction values of the abrasive grain coverage area index, the abrasive grain number and the maximum abrasive grain chain width with the true data in the future 30 time points in (a) of Figure 8 , (b) of Figure 8 and (c) of Figure 8 are respectively, the overall trend of the prediction values is stable, the experimental values jump greatly, the overall prediction results of the three characteristics of the abrasive grain coverage area index, the abrasive grain number and the maximum abrasive grain chain width are consistent with the trend of the true data, and the prediction results of individual values are deviated, in which the prediction result of the abrasive grain coverage area index is the closest.

[0073] Second time period model prediction: The prediction models of the three time series of the abrasive grain coverage area index, the abrasive grain number and the maximum abrasive grain chain width are respectively ARIMA(1, 1, 14), ARIMA(1, 1, 10) and ARIMA(3, 1, 11) after the time series of the second time period are subjected to stationarity test, model order determination, parameter estimation and test, as shown in (a) of Figure 9 , Figure 10 and (b) of Figure 10 .

[0074] From the comparison of the experimental values and the prediction values in (a) of Figure 11 , (b) of Figure 11 and (c) of Figure 11 , it can be seen that the overall trend of the prediction values of the abrasive grain coverage area index, the abrasive grain number and the maximum abrasive grain chain width in the second time period is the same as that of the experimental values, and the prediction results are basically consistent, the trend of the predicted 30 values is relatively stable and does not show a jump change, and the prediction values of individual time points have a certain difference from the experimental values.

[0075] The predicted value is generally stable, and some predicted values have large differences with the experimental values, because the prediction model of ARIMA is based on the overall trend analysis of previous data, mainly analyzes the general law, and the predicted value is generally stable, and the analysis ability for randomness is poor, so compared with the experimental value, the prediction of some values is inaccurate, and the following judgments can be made through the above comparison and analysis: for different time series of different characteristics, the future value can be predicted by establishing an ARIMA model, and the state of gear wear is described.

[0076] The present application has the following beneficial effects: I. For the constructed abrasive particle group characteristic time series, the wear state is predicted by establishing a time series ARIMA prediction model, the wear severity can be analyzed and judged in advance, and the mechanical equipment failure rate is effectively reduced; II. According to the model establishment steps, the initial wear-stable wear period (the first 48 hours) and the initial wear-severe wear (the first 78 hours) of three characteristic time series of abrasive particle coverage area index, abrasive particle number and maximum abrasive particle chain width are selected, six different prediction models are established, and the comparison of the predicted value and the experimental value further shows that the established prediction model can be applied to the prediction of characteristic time series; III. The ARIMA prediction model based on the characteristic time series realizes the prediction of the future value by using the historical data change information, provides necessary analysis conditions for the diagnosis and monitoring of mechanical equipment, and the selected three abrasive particle group characteristics can be used as information representing wear, and the prediction model can be used for the analysis and judgment of the severity of gear wear.

[0077] The above is only some specific embodiments of the present application, but the design concept of the present application is not limited thereto, and any non-essential modification of the present application using this concept should belong to the behavior of infringing the protection scope of the present application.

Claims

1. A gear wear state prediction method based on a time series ARIMA model, characterized by: Comprising the following steps: Step S10, constructing a prediction model based on ARIMA( p , d , q ) The specific steps are as follows: Step S11, constructing a characteristic time series of abrasive particle population; Step S12, stationarity test: the stationarity of the characteristic time series is comprehensively judged by the trend of the characteristic time series itself and the tailing and truncation principles of analyzing the autocorrelation function and the partial autocorrelation function. When the stationarity test result of the characteristic time series is non-stationary, the stationarity of the characteristic time series is processed by using a difference processing mode, and the difference order is determined according to the processing effect d ; Step S13, model order determination: determine the autocorrelation order of the prediction model by using the order determination method p and the moving average order q ; Step S14, parameter estimation: predict the characteristic time series to obtain data To estimate the value of , we need to calculate the autoregressive coefficient in the prediction model and the sliding average coefficient , and determine the final prediction model; Step S15, model verification: I. Model adaptability test: The model adaptability test is a white noise test, which is verified by residual series to determine whether the obtained residual series is white noise; II. Model parameter significance test: The estimated parameter values in the prediction model are tested to determine whether they are significantly non-zero; Step S20, analysis and verification based on ARIMA model prediction results: grit coverage area index , number of grits , maximum grit chain width The two different time series of stable wear period and severe wear period under three characteristic parameters are modeled and predicted. The prediction effect of the prediction model is illustrated by comparing the experimental value with the predicted value, and then the wear severity of the gear is judged.

2. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: Based on ARIMA( p , d , q ) is expressed as: Where: — non-stationary time series; —autoregressive coefficient; — sliding mean coefficient; —white noise; —autoregressive order; — sliding average order; — difference factor; The models are Errors at different times.

3. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: In step S12, the stationarity judgment criteria of the characteristic time series are as follows: I. The horizontal axis of the autocorrelation function (ACF) graph and the partial autocorrelation function (PACF) graph represents the lag k, and the vertical axis is the correlation coefficient. The upper and lower horizontal lines represent the standard deviation interval of the coefficient. The tail refers to the autocorrelation function and the partial autocorrelation function in the entire order value greater than 2 times the standard deviation range, showing a weak trend or suddenly decreasing to zero at the initial order, and then alternating inside and outside the 2 times standard deviation. The truncation refers to the sudden decrease to zero at the initial order, and then the correlation coefficient values at the order fall within the 2 times standard deviation range; II. The characteristic time series with a monotonic trend is a non-stationary time series. The characteristic time series with a periodic change is a stationary time series. For the establishment of the prediction model, from the initial order, if the autocorrelation function and the partial autocorrelation function are always controlled within the two times standard deviation range and fluctuate around the zero axis, the characteristic time series is a very strong random stationary time series.

4. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: In step S12, the difference processing mode is to convert the ARMA( d , p , q ) model into an ARIMA( p , d , q ) model by first-order difference, and the difference form is as follows: 。 5. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: In step S13, the order determination method is Bayesian information criterion. When the sample sequence length The model order determined by the Bayesian information criterion converges to the true value according to probability, and the smaller the BIC value in the regression model, the better the fitting effect. The judgment criterion is: In the formula: The number of model independent parameters; The number of samples; The likelihood function; The penalty term avoids the dimension disaster phenomenon in the case of excessive dimension.

6. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: In step S14, the parameter estimation method is Yule-Walker estimation, and the autocovariance function, autocorrelation function and sample partial correlation function of the sample under the characteristic time sequence are calculated by using Yule-Walker estimation, and then the autoregressive coefficients are solved with the moving average coefficients .

7. The gear wear state prediction method based on the time series ARIMA model according to claim 6, characterized in that: The autocorrelation function is the degree of autocorrelation between variables, Indicates that for the extracted feature time series , after differential processing, a stationary characteristic time series with a mean of zero is obtained , using the sample autocovariance function to solve the delay Autocorrelation function of order , solve the sample data autocorrelation function formula: Where: is the time series sample autocovariance function; is the mean of the sequence sample points; the purpose of the partial correlation function is to eliminate the lag effect on the characteristic time series, calculate PACF, and have a partial correlation coefficient , according to the autocorrelation function The partial correlation function can be obtained by the Yule-Walker equation , the expression is as follows Through the above matrix operations, we can get , is also calculated using the Levinson recursive formula. The specific derivation formula is as follows: Where: , in the partial correlation function, take When , therefore, based on ARIMA( p , d , q ) is the autoregressive coefficient of the prediction model In fact, the partial correlation function Select The value of ; Computing the autoregressive coefficients Only the autocorrelation function in is expressed as follows: According to the above calculation results, the moving average coefficient and the error sequence variance , let In the formula: is the model of MA( q ), the autocovariance function can be expressed as: Substitute in the formula into the following formula, and solve the nonlinear equation set to get the moving average coefficient and : .

8. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: In step S20, the following three conditions are set for the establishment of the prediction model: I. Abrasive grain coverage area index II. Abrasive grain number III. Maximum abrasive grain chain width The time series points of the three characteristic parameters are the same, and the first time period is selected from the initial wear to the stable wear period; the second time period is selected from the initial wear to the severe wear. II. Based on historical data prediction, 100 characteristic points in the future are predicted; III. Select 30 characteristic points under the initial condition for experiment and comparison analysis of predicted values.

9. The gear wear state prediction method based on the time series ARIMA model according to claim 1, characterized in that: In step S15, if the prediction model does not pass the test, the order of the prediction model needs to be reset p and q model fitting is performed again.

10. The gear wear state prediction method based on a time series ARIMA model according to claim 1, characterized in that: In step S15, the Box-Ljung statistic is used to test whether the autocorrelation coefficient is statistically significant.

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