An adaptive sampling method for equipment degradation state monitoring

Abstract

The application discloses a self-adaptive sampling method for equipment degradation state monitoring, and the method comprises the following steps: acquiring an initial time sequence representing a degradation state through an equal-time-interval sampling strategy; interchanging independent variables and dependent variables in the time sequence to realize conversion of the time sequence into a degradation sequence; converting the irregular degradation sequence into a regular degradation sequence through an interpolation method; performing degradation prediction through a difference integrated moving average autoregressive model; obtaining a next sampling interval and performing sampling; and obtaining a final sample set until a failure threshold is reached.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of state monitoring, and more specifically relates to a self-adaptive sampling method for equipment degradation state monitoring. BACKGROUND

[0002] Condition Monitoring (CM) originated in the early stage of mechanical development and has been widely used in various fields of industry. With the popularity of sensors and the rise of the Internet of Things, it has gradually expanded to more extensive fields, including medical care, climate environment, and autonomous driving. At the same time, real data often presents a skew distribution with a tail. Therefore, there are two prominent problems in real data collection.

[0003] (1) Data explosion. The explosive growth of data volume not only brings huge pressure on storage, but also exponentially increases the subsequent data cleaning and data mining work.

[0004] (2) Data imbalance. Data imbalance is manifested in local information redundancy, local information loss, and uneven overall data distribution. In view of the non-negligible influence of unbalanced classification and unbalanced regression on the accuracy of state recognition and state prediction, people have conducted extensive research on it. However, the ultimate purpose of related research is only to alleviate the impact of data imbalance, not to eliminate it.

[0005] To fundamentally solve the above problems, it ultimately focuses on how to obtain an efficient data set, and sampling strategy is an important part of it. Among the control variables involved in the sampling strategy, sampling frequency, sampling interval, and sample length are common control variables involved in all sampling. Among them, sampling interval has great potential for solving the existing problems because it can simultaneously affect data volume and data imbalance. There are the following problems in the current research on sampling interval adjustment.

[0006] Problem 1: The sampling target is not clear.

[0007] Problem 2: Irregular Time Series Prediction (ITSP) method is not mature.

[0008] Problem 3: The existing method has a time lag problem, that is, using the current state to guide future sampling without considering the time-varying characteristics of the state.

[0009] Problem 4: There is a theoretical deviation in predicting the sampling time. Time series prediction research estimates the state at a given time, which is exactly the opposite of our actual needs.

[0010] Due to the huge difference in data characteristics, it is impossible to find a general solution to solve the problems in all fields, and a practical idea is to explore specific solutions by focusing on specific scenarios.

[0011] Degradation is ubiquitous in nature, and the accumulation of degradation will gradually lead to a critical point of failure, which may have disastrous consequences. In order to avoid the huge risks brought by the accumulation of degradation, the development of sensors and the use of data have attracted widespread attention. However, they are respectively related to information acquisition ability and information mining ability, and the importance of sampling strategy between them is seriously underestimated, especially the sampling strategy problem about sampling interval adjustment.

[0012] Therefore, the research on sampling interval adjustment in degradation monitoring is of great significance. SUMMARY

[0013] The purpose of the present application is to overcome the problem of unbalanced degradation information acquisition and explosive sampling data in current degradation monitoring, and to provide an adaptive sampling method for equipment degradation state monitoring, which realizes the degradation state monitoring of equipment by transforming time series into degradation sequence and predicting degradation sequence, and outputting sampling interval.

[0014] In order to achieve the above-mentioned purpose of the application, the adaptive sampling method for equipment degradation state monitoring comprises the following steps:

[0015] (1) initialize the time-based sampling strategy;

[0016] The sampling target in equipment degradation monitoring is subject to uniform distribution, and the initial sampling interval SI d is set.

[0017] Set the sampling boundary, including: failure threshold h thr , upper limit of sampling interval I max , lower limit of sampling interval I min and minimum number of degradation sequences V1;

[0018] (2) obtain the initial time sequence representing the degradation state;

[0019] The initial degradation state indicators of p samples and the corresponding sampling time are obtained according to the initial sampling interval SI d based on the equal time interval sampling strategy, and then the initial state time sequence is constructed: x={(t i ,h i ):i=1,2,…,p}, wherein t i represents the sampling time of the i-th sample, h i represents the degradation state indicator value corresponding to the i-th sample, and p represents the number of samples.

[0020] Let h new = h p , X = x;

[0021] (3) Transforming time series into degradation series;

[0022] (3.1) Out-of-limit detection;

[0023] If h new ≥ h thr , stop sampling and output the final sampling time series X; otherwise, go to step (3.2);

[0024] (3.2) Smoothing processing;

[0025] Let the number of samples in X be n, and use robust local weighted regression algorithm to smooth the degradation state indicators in X, and obtain time series

[0026] (3.3) Monotonicity detection;

[0027] Let If all elements in h 1 are greater than 0, let h i = h 3 i = h 1 , and then jump to (3.5); otherwise, let h i = h 2 i = h 1 , and then go to step (3.4);

[0028] (3.4) Monotonicity processing;

[0029] Get the serial number of non-positive elements in h 1 , and for each non-positive element with serial number m, let h m+1 = h 2 m = h 2 + ε, where ε is a constant less than 0.0001*h thr ; let h i = h 1 i = h 2 , and then return to (3.3);

[0030] (3.5) Variable exchange;

[0031] In the state time series, take the sampling time of each sample as the independent variable and the corresponding degradation state indicator as the dependent variable, exchange the independent variable and the dependent variable, and obtain time series {(t i , h i3 ):i = 1, 2, …, n} into a degenerate sequence {(h i 3 ,t i ):i = 1, 2, …, n};

[0032] (4), degenerate prediction

[0033] (4.1), regularizing the degenerate sequence by using interpolation method;

[0034] (4.1.1), calculating the maximum allowed degenerate interval MADI:

[0035] MADI = (h last -h1) / V1

[0036] where h1 and h last represent the first element and the last element of the independent variable in the degenerate sequence respectively, and V1 is the minimum number of points of the degenerate sequence;

[0037] (4.1.2), determining the actual sampling state interval SI s of the sampling strategy;

[0038] SI s = min(SI d , MADI)

[0039] where SI d is the target sampling state interval;

[0040] (4.1.3), scaling the degenerate sequence S according to the actual sampling state interval SI s ;

[0041] S t = S / SI s

[0042] where S t represents the degenerate sequence after scaling;

[0043] (4.1.4), constructing an interpolation point sequence {H k};

[0044] The independent variable of the degenerate sequence after scaling is represented as {th i , i = 1, 2, …, n}, and then an interpolation point sequence {H k , k = 1, 2, …, K, represents the floor function;

[0045] (4.1.5), selecting the interpolation method of piecewise cubic Hermite interpolation polynomial to obtain the regular degenerate sequence;

[0046] In the interpolation point sequence {H k}, for the sub-interval [h k , h k+1 ], the label l k is its length, d k is its first-order difference, that is:

[0047] l k = h k+1 - h k

[0048] d k = (t k+1 - t k ) / l k

[0049] Let s k be the slope at point h k :

[0050] s k = F'(h k )

[0051] Where, for piecewise linear interpolation, s k = d k or d k+1 , for h k ≤ h ≤ h k+1 , the cubic polynomial F(h) is expressed as:

[0052]

[0053] Δ = h - h k

[0054] Bring {H k} into F(h) on the corresponding sub-interval to obtain a new time sequence {T k : i = 1, 2, …, K}, and then obtain the regular degenerate sequence {(H k , T k )};

[0055] (4.2) Degenerate sequence prediction;

[0056] Set the autoregressive integrated moving average model ARIMA(p, d, q), where p represents the lag order, d represents the difference order, and q represents the moving average order;

[0057] Use the model ARIMA(p, d, q) to make a single-step prediction on {(H k , T k )}, and the prediction result is denoted as T l ;

[0058] (5), output the adjusted sampling interval;

[0059] (5.1), calculate the next sampling interval prediction value SI l = T l -T K ;

[0060] (5.2), determine the actual sampling interval SI a :

[0061]

[0062] (5.3), obtain a new state indicator h a with the actual sampling interval SI new , update the sample set X = X∪(T l , x new ), and then return to step (3).

[0063] The application aims to achieve the following:

[0064] The application is a self-adaptive sampling method for equipment degradation state monitoring, which obtains an initial time series representing the degradation state based on an equal-time-interval sampling strategy; then, the independent variable and the dependent variable in the time series are interchanged to realize the conversion of the time series into a degradation sequence, and an interpolation method is used to convert the irregular degradation sequence into a regular degradation sequence; finally, a difference integrated moving average autoregressive model is used for degradation prediction to obtain the next sampling interval and perform sampling until the failure threshold is reached to obtain the final sample set.

[0065] Meanwhile, the application also has the following beneficial effects:

[0066] The application introduces a sampling target numericalization module to solve the fuzziness of the sampling target, proposes to solve the ITSP problem by converting the regular sequence, migrating the existing ITSP method, and using machine learning methods, uses the prediction results of the sequence prediction model to guide sampling to solve the time lag problem of the existing method, and solves the problem that step prediction will introduce errors by interchanging variables. In this way, the proposed adaptive sampling framework improves the existing problems to some extent. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is a flowchart of the application, a self-adaptive sampling method for equipment degradation state monitoring;

[0068] Figure 2 are three typical equipment degradation curves;

[0069] Figure 3is a logic function schematic diagram in the comparison method based on the logic function sampling strategy in this embodiment;

[0070] Figure 4 is a data distribution comparison diagram of data obtained by different sampling strategies under exponential simulation data in this embodiment;

[0071] Figure 5 is a comparison diagram of index intervals and time intervals of data obtained by different sampling strategies under exponential simulation data in this embodiment;

[0072] Figure 6 is a data distribution comparison diagram of data obtained by different sampling strategies under mutation J type simulation data in this embodiment;

[0073] Figure 7 is a comparison diagram of index intervals and time intervals of data obtained by different sampling strategies under mutation J type simulation data in this embodiment;

[0074] Figure 8 is a data distribution comparison diagram of data obtained by different sampling strategies under inverted S type simulation data in this embodiment;

[0075] Figure 9 is a comparison diagram of index intervals and time intervals of data obtained by different sampling strategies under inverted S type simulation data in this embodiment; DETAILED DESCRIPTION

[0076] The specific embodiments of the present application will be described below with reference to the accompanying drawings, so that those skilled in the art can better understand the present application. It should be particularly noted that in the following description, when the detailed description of known functions and designs may obscure the main content of the present application, these descriptions will be omitted here.

[0077] EMBODIMENT

[0078] Figure 1 is a flowchart of an adaptive sampling method for equipment degradation state monitoring.

[0079] In this embodiment, as shown in the figure, an adaptive sampling method for equipment degradation state monitoring comprises the following steps: Figure 1

[0080] S1, initialize the hyperparameters of the sampling strategy;

[0081] ​The ideal sampling is the uniform distribution, and only a proper degradation interval needs to be determined; otherwise, the distribution and engineering practice need to be combined for specific analysis. It should be noted that even if the same degradation amount, different states may also produce different effects, just like the sensitivity of people to pain is different in different life stages. Another quantity to be quantified is the initial sampling strategy, which generally adopts a time-based sampling strategy for data accumulation before the sampling cycle. In addition, the sampling boundary should also be specified to prevent sudden changes in the condition law and reduce the impact of large errors that may occur in prediction.

[0082] In the following, we set the following parameters for the degradation state monitoring in the mechanical field:

[0083] The sampling target in the equipment degradation state monitoring obeys the uniform distribution, and the initial sampling interval SI is set d ;

[0084] The sampling boundary is set, including: the failure threshold h thr , the upper limit of the sampling interval I max , the lower limit of the sampling interval I min , and the minimum number of degradation sequences V1;

[0085] In this embodiment, the present application is not limited to the mechanical field, and can be used in medical treatment, climate environment, automatic driving, and other fields to realize degradation state monitoring.

[0086] S2, an initial time sequence representing the degradation state is obtained;

[0087] Based on the equal time interval sampling strategy, the initial degradation state index sample and the corresponding sampling time are obtained according to the initial sampling interval SI d , and the initial state time sequence is represented as: x={(t i ,h i ):i=1,2,…,p}, wherein t i represents the sampling time of the i th sample, h i represents the i th degradation state index sample collected, and p represents the number of collected samples; h new =h p , and X=x.

[0088] S3, the conversion of the time sequence to the degradation sequence is realized;

[0089] Usually physical degradation state indicators do not need additional processing, while the data relied on by feature indicators often need to be filtered and denoised first due to inevitable environmental noise and interference from useless components. In addition, since feature indicators do not obey the law of degradation irreversibility in most cases, they need to be monotonized and smoothed to make them more approximate to the actual degradation law. On this basis, by exchanging the independent variable and dependent variable of the time series obtained, the time series is converted into a degradation sequence. In this way, the next sampling interval can be predicted without error in theory. The process is described as follows:

[0090] S3.1, overrun detection;

[0091] If h new ≥ h thr , stop sampling and output the final sampling time series sample X; otherwise, go to step S3.2;

[0092] S3.2, smoothing processing;

[0093] Assume that the number of samples in X at this time is n, and the time series obtained by smoothing the degradation state indicators in X using the robust locally weighted regression (Robust Locally Weighted Regression) algorithm is {(t i , h i 1 ): i = 1, 2, …, n};

[0094] S3.3, monotonicity detection;

[0095] Let h If all elements in h 1 are greater than 0, let h i 3 = h i 1 , and then jump to S3.5; otherwise, let h i 2 = h i 1 , and then go to step S3.4;

[0096] S3.4, monotonization processing;

[0097] Get the serial number of non-positive terms in h 1 , and for each non-positive term with serial number m, let h m+1 2 = h m 2 + ε, where ε is a constant less than 0.0001*h thr ; let h i 1= h i 2 Return to S3.3; for example, if h 1 is a non-positive term, modify the value of the 6th term h6 1 in the time series and assign it to h6 2 ; if h 1 is a positive term, directly assign the value of the 10th term h 10 1 in the time series to h 10 2 ; finally, assign h i 2 to h i 1 so as to perform monotonicity detection again;

[0098] S3.5, variable exchange;

[0099] In the state time series, take the sampling time of each sample as the independent variable and the corresponding degradation state index as the dependent variable, exchange the independent variable and the dependent variable, realize the transformation of the time series {(t i , h i 3 ): i = 1, 2,..., n} to the degradation sequence {(h i 3 , t i ): i = 1, 2,..., n};

[0100] S4, degradation prediction

[0101] Since the degradation law is mostly nonlinear, whether the collected time series is irregular or not, the degradation sequence obtained after variable exchange is usually irregular, and its prediction is an ITSP problem. A feasible method is to convert the irregular sequence into a regular sequence and then use mature time series prediction methods for prediction, the specific operation of which is as follows:

[0102] S4.1, regularize the degradation sequence by using interpolation method;

[0103] S4.1.1, calculate the maximum allowed degradation state interval MADI:

[0104] MADI = (h last - h1) / V1

[0105] In the formula, h1 and h last represent the first element and the last element of the independent variable in the degradation sequence respectively, and V1 is the minimum point number of the degradation sequence;

[0106] S4.1.2, determine the actual sampling state interval SI s of the sampling strategy;

[0107] SI s =min(SI) d MADI)

[0108] In the formula, SI d The target sampling state interval;

[0109] S4.1.3, according to the actual sampling interval SI s Scaling transformation is performed on the degraded sequence S;

[0110] S t =S / SI s

[0111] In the formula, S t This represents the degraded sequence after scaling.

[0112] S4.1.4 Constructing the interpolation point sequence {H} k};

[0113] The independent variable of the degraded sequence after scaling is represented as {th}. i Given the sequence {i = 1, 2, ..., n}, construct the interpolation point sequence {H}. k}, k = 1, 2, ..., K, Indicates rounding down;

[0114] In this embodiment, since SI is used in the scaling transformation s The degenerate sequence was normalized, i.e., {th i The actual sampling interval in {H} is converted to a unit length. Therefore, {H} k} is an arithmetic sequence with a difference of 1, and the number of columns is floor(th). n -th1).

[0115] S4.1.5. Select the piecewise cubic Hermite interpolation polynomial method to obtain the degenerate sequence of the rule;

[0116] In the interpolation point sequence {H k In}, for the subinterval [h k ,h k+1 ], mark l k For its length, d k Its first difference is:

[0117] l k =h k+1 -h k

[0118] d k =(t k+1 -tk ) / l k

[0119] Let s k For point h k Slope at:

[0120] s k =F′(h k )

[0121] In the formula, for piecewise linear interpolation, s k =d k or d k+1 For h k ≤h≤h k+1 The fitted cubic polynomial F(h) is expressed as:

[0122]

[0123] Δ=hh k

[0124] {H k Substituting this into F(h) in the corresponding sub-interval, we obtain the new time series {T}. k :i=1,2,…,K}, and thus obtain the regular degenerate sequence {(H k ,T k The monotonic function is generated by fitting a monotonic sequence using a piecewise cubic Hermite interpolation polynomial. This method preserves the shape of the data and the corresponding monotonicity, which is exactly what we need.

[0125] S4.2 Degradation Time Prediction;

[0126] Set up an autoregressive integral moving average model ARIMA(p,d,q), where p represents the lag order, d represents the difference order, and q represents the moving average order.

[0127] Using the model ARIMA(p,d,q) to analyze {(H k ,T k Perform a single-step prediction, and denot the prediction result as T. l ;

[0128] S5, Output sampling interval;

[0129] S5.1 Calculate the predicted value SI for the next sampling interval. l =T l -T K ;

[0130] S5.2 Determine the actual sampling interval SI a :

[0131]

[0132] S5.3, with actual sampling interval SI a obtain new state indicator h new , update sample set X = X∪(T l , x new ), and return to step S3. Until failure threshold is reached and final sample is obtained.

[0133] To better illustrate the technical effects of the present application, a specific embodiment is used to test and verify the present application. The embodiment uses equipment degradation simulation data, and selects three typical equipment degradation shapes as shown in Figure 2 (a) exponential, (b) mutation J type and (c) inverted S type curve to simulate the degradation process.

[0134] Three comparison methods are introduced. The first is a time-based sampling strategy, i.e. fixed time sampling. The second is a fixed proportion adjusted sampling strategy, which uses a proportion coefficient of (1, +∞) and (0, 1) to multiply the sampling interval for slow and fast degradation, respectively, to adjust the sampling interval, otherwise the sampling interval remains unchanged. The third is a sampling adjustment strategy based on a logic function. It uses a sigmoid function to continuously adjust the sampling, and the schematic diagram is shown in Figure 3 .

[0135] SI a represents the actual sampling interval, and the reciprocal of SI a can be regarded as a sigmoid function of the level movement of the degradation rate Rate. Let y = 1 / SI a , and the logic function can be expressed as:

[0136]

[0137] In the formula, y min = 1 / I max , y max = 1 / I min , and l hm represents the horizontal movement length of the sigmoid function, and coef is the coefficient of the adjustment speed change rate. Substituting it into the formula, the expression of SI a is obtained:

[0138]

[0139] The embodiment designs four indicators to evaluate the severity of existing problems in data acquisition, and uses the average deviation value from ideal sampling as the quality evaluation of the sampling strategy. The indicators and symbols are shown in Table 1.

[0140] Problem Evaluation index Symbol Data explosion Total data volume V t ]]> Data imbalance Information loss rate [R m <!-- 7 -->]]> Data imbalance Information honor volume V r ]]> Data imbalance Information redundancy rate [R r ]]> Data bias Average bias

[00020] D a ]]>

[0141] Table 1

[0142] For the initial sample's state index set {h i ,i=1,2,…,n}, using the target sampling state interval SI d As the interval length, the failure threshold h thr The sampling requirement set {S} is constructed as the endpoint. m}. Let I j Let {S} represent the j-th subinterval. m}={I1U I2 U … UI m |I j =[h n +(j-1 / 2)*SI d ,h n +(j+1 / 2)*SI d Then obtain the final sample {x}. i After i = 1, 2, ..., v, the state index in {S} is observed and calculated. m The quality of the sampling strategy is judged by the data distribution in the table. For ease of comparison, all evaluation indicators in Table 1 are relative values, and their expressions are as follows:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] In the formula, IN m IN r These represent the number of missing subintervals and the number of redundant subintervals, respectively.

[0149]

[0150] Table 2

[0151] The parameters for each sampling strategy were assigned using Table 2, and the results are as follows: Figures 4-9 As shown. From the perspective of data distribution, time-based strategies are prone to losing some information during rapid degradation and generating redundancy during slow degradation. Proportion-based and logistic function-based strategies improve upon these two problems to some extent. However, they may introduce side effects. For example, Figure 6 Information loss occurred while attempting to reduce redundancy, and Figure 4 and8 Information redundancy occurs when reducing information loss. The reason is that they are essentially qualitative methods. The proportional-based strategy obtains different data amounts in different states because the proportional coefficient is constant. Although the logic function-based strategy is more adaptive to different states, it is impractical to find a universal function to adapt to the changing degradation law. In contrast to its unstable performance, the proposed strategy achieves almost perfect performance overall. Although information loss and redundancy still occur when the state changes, it can quickly recover, which is also reflected in the changes of the upper subgraph state indicators of Figure 5 and Figure 9 Observing the changes of the state indicators and the time interval, the proportional-based strategy adjusts the fastest, the logic function-based strategy is slower but smooth, and the proposed method exhibits different characteristics in different states.

[0152] All the above observations are reflected in the quantitative indicators of Table 3. The values in the first row are ideal values, and the red bold numbers represent the best values under a certain degradation law. Consistent with the previous analysis, the proposed strategy performs better than other strategies in almost all indicators. The only parameter that seems not optimal is the data amount under the inverse S degradation. However, the data amount of the time-based strategy is the smallest, which is obtained based on the loss of a large amount of degradation information, making its data amount advantage meaningless. Therefore, the proposed strategy achieves the optimal effect on all simulated degradation data sets.

[0153]

[0154] Table 3

[0155] Although the above describes the specific embodiments of the present application in detail, so that those skilled in the art can understand the present application, it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

Claims

1. An adaptive sampling method for equipment degradation state monitoring, characterized in that, Includes the following steps: (1) Initialize the time-based sampling strategy; In device degradation monitoring, sampling targets obey uniform distribution, and initial sampling intervals are set ; Setting a sampling boundary, including: a failure threshold , an upper limit of a sampling interval , a lower limit of a sampling interval , and a minimum number of degenerate sequences ; (2) Obtain the initial time series representing the degradation state; The equal-time-interval-based sampling strategy is according to an initial sampling interval acquiring an initial degradation state indicator of each sample and a corresponding sampling time, and then forming an initial state time sequence: , wherein, denotes a sampling time of the i th sample, denotes a sampling time of the i th sample, denotes a degradation state indicator value corresponding to the i th sample, denotes a degradation state indicator value corresponding to the i th sample, denotes a sample number; make , ; (3) To realize the transformation of time series into degenerate series; (3.1) Over-limit detection; like If the sampling stops, the final sampling time series is output. Otherwise, proceed to step (3.2); (3.2) Smoothing process; Suppose at this time The number of samples in the middle is Using the robust locally weighted regression algorithm to The degradation state index in the data is smoothed to obtain the time series. ; (3.3) Monotonicity detection; remember ,like All elements in the set are greater than 0, let Then jump to (3.5); otherwise, let Then proceed to step (3.4); (3.4) Monotonicization process; Get The sequence number of the positive term in the non-Chinese section, for each sequence number is The non-positive term, let In the formula, Less than r The constant; let Then return to (3.3); (3.5) Variable interchange; In a state time series, the sampling time of each sample is used as the independent variable, and the corresponding degradation state index is used as the dependent variable. By interchangeding the independent and dependent variables, the time series... Transform into a degenerate sequence ; (4) Degradation prediction; (4.1) Regularize the degenerate sequence using interpolation; (4.1.1) Calculate the maximum allowable degradation interval. : ； in, and Let represent the first and last elements of the independent variable in the degenerate sequence, respectively. The minimum number of points in the degenerate sequence; (4.1.2) Determine the actual sampling state interval of the sampling strategy. ; ； in, The target sampling state interval; (4.1.3) According to the actual sampling interval For degenerate sequences Perform scaling transformation; ； in, This represents the degraded sequence after scaling. (4.1.4) Constructing the interpolation point sequence ; The independent variable of the degraded sequence after scaling is expressed as: Then construct the interpolation point sequence. , , , Indicates rounding down; (4.1.5) Select the piecewise cubic Hermite interpolation polynomial method to obtain the degenerate sequence of the rule; In the interpolation point sequence In the middle, for sub-intervals ,mark For its length, Its first difference is: ； ； make For point Slope at: ； For piecewise linear interpolation, or ,for Fitting a cubic polynomial Represented as: ； ； ； Will Substitute into the corresponding sub-interval In this process, a new time series is obtained. This leads to the rule degeneration sequence. ; (4.2) Degenerate sequence prediction; Set up an autoregressive integral moving average model In the formula, Indicates the lag order. Indicates the difference order. Indicates the order of the moving average; Using the model right Perform a single-step prediction, and record the prediction result as... ; (5) The adjusted sampling interval; (5.1) Calculate the predicted value for the next sampling interval. ; (5.2) Determine the actual sampling interval : ； (5.3) Based on the actual sampling interval Obtain new status indicators Update the sample set Then return to step (3).

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