CN112100711B - ARIMA and PSO-ELM based concrete dam deformation combined forecasting model construction method - Google Patents

ARIMA and PSO-ELM based concrete dam deformation combined forecasting model construction method Download PDF

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CN112100711B
CN112100711B CN202010795157.3A CN202010795157A CN112100711B CN 112100711 B CN112100711 B CN 112100711B CN 202010795157 A CN202010795157 A CN 202010795157A CN 112100711 B CN112100711 B CN 112100711B
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CN112100711A (en
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魏博文
罗绍杨
贾璐
程颖新
徐富刚
黄伟
李火坤
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Nanchang University
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Abstract

The invention provides a concrete dam deformation combined forecasting model building method based on ARIMA and PSO-ELM, aiming at the characteristics of high nonlinearity and uncertainty caused by mutual influence of multiple factors in the dam deformation process, irregular chaos characteristic caused by complex noise pollution and the like, self-adaptive analysis and processing are carried out on a residual sequence of a displacement mixed model by using an Ensemble Empirical Mode (EEMD), a Particle Swarm Optimization (PSO) ELM selects an optimal input weight matrix and hidden layer deviation, a PSO-ELM model is built to optimize nonlinear high-frequency induction signals, and meanwhile, a low-frequency trend signal of the PSO-ELM model is fitted and predicted by means of an autoregressive integral sliding average model (ARIMA), so that a multi-scale deformation optimized combined forecasting model is built. Compared with the traditional model, the model built by the invention has higher prediction precision, can overcome noise interference in the monitoring sequence, reflects the multi-scale characteristic of the dam monitoring sequence, and can more clearly and comprehensively analyze and judge the dam monitoring data time sequence.

Description

ARIMA and PSO-ELM based concrete dam deformation combined forecasting model construction method
Technical Field
The invention relates to the technical field of dam operation safety monitoring and management, in particular to a concrete dam deformation combined forecasting model construction method based on ARIMA and PSO-ELM.
Background
The dam is affected by a plurality of complex factors such as external load environment and the like in the service process, the local and overall safety performance of the dam is gradually faded over time, the dam deformation is an important index for evaluating the active performance of the dam, the dynamic evolution process of the dam body under the double coupling action of external environment load and internal dam material performance evolution is reflected, a real-time forecasting model is established by acquiring and sorting deformation monitoring data, deeply excavating the deformation evolution rule and processing chaotic signals of the monitoring signals, and the real-time forecasting model has important significance for evaluating the operation condition of the dam and guaranteeing the safety of the dam.
Based on prototype observations and seepage of the influence of the dam body, the dam foundation, the high slope surrounding environment and landslides on the reservoir dam, some mathematical, mechanical and artificial intelligence theories and methods are commonly used to analyze and evaluate the behavior of the dam. The method is considered as an effective way for ensuring the use safety of dam engineering, but the complex nonlinear relation between dam deformation and influence factors thereof is not excavated, the commonly used dam deformation safety monitoring data analysis models mainly comprise 3 types, namely a statistical model, a deterministic model and a mixed model, the statistical model is high in efficiency, simple and convenient to calculate and considers static water load, but cannot reflect the property state of the dam from the concept of mechanics, the deterministic model calculates the effect fields of the dam and the dam foundation under the load action by using a finite element method, although an expression of physical properties is established, complete data is needed to determine the material properties of the dam and the dam foundation and the setting of boundary slope conditions, so the two models have certain limitations, the mixed model makes up the defects of the two models, exerts the respective advantages of the two models, is constructed on the basis of the two models, the precision of the model is effectively improved, but the single mixed model cannot solve the influence of noise caused by environment, human and other uncertain factors on monitoring data, and the like utilize wavelet analysis tools to carry out wavelet decomposition on the monitoring data sequence, and utilize the time-frequency space reconstruction technology of each chaotic space to reconstruct each subsequence. And establishing a dam deformation behavior support vector machine prediction model according to the denoised and reconstructed deformation subsequence. Compared with other models, the method has obvious advantages in the aspects of solving the problems of small samples, nonlinearity and high dimension number. However, most of the models only consider the main influence factors of the models but not the influence of the chaotic effect in the residual sequence, so that the improvement of the fitting precision and the reliability of the prediction result is limited, and many scholars try to introduce an EMD non-stationary data analysis method into dam deformation analysis, such as Zhao and the like, decompose dam deformation data by using an empirical mode decomposition algorithm, obtain deformation components with different physical characteristic scales, and analyze the characteristics of each deformation component and the related influence factors thereof. And respectively establishing a prediction model of each deformation component based on the GA-SVM according to the characteristics of each deformation component, adding the prediction models of each component, and finally constructing a multi-scale deformation prediction model based on empirical mode decomposition and a support vector machine. However, in the signal decomposition process, the EMD method adopts cubic spline interpolation function fitting according to the extreme points of the signal to obtain the upper and lower envelope curves with boundary effect and other problems, which affects the precision of each component obtained by decomposition and is not beneficial to analyzing the signal change characteristics hidden in the signal. Therefore, how to perform noise reduction processing on the deformation residual sequence and perform phase space reconstruction on the chaotic components has important significance for accurate prediction of dam deformation performance.
In consideration of the uncertainty of factors existing in deformation monitoring residual data, the nonlinear problem is the key to improving the anti-noise capability of a model and the like, the invention provides a multiscale dam deformation prediction model based on ARIMA and PSO-ELM, an integrated empirical mode capable of inhibiting modal aliasing of sequence Intrinsic Mode Functions (IMF) is utilized, noise reduction processing is carried out on a residual sequence with chaotic characteristics, the residual sequence is decomposed into multiple high-frequency induction signals and a low-frequency trend signal, the parameter optimization characteristic of a particle swarm algorithm is utilized, the input matrix weight and the hidden layer deviation of an extreme learning machine are optimized, the high-frequency induction signals and the low-frequency trend signal of the ARIMA are processed and predicted by combining the data training advantages of the ARIMA model, and the residual prediction item and the regression prediction value of the regression model are superposed to establish a functional residual prediction combination model with good self-adaptive learning capability, cross fault-tolerant correction and the like.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, a Particle Swarm Optimization (PSO) global optimization ELM is utilized to select an optimal input weight matrix and hidden layer deviation, a PSO-ELM model is constructed to carry out optimization training on a nonlinear high-frequency induction signal, meanwhile, a low-frequency trend signal is subjected to fitting prediction by virtue of the linear training capability advantage of an autoregressive integrated sliding average model (ARIMA), and a combined prediction model based on mixed model concrete dam deformation residual signal optimization is established, so that the prediction precision of the prediction model is improved, noise interference in a monitoring sequence is overcome, the multi-scale characteristic of a dam monitoring sequence is reflected, and the prediction model can more clearly and comprehensively analyze and judge a dam monitoring data time sequence.
In order to achieve the purpose, the invention provides a concrete dam multi-scale deformation combined forecasting model based on ARIMA and PSO-ELM, which is realized by the following scheme:
a concrete dam deformation combined forecasting model building method based on ARIMA and PSO-ELM is characterized by comprising the following steps:
s1, selecting a proper dam section according to existing dam displacement data, establishing a finite element model through ANSYS, calculating a deformation value of a dam body measuring point under the load action by using an elastic mechanics finite element method to obtain a water pressure component, a temperature component and an aging component, and establishing a mixed model by using a statistical model method;
and S2, constructing a residual error corrected concrete dam deformation combined forecasting model.
In the step S2, the residual error corrected concrete dam deformation combined forecasting model is constructed by the following method:
s3, utilizing an EMD signal processing method EEMD, enabling the signal to have continuity on different scales through the uniform distribution characteristic of Gaussian white noise frequency, offsetting noise through multiple times of average processing, restraining or even completely eliminating noise influence, solving the easy-mixed-mode effect of EMD, and decomposing mixed signals formed by various different frequencies which are interwoven into a plurality of groups of high-frequency induction IMFs and 1 group of low-frequency trend signals;
s4, high-frequency induction signal processing of a PSO-ELM dam deformation residual sequence;
s5, low-frequency trend signal processing of ARIMA (p, d, q) dam deformation residual sequence: establishing an ARIMA (p, d, q) model forecasting model;
and S6, constructing a concrete dam deformation combined forecasting model based on PSO-ELM and ARIMA residual error correction.
And S4, processing the high-frequency induction signal of the PSO-ELM dam deformation residual sequence, wherein the processing process comprises the following steps:
with N training data sets (x) i ,y i ) Input data set x i ＝[x i1 ,x i2 ,...,x in ] T ∈R n Outputting the data set
y i ＝[y i1 ,y i2 ,...,y im ] T ∈R m And comprises L (N) 0 ≧ L) hidden nodes and activation function g (x) expressed as
Figure BDA0002625321480000031
I.e. H β = T (1)
The connection weight w can be randomly input i And implicit layer deviation b i Determining a hidden layer output matrix H, training an ELM neural network, converting the ELM neural network into a linear system H beta = T so as to determine an output weight beta, and then applying a particle swarm optimization algorithm to optimization processing of ELM key parameters.
The process of establishing the ARIMA (p, d, q) model forecasting model in the step S5 comprises the following steps:
s51, stationarity checking and stabilizing treatment
The stationarity of the time sequence is checked by using a scatter diagram, an autocorrelation function ACF, a partial autocorrelation function diagram PACF and a unit root ADF of the time sequence, and if the data sequence is non-stationary and has a certain increasing or decreasing trend, d-order difference processing needs to be carried out on the data;
s52, identifying and fixing the order of the model
After stationarity is checked and a difference order d is determined, an ARIMA (p, d, q) model form suitable for the sequence is determined according to an autocorrelation function ACF and a partial autocorrelation function PACF, namely the model form is judged to be an AR (p), MA (q) or ARMA (p, q) model; after the model form is determined, the order of the model form is determined by adopting AIC standard order determination;
s53, parameter estimation
The model parameters include phi 1 ,φ 2 ,…,φ p And theta 1 ,θ 2 ,…θ q And
Figure BDA0002625321480000032
estimating the model parameters by adopting a least square method;
s54, diagnosis and inspection
According to the residual error of the fitting time interval, analyzing the model precision to test the applicability of the model, carrying out statistical test on the model by an autocorrelation function method, and if the training value and the residual error sequence of the ARIMA model estimation value
Figure BDA0002625321480000041
The model established for the white noise sequence is feasible and can be used for forecasting the system signal of the residual sequence.
In the step S6, the construction of the concrete dam deformation combined forecasting model based on PSO-ELM and ARIMA residual error correction comprises the following contents:
the PSO-ELM model and the ARIMA model give full play to the fitting advantages of the PSO-ELM model and the ARIMA model under different learning conditions, and a combined model aiming at the stepwise regression residual error of the dam monitoring data is constructed; the fit accuracy of the model is evaluated using measures of prediction accuracy in the field of statistics, including Mean Absolute Error (MAE), mean Squared Error (MSE), mean Absolute Percent Error (MAPE), and coefficient of determination (R) 2 ) The calculation formula of each measurement index is as follows:
Figure BDA0002625321480000042
Figure BDA0002625321480000043
Figure BDA0002625321480000044
Figure BDA0002625321480000045
in the formula: n is the number of samples; delta i Is the measured value of dam displacement;
Figure BDA0002625321480000046
is a calculated value of dam displacement.
In step S52, the order is fixed by using AIC standard, and the order fixing method includes:
Figure BDA0002625321480000047
in the formula: l is a preset upper limit of the model order;
Figure BDA0002625321480000048
variance estimation for ARIMA model residual sequence; n is the sample volume; the (p, q) corresponding to the minimum AIC value is the determined order.
In step S54, the model is statistically tested by an autocorrelation function method, which is as follows:
suppose H 0 :{ε t Constructs a statistic for white noise sequences
Figure BDA0002625321480000049
In the formula: n is the sample volume;
Figure BDA00026253214800000410
for the sample autocorrelation coefficients, M is taken to be N/10,
for a given level of significance, α, the table is looked up
Figure BDA0002625321480000051
Then the hypothesis H0 is negated at the significance level α and reselection is more appropriateThe model of (2); otherwise, the model is considered to be well fitted, and the optimal prediction model obtained through the steps can be used for prediction of the residual sequence system signal.
The invention has the beneficial effects that:
the invention utilizes Particle Swarm Optimization (PSO) to optimize ELM to select the optimal input weight matrix and hidden layer deviation, constructs a PSO-ELM model to optimize and train nonlinear high-frequency induction signals, and simultaneously performs fitting prediction on low-frequency trend signals by virtue of the linear training capability advantage of an autoregressive integrated sliding average model (ARIMA), establishes a combined prediction model based on mixed model concrete dam deformation residual signal optimization, improves the prediction accuracy of the prediction model, overcomes noise interference in a monitoring sequence, can accurately reflect the multi-scale characteristics of a dam monitoring sequence, enables the prediction model to more clearly and comprehensively analyze and judge dam monitoring data time sequences, and provides new ideas and references for processing deformation monitoring data of dams and the like.
Drawings
FIG. 1 is a flow chart of combinatorial forecasting model construction;
FIG. 2 is a view showing a vertical arrangement of a dam;
FIG. 3 is a diagram of an ELM model structure;
FIG. 4 shows the measured displacement of the measuring point PL23, the change process of the upstream water level and the local air temperature;
FIG. 5 is a 23# dam section finite element model;
FIG. 6 shows the water pressure component at point PL23 and the corresponding upstream water level variation process;
FIG. 7 is a process line of horizontal displacement stepwise regression fit comparison and residual error sequences for measurement point PL 23;
FIG. 8 shows the EEMD decomposition results of the regression model residual sequence of the measurement point PL 23;
FIG. 9 is a variation process of the residual sequence and low frequency components of the regression model of the measuring point PL 23;
FIG. 10 shows the results of the deformation model fitting and prediction for measurement point PL 23;
FIG. 11 shows the result of the sequence of the deformation model residuals at the measurement point PL 23.
Detailed Description
For a better understanding of the present invention, reference is made to the following examples and accompanying drawings.
Example (b): see fig. 1-11.
Fig. 1 is a flow chart of the construction of a concrete dam multi-scale deformation combined prediction model based on ARIMA and PSO-ELM in the present invention, and the embodiment is as follows: the maximum dam height of a certain concrete gravity dam is 105.0m, the dam top elevation is 115.0m, the normal water storage level and the check flood level elevation are 108.0m and 111.4m respectively, and the regulated storage capacity and the total storage capacity are 102.7 hundred million m3 and 220 hundred million m3 respectively. The dam is provided with more comprehensive monitoring items including deformation, seepage, temperature, stress strain and the like, the items for monitoring dam displacement mainly comprise a Plumb Line (PL), an inverted plumb line (IP), a tension line, a sight line and the like, wherein the displacement of the water flow direction and the water flow direction is monitored by the plumb line and the inverted plumb line, and the dam plumb line arrangement scheme is shown in figure 2.
As the non-overflow dam section is less disturbed by water flow such as flood discharge and the like, and the monitoring data is regular, long-term monitoring data (shown in table 1) of the horizontal displacement of the measuring point PL23 (71.4 m) of the dam top in the No. 23 non-overflow dam section from 1 month and 1 day in 2013 to 10 months and 1 day in 2019 are selected for analysis, and input quantities such as a water pressure component, a temperature component and an aging component are subjected to zero return processing on the first monitoring day (namely 1 month and 1 day in 2009). The process line of the upstream water level, the process line of the rainfall amount in the dam site area and the process line of the temperature measurement value in the monitoring period are shown in fig. 4.
TABLE 1 monitoring data of horizontal displacement of measuring point PL23 (71.4 m) on dam crest of non-overflow dam section
Figure BDA0002625321480000061
And (3) establishing a mixed model for the measuring points PL23 respectively:
and establishing finite element analysis by using ANSYS finite element calculation software, setting the simulated foundation range to respectively extend about 2 times upstream at the dam heel, about 2 times downstream at the dam site, and 1.5 times the dam height at the bottom of the dam foundation, wherein the number of model units built by grid division is 156369, the number of nodes is 176135, and the model finite element grid is shown in figure 5. And (3) calculating the deformation of the dam body measuring point under the hydraulic load in the 1 st 1 th 2013 by using an elastic mechanics finite element method, and taking the deformation as the initial deformation. And then, selecting the actually measured water levels of the upstream and the downstream as hydrostatic pressure loads, and calculating the deformation value of the dam body measuring point under the action of the hydrostatic pressure loads by using an elastic mechanics finite element method. The actual measurement value change process line and the water pressure component change process line of the measuring point of the Xinanjiang dam arch 23# dam section PL23-1 under the corresponding water level are shown in FIG. 6.
From the calculation result of the hydraulic pressure displacement component, regression analysis is performed on the formula (7), and the undetermined coefficient a in the formula is obtained i . The hydraulic component of the hybrid model is therefore:
δ H ＝-0.00469-0.0125H 1 +0.0018H 2 ⑧
the temperature component is only considered by boundary temperature change, namely air temperature and water temperature, because the concrete hydration heat of the dam is dissipated and the internal temperature of the dam body reaches a quasi-stable temperature field after the dam operates for years. Because of lack of water temperature monitoring data and simple harmonic change of two temperatures, the temperature component of the dam is selected from multi-period harmonic as a factor, and meanwhile, for a dam which is in service for a long time, the time-effect component of the dam can be gradually transited from nonlinear change to linear change and can be represented by a linear function. The adjustment coefficient X and the coefficients of the temperature displacement component and the aging displacement component are calculated by adopting a regression analysis method, the coefficients are shown in table 2, and the process line of the horizontal displacement fitting of the measuring point and the process line of the residual sequence are shown in fig. 7.
TABLE 2 adjustment coefficient X and coefficient calculation results for temperature displacement component and aging displacement component
Figure BDA0002625321480000071
It can be known from the fitting result of the conventional stepwise regression model built in fig. 7 that accurate prediction cannot be performed, information still remains in the residual error, more information can be obtained through deep analysis, the residual error sequence in fig. 7 is subjected to multi-scale EEMD decomposition, and is decomposed into 4 sets of high frequency Induction (IMF) and 1 set of low frequency trend signals, and the decomposition result is shown in fig. 8.
As shown in fig. 9, the frequencies of the 5 IMF components are gradually decreased, which shows the fluctuation characteristics under the influence of different factors, and the characteristic of periodic fluctuation is obvious, and the period of the fluctuation is unstable and has the characteristic of non-uniform change. The preliminary analysis is the nonlinearity of the combined action of internal and external factors such as dam water level, temperature and dam body structure change. The residual belongs to low-frequency components and represents the time-varying trend in the original deformation sequence.
As can be seen from FIG. 9, the EEMD decomposed low-frequency sequence has the same general trend with the regression model residual sequence, but is smoother and more stable than the regression model residual sequence, and the ARIMA model is used for modeling and forecasting the low-frequency signal of the residual sequence, and the residual forecast value is recorded as
Figure BDA0002625321480000072
The high-frequency signal sequence of the method shows obvious discreteness, is unstable data and is suitable for being obtained by adopting PSO-ELM modeling prediction
Figure BDA0002625321480000073
Residual prediction term [ delta ] 0 I.e. that
Figure BDA0002625321480000074
And superposing the prediction values to a regression model prediction value to form a deformation combined prediction model considering residual error correction. In order to check the effectiveness of the combined model, a PSO-ELM model of the measuring point is established at the same time, and the fitting and forecasting results of the regression model and the combined forecasting model established by the invention and the residual sequence thereof are respectively drawn in a graph of FIG. 10 and a graph of FIG. 11.
In order to deeply compare the prediction accuracy of the three models, the present embodiment quantitatively calculates the statistical indexes of the three measuring points, such as Mean Absolute Error (MAE), mean Square Error (MSE), mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R2), as shown in table 3.
TABLE 3 comparison of prediction accuracy between the combined model and the conventional model
Figure BDA0002625321480000081
As can be seen from Table 3, compared with the conventional model, the MAE, MSE and MAPE are closer to 0, namely closer to the perfect model, which shows that the forecasting precision of the combined forecasting model constructed by the method is better than that of the conventional monitoring model, thereby verifying the rationality and practicability of the method.
Although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention.

Claims (3)

1. A concrete dam deformation combined forecasting model building method based on ARIMA and PSO-ELM is characterized by comprising the following steps:
s1, selecting a proper dam section according to existing dam displacement data, establishing a finite element model through ANSYS, calculating a deformation value of a dam body measuring point under the load action by using an elastic mechanics finite element method to obtain a water pressure component, a temperature component and an aging component, and establishing a mixed model by using a statistical model method;
s2, constructing a residual error corrected concrete dam deformation combined forecasting model;
s3, utilizing an EMD signal processing method EEMD, enabling the signal to have continuity on different scales through the uniform distribution characteristic of Gaussian white noise frequency, offsetting noise through multiple times of average processing, restraining or even completely eliminating noise influence, solving the easy-mixed-mode effect of EMD, and decomposing mixed signals formed by various different frequencies which are interwoven into a plurality of groups of high-frequency induction IMFs and 1 group of low-frequency trend signals;
s4, high-frequency induction signal processing of a PSO-ELM dam deformation residual sequence;
is provided with N training numbersData set (xi, yi), input data set x i ＝[x i1 ,x i2 ,...,x in ] T ∈R n Output data set y i ＝[y i1 ,y i2 ,...,y im ] T ∈R m And comprises L (N) 0 ≧ L) hidden nodes and activation function g (x) expressed as
Figure FDA0003838423830000011
The connection weight w can be randomly input i And implicit layer deviation b i Determining a hidden layer output matrix H, training an ELM neural network, converting the ELM neural network into a linear system H beta = T so as to determine an output weight beta, and then applying a particle swarm optimization algorithm to optimization processing of ELM key parameters;
s5, low-frequency trend signal processing of ARIMA (p, d, q) dam deformation residual sequence: establishing an ARIMA (p, d, q) model forecasting model;
s51, stationarity checking and stabilizing treatment
Using a scatter diagram, an autocorrelation function ACF, a partial autocorrelation function diagram PACF and a unit root ADF of a time sequence to check the stationarity of the time sequence, and if the data sequence is non-stationary and has a certain increasing or decreasing trend, performing d-order difference processing on the data;
s52, identifying and fixing the order of the model
After stationarity is checked and the difference order d is determined, an ARIMA (p, d, q) model form suitable for the sequence is determined according to the analysis of an autocorrelation function ACF and a partial autocorrelation function PACF, namely the model form is judged to be an AR (p), MA (q) or ARMA (p, q) model; after the model form is determined, the order of the model form is determined by adopting AIC standard order determination;
s53, parameter estimation
The model parameters include phi 1 ,φ 2 ,…,φ p And theta 1 ,θ 2 ,…θ q And
Figure FDA0003838423830000021
estimating the model parameters by adopting a least square method;
s54, diagnosis and inspection
Analyzing the accuracy of the model according to the residual error of the fitting time period to check the applicability of the model, carrying out statistical check on the model by an autocorrelation function method, and if the training value and the residual error sequence of the estimated value of the ARIMA model are the same
Figure FDA0003838423830000022
The model established for the white noise sequence is feasible and can be used for forecasting the system signal of the residual error sequence
S6, constructing a concrete dam deformation combined forecasting model based on PSO-ELM and ARIMA residual error correction;
the PSO-ELM model and the ARIMA model give full play to the fitting advantages of the PSO-ELM model and the ARIMA model under different learning conditions, and a combined model aiming at the stepwise regression residual error of the dam monitoring data is constructed; the fitting accuracy of the model is evaluated by using the measurement indexes of prediction accuracy in the field of statistics, the measurement indexes comprise Mean Absolute Error (MAE), mean Square Error (MSE), mean Absolute Percentage Error (MAPE) and a decision coefficient (R2), and the calculation formula of each measurement index is as follows:
Figure FDA0003838423830000023
Figure FDA0003838423830000024
Figure FDA0003838423830000025
Figure FDA0003838423830000026
in the formula: n is the number of samples; delta. For the preparation of a coating i Is largeThe measured value of dam displacement;
Figure FDA0003838423830000027
is a calculated value of dam displacement.
2. The method for constructing the combined forecast model of concrete dam deformation based on ARIMA and PSO-ELM as claimed in claim 1, wherein in step S52, said AIC standard scaling is used to scale the order, and the scaling method is:
Figure FDA0003838423830000028
in the formula: l is a preset model order upper limit;
Figure FDA0003838423830000029
variance estimation for ARIMA model residual sequence; n is the sample capacity; the (p, q) corresponding to the minimum AIC value is the determined order.
3. The method for constructing a combined forecasting model for deformation of concrete dam based on ARIMA and PSO-ELM as claimed in claim 1, wherein the statistical test of the model by the autocorrelation function method in step S54 is as follows:
hypothesis H 0 :{ε t And 5, constructing a statistic as a white noise sequence:
Figure FDA0003838423830000031
in the formula: n is the sample volume;
Figure FDA0003838423830000032
for the sample autocorrelation coefficients, M is taken as N/10,
for a given level of significance, α, the table is looked up
Figure FDA0003838423830000033
Then H0 is negatively assumed on the significance level alpha, and a more appropriate model is reselected; otherwise, the model is considered to be well fitted, and the optimal prediction model obtained through the steps can be used for prediction of the residual sequence system signal.
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