CN112100711A - 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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CN112100711A
CN112100711A CN202010795157.3A CN202010795157A CN112100711A CN 112100711 A CN112100711 A CN 112100711A CN 202010795157 A CN202010795157 A CN 202010795157A CN 112100711 A CN112100711 A CN 112100711A
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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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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 an 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 service performance of the dam, the dynamic evolution process of the dam body under the double coupling action of external environmental load and internal dam material performance evolution is reflected, a real-time forecasting model is established by collecting and arranging 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 relationship between dam deformation and the 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 the hydrostatic load, but cannot reflect the behavior of the dam from the concept angle 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 thereof, is constructed by taking the two models as the basis, and effectively improves the precision of the models, however, a single hybrid model cannot solve the influence of noise caused by environment, human factors and other uncertain factors on the monitored data, and the Poplar and the Beibei utilize a wavelet analysis tool to perform time-frequency decomposition on the monitored data sequence, and reconstruct the phase space of each subsequence by means of a chaotic phase space reconstruction technology. 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 consider 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 are limited, and many scholars try to introduce an EMD non-stationary data analysis method into dam deformation analysis, such as Zhanghao and the like, decompose dam deformation data by using an empirical mode decomposition algorithm to 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 of 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 with mode aliasing capable of inhibiting sequence Intrinsic Mode Functions (IMF) is utilized, the noise reduction processing is carried out on a residual sequence with chaotic characteristics, the residual sequence is decomposed into a plurality of 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 are processed and predicted by combining the data training advantages of the ARIMA model, and the residual prediction item and a regression prediction value are superposed to establish a residual prediction combination model with the functions of better self-adaptive learning capability, cross fault-tolerant correction and the like, compared with the conventional model, the combined forecasting model provided by the invention has the advantages that the forecasting precision is obviously improved, and a convenient and efficient new method is provided for forecasting the deformation of other hydraulic buildings.
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 error signal optimization is established, so that the prediction precision of the prediction model is improved, the 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 step S2, the method for constructing the residual error corrected concrete dam deformation combined prediction model includes:
s3, utilizing an EMD signal processing method EEMD, enabling signals to have continuity on different scales through the uniform distribution characteristic of Gaussian white noise frequency, offsetting noise through multiple times of average processing, inhibiting 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, processing a high-frequency induction signal 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 step S4, the high-frequency induction signal processing of the PSO-ELM dam deformation residual sequence comprises the following steps:
with N training data sets (x)i,yi) Input data set xi＝[xi1,xi2,...,xin]T∈RnOutputting the data set
yi＝[yi1,yi2,...,yim]T∈RmAnd comprises L (N)0≧ L) hidden nodes and activation function g (x) whose expression is
Figure BDA0002625321480000031
I.e. H β ═ T — (r)
The connection weight w can be randomly inputiAnd implicit layer deviation biDetermining hidden layer output matrix H, training ELM neural network, and converting itAnd determining an output weight beta for a linear system H beta-T, and then applying a particle swarm optimization algorithm to the optimization process of the ELM key parameters.
The process of establishing the ARIMA (p, d, q) model forecasting model in the step S5 is as follows:
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 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 judgment model form is 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 phi1,φ2,…,φpAnd theta1,θ2,…θqAnd
Figure BDA0002625321480000032
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 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 step S6, constructing a combined prediction model of concrete dam deformation based on PSO-ELM and ARIMA residual correction includes the following steps:
the PSO-ELM model and the ARIMA model are used for fully exerting 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 statistical domain, 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;iis 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 is:
Figure BDA0002625321480000047
in the formula: l is a preset model order upper limit;
Figure BDA0002625321480000048
estimating the variance of the residual sequence of the ARIMA model; n is the sample volume; the minimum AIC value corresponds to (p, q) i.eIs of a given order.
In step S54, the model is statistically tested by the autocorrelation function method, which is as follows:
suppose H0:{tConstructs statistics for white noise sequence
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 H0 assumption is negated at the significance level α and the 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.
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 architecture;
FIG. 4 shows the measured displacement of measurement point PL23, the variation process of upstream water level and 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 stepwise regression fit comparison and residual sequence for horizontal displacement of measurement point PL 23;
FIG. 8 shows the EEMD decomposition results of the regression model residual sequence at the measurement point PL 23;
FIG. 9 shows the variation process of the residual sequence and low frequency component of the regression model at the measurement point PL 23;
FIG. 10 shows the results of the deformation model fitting and prediction at PL 23;
FIG. 11 shows the sequence of the deformation model residuals at 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(71.4m) of No. 23 non-overflow dam section in 2013, 1 month and 1 day to 2019, 10 month and 1 day are selected for analysis, and input quantities such as a water pressure component, a temperature component and an aging component are all subjected to zeroing treatment 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 at PL23(71.4m) measuring point of dam crest of non-overflow dam section
Figure BDA0002625321480000061
And (3) respectively establishing a mixed model for the measuring points PL 23:
and establishing finite element analysis by using ANSYS finite element calculation software, setting the simulated foundation range to respectively extend about 2 times upstream of the dam heel, about 2 times downstream of the dam address, and 1.5 times dam height at the bottom of the dam foundation, dividing the number of the built model units by grids into 156369, setting the number of nodes to be 176135, and showing a model finite element grid in a 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 at the upper and lower streams 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 measured 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.
Carrying out regression analysis on the formula (c) according to the calculation result of the water pressure displacement component, and solving the undetermined coefficient a in the formulai. The hydraulic component of the hybrid model is therefore:
H＝-0.00469-0.0125H1+0.0018H2 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 trend of the original deformation sequence changing along with time.
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
Subjecting residual forecast item to final check0I.e. that
Figure BDA0002625321480000074
And (4) superposing the prediction values into 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 10 and a graph 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 prediction precision of the combined prediction 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 above embodiments, it should be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (7)

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;
and S2, constructing a residual error corrected concrete dam deformation combined forecasting model.
2. The method for constructing a combined forecasting model of concrete dam deformation based on ARIMA and PSO-ELM as claimed in claim 1, wherein the step S2 of constructing the residual error modified combined forecasting model of concrete dam deformation comprises the following steps:
s3, utilizing an EMD signal processing method EEMD, enabling signals to have continuity on different scales through the uniform distribution characteristic of Gaussian white noise frequency, offsetting noise through multiple times of average processing, inhibiting 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, processing a high-frequency induction signal 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.
3. The method for constructing a combined forecasting model of concrete dam deformation based on ARIMA and PSO-ELM as claimed in claim 2, wherein the step S4 is a high frequency induction signal processing of the PSO-ELM dam deformation residual sequence, the processing procedure is as follows:
with N training data sets (x)i,yi) Input data set xi＝[xi1,xi2,...,xin]T∈RnOutput data set yi＝[yi1,yi2,...,yim]T∈RmAnd comprises L (N)0≧ L) hidden nodes and activation function g (x) whose expression is
Figure FDA0002625321470000011
The connection weight w can be randomly inputiAnd implicit layer deviation biDetermining 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 the optimization processing of the ELM key parameters.
4. The method for constructing a combined forecasting model of deformation of concrete dam based on ARIMA and PSO-ELM as claimed in claim 2, wherein the process of establishing ARIMA (p, d, q) model forecasting model in step S5 is:
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 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 judgment model form is 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 phi1,φ2,…,φpAnd theta1,θ2,…θqAnd
Figure FDA0002625321470000021
by using the mostEstimating model parameters by using the small two multiplication;
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 FDA0002625321470000022
The model established for the white noise sequence is feasible and can be used for forecasting the system signal of the residual sequence.
5. The method for constructing a combined forecasting model of deformation of concrete dam based on ARIMA and PSO-ELM as claimed in claim 2, wherein said constructing a combined forecasting model of deformation of concrete dam based on PSO-ELM and ARIMA residual correction in step S6 includes the following steps:
the PSO-ELM model and the ARIMA model are used for fully exerting 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 statistical domain, 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 FDA0002625321470000023
Figure FDA0002625321470000024
Figure FDA0002625321470000025
Figure FDA0002625321470000026
in the formula: n is the number of samples;iis the measured value of dam displacement;
Figure FDA0002625321470000031
is a calculated value of dam displacement.
6. The method for constructing a combined forecasting model of concrete dam deformation based on ARIMA and PSO-ELM as claimed in claim 4, wherein in step S52, the AIC standard is adopted to determine the order, and the method comprises:
Figure FDA0002625321470000032
in the formula: l is a preset model order upper limit;
Figure FDA0002625321470000033
estimating the variance of the residual sequence of the ARIMA model; n is the sample volume; the (p, q) corresponding to the minimum AIC value is the determined order.
7. The method for constructing a combined forecasting model for deformation of concrete dam based on ARIMA and PSO-ELM as claimed in claim 4, wherein the statistical test of the model by the autocorrelation function method in step S54 is performed by:
suppose H0:{tAnd 5, constructing a statistic as a white noise sequence:
Figure FDA0002625321470000034
in the formula: n is the sample volume;
Figure FDA0002625321470000035
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 FDA0002625321470000036
Then the H0 assumption is negated at the significance level α and the 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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