A method for dynamic interval prediction and anomaly identification of a diversion channel slope displacement based on DeepAR

Abstract

The application relates to the technical field of water conservancy engineering safety monitoring, in particular to a diversion channel side slope displacement dynamic interval prediction and abnormality identification method based on DeepAR, which comprises the following steps: input variable selection; correlation calculation; DeepAR model construction; model training and prediction; prediction effect evaluation; displacement prediction abnormality identification; the method has the beneficial effects that the displacement probability distribution at different time points is obtained, the mean value and the variance of the displacement prediction are dynamically calculated, the prediction interval changing with time under different confidence degrees is calculated through the probability distribution, the interval prediction model with the bandwidth changing with time is constructed, the prediction precision is improved, and the side slope displacement state is more comprehensively obtained.

Description

Technical Field

[0001] The present invention relates to the field of water conservancy project safety monitoring, and specifically to a method for dynamic interval prediction and anomaly identification of water diversion channel slope displacement based on DeepAR. Background Art

[0002] As a crucial component of water diversion projects, the stability of diversion channel slopes is directly linked to their safety and normal operation. Therefore, it is crucial to strengthen the monitoring and management of diversion channel slope safety to prevent slope accidents. Displacement is a key indicator of slope instability, and predicting future displacement trends is crucial for ensuring diversion channel slope safety.

[0003] Models commonly used in slope displacement prediction, such as back propagation neural network

[0004] Backpropagation Neural Network (BP), Support Vector Machine (SVM), Recurrent Neural Network (RNN), etc. typically output a single displacement prediction value, or a point prediction result. Due to the limitations of understanding the diversion channel slope system, noise interference in monitoring data, and other uncertain factors, uncertainty in displacement prediction is inevitable.

[0005] Therefore, a dynamic interval prediction and anomaly identification method for diversion channel slope displacement based on DeepAR is needed to solve the above technical problems. Summary of the Invention

[0006] The purpose of the present invention is to provide a dynamic interval prediction and anomaly identification method for water diversion channel slope displacement based on DeepAR, obtain the displacement probability distribution at different time points, dynamically calculate the mean and variance of the displacement prediction, calculate the prediction interval that changes with time under different confidence levels through the probability distribution, construct an interval prediction model whose bandwidth changes with time, improve the prediction accuracy, and obtain the slope displacement state more comprehensively to solve the problems raised in the above background technology.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for dynamic interval prediction and anomaly identification of diversion channel slope displacement based on DeepAR, the method comprising the following steps:

[0008] Selection of input variables;

[0009] Correlation calculation;

[0010] Construction of DeepAR model;

[0011] Model training and prediction;

[0012] Prediction effect evaluation;

[0013] Anomaly identification for displacement prediction.

[0014] Preferably, the selection of the input variables specifically includes: the factors affecting the displacement of the water diversion channel slope mainly include water level, time and rainfall.

[0015] Preferably, the correlation calculation specifically includes:

[0016] Displacement has a certain correlation with water level and its higher power. 2 , H 3 As the water level influencing factors, the Pearson correlation coefficient method is used to calculate the correlation between the previous rainfall and time effect and displacement, and the rainfall and time effect influencing factors with strong correlation are selected, as follows:

[0017] Suppose two variable sequences are X=(x1,x2…x n ), Y=(y1,y2…y n ), the Pearson correlation coefficient is calculated using the following formula:

[0018]

[0019] in are the means of the sequences of the corresponding variables, x t ,y t are the monitoring values ​​of different variables at different time points, and n is the sample size.

[0020] Preferably, the construction of the DeepAR model specifically includes:

[0021] The hidden layer output h at the current moment t As shown in the following formula:

[0022] h t =h(h t-1 , z t-1 , x t )=f(W hz z t-1 +W hx x t +W hh h t-1 +b) (2)

[0023] Where: z t represents the displacement value at time t, X t Represents the influencing factor at time t. At time t, the input of the network includes the influencing factor x t , the value z at the previous moment t-1 , and the hidden layer output h at the previous momentt-1 , h t is the output of the hidden layer at time t, W hz is the weight corresponding to the input layer displacement data to the hidden layer, W hx is the weight corresponding to the input layer influence factor to the hidden layer, W hh is the weight of the hidden layer output at the previous time point to the hidden layer output at the next time point, b is the bias term of the input layer to the hidden layer, and f(x) is the hyperbolic tangent activation function, which is specifically expressed as follows:

[0024]

[0025] After obtaining the hidden layer output h t , the mean and standard deviation of the Gaussian distribution are calculated:

[0026] μ t = W μh h t +b μ (4)

[0027] σ t = ln [1 + exp (W σh h t +b σ )] (5)

[0028] wherein W μh , b μ are the weight and bias term corresponding to the calculation of the output layer μ t , W σh , b σ are the weight and bias term corresponding to the calculation of the output layer σ t , and the Gaussian likelihood function is obtained by calculating the mean and variance at each time point as follows:

[0029]

[0030] Preferably, the training and prediction of the model specifically include:

[0031] In the training phase, the input of the network includes the influence factor and the displacement value at the previous time, as well as the hidden layer output at the previous time, so as to calculate the parameter mean μ and standard deviation σ of the likelihood function. It is considered that the fitting distribution output by the network is closer to the real situation, that is, the fitting distribution has a great probability of taking value at z t , and the maximum value is obtained at z t , and the objective function for training is constructed as follows:

[0032]

[0033] In the formula: t0 is the time of starting prediction, and the negative form of the target function is taken in the DeepAR model, that is The loss function is used for training. In actual training, when the loss function tends to be stable, it is considered that the network training is completed, that is, the target function reaches the maximum;

[0034] In the prediction stage, the goal of DeepAR is to obtain the probability distribution of the current time according to the displacement value and the value of the influence factor at the historical time. The joint distribution is composed of the product of Gaussian likelihood functions at different time points;

[0035]

[0036] In the formula: T is the time when the prediction ends, represents the displacement value in the prediction time period, represents the displacement value in the training time period, and x1: T is the influence factor; Q(z t |z 1：t-1 , x 1：T ) is a conditional probability distribution, that is, the displacement probability distribution under the condition of z 1：t-1 and x 1：T . is the joint distribution of the model, which is the product of the conditional probability Q(z t |z 1：t-1 , x 1：T ).

[0037] Preferably, the prediction effect evaluation specifically includes:

[0038] The point prediction evaluation indexes root mean square error E RMSE , mean absolute percentage error E MAPE , and interval evaluation indexes interval coverage probability P PICP , and normalized average width of prediction interval P PINAW are used as the evaluation indexes of the model performance, and the corresponding calculation formulas are as follows:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] In the formula: N is the number of prediction samples, z t is the measured displacement value, is the output displacement value of the model, is the minimum and maximum value of the prediction interval at time t, z max , z min is the maximum and minimum displacement within the prediction period; P PICP The larger it is, the more true values ​​fall within the prediction interval; PICP It is necessary to achieve the corresponding confidence level, namely the nominal confidence level, as much as possible, otherwise the obtained prediction interval is considered to be insufficiently reliable; P PINAW The smaller the value, the narrower the prediction interval. PICP When the same P PINAW The smaller it is, the better the model's prediction effect.

[0045] Preferably, the abnormality identification of the displacement prediction specifically includes:

[0046] The interval prediction result with a confidence level of 90% is selected as the standard for judging abnormalities. When the actual displacement value falls within the prediction interval corresponding to this confidence level, it is determined that the actual displacement value is in a normal state under this confidence level; on the contrary, if the actual displacement value exceeds the range of the prediction interval, it is determined that the actual displacement value under this confidence level is abnormal, and the alarm mechanism is triggered accordingly.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The DeepAR-based dynamic interval prediction and anomaly identification method for diversion channel slope displacement proposed in this paper obtains the displacement probability distribution at different time points, dynamically calculates the mean and variance of the displacement prediction, calculates the prediction interval that changes with time at different confidence levels through the probability distribution, and constructs an interval prediction model whose bandwidth changes with time, thereby improving the prediction accuracy and obtaining a more comprehensive picture of the slope displacement status. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is the displacement and rainfall data graph of the present invention;

[0050] Figure 2 This is the loss function curve of DeepAR training period of the present invention

[0051] Figure 3 This is the displacement prediction effect diagram of the DeepAR model in 2015 of the present invention. DETAILED DESCRIPTION

[0052] In order to make the purposes, technical solutions of the present application clear, complete and the advantages more clear and apparent, the embodiments of the present application are further described in detail below with reference to the drawings. It should be understood that the specific embodiments described herein are part of the embodiments of the present application, rather than all the embodiments, and are only used to explain the embodiments of the present application, and are not used to limit the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0053] Embodiment one, please refer to Figures 1-2 The present application provides a technical solution: a DeepAR-based diversion channel slope displacement dynamic interval prediction and anomaly identification method, the method comprising the following steps:

[0054] Selection of input variables; the influencing factors of the diversion channel slope displacement mainly include water level, time effect and rainfall.

[0055] Correlation calculation; the displacement has certain correlation with the water level and the high order of the water level, and H, H 2 , H 3 are selected as the water level influencing factors, the correlation between the early rainfall and the time effect and the displacement is calculated by using the Pearson correlation coefficient method, the rainfall and the time effect influencing factors with strong correlation are selected, and the specific process is as follows:

[0056] Suppose two variable sequences are X=(x1,x2…x n ), Y=(y1,y2…y n ), and the Pearson correlation coefficient is calculated by using the following formula:

[0057]

[0058] Among them are the mean values of the corresponding variable sequences, x t , y t are the monitoring values of different variables at different time points, and n is the sample number.

[0059] Construction of DeepAR model; the current time hidden layer output h t is shown in the following formula:

[0060] h t =h(h t-1 , z t-1 , x t )=f(W hz z t-1 +W hx x t +W hh h t-1 +b) (2)

[0061] In the formula: zt denotes the displacement value at time t, X t denotes the influence factor at time t, at time t, the input of the network includes the influence factor x t , the value of z at the previous time t-1 , and the hidden layer output h at the previous time t-1 , h t is the output of the hidden layer at time t, W hz is the weight corresponding to the input layer displacement data to the hidden layer, W hx is the weight corresponding to the input layer influence factor to the hidden layer, W hh is the weight of the hidden layer output at the previous time point to the hidden layer output at the next time point, b is the bias term of the input layer to the hidden layer, and f(x) is the hyperbolic tangent activation function, which is specifically expressed as follows:

[0062]

[0063] After obtaining the hidden layer output h t , the mean and standard deviation of the Gaussian distribution are calculated:

[0064] μ t = W μh h t +b μ (4)

[0065] σ t = ln[1+exp(W σh h t +b σ )] (5)

[0066] In the formula: W μh , b μ are the weight and bias term corresponding to the calculation of the output layer μ t , W σh , b σ are the weight and bias term corresponding to the calculation of the output layer σ t , the Gaussian likelihood function is obtained by calculating the mean and variance at each time point as follows:

[0067]

[0068] Model training and prediction; in the training phase, the input of the network includes the influence factor and the displacement value at the previous time, and the hidden layer output at the previous time, so as to calculate the parameters of the likelihood function mean μ and standard deviation σ, the closer the fitting distribution output by the network distribution is to the real situation, that is, the fitting distribution has a great probability of taking value at z t , and it takes the maximum value at z t , and the objective function of the training is constructed as follows:

[0069]

[0070] Where t0 is the time when prediction starts, and in the DeepAR model, the negative form of the objective function is Training is done for the loss function. In actual training, when the loss function tends to be stable, the network training is considered complete, that is, the objective function reaches its maximum;

[0071] In the prediction phase, DeepAR aims to find the probability distribution of the current moment based on the displacement values ​​and impact factor values ​​at historical moments. The joint distribution is composed of the product of Gaussian likelihood functions at different time points.

[0072]

[0073] Where: T is the prediction end time, represents the displacement value of the prediction time period, Indicates the displacement value of the training period, x 1：T is the impact factor; Q(z t |z 1：t-1 , x 1：T ) is the conditional probability distribution, that is, given z 1：t-1 and x 1：T Probability distribution of displacement under conditions; is the joint distribution of the model, which is the conditional probability Q(z t |z 1：t-1 , x 1：T ) is the product of .

[0074] Evaluation of prediction effect; use the point prediction evaluation index root mean square error E RMSE , mean absolute percentage error E MAPE , and interval evaluation index interval coverage probability P PICP , the normalized mean width of the prediction interval P PINAW As an evaluation indicator of model performance, the corresponding calculation formula is as follows:

[0075]

[0076]

[0077] Where: N is the number of prediction samples, z t is the measured displacement value, Output displacement values ​​for the model, is the minimum and maximum value of the prediction interval at time t, z max , z min is the maximum and minimum displacement within the prediction period; P PICP The larger it is, the more true values ​​fall within the prediction interval;PICP The corresponding confidence, i.e. nominal confidence, needs to be reached as much as possible, otherwise the reliability of the obtained prediction interval is considered insufficient; P PINAW The smaller, the narrower the range of the prediction interval, and when P PICP The same P PINAW The smaller, the better the prediction effect of the model.

[0078] Abnormal identification of displacement prediction, the interval prediction result of 90% confidence is selected as the standard for judging abnormality, when the actual displacement value falls within the prediction interval corresponding to this confidence, it is determined that the actual displacement value is in a normal state under this confidence; on the contrary, if the actual displacement value exceeds the range of the prediction interval, it is judged that the actual displacement value has appeared abnormal under this confidence, and the alarm mechanism is triggered accordingly.

[0079] Example two, referring to the attached Figure 3 Fig. 2, on the basis of example one, taking the middle line of a certain channel slope as the research object, the channel is located in the north section of Zhanghe River to the south section of Goyunhe River, the design water depth is 6m, the cross section of the channel is trapezoidal, the design slope coefficient is 2.35, and 8 monitoring sections are arranged on the channel slope, taking the displacement data of monitoring point QDBM503 of high fill section 103+658 as an example for analysis. Considering the uncertainty of displacement, a displacement interval prediction model based on DeepAR is constructed, the mean and variance of displacement prediction value at different time points are calculated to obtain the probability distribution of displacement with time difference, the range of possible changes of future values is predicted through the confidence interval under a certain confidence, the dynamic change of uncertainty is analyzed, and the dynamic interval prediction of displacement is realized, as follows:

[0080] The rainfall influence factors Q 1 , Q 3 , Q 5 , Q 7 , Q 9 , Q 11 , Q 13 , and the time effect factor T, T 0.5 , T -0.5 , lnT, 1-e -T / 100 , T / (T+1) are selected respectively, and the correlation between different influence factors and displacement is calculated by formula (1), wherein Q 1 represents the rainfall of the previous day, Q 3 represents the rainfall of the previous three days, and the others are similar. T is the number of days from the observation date to the initial measurement date. The correlation between different influence factors and displacement is calculated by using 29 groups of displacement, rainfall and time effect sequences from August 2014 to May 2015. The displacement and rainfall data in this period are shown in Figure 1 Table 1, and the correlation calculation results are shown in Table 1.

[0081] Table 1 Pearson correlation coefficient calculation results of rainfall, time and displacement

[0082]

[0083] The absolute value of Pearson correlation coefficient is closer to 1, the higher the correlation between two variables. From Table 1, Q 5 , Q 11 , Q 13 , T, T 0.5 , lnT have higher correlation with displacement, so they are used as the influence factors of rainfall and time in the model.

[0084] DeepAR model with 3 layers of recurrent neural network hidden layer is constructed, learning rate is 0.001, number of neurons is 15, and iteration number is 100. Displacement data from August 2014 to May 2015 is used as training set, and model loss function is calculated, its change process is shown in Figure 2 .

[0085] It can be seen that the model tends to be stable when the iteration number is 20, at this time the model training is completed, and the trained model is used to predict the displacement of the next three months, the prediction result is shown in Figure 3 .

[0086] It can be seen from Figure 3 that the model prediction result and the actual displacement trend are consistent. P PICP under 50% confidence is 71%, the maximum bandwidth is 0.35mm, and the minimum bandwidth is 0.24mm. P PICP under 90% confidence is 100%, the maximum bandwidth is 0.96mm, and the minimum bandwidth is 0.67mm. P PICP are all greater than the corresponding nominal confidence, the reliability of interval prediction is high, and the interval width under different confidence levels changes dynamically with time.

[0087] DeepAR interval prediction model is used to predict the displacement interval value from May 14, 2015 to August 27, 2015, and further abnormal identification of slope displacement is carried out. Taking the interval prediction result under 90% confidence as an example, the slope displacement is analyzed. The displacement interval prediction result under 90% confidence is shown in Table 2.

[0088] Table 2 Displacement interval prediction result under 90% confidence

[0089]

[0090] Take the minimum prediction bandwidth in the table as an example to identify the abnormality of the slope displacement. The displacement prediction interval bandwidth of May 23, 2015 in the table is the minimum, which is 0.67 mm, the displacement prediction interval is [17.86 mm, 18.53 mm], and the actual measured displacement value of the slope displacement on that day is 17.9 mm. The actual displacement value falls within the prediction interval, so under the confidence of 90%, the displacement at this time point is within the normal range and is not abnormal.

[0091] Take the maximum bandwidth in the prediction period as another example. The interval bandwidth of July 11, 2015 is 0.96 mm, which is the maximum bandwidth in the prediction period. The prediction interval is [18.90 mm, 19.86 mm], and the actual measured displacement value of the slope displacement on that day is 19.3 mm. The actual displacement value also falls within the prediction interval, so under the confidence of 90%, the displacement prediction value at this time point is also within the normal range and is not abnormal.

[0092] Although the embodiments of the present application have been shown and described, it can be understood by those of ordinary skill in the art that various changes, modifications, replacements and variations can be made to these embodiments without departing from the principles and spirits of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for dynamic interval prediction and anomaly identification of diversion channel slope displacement based on DeepAR, characterized by: The method comprises the following steps: Selection of input variables; Correlation calculation; Construction of DeepAR model; Model training and prediction; Prediction effect evaluation; Anomaly identification for displacement prediction; The selection of the input variables specifically includes: factors affecting the displacement of the diversion channel slope include water level, time effect and rainfall; The correlation calculation specifically includes: Displacement has a certain correlation with water level and its higher power. 2 , H 3 As the water level influencing factors, the Pearson correlation coefficient method is used to calculate the correlation between the previous rainfall and time effect and displacement, and the rainfall and time effect influencing factors with strong correlation are selected, as follows: Suppose two variable sequences are X= ( 1 , 2… n ) ，Y= ( 1 , 2… n ), the Pearson correlation coefficient is calculated using the following formula: （1） in are the means of the sequences of the corresponding variables, t , Monitor values ​​for different variables at different time points, is the sample size; The construction of the DeepAR model specifically includes: Hidden layer output at the current moment h t As shown in the following formula: （2） Where: z t express t The displacement value at the moment, x t express t The impact factor of time, t At this moment, the network input includes the influencing factors x t , the value at the previous moment z t-1 , and the hidden layer output at the previous moment h t-1 , h t for t The output of the hidden layer at time t, W hz is the weight corresponding to the displacement data from the input layer to the hidden layer, W hx is the weight corresponding to the input layer impact factor to the hidden layer, W hh is the weight from the hidden layer output at the previous time point to the hidden layer output at the next time point, b is the bias from the input layer to the hidden layer, f(x) is the hyperbolic tangent activation function, which is expressed as follows: （3） Get the hidden layer output h t Finally, calculate the mean and standard deviation of the Gaussian distribution: （4） （5） Where: μh , b μ Calculate the output layer μ t The corresponding weights and bias terms, σh , σ Calculate the output layer σ t The corresponding weights and bias terms are obtained by calculating the mean and variance at each time point to obtain the Gaussian likelihood function as follows: （6）。 2. The method for dynamic interval prediction and anomaly identification of diversion channel slope displacement based on DeepAR according to claim 1 is characterized by: The training and prediction of the model specifically include: During the training phase, the network input includes the influencing factor and the displacement value at the previous moment, as well as the hidden layer output at the previous moment, so as to calculate the parameter mean of the likelihood function μ and standard deviation σ , it is believed that the closer the fitting distribution of the network distribution output is to the real situation, that is, the fitting distribution is z t There is a great probability value at z t Get the maximum value and construct the objective function of training as follows: （7） Where: 0 is the moment when prediction starts. In the DeepAR model, the negative form of the objective function is taken, that is, Training is done for the loss function. In actual training, when the loss function tends to be stable, the network training is considered complete, that is, the objective function reaches its maximum; In the prediction phase, DeepAR aims to find the probability distribution of the current moment based on the displacement values ​​and impact factor values ​​at historical moments. The joint distribution consists of the product of Gaussian likelihood functions at different time points. （8） Where: To predict the end time, represents the displacement value of the prediction time period, represents the displacement value of the training time period, is the impact factor; is the conditional probability distribution, that is, and Probability distribution of displacement under conditions; is the joint distribution of the model, which is the conditional probability The product of .

3. The method for dynamic interval prediction and anomaly identification of diversion channel slope displacement based on DeepAR according to claim 1 is characterized by: The prediction effect evaluation specifically includes: Use the root mean square error (RMS) to evaluate point predictions , mean absolute percentage error , and interval evaluation index interval coverage probability , normalized mean width of prediction interval As an evaluation indicator of model performance, the corresponding calculation formula is as follows: （9） （10） （11） （12） （13） Where: To predict the number of samples, for Measured displacement value, Output displacement values ​​for the model, for t The minimum and maximum values ​​of the moment prediction interval, are the maximum and minimum displacements within the prediction period; The larger it is, the more true values ​​fall within the prediction interval; It is necessary to achieve the corresponding confidence level, namely the nominal confidence level, as much as possible, otherwise the obtained prediction interval is considered to be insufficiently reliable; The smaller the value, the narrower the prediction interval. Same The smaller it is, the better the model's prediction effect.

4. The method for dynamic interval prediction and anomaly identification of diversion channel slope displacement based on DeepAR according to claim 1 is characterized by: The abnormality identification of the displacement prediction specifically includes: The interval prediction result with a confidence level of 90% is selected as the standard for judging abnormalities. When the actual displacement value falls within the prediction interval corresponding to this confidence level, it is determined that the actual displacement value is normal under this confidence level. On the contrary, if the actual displacement value exceeds the range of the prediction interval, it is determined that the actual displacement value under this confidence level is abnormal, and the alarm mechanism is triggered accordingly.

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