A foundation pit settlement prediction method based on FNN neural network and autoregressive model

Abstract

The application discloses a foundation pit settlement prediction method based on a FNN neural network and an autoregressive model, and comprises the following steps: acquiring foundation pit settlement monitoring data, and using a cubic spline interpolation method to interpolate a settlement observation sequence into an equal-time interval sequence with a settlement amount every half day; taking previous four period observation values as input and a next period observation value as output to construct training samples and test samples; using the training samples to construct an autoregressive model, and calculating a next period settlement prediction value of the autoregressive model; using the training samples to determine a residual error of the next period settlement result predicted by the autoregressive model; constructing an FNN neural network model to represent a nonlinear relationship between the values and the residual error; using the data to construct training samples of the FNN model, and iteratively training the FNN model; adding an output result of the FNN model and a calculated value of the autoregressive model to form an FNN neural network and autoregressive fusion model and verify the precision of the FNN neural network and autoregressive fusion model. The precision and stability of the application are significantly improved compared with a common model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of construction engineering construction quality monitoring control management, relates to the technical field of deep foundation pit deformation prediction, and in particular to a foundation pit settlement prediction method based on an FNN neural network and an autoregressive model. BACKGROUND

[0002] With the rapid development of China's economy, urban construction is continuously advancing, and the construction land is increasingly nervous and the construction space is increasingly narrow and crowded in urban construction, and buildings tend to be super high and deep longitudinal development. Safety monitoring of deep foundation pit engineering is very important in this type of super high or super deep building, and is the basis and guarantee for smooth construction.

[0003] The conventional foundation pit deformation prediction method is based on historical monitoring data of a certain deformation variable, analyzes the deformation characteristics, constructs a regression model, and then predicts the future trend. This type of method has simple principle and fast calculation, but is greatly affected by subjective factors, and generally has the problem of underfitting of the regression model. At the same time, the prediction accuracy of this type of analysis method often decays with time, and cannot fully tap the time sequence law of the foundation pit monitoring data. With the development of computer technology, wavelet analysis, grey theory, artificial neural network and other methods have been applied to deformation prediction. Artificial neural network can fully tap the implicit law in the learning sample due to its strong adaptability and nonlinear mapping ability, and more accurately approximates the deformation characteristics of the building, and thus is widely used. The conventional neural network model still has problems such as poor stability and easy to fall into local minimum, and the prediction residual increases with time. SUMMARY

[0004] The application discloses a fusion model of an autoregressive model and an FNN neural network algorithm to improve the accuracy of foundation pit deformation prediction and provide reliable guidance for safe construction.

[0005] The application achieves the following technical solutions:

[0006] The application discloses a foundation pit settlement prediction method based on an FNN neural network and an autoregressive model, comprising the following steps:

[0007] S1: Obtain foundation pit settlement monitoring data, and interpolate the settlement observation sequence into an equal-time interval sequence with a settlement amount every half day by using a cubic spline interpolation method. Take the previous 4 observation values as input and the next 1 observation value as output to construct training samples and test samples;

[0008] S2: Use the training samples obtained in S1 to construct an autoregressive model, and calculate the next 1 settlement prediction value of the autoregressive model;

[0009] S3: Determine the residual error (RSE) of the autoregressive model prediction of the settlement result in the next period using the training sample obtained in S1;

[0010] S4: Construct a 5x5x1 FNN neural network model to represent the nonlinear relationship between the observed values of the previous four periods, the predicted value of the settlement in the next period obtained by the autoregressive model, and the residual error (RES) of the autoregressive model prediction result;

[0011] S5: Use the data obtained in S1, S2, and S3 to construct the training sample of the FNN model, and iteratively train the FNN model;

[0012] S6: Use the observed settlement values x n-1 , x n-2 , x n-3 , x n-4 of the previous four periods and the settlement x′ n in the next period calculated by the autoregressive model to calculate the residual error RES of the autoregressive model using the FNN model trained in S4 and S5, and finally calculate the settlement prediction value in the next period obtained by the new model and evaluate the accuracy of the new model.

[0013] The modeling data in step S1 uses the support pile settlement observation data, and a cubic spline interpolation is used to obtain an equal-interval settlement observation sequence every half day. The input of the training sample is the settlement observation data of the previous four periods, and the output is the settlement result in the next period.

[0014] The autoregressive model in step S2 uses the settlement observation data of the previous four periods to predict the settlement result in the next period. The autoregressive model is shown in formula (1):

[0015] x n = β0+ β1x n-1 + β2x n-2 + β3x n-3 + β4x n-4 (1)

[0016] Where x n is the observed settlement value in the next period, x n-1 , x n-2 , x n-3 , x n-4 are the observed settlement values of the previous four periods. The undetermined coefficients β0, β1, β2, β3, β4 are determined by the least squares method. The settlement in the next period calculated by the autoregressive model is denoted as x′ n ;

[0017] The RES in step S3 is shown in formula (2):

[0018] RES = x n -x′n (2)

[0019] wherein, x n is the settlement observation value of the last 1 period, x′ n is the settlement of the last 1 period calculated by the autoregressive model.

[0020] The FNN network in step S4 is composed of an input layer, a hidden layer and an output layer, the input layer node number is 5, representing the previous 4 period settlement observation data and the autoregressive model prediction data respectively, the hidden layer node number is 5, and the output layer node number is 1, representing the prediction error of the autoregressive model, and the activation function is selected as Tan-Sigmoid function, and the expression is as follows:

[0021]

[0022] wherein, x is the input signal value of the neuron, f(x) is the output signal value, the target error of the FNN is 0.0001mm, the maximum training number is 200 times, and the gradient descent method is adopted for training.

[0023] The final prediction value of the settlement of the last 1 period in step S6 is shown in formula (3):

[0024]

[0025] wherein, is the final prediction value of the AR+FNN model, x′ n is the prediction value of the autoregressive model, and RES is the residual error of the autoregressive model obtained by constructing the FNN model in steps S4 and S5.

[0026] The verification accuracy is that the settlement observation value x i which does not participate in the calculation of steps S1-S5 is taken as the true value, the root mean square error is taken as the evaluation standard, and the calculation formula is as follows:

[0027]

[0028] Compared with the prior art, the present application has the following advantages:

[0029] 1. The new model is superior to the commonly used autoregressive model and the traditional FNN model, and the precision of the new model is significantly improved compared with the above two models.

[0030] 2. The autoregressive+FNN fusion model has good stability and can obtain good prediction results at all monitoring points.

[0031] 3. With the passage of monitoring time, the precision of the autoregressive model and the conventional FNN model decreases, and the autoregressive+FNN fusion model can obtain higher precision in the whole prediction period.

[0032] 4. The deformation characteristics of some monitoring points are quite complex, and there are still significant changes at the end of construction. In this case, the autoregressive model and the traditional FNN model do not perform well in predicting these types of monitoring points, but the autoregressive + FNN model can still achieve high prediction accuracy. Attached Figure Description

[0033] Figure 1 This is a flowchart of the steps of the present invention;

[0034] Figure 2 This is a sequence diagram of the cumulative settlement test error in this embodiment; in the diagram, the horizontal axis of each sequence diagram represents the sample observation time, and the vertical axis represents the model residual. Detailed Implementation

[0035] The present invention will be further described below with reference to specific embodiments. These specific embodiments are further explanations of the principles of the present invention and are not intended to limit the present invention in any way. Any technology that is the same as or similar to the present invention does not exceed the scope of protection of the present invention.

[0036] Refer to the attached diagram.

[0037] like Figure 1 As shown in the figure, this specific embodiment discloses a new method for predicting foundation pit settlement based on FNN neural network and autoregressive model, including the following steps:

[0038] S1: Obtain the settlement monitoring data of the foundation pit, and interpolate the settlement observation sequence into an equal time interval sequence of settlement amount per half-day using cubic spline interpolation. Use the first four observations as input and the last observation as output to construct training and validation samples. Details are as follows:

[0039] This specific implementation method selects continuous data from a certain project from August 3rd, 20** to January 4th of the third year, obtaining a total of 152 data periods. Cubic spline interpolation is used to obtain one observation data point per half-day. The first four observations are used as input, and the last observation is used as output to construct training and validation samples, resulting in a total of 1039 observation samples. The first 500 periods are used as training samples, and the last 535 periods as validation samples.

[0040] S2: Using the training samples obtained in S1, an autoregressive model is constructed, and the predicted settlement value for the next period is calculated. The autoregressive model uses the settlement observation data from the previous four periods to predict the settlement result for the next period. The autoregressive model is shown in formula (1):

[0041] x n =β0+β1x n-1 +β2x n-2 +β3x n-3 +β4x n-4 (1)

[0042] where x n is the observed settlement value of the last period, x n-1 , x n-2 , x n-3 , x n-4 are the observed settlements of the previous four periods. The undetermined coefficients β0, β1, β2, β3, β4are determined by the least square method. The settlement of the last period calculated by the autoregressive model is denoted as x′ n .

[0043] S3: Using the training samples obtained in S1, determine the residual error (RES) of the autoregressive model in predicting the settlement of the last period;

[0044] where RES is shown in equation (2):

[0045] RES = x n -x′ n (2)

[0046] In equation (2), x n is the true observed settlement value of the last period, and x′ n is the settlement of the last period calculated by the autoregressive model.

[0047] S4: Construct a 5x5x1 FNN neural network model to fit the nonlinear relationship between the observed values of the previous four periods, the predicted value of the settlement of the last period obtained by the autoregressive model, and the residual error (RES) of the autoregressive model in predicting the settlement of the last period;

[0048] where the FNN network consists of an input layer, a hidden layer, and an output layer, the input layer node number is 5, representing the observed settlement data of the previous four periods and the predicted data of the autoregressive model; the hidden layer node number is 5; the output layer node number is 1, representing the prediction error of the autoregressive model; the activation function is selected as the Tan-Sigmoid function, whose expression is:

[0049]

[0050] where x is the input signal value of the neuron, f(x) is the output signal value, the target error of the FNN is 0.0001 mm, the maximum training times is 200, and the gradient descent method is used for training.

[0051] S5: Using the data obtained in S1, S2, and S3, construct the training samples of the FNN model, and iteratively train the FNN model.

[0052] S6: Using the test samples obtained in S1 and the settlement of the last period calculated by the autoregressive model x′ n, the final prediction value of the settlement of the next period is calculated by the new model, and the accuracy of the new model is evaluated.

[0053] the final prediction value of the settlement of the next period calculated by the new model As shown in equation (3):

[0054]

[0055] wherein is the final prediction value of the autoregressive + FNN model, x' n is the prediction value of the autoregressive model, and RES is the residual error of the autoregressive model obtained by constructing the FNN model in steps S4 and S5.

[0056] The verification accuracy is to take the settlement observation value x i of the 535 test samples in step S1 as the true value, and the root mean square error is used as the evaluation standard, and the calculation formula is:

[0057]

[0058] In order to analyze the accuracy of the autoregressive + FNN fusion model, the modeling error and the test error of the autoregressive model, the FNN model and the autoregressive + FNN fusion model are calculated and compared, and the specific results are shown in Table 1; in order to further analyze the stability of the new model, the error sequence diagram of each test sample is drawn.

[0059] Table 1 Precision comparison of the support pile settlement prediction method of the embodiment

[0060]

[0061] From Table 1, Figure 2 It can be seen that:

[0062] (1) The three models can all achieve high prediction accuracy, among which the autoregressive + FNN fusion model has the highest accuracy, the accuracy is increased by 39% on average compared with the autoregressive model, and the accuracy is increased by 41% on average compared with the traditional FNN model, which can fully meet the deformation prediction requirements of the foundation pit horizontal displacement, settlement and adjacent building and adjacent road settlement.

[0063] (2) The modeling accuracy of the traditional FNN model is high, but its stability is poor, and the prediction effect at some monitoring points is not good. The autoregressive + FNN fusion model has good stability and can achieve good prediction results at all monitoring points.

[0064] (3) With the passage of monitoring time, the accuracy of the autoregressive model and the FNN model decays, but the autoregressive+FNN fusion model does not have this phenomenon, and can achieve higher accuracy throughout the prediction period.

[0065] (4) The deformation characteristics of some monitoring points are relatively complex, and there is still a large fluctuation at the end of construction. The autoregressive model and the traditional FNN model do not perform well in the prediction of this type of monitoring point, but the autoregressive+FNN fusion model can still achieve high prediction accuracy.

[0066] From the above conclusions, it can be seen that the autoregressive+FNN model combines the stability of the autoregressive model and the powerful nonlinear fitting ability of the FNN algorithm, and has good generalization ability. Through the verification of the settlement monitoring point data in this embodiment, the AR+FNN model can meet the needs of various high-precision deformation prediction in the process of foundation pit construction.

Claims

1. A foundation pit settlement prediction method based on FNN neural network and autoregressive model, characterized by The method comprises the following steps: S1: obtaining foundation pit settlement monitoring data, using cubic spline interpolation to interpolate the settlement observation sequence into an equal-time interval sequence with a settlement amount every half day, and using the previous four observation values as input and the next observation value as output to construct training samples and test samples; S2: using the training samples obtained in S1 to construct an autoregressive model and calculate the next period settlement prediction value of the autoregressive model; The autoregressive model in step S2 is shown in formula (1): （1） wherein, is the settlement observation value of the next period, , , , are the settlement observation values of the previous four periods; the undetermined coefficients are determined by the least square method , , , , ; the settlement of the next period calculated by the autoregressive model is ; S3: using the training samples obtained in step S1 to determine the residual error (RES) of the autoregressive model prediction result; The residual error (RES) in step S3 is shown in formula (2): （2） wherein, is the observed settlement value of the next period, is the settlement of the next period calculated from the autoregressive model; S4: constructing a 5*5*1 FNN neural network model to represent the nonlinear relationship between the previous four observation values, the next period settlement prediction value obtained by the autoregressive model and the residual error (RES) of the autoregressive model prediction result; The input layer of the FNN neural network model in the step S4 includes the settlement observation values of the first four periods , , , , the next period settlement calculated by the autoregressive model ; the hidden layer has 5 nodes; and the output layer is the residual (RES) of the prediction result of the autoregressive model. S5: using the data obtained in S1, S2 and S3 to construct the training samples of the FNN model, and iteratively training the FNN model; S6: the settlement of the next period is calculated by using the settlement observation values of the previous four periods , , , and the autoregressive model , the residual error (RES) of the autoregressive model is calculated by the FNN model trained in S4 and S5, the settlement prediction value of the next period is finally calculated by the FNN neural network and the autoregressive model, and the accuracy of the new model is evaluated.

2. The FNN neural network and autoregressive model-based foundation pit settlement prediction method according to claim 1, characterized in that: The modeling data in step S1 uses support pile settlement observation data, and obtains an equal interval settlement observation sequence with one every half day by cubic spline interpolation; the input of the training sample is the previous four settlement observation data, and the output is the next period settlement result.

3. The FNN neural network and autoregressive model-based foundation pit settlement prediction method according to claim 1, characterized in that: The autoregressive model in step S2 uses the previous four settlement observation data to predict the next period settlement result.

4. The FNN neural network and autoregressive model-based foundation pit settlement prediction method according to claim 1, characterized in that: The FNN network in step S4 is composed of an input layer, a hidden layer and an output layer, the number of nodes of the input layer is 5, representing the previous four settlement observation data and the autoregressive model prediction data; the number of nodes of the hidden layer is 5; the number of nodes of the output layer is 1, representing the prediction error of the autoregressive model, and the activation function is selected as Tan-Sigmoid function, and its expression is: wherein, is the input signal value of the neuron, is the output signal value, the target error of the FNN is 0.0001 mm, the maximum training times is 200, and the gradient descent method is used for training.

5. The FNN neural network and autoregressive model-based foundation pit settlement prediction method according to claim 1, characterized in that, The final prediction value of the next period settlement amount in step S6 is shown in formula (3): （3） wherein, is the final prediction value of the autoregressive+FNN model, is the settlement of the next period calculated by the autoregressive model, and the residual (RES) is the residual (RES) of the autoregressive model obtained by constructing the FNN model in steps S4 and S5.

6. The FNN neural network and autoregressive model-based foundation pit settlement prediction method according to claim 1, wherein the accuracy of the new model is evaluated by using the settlement observation values that are not involved in the calculation of steps S1-S5 in step S6. As the true value, the root mean square error is used as the evaluation standard, and the calculation formula is: 。

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