Application of neural network merging model in dam deformation analysis

Zhang Fan Hu Wusheng

(School of Transportation, Southeast University, Nanjing 210096, China)

As it is known to all, building dams is one of the most important engineering measures for the comprehensive utilization of water resources, and all the countries in the world are now attaching great importance to it. The water conservancy and hydropower engineering have brought huge economic benefits to human beings, such as flood controlling, power generation, water supply, shipping, irrigation, tourism, cultivation and so on. However, there is a certain degree of risk in constructing dams since the dam-break phenomenon will cause huge economic losses and even serious casualties. Therefore, dam safety becomes more prominent and important, and the establishment of a good dam deformation analysis model is exactly an important means to ensure the safe operation of the dam.

Since the 1950s, methods of dam deformation analysis have been put forward in succession by many scholars in Italy[1], Austria[2]and Korea[3]. Compared with other countries, the analysis of dam monitoring data started later in China, but some effective progress has also been made by domestic scholars[4-6]. At present, the conventional models of dam deformation analysis are divided into three classes: the statistical model, the deterministic model and the mixed model. There is no doubt that these classical deformation analysis models have played very important roles for dam deformation prediction in the past several decades. But it is undeniable that because of the complexity of the actual engineering, the under fitting problem which commonly exists in regression models results in a low prediction accuracy in such kind of models.

In recent years, with the continuous development of new disciplines, the wavelet analysis[7], the grey theory[8], fuzzy mathematics[9]and the artificial neural network[10-11]have been applied to the analysis of dam monitoring data, which enrich the dam deformation analysis models. Because of its self-organization, self-adaptability, association ability, self-learning ability and very strong nonlinear mapping ability, the neural network has now been used in a wide range of applications. Based on the vertical displacement observation data of the dam, the statistical model, the conventional BP neural network model and the merging model are built up in this paper, and the prediction effects of the three models are compared and analyzed.

1 OverviewofThreeDamDeformationAnalysisModels

1.1 Statisticalmodel

The statistical model is the most mature and widely used model in dam safety monitoring. By qualitative analysis we know that the vertical displacement of a gravity arch dam at any point can be divided into three main parts: hydraulic pressure component, thermal component and aging component[5]. Combined with the specific circumstance of the dam, the statistical model for the vertical displacement is

δ=δH+δT+δA

(1)

whereδis the vertical displacement;δHis the hydraulic pressure component;δTis the thermal component; andδAis the aging component.

The expression of the hydraulic pressure component of the vertical displacement is

(2)

whereHis the water depth in front of the dam, namely the reservoir water level; andaiis the hydraulic factor regression coefficient.

The thermal component is mainly due to the temperature variations of the dam body and the bedrock. The Chencun Dam has been in operation for more than thirty years, and the dam body is in the state of the quasi-stationary temperature field. Therefore, the thermal component can be represented by a periodic function

(3)

wheretis the cumulative number of days between the observation day and the first observation day of the modeling time; andb1j,b2jare the thermal factor regression coefficients.

The aging component is a comprehensive reflection of many effects such as concrete creep and so on, and its causes are very complex. In this paper, we use the model as follows:

δA=c1θ+c2lnθ

(4)

whereθis the cumulative number of days between the observation day and the first measuring day divided by 100, andc1,c2are the aging factor regression coefficients.

In summary, the statistical model of the vertical displacement is

(5)

wherea0is the constant term.

1.2 Conventional BP neural network model

The error back-propagation network is the most widely used and effective one in the existing dozens of artificial neural network models. Usually, the BP neural network consists of the input layer, the hidden layer and the output layer. The main idea of the BP algorithm is to divide the learning process into two stages[12].

1) The forward propagation process: The input information is given, and the actual output value of each unit is calculated layer-by-layer.

2) The back propagation process: If the expected output value is not obtained in the output layer, then we calculate the difference between the actual output and the expected output layer-by-layer recursively in order to adjust the weights.

Use these two processes repeatedly and obtain the minimum error signal, and when the error achieves the expected requirements, the learning procedure of the network ends. The structure of the BP neural network model is shown in Fig.1.

Fig.1 Structure of the BP neural network model

The specific structure of the BP neural network model in this paper is as follows:

2) The number of hidden layer nodes isP, which is always determined by tentative calculation or experience. In this paper,P=16.

3) The output layer is the measured vertical displacement valuey0. So the structure of the BP neural network model is 9×16×1 in this paper.

1.3 Neural network merging model

The merging model is a method to compensate for the error of the hypothetical model based on the BP neural network model[13]. The specific structure of the neural network merging model in this paper is as follows:

2) The number of hidden layer nodes isP, which is always determined by tentative calculation or experience. In this paper,P=16.

3) The output layer is the difference between the measured vertical displacement valuey0and the fitted value of the statistical modelys. Note that the final result of the merging model is the sum of the simulated value of the neural network and the fitted value of the statistical modelys. So the structure of the neural network merging model is (9+1)×16×1 in this paper.

2 Case Study

2.1 Projectoverviewandmodelingdataselection

Located in the upper reaches of the Qingyi River, the Chencun Dam is a comprehensive medium-sized water conservancy and hydropower project. The concrete gravity arch dam has 28 sections from left to right, and the total reservoir capacity of the dam is 2.825×106m3.

The observation data of the vertical displacement of a certain observation point in Chencun Dam between January 1999 and December 2006 are used for deformation analysis. The gross error is eliminated by data preprocessing and finally 96 samples are selected, 12 samples for each year. Now the 96 samples are divided by the following three conditions:

1) Sample classification 1: The 60 samples from 1999 to 2003 are selected as the learning samples, and the rest 36 samples from 2004 to 2006 are selected as the testing samples.

2) Sample classification 2: The 72 samples from 1999 to 2004 are selected as the learning samples, and the rest 24 samples from 2005 to 2006 are selected as the testing samples.

3) Sample classification 3: The 84 samples from 1999 to 2005 are selected as the learning samples, and the rest 12 samples in 2006 are selected as the testing samples.

2.2 Comparison of prediction accuracy

After modeling by the statistical model, the BP neural network model and the neural network merging model respectively for the three kinds of sample classification above, the RMSEs of the testing samples are shown in Tab.1.

Tab.1 RMSEs of testing samples of different models mm

From Tab.1, we can see that the prediction accuracy of the statistical model is general. The effect of the BP neural network model is improved, while the neural network merging model is the best, since the average prediction accuracy of the merging model is improved by 33% and 18%respectively compared with the other two models. From the comparison of different sample classifications for each model, we can see that with the increase in the learning samples, the RMSEs of the statistical model reduce significantly, while the RMSEs of the BP neural network model and the merging model change slowly. This shows that the prediction accuracy of the statistical model is more dependent on the number of learning samples for modeling, which is determined by its statistical characteristics.

2.3 Analysis of generalization ability

In order to test the generalization ability of the neural network merging model, we choose sample classification 2 to compare the forecast values in 2005 and 2006 predicted by the statistical model and the neural network merging model. The results are shown in Tab.2 and Tab.3.

Tab.2Comparison of prediction results in 2005 mm

Tab.3 Comparison of prediction results in 2006 mm

From Tab.2 and Tab.3, we can see that the residual errors of the statistical model in 2005 are significantly smaller than those in 2006, and the RMSEs are±0.363 and ±0.613 mm, respectively. Compared with the statistical model, the amplitude of variation of the neural network merging model is less, and the RMSEs are ±0.277 and ±0.373 mm, respectively. This shows that the neural network merging model has a better generalization ability.

3 Conclusion

Dam deformation observation data is important for dam safety monitoring, and dam deformation analysis is the most effective use of these data, so the quality of the deformation analysis models directly determines whether the dam can operate under a safe condition or not. From the instance in this paper, we can see that the statistical model has been widely used. But in some cases, due to the complexity of influencing factors of the dam, the fitting accuracy is often not very good. The neural network merging model has not only a higher prediction accuracy but also a stronger generalization ability, so it can be used as a good method for deformation analysis of dam monitoring data.

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