Mathematical Problems in Engineering

Volume 2017, Article ID 2586107, 13 pages

https://doi.org/10.1155/2017/2586107

## Study on MPGA-BP of Gravity Dam Deformation Prediction

^{1}College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China^{2}College of Water Conservancy and Hydropower, Hohai University, Nanjing 210098, China

Correspondence should be addressed to Xiaoyu Wang; moc.361@draz_reverof

Received 2 June 2016; Accepted 21 November 2016; Published 3 January 2017

Academic Editor: Ziran Wu

Copyright © 2017 Xiaoyu Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Displacement is an important physical quantity of hydraulic structures deformation monitoring, and its prediction accuracy is the premise of ensuring the safe operation. Most existing metaheuristic methods have three problems: (1) falling into local minimum easily, (2) slowing convergence, and (3) the initial value’s sensitivity. Resolving these three problems and improving the prediction accuracy necessitate the application of genetic algorithm-based backpropagation (GA-BP) neural network and multiple population genetic algorithm (MPGA). A hybrid multiple population genetic algorithm backpropagation (MPGA-BP) neural network algorithm is put forward to optimize deformation prediction from periodic monitoring surveys of hydraulic structures. This hybrid model is employed for analyzing the displacement of a gravity dam in China. The results show the proposed model is superior to an ordinary BP neural network and statistical regression model in the aspect of global search, convergence speed, and prediction accuracy.

#### 1. Introduction

Dam cracks and displacement monitoring that reflect the structural aging and disease are widely used in various forms of dams (e.g., Xianghongdian Dam [1], Chencun Dam [2], and Dokan Dam [3]). Dam deformation is generally caused by three primary factors: temperature variation, chemical reactions, and live loads [4]. Many ideas have been proposed to monitor dam deformation with statistical regression analysis or mechanical calculation. Tonini [5] proposed that dam displacement may come from three causative influences: water pressure, temperature variation, and aging. Other scholars further researched these influences and proposed various models.

Statistical regression models [6] have been proposed to analyze and describe dam deformation data quantitatively. Improved models used the average temperature, certain interval number of days before the observation, to analyze Castelo Arch Dam utilizing hysteresis of air temperature in the dam [7]. Rocha used the power-polynomial of the reservoir water level value to express hydrostatic pressure factor [6]. It was not until the failure of Malpasset Arch Dam in France in 1959 and Arch Dam’s reservoir-bank landslide that we began to realize the importance of dam safety and value safety monitoring work. Thus, statistical regression model was used through the finite-element method to calculate influence factor of the dam deformation [8].

Researchers further studied and proposed deterministic models [9]. Deterministic model can be used to analyze quantitatively and qualitatively dam time observation sequence [10]. Multiple linear regression approaches, which are simple and require no prior knowledge of the structure material properties, became popular in analyzing the relationship between environment quantity and effect size [11]. Hybrid models, a combination of the deterministic models and purely statistical (regression) models, can be used to analyze dam displacement through the finite-element theory.

In the last 10 years, artificial intelligence algorithms, such as the grey system, the fuzzy mathematic theory, the time series, the wavelet theory, and bionics algorithm, were also gaining popularity. The grey system has been proposed and applied to the dam stress grey forecasting model [12, 13]. The fuzzy mathematic theory is used to analyze gravity dam instability due to interval risk [14]. The method based on the wavelet theory describes the effect of dam monitoring data of quantity separating into effect size and environment quantity [15]. Recent studies such as artificial neural network [16] and artificial bee colony algorithm (ABC) [17] provided excellent fitting precision to assess feasibility and practicability of dam safety monitoring model.

Artificial neural network, which possesses strong ability of nonlinear function approximation and self-organizing and self-adaptive function, has been applied to the data of dams safety monitoring analysis and forecasting to remove data irregularity. Backpropagation neural networks have been proposed to monitor and predict the dam deformation while based on the actual values of a concrete gravity dam’s horizontal displacement [16]. The prediction accuracy was greatly improved from previous statistical model. In addition, space displacement analysis [18] and the forward-inversion analysis method [19] were also proposed to supervise dam deformation. That BP network model’s shortcomings were optimizing the structure of the network model and establishing the dam deformation forecasting model whose BP neural network was improved [20]. Recent studies [21, 22] have revealed that the artificial neural network can be applied to monitor deformation and monitor seepage of earth-rock dams.

Many studies [23, 24] demonstrated that BP neural network has some defects, such as slow learning convergence speed, local extremism, and the inconsistency and unpredictability of the structure. Therefore, many scholars combined BP neural network and other theories to improve prediction accuracy, such as fuzzy mathematics theory [25, 26]. Such combination provides better results than regression models. The combination with wavelet decomposition on the function approximation improved the fitting and prediction accuracy of dam deformation monitoring [27]. The combination with particle swarm also received good forecasting results [28]. A hybrid wavelet neural network methodology shows the superiority in improving prediction precision of time-varying behavior of engineering structures [29].

As a new type of search methods, genetic algorithm (GA) has many advantages, such as simple general, high global searching capability, strong robustness, and wide application range. Many studies have shown that these advantages can be used to optimize BP neural network’s structure, the weight, threshold value, and parameters and improve the prediction accuracy. Fu et al. [30] combined genetic algorithm backpropagation neural network prediction and finite-element model simulation to improve the process of multiple-step incremental air-bending forming of sheet metal. However, little research has been conducted in dam deformation analysis. Yin et al. [31] proposed the use of the GA-BP to optimize the injection molding process parameters. Chen et al. [32] suggested that GA-based BP neural network could be a promising approach for anticipating MMP in CO_{2}-EOR process. However, the results [30–32] may have been more beneficial if the phenomenon of premature convergence in the GA was considered; because all individuals in the population tended to have the same status and stopped evolution, the algorithm fails to give a satisfactory solution. Furthermore, when using normal GA to solve practical problems, we could have been puzzled by setting control parameters and designing the genetic operator. They tend to be given based on the actual problem tentatively. As aforementioned, the inappropriate setting will largely influence the performance of the algorithm. Thus further studies are required for exploring the applicability and reliability of GA-BP in dam deformation and seeking better methods of improvement.

The objective of this study is to analyze the feasibility of GA-BP in dam deformation, to explore the usefulness of proposed multiple population genetic algorithm backpropagation (hybrid MPGA-BP model), and to compare it with statistical regression model and conventional BP network model with the same parameter for dam deformation analysis. The rest of the paper is arranged as follows. Section 2 points out the pertinence between the loads and the dam behavior and then presents a brief review of BP neural network and MPGA and introduces proposed MPGA-BP model. Section 3 provides a case study of a gravity dam, which includes model setting-up, the results of model analysis, and evaluation. Several figures and tables are presented to illustrate the comparison among the statistical regression model, BP neural network model, and MPGA-BP model. Section 4 presents concluding remarks.

#### 2. Material and Methods

##### 2.1. Statistical Relation between the Loads and the Dam Behavior

Dam structure is influenced by hydraulic, environmental, and geomechanical factors. Therefore, the situation requires us to study the variables that affect the dam behavior before applying the improved artificial neural network approaches. Based on the results of the study of [33, 34], the approved formulation for deformation of an observing point located on the dam can be generated as follows:where , , and are the displacements contributed by hydrostatic pressure, temperature variation, and aging, respectively.

As an important factor of deformation, hydrostatic pressure can be expressed as a polynomial function for the reservoir water level above the foundation as follows:where and are determined by regression analysis; is the number of water pressure factors ( for the concrete gravity dam).

The displacement contributed by temperature variation can be modeled in two ways. If temperature measurements within the dam body and foundation are adequate and available, thenwhere is the temperature measured values at temperature measuring point at point ; and are determined by regression analysis; is the number of temperature factors.

If temperature measurements are inadequate and unavailable, the form of measured temperature cannot be used to describe temperature field’s variation. When dam temperature field closes to the quasi-stable temperature field, we can describe approximatively the changes of temperature field within dam body through the changes of temperature outside. But there is a lag effect on the dam body internal temperature variation which was influenced by air temperature changes. So, the influence of air temperature variation on monitoring effect-quantity also causes a lag effect. As a consequence, average temperature of several days before the day of monitoring effect-quantity was served as temperature factors. Therefore the form of temperature temporal loadings can be described as follows:where is the average value of the temperature factors in the day to the day before observational days; and are determined by regression analysis; is the number of temperature factors. The influence contributed by aging can be modeled as follows: where is the relation function of the aging factor; is order value of observational days; is the order value of base day; is the number of temperature factors. is the regression constant; is the regression coefficient; and are determined by regression analysis.

##### 2.2. Structure of BP Neural Network

W. McCulloch and W. Pitts opened an era of neuroscience research in 1943 since they created the mathematical model of neuron formation and imitation of biological neuron activity function. As a mathematical analogue of the biological system, it can be used to highlight processes, to deal with fuzzy information, or to display chaotic properties. BP neural network is by far the most widely used neural network, whose training method is based on the error backpropagation (BP) to the multilayer neural network. The topology of the BP neural network structure is as in Figure 1. In the figure, a three-layer structure of BP neural network divides into input layer, one hidden layer, and output layer. The individual neurons connected between two layers; there is only a connection weight between adjacent two layers. When a set of data enter the network structure from the input layer, the value of each hidden layer node can be obtained, combining with the weights between input layer and hidden layer and related algorithm. Then the value of each output node will arise by combining with the weights between hidden layer and output layer and the related algorithm. Nevertheless, the expected output and actual output had certain error; the model would utilize predetermined error values to adjust the weights between layers. This process will repeat until the predetermined error values present.