A high-performance displacement prediction model of concrete dams integrating signal processing and multiple machine learning techniques
Introduction
Concrete dams during the operation period are bound to suffer from various dynamic and static cyclic environmental loads, such as hydrostatic and temperature loads, and accidental disasters like earthquakes and catastrophic floods [1]. And such external forces would lead to the deterioration of material properties and the reduction of structural resistances. The operation safety of dams directly affects the benefit's exertion of the projects, national economy development and regional stability. Dam failure will pose a serious threat to the life security of citizens in the downstream [2,3]. Recently, with the exploitation of water resources and the development of dam construction technology, Xiaowan, Xiluodu, Jinping I and some other super high concrete dams have been put into operation. The project scale and difficulty in security management of such engineered systems have far exceeded those of dams in the previous generation. The operation safety issue of dams has aroused common concern of the whole society.
The measured data-driven structural health monitoring (SHM) is a crucial method to provide vital theoretical basis and technical support for safeguarding healthy operation of concrete dams. Displacement can intuitively reflect the comprehensive operation behavior of concrete dams under the synergistic action of dynamic changes of environmental loads and nonlinear evolutions of material and structural properties [4,5]. Therefore, the measured displacement-based SHM model has become a research hotspot for real-time diagnosis of health status, identification of structural damage and prediction of future operational behavior [6], [7], [8]. The measured displacement-based SHM model can be classified into HST and hydrostatic-thermal-time (HTT) models [9], [10], [11]. Among which, HST model usually employs multicycle harmonic functions to simulate the periodic variation behavior of thermal displacement. Due to the simple structure, HST model is popularly used for dam displacement prediction [7,10,11]. However, harmonic functions cannot reasonably depict the short-term dynamic fluctuation behavior of thermal displacement induced by the temperature difference. Therefore, HST model cannot well elaborate the detailed variation behavior of thermal displacement when the ambient temperature is obviously colder or warmer than usual [1,10].
The mathematical analysis method-based model established via the causal relationship between dam displacement and its explanatory variables is the most popular modelling approach of the measured displacement-based SHM model due to its high computational efficiency. And with the development of computer technology, a large number of machine learning (ML) techniques, such as support vector machine (SVM) [2,12], extreme learning machine (ELM) [4], radial basis function network (RBFN) [6], boosted regression trees (BRT) [8], long-short term memory (LSTM) [13,14] and TSVR [1], have been successfully utilized in the measured displacement-based SHM model nowadays. The ML techniques effectively overcome the problem of multicollinearity among the explanatory variables in the linear regression analysis methods, such as multiple linear regression (MLR) and stepwise regression (SR). And they perform with excellent predictive accuracy. The application of such ML techniques dramatically facilitates the development of the measured displacement-based SHM model. In addition, decomposition-ensemble models integrating multiple techniques further enriched the modelling approach of the measured displacement-based SHM models. And the decomposition-ensemble models exhibit superior predictive performance to the single technique-based models. For instance, Li et al. [5] proposed a distributed time series evolution-based displacement prediction model using locally estimated scatterplot smoothing, non-linear least squares and dynamic time warping. Zhang and Xu [15] adopted empirical mode decomposition (EMD) to decompose the measured displacement into several displacement components with different variation behaviors, and then the displacement components were predicted by the optimized SVM. Bian and Wu [16] utilized EMD to decompose the measured displacement into periodic and irreversible displacements, and tested the modelling performances of ELM, SVM and back propagation neural network on periodic displacement. Cao et al. [17] utilized VMD to decompose the measured displacement into several components, and the decomposed components were predicted with ELM.
Considering the strong nonstationary and nonlinear variation behavior of the measured displacement, and the insufficiency of HST model on the interpretative capability of thermal displacement, a high-performance displacement prediction model of concrete dams is proposed based on signal processing and multiple ML techniques. Firstly, VMD is adopted to decompose the measured displacement into several time series, and SE method is used to avoid over-decompostion. Secondly, according to the modelling factors in HST model, the decomposed signals are categorized into trend, periodic, semi-periodic and stochastic signals via K-means clustering algorithm. Meanwhile, the trend, periodic and semi-periodic signals are utilized to reconstruct the displacement. Thirdly, TSVR is adopted to establish HST-based prediction model for the reconstructed displacement, and the stochastic signals are predicted with GRU network-based model. To improve the modelling performance, the parameters of TSVR and GRU are optimized by SOA. Finally, a high-performance displacement prediction model is established by superimposing the predicted values of TSVR-based and GRU-based models. The modelling procedure of the proposed model is elaborated and the predictive accuracy is tested with the measured displacements of a gravity dam. Modelling results demonstrate that the proposed model has excellent predictive performance. A novel prediction technique is provided for accurately predicting dam displacement.
Section snippets
HST-based displacement prediction model
Displacement of concrete dams consists of hydrostatic pressure-driven and ambient temperature-driven reversible displacements and irreversible displacement caused by the nonlinear evolutions of material and structural properties [[2], [3],7]. HST model is usually written aswhere δ(h) and δ(s) are the reversible displacements caused by hydrostatic and temperature loads, respectively; δ(t) is the irreversible displacement.
Water pressure component δ(h) is usually computed
Decomposition and reconstruction of the measured displacement
In this section, VMD is firstly adopted to decompose the measured displacement into several signals with different frequency characteristics [18]. To avoid over-decomposition, SE method is used for determining the appropriate number of the signal decomposition [19]. Then, according to the modelling factors of HST model, the decomposed signals are categorized into trend, periodic, semi-periodic and stochastic signals via K-means clustering algorithm [20], and the trend, periodic and
Optimized ML techniques-based displacement prediction
To improve the modelling efficiency, the trend, periodic and semi-periodic signals are firstly employed to reconstruct the displacement. And then, the reconstructed displacement is predicted with TSVR-based HST model, and the stochastic signals are predicted with GRU-based model. In addition, to improve the modelling performance, the parameters of TSVR and GRU are optimized by SOA algorithm. The adopted methodologies are introduced as follows.
Project background and data acquisition
A gravity dam is taken to elaborate the implementation process of the proposed prediction model. This dam is composed of 87 dam sections, which undertakes the tasks of flood control, power generation and so on. The crest length and the maximum height are 1570.0 m and 121.5 m, respectively. The total and regulating storage capacities are 2419 and 1918 million m3, respectively. The downstream view of this dam is shown in Fig. 5.
The horizontal displacement behavior of this dam is automatically
Conclusions
Considering the limitations of HST model and the strong nonstationarity, nonlinearity of the measured displacement, this study proposed a high-performance dam displacement prediction model via signal processing and multiple ML techniques. And the predictive performance of the proposed model is tested with the measured horizontal displacements of a gravity dam. The main conclusions are as follows.
- (1)
VMD technique can effectively decompose the measured displacement into trend, periodic,
Declaration of Competing Interest
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Acknowledgments
This work is supported by National Natural Science Foundation of China (Grants 51739003, 52169025), Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant KYCX21_0515), China Postdoctoral Science Foundation (Grant 2021M702949) and the Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant 2021492111).
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