Elsevier

Engineering Structures

Volume 119, 15 July 2016, Pages 230-251
Engineering Structures

Interpretation of dam deformation and leakage with boosted regression trees

https://doi.org/10.1016/j.engstruct.2016.04.012Get rights and content

Highlights

  • Boosted regression trees were used to analyse dam monitoring data.

  • An 100-m height double-curvature arch dam was considered as a case study.

  • The models were interpreted and conclusions on dam behaviour were drawn.

  • The evolution over time was clearly identified.

Abstract

Predictive models are essential in dam safety assessment. They have been traditionally based on simple statistical tools such as the hydrostatic-season-time (HST) model. These tools are well known to have limitations in terms of accuracy and reliability. In the recent years, the examples of application of machine learning and related techniques are becoming more frequent as an alternative to HST. While they proved to feature higher flexibility and prediction accuracy, they are also more difficult to interpret. As a consequence, the vast majority of the research is limited to prediction accuracy estimation. In this work, one of the most popular machine learning techniques (boosted regression trees), was applied to model 8 radial displacements and 4 leakage flows at La Baells Dam. The possibilities of model interpretation were explored: the relative influence of each predictor was computed, and the partial dependence plots were obtained. Both results were analysed to draw conclusions on dam response to environmental variables, and its evolution over time. The results show that this technique can efficiently identify dam performance changes with higher flexibility and reliability than simple regression models.

Introduction

Dam monitoring is essential to ensure its proper operation and its long-term safety [1]. One of the main tasks to be carried out is the comparison between the expected response and that registered by the monitoring system, to understand the dam behaviour and to detect potential anomalies. In this context, predictive models are necessary to estimate the dam response in a given situation.

Data-based tools allow building predictive models based on monitoring data, i.e., without explicitly considering the physical properties of the dam and the foundation. The hydrostatic-season-time (HST) model [2] is the most widely applied, and the only generally accepted by practitioners.

HST is based on multiple linear regression considering the three most influential external variables: hydrostatic load, air temperature and time. The main advantages of HST are:

  • 1.

    It frequently provides useful estimations of displacements in concrete dams [3].

  • 2.

    It is simple and thus easily interpretable: the effect of each external variable can be isolated in a straightforward manner, since they are cumulative.

  • 3.

    Since the thermal effect is considered as a periodic function, the time series of air temperature are not required. This widens the possibilities of application, as only the reservoir level variation is needs to be available to build an HST model.

  • 4.

    It is well known by practitioners and frequently applied in several countries [3].

Nonetheless, HST also features conceptual limitations that damage the prediction accuracy [3] and may lead to misinterpretation of the results [4]. For example, it is based on the assumption that the hydrostatic load and the temperature are independent, whereas it is obviously not the case: the thermal field in the dam body, especially in the vicinity of the water surface, is strongly dependant on the water temperature in the upstream face [5]. In turn, the thermal load influences the stress and displacement fields.

Several modifications to the original HST model have been proposed to overcome these drawbacks. They focus on improving the consideration of the thermal load, by taking into account the actual air temperature instead of the historical mean [6], or the effect of the water temperature on the upstream face [3], [7].

In the recent years, non-parametric techniques have emerged as an alternative to HST for building data-based behaviour models [8], e.g. support vector machines (SVN) [9], neural networks (NN) [10], adaptive neuro-fuzzy systems (ANFIS) [11], among others [8]. In general, these tools are more suitable to model non-linear cause-effect relations, as well as interaction among external variables, as that previously mentioned between hydrostatic load and temperature. On the contrary, they are typically more difficult to interpret, what led them to be termed as “black box” models (e.g. [12]).

Most of the published works focused on building predictive models whose accuracy was generally higher than that offered by HST (e.g. [10], [13], [14]). Since the resulting model was seldom analysed, little information was provided for dam safety assessment. Some exceptions worth mentioning, though simple, were due to Santillán et al. [15], Mata [10] and Cheng and Zheng [16].

Therefore, dam engineers face a dilemma: the HST model is widely known and used and easily interpretable. However, it is based on some incorrect assumptions, and its accuracy can be increased. On the other hand, more flexible and accurate models are available, but they are more difficult to implement and analyse. The same problem arose in the field of statistics [17].

The objective of this work is to investigate the possibilities of interpretation of one of these black box models to:

  • 1.

    Identify the effect of each external variable on the dam behaviour.

  • 2.

    Detect the temporal evolution of the dam response.

  • 3.

    Provide meaningful information to draw conclusions about dam safety.

Among the plethora of machine learning techniques available [18], a previous comparative study [13] showed boosted regression trees (BRT) as one of the more appropriate tools for the prediction of dam response. In this paper, the technique was further explored, with focus on the interpretation of the results for dam behaviour identification. In particular, the partial dependence plots were examined to isolate the effect of each action, and the relative influence (RI) was computed to identify the strength of each input–output relation. Furthermore, the results were interpreted from an overall viewpoint to draw conclusions on the dam behaviour.

The method was applied to the analysis of La Baells Dam, as compared to the conventional HST model.

The rest of the paper is organised as follows. A brief introduction to BRT is presented, including the methods for interpretation. Then, the case study and the HST version taken as reference are described. The results are included and interpreted in terms of the dam behaviour, and the differences between both methods are discussed.

Section snippets

Boosted regression trees

The objective of a predictive model is to estimate the value of an output variable YR (i.e. radial displacement or leakage), based on a set of predictors (reservoir level, air temperature, etc.) XRp, i.e. YŶ=F(X). The observed values are denoted as (xi,yi),i=1,,N, where N is the number of observations. Note that each xi is a vector with p components, each of which is referred to as xij, when necessary. Similarly, Xj,j=1,,p stands for each dimension of the input space.

BRT models are built

Model accuracy

Although the work focused on model interpretation and its implications on dam safety, the goodness of fit was also checked in order to (a) observe the effect of variable selection, and (b) check the prediction accuracy of the model used for interpretation (M3).

Table 2 contains the error indices for each target, while more detailed results are included in Appendix A. For those models with variable selection, the predictors are also listed. The results show that BRT efficiently discarded

Summary and conclusions

BRT models with different degree of variable selection were fitted to 8 radial displacements and 4 leakage flows at La Baells Dam. The relative influence of each input was computed and depicted via word clouds, which offered an efficient visualisation of the overall response of the dam. These graphs, together with the univariate and bivariate partial dependence plots, allowed interpretation of the BRT models: useful information regarding dam behaviour was obtained, such as the thermal inertia,

Acknowledgements

The authors thank Carlos Barbero, dam safety manager at the Catalan Water Agency, for providing the monitoring data.

The research was supported by the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía y Competitividad, MINECO) through the projects iComplex (IPT-2012-0813-390000) and AIDA (BIA2013-49018-C2-1-R and BIA2013- 49018-C2-2-R).

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