Suspended sediment concentration estimation by stacking the genetic programming and neuro-fuzzy predictions
Graphical abstract
Introduction
In the new decade due to lack of water resources, it is vital to have an accurate sediment prediction for different purposes such as dam service life evaluation or water management. In order to predict the sediment, because of its paramount importance and its nonlinear nature, there have been great challenges for water and hydraulic structures engineers. Sediment has severe effects on hydraulic and geomorphologic features of the rivers and hydraulic structures. Furthermore, prediction of sediment has detrimental effects on the dams’ reservoirs. So, incorrect estimation of sediment rate reduces the amount of waters stored behind the dams and consequently has a huge negative effect on supplying drinking water and agricultural water. This is why scientists and experts are constantly seeking for new ways to predict the sediment accurately and suggesting various empirical formulas for this purpose [1], [2], [3], [4]. Accuracy of these empirical formulas was evaluated by some researchers [5], [6]. Due to some innate errors in measuring the input parameters, applying empirical methods leads to uncertainties in the final results [7]. The nonlinear and seasonal nature of the related parameters in estimating sediment, inaccurate measurement and lack of sufficient data are some factors that cause uncertainties in the results obtained by empirical models [8].
Besides the empirical formulas, the sediment rating curve has been used for estimating the sediment in the both gauged and ungauged stations as well [9], [10], [11], [12], [13]. Heng and Suetsugi [13] showed that using sediment rating curve could increase the uncertainties. Thus, it is essential to use a method which is able to estimate the sediment more accurately and confidently. Soft computing methods, which are widely used in various fields, are able to help us in this way as well. In this study, among various methods of soft computing, our attention is focused on three methods of soft computing. These methods are artificial neural network, neuro-fuzzy, and genetic programming. Researches done by these methods for predicting sediment will be reviewed in Section 2.
In order to improve the prediction accuracy of soft computing methods, a combination of several predicting algorithms can be used. These methods, called ensemble learning [14], have such different varieties as Bayesian model averaging, bagging, boosting, model tree ensembles, and stacking. In some previous studies, to enhance accuracy, some ensemble learning methods such as bagging, boosting, and model tree ensembles were used to predict the hydrological quantities. These studies will be reviewed in Section 2. However, as will be shown, in all of these researches, the hydrological quantities other than sediment have been predicted and none of them was related to the prediction of sediment. Also, to the best of our knowledge, among various methods of ensemble learning, none of the previous studies used the stacking method to predict any hydrological quantity.
In the stacking method, at first, some predicting algorithms are trained by using the existing data. Then the predicted data are used as the inputs for training the combining model. Normally, this method performs better than using a single algorithm [14].
As it will be reviewed in Section 2, former studies show that some of the soft computing methods are able to predict the suspended sediment successfully. On the other hand, as mentioned above, combining the results of single algorithms based on stacking method usually performs better than using them separately. Considering these facts, it is expected that stacking and combining the results of the successful soft computing methods for predicting the suspended sediment can improve the prediction accuracy. This is the main contribution of our work; in this paper, a new method is proposed to predict the sediment of river based on stacking method. In our proposed method, to obtain the accurate prediction, neural network is applied as a combining meta-model to combine the predictions made by linear genetic programming and neuro-fuzzy based on cross validation.
The paper proceeds as follows: In Section 2, the previous researches conducted on predicting sediment and hydrological data by soft computing methods are reviewed. In Section 3, our proposed method will be presented for using stacking to predict the suspended sediment. In Section 4, case studies on which the proposed method will be evaluated are brought and the results of the proposed method will be analyzed, comparing with those of other methods. Finally, in Section 5, conclusions are presented briefly.
Section snippets
Literature review
In this section, first, all previous studies regarding artificial neural networks, neuro-fuzzy, and genetic algorithm (including genetic programming) that focus on predicting sediment are reviewed. Then, the studies related to the use of ensemble learning methods for predicting hydrological quantities are reviewed. Table 1 presents a summary of the reviewed studies. This summary includes input variables, predicted quantities, and the soft computing methods used to predict the hydrological
The proposed method: applying stacking method for predicting the suspended sediment
Ensemble learning methods are designed to obtain more accurate prediction by aggregating the predictions of multiple machine learning models [54]. Stacking is an ensemble learning method that was first introduced by Wolpert [14] for combining the N classifier models. Then, this method was extended by Breiman [55] to combine the N predictor models. The main idea behind the stacking is to form a combination of N learning models by using cross validation [56]. The stacking procedure is performed
Evaluation
In this section, first, the case studies which will be used for evaluation of the proposed procedure are introduced. These case studies include data of Rio Valenciano and Quebrada Blanca stations. Next, the proposed method is applied on data of these stations and the results are compared with linear genetic programming [42], artificial neural network [33], and neuro-fuzzy [33] methods. Two statistics – Root Mean Square Errors (RMSE) and – are used for comparison. RMSE can be used for
Conclusion
Stacking method can be used to accurate prediction by combining the results of various individual methods. In this study, an approach was proposed based on stacking as an innovative method to predict the suspended sediment. The results were compared with some powerful methods like linear genetic programming, neural network, and neuro-fuzzy, which had been used before to predict the sediment by Kisi and Guven [42] and Kisi [33]. The results clearly prove that our proposed method is able to
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2022, International Journal of Sediment ResearchA stacking ensemble model for hydrological post-processing to improve streamflow forecasts at medium-range timescales over South Korea
2021, Journal of HydrologyCitation Excerpt :We note that the term “ensemble” in the stacking ensemble model is slightly different from the general term “ensemble” in hydrology and can be explained as the estimated quantities obtained from the spread of the ensemble members originating from diverse prediction models (Gneiting et al., 2005). The stacking ensemble model has been applied to various fields of hydrological and climatological modeling, such as river ice breakup timing (Sun, 2018; Sun and Trevor, 2018), daily streamflow prediction (Li et al., 2020; Tyralis et al., 2019), low flow frequency analysis (Worland et al., 2018), and suspended sediment yield estimation (Shamaei and Kaedi, 2016). The above studies commonly reported that the stacked ensemble learning is effective because it allows for the correction of forecast biases.
Ensemble machine learning paradigms in hydrology: A review
2021, Journal of HydrologyCitation Excerpt :It was claimed that better prediction results were attained by the usage of the ensemble technique in comparison to the previous investigations (more than 7% improvement in the accuracy). Shamaei and Kaedi (2016) employed the stacking method for improving the suspended sediment prediction results of individual ML models including Linear Genetic Programming (LGP) and Neuro-Fuzzy (NF). The results revealed that the applied ensemble method improved the performance of the individual models (around 40% improvement in the RMSE values).
Two decades on the artificial intelligence models advancement for modeling river sediment concentration: State-of-the-art
2020, Journal of HydrologyCitation Excerpt :WLSSVM and WANN models showed same subsequences in daily and different in monthly SSL estimations. Shamaei and Kaedi (2016) proposed a method called stacking to predict the SSC. They compared performance of LGP, ANN, NF methods with stacking model.