Combining Outlier Robust Extreme Learning Machine (ORELM) with seasonal autoregressive moving average linear model (SARIMA) to improve the accuracy of runoff modeling

Document Type : Research Paper

Authors

• Fereshteh Nourmohammadi Dehbalaei ¹
• Arash Azari ²
• Ali Akbar Akhtari ³

¹ Department of Information Science, Faculty of Management, University of Tehran, Tehran,

² Assistant Professor, Department of Water Engineering, Razi University, kermanshah. Iran

³ Department of Civil Engineering, Razi University,Kermanshah, Iran Iran.

Abstract

Keywords

• Hybrid model
• MLP
• Monthly Runoff
• ORELM
• SARIMA

Main Subjects

• هیدرولوژی

EXTENDED ABSTRACT

Introduction

Runoff is an important factor in a hydrological system and is influenced by various factors such as geographic location, topography, and climate. Runoff forecasting plays an essential role in reducing the effects of floods and droughts, controlling erosion and sedimentation in the basin. Various hydrological models including empirical models, physical models and data-based models have been developed for runoff modeling. The data-driven methods due to the need for less knowledge of the physical behavior of the phenomenon have become more popular.

Materials and Methods

At first, the data were divided into two categories, training (70% of the total data measured) and testing (30% of the total data measured). The value of the Hurst coefficient for the data was 0.63, which indicates that the length of the time series is sufficient for modeling. The results of the normality and stationarity test showed that the data have a non-normal distribution and a non-stationary behavior. Therefore, by performing normalization through normalizing functions and removing definite terms from the time series by performing seasonal differentiation, the data were normalized and stationary. By defining two scenarios (without preprocessing and with preprocessing) and by performing different modeling, the best linear model was selected. By calculating the residual of the linear model and checking the independence of the residuals through the Ljung–Box test, nonlinear modeling was performed by outlier robust extreme learning machine (ORELM) and multilayer perceptron (MLP) models. Then, the output of the nonlinear model was summed with the linear model.

Results and Discussion

For linear modeling with SARIMA model, two scenarios were defined. The best linear model in the first scenario was obtained with MAE=13.28, RMSE=17.23, R=0.62 and AIC=267.54 using seasonal parameters and without preprocessing. In the second scenario, four sub-scenarios were implemented. Sub-scenario 4 using preprocessing through the standardization with MAE=12.76, RMSE=13.11, R=0.57 and AIC=264.41 shows better results than other sub-scenarios. The comparison of the results obtained from the implementation of different nonlinear models showed that model 6 with MAE=10.25, RMSE=13.48 and R=0.7 has the lowest error value and the highest correlation compared to other models. The comparison of the results obtained from the SARIMA-MLP models showed that model 4 with MAE=11.35, RMSE=14.67, AIC=254.41 and R=0.65 has the lowest error and the highest correlation as well as the least complexity compared to other combinations. Comparing the results obtained from the SARIMA-ORELM model showed that model 6 with AIC=249.29, R=0.71, MAE=11.2 and RMSE=14.33 has the best performance in terms of accuracy and complexity compared to other models. By comparing the statistical indicators, the best SARIMA-ORELM and SARIMA-MLP models were selected. The comparison of the results obtained from the implementation of different linear models through the two scenarios showed that preprocessing through standardization increases the accuracy of the model and reduces the complexity of the model.

Conclusion

A summary of the comparison of the results of the hybrid models with the results obtained from modeling through SARIMA and MLP models is given below:

The results of comparing the predictions of the models through statistical indicators show SARIMA-ORELM model performs better than SARIMA-MLP model in all mathematical criteria.

SARIMA-MLP and SARIMA-ORELM models reduced the complexity of the model by 4.9% and 6.8%, respectively, compared to the linear modeling mode without preprocessing.

Among the six different models selected for runoff modeling, the weakest performance in terms of error and complexity criteria is achieved by modeling through the SARIMA model without preprocessing.

Author Contributions

F.N.D.: Writing – original draft, Formal analysis, Conceptualization, Data curation, Methodology, Validation, Writing – review & editing. A.A.: Writing – original draft, Formal analysis, Conceptualization, Data curation, Methodology, Validation, Writing – review & editing. A.A.A.: Conceptualization, Data curation, Writing – review & editing.

Data Availability Statement

Data is available on reasonable request from the authors.

Acknowledgements

The authors would like to thank all participants of the present study.

Ethical considerations

The authors avoided data fabrication, falsification, plagiarism, and misconduct.

Conflict of interest

The authors declare no conflict of interest