Artificial neural network based generalized storage–yield–reliability models using the Levenberg–Marquardt algorithm

Abstract

Generalised storage–yield–reliability models are developed using multi-layer perceptrons artificial neural networks (ANNs), trained using the Levenberg–Marquardt algorithm. These ANNs provide, for the first time, generalised models for simultaneously predicting within-year and over-year storage capacities, given the yield, reliability and readily obtainable streamflow statistics. The training, validation and testing of the models used time series data from 18 streams located in different parts of the world, which were carefully selected so that they nearly cover the range of flow variability observed in world streams. The performance of the models was very good. Further comparison of the ANN models with existing regression models revealed that the latter are marginally better; however, given that the regression models require the over-year capacity to be known a priori, the ANN models are more generic and should be preferred.

Introduction

Reservoir planning involves the determination of storage capacity of the reservoir, which will satisfy the demand with an acceptable level of reliability. This information can be provided by developing the storage–yield–reliability (S–Y–R) relationship for the site under investigation. The development of the S–Y–R function is generally achieved by carrying out a sequential analysis of time series data using one of a variety of traditional techniques such as behaviour simulation and the Sequent Peak Algorithm (see McMahon and Adeloye, 2005). However, more recently, other techniques have been developed which by-pass the sequential analysis of time series data. Because they do not require the sequential analysis of time series data, these generalised techniques, as they are commonly known (see Vogel and Stedinger, 1987) are much faster to implement, which makes them very useful during preliminary design stage, and are potentially more suited to application at ungauged sites as described by Adeloye et al. (2003). However, these desirable aspects of having generalised S–Y–R models are marred by the fact that nearly all the existing ones only predict the over-year capacity; in situations where significant within-year capacity exists, such as when the annual flow variability is low or the level of development is low, the existing generalised models will underestimate the total storage requirements.

Tentative solutions to this problem have included subjectively adjusting predicted over-year capacity estimate for within-year contribution (e.g. Hardison, 1965) and using more formal regression equations relating total (i.e. over-year plus within-year) capacity to the over-year capacity (e.g. Adeloye et al., 2003). However, both of these are limited in scope because they assume that the over-year storage is known a priori. In addition, the procedure by Hardison (1965) used data from the USA and hence may not be valid elsewhere. Finally, Adeloye et al. (2003) assumed a linear relationship between capacity and input factors such as the demand, reliability and coefficient of variation (Cv) of annual flows, whereas the true relationship is non-linear.

The aim of this study was to develop ANN-based generalized S–Y–R models for reservoirs, which will predict both the within-year and over-year capacities simultaneously. ANNs are most suitable for this task because they are capable of mapping most non-linear functions, which S–Y–R functions are, without specifying explicitly the form of the functions (Shamseldin, 1997). According to Haykin (1994) an artificial neural network is “a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use. It resembles the brain in two aspects: knowledge is acquired by the network through a learning process and interneuron connection strengths known as synaptic weights are used to store knowledge.”

In Section 2, a brief introduction to ANNs is given together with a short review of its numerous applications in hydrology and water resources. This is then followed by a description of the methodology used in the study. Finally, the results are presented and discussed.