**1. Introduction**

256 Genetic Programming – New Approaches and Successful Applications

[44] Arganis JML, Val SR, Prats RJ, ,Rodríguez VK, Domínguez MR, Dolz RJ (2009). "Genetic programming and standardization in water temperature modelling,"

Advances in Civil Engineering. Hindawi Publishing Corporation. 2009: 10.

The experience of applying evolutionary computing to time series describing local physical problems has benefited the modelling culture by showing that many different mathematical formulae can be produced to describe the same problem. This experience brings into the focus the roles of pluralism in the modelling culture as opposed to searching for the best model, where physical problems provide relevance and context to the choice of modelling techniques. Both of these roles are often overlooked and do not directly influence research agenda. Although the focus of this paper is on evolutionary computing, it also promotes a pluralistic modelling culture by studying other modelling techniques, as well as by keeping the role of physical problems in the foreground.

Estimating suspended sediment loads is a problem of practical importance and includes such problems as changing courses in rivers, loss of fertile soil, filling reservoirs and impacts on water quality. The study of these problems in the short-run are referred to as sediment transport and erosion for those in the long-run. Past empirical capabilities remain invaluable but are not sufficient on their own as management and engineering solutions often require an insight into the problem. Empirical knowledge has been incorporated into the body of distributed modelling techniques giving rise to sophisticated modelling software tools but their applications require a great deal of resources. There remains a category of problems, often referred to as time series analysis, which uses the sequences of time variations and predicts the future values. This category of models provides useful information to management of local problems. For instance, such models may be used to schedule dredging requirements or other maintenance activities. Time series analysis is developing into local management tools and it is a focus of this chapter.

© 2012 Khatibi et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Khatibi et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The aim of this chapter is to predict suspended sediment load of a river into the future. Besides the traditional empirical Sediment Rating Curve (SRC), there are several strategies for analysing such time series and *evolutionary computing* is one of Artificial Intelligence (AI) approaches, which broadly include capabilities for searching and recognising patterns among others. This chapter also employs Artificial Neural Network (ANN), which is another AI approach. Yet another strategy is to regard time series as outcomes of many random drivers and this assumption is supported by a whole body of probabilistic approaches, where this chapter uses Multi-Linear Regression (MLR) analysis to model the same data. Over the past few decades, research has increasingly focused on the application of deterministic chaos (or chaos theory or dynamic systems) showing that many of apparently randomly varying system behaviours can be explained by deterministic chaos. The concept behind this modelling strategy is that the particular data can largely be explained by deterministic behaviour, where in time the system evolves asymptotically towards an *attractor*. Its random-looking variations are assumed to be an internal feature of the system and depending on its initial conditions, its state under a certain range may become highly erratic but with a predictable behaviour. Evidently, none of these strategies are identical and different models rarely produce identical results. This chapter therefore compares the performance of these modelling strategies for solving an engineering problem.

Inter-Comparison of an Evolutionary Programming

Model of Suspended Sediment Time-Series with Other Local Models 259

of ANN to suspended sediment include that by Wang et al (2008), who applied ANN to

Aytek and Kishi (2008) used the GP approach to model suspended sediment for two stations on the Tongue River in Montana, USA, and indicate that the GP formulation performs quite

Chaotic signals have also been identified in time series of suspended sediment loads by Sivakumar and Jayawardena (2002, 2003), Farmer and Sidorowich, 1987). The outcomes

Overall, a general understanding of the analysis of suspended sediment load is yet to emerge and one way to gain an insight into the problem is to carry out inter-comparison studies of the performance of a host of models applied to diversity of rivers of different

Sediment transport is concerned with entrained soil materials carried in water by erosion on the catchment and within channels. Sediment particles are categorised as follows (i) the saltation load (not discussed here); (ii) bedload (not discussed here) and (iii) suspended load including clay (< 62*μm* in particle diameter), silt and sand. Suspended load (both as "finegrained sediment" and "wash load") is directly a result of the turbulence in water and forms a large proportion of the transported load, where the turbulence is a measure of the energy

*Sediment discharge* is a measure of the mass rate of sediment transport at any point in space and time and determines whether the load is being transported or deposited. The whole process comprises soil erosion, sediment transport and sediment yield, where the deposited load delivered to a point in the catchment is referred to as sediment yield and is expressed as tons per unit area of the basin per year, measured at a point. Estimation of sediment yield (and soil erosion) is essential for management but these and mathematical models are used to gain an insight into the underlying processes. Sediment yield is estimated by (i) direct measurement, (ii) using local time series models to predict future states; (iii) using

Suspended sediment forms most of the transported load and can be affected by many parameters including rainfall, land use pattern, slope, soil characteristics, e.g. soil moisture content but their considerations lead to distributed models, which are complex. Recorded suspended sediment derives distributed models by serving them as boundary conditions or input sources but their inherent information is not tapped on. There is a case for local models to study the information contained in recorded sediment loads alone in terms of flow and sediment hydrographs. This chapter is concerned with the study of the suspended

mathematical models to study jointly both erosion and sediment processes.

derive the coefficients of regression analysis for their SRC model.

shapes and sizes.

**3. Study area and data** 

in the water to carry the load.

load of a river, as discussed below.

**3.1. Understanding the problem** 

well compared to sediment rating curves and multi linear regression models.

revealed the usefulness of these methods towards an effective prediction capability.

The study employs 26 years of the Mississippi River data recorded at Tarbert + RR Landings and involve both flows and suspended sediment load. The river discharges about 200 million metric tons of suspended sediment per year to the Gulf of Mexico, where it ranks about sixth in the world today.
