A novel application of a multi-objective evolutionary algorithm in open channel flow modelling

Abstract

The Shiono and Knight method (SKM) is a simple depth-averaged flow model, based on the RANS equations which can be used to estimate the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels with the minimum of computational effort. However, in order to apply the SKM, detailed knowledge relating to the lateral variation of the friction factor ( f ), dimensionless eddy viscosity (l) and a sink term representing the effects of secondary flow (G) are required. In this paper a multi-objective evolutionary algorithm is used to study the lateral variation and value of these parameters for simple trapezoidal channels over a wide range of aspect ratios through the model calibration process. Based on the available experimental data, four objectives are selected and the NSGA-II algorithm is applied to several datasets. The best answer for each set is then selected based on a proposed methodology. Rules relating f, l and G to the wetted parameter ratio (P b /P w ) for a variety of situations have been developed which provide practical guidance for the engineer on choosing the appropriate parameters in the SKM model.

River hydraulics – a view from midstream

“…Until such work is undertaken, this will inevitably limit the application of this type of model. Recent work by Sharifi et al (2009Sharifi et al ( , 2010 on the application of evolutionary computation to open-channel modelling, and by Chlebek and Knight (2006), indicate that it is possible to investigate numerically the physical parameters more thoroughly than hitherto. The use of 2D and 3D models poses particular difficulties with respect to calibration.…”

The end depth ratio and principal component analysis

“…side weirs - Ramamurthy et al, 2006) and as such lend themselves to analysis of the free overfall. However, more recently Sharifi (2009) and Sharifi et al (2009aSharifi et al ( , 2009b have applied genetic programming to examine the problem and, as will be explained below, it was this work which motivated the current analysis.…”

“…Table 1 illustrates the top five expressions which were deemed to perform the best for a rectangular channel using such an approach. The evaluation of these expressions and the criteria used to establish which were the best are beyond the scope of this paper but these issues are fully discussed elsewhere by Sharifi (2009) and Sharifi et al (2009b). However, for the benefit of the reader it is noted that in the present context, the 'best' model was evaluated by analysing the complexity of the model and its goodness of fit.…”

“…Expression Table 1. The five best expressions found using genetic programming relating h c to h e (adapted from Sharifi, 2009) The expressions given in Table 1 were developed using both sub-and super-critical flow data and as such relate to both types of flow. A similar analysis was undertaken for channels with circular and trapezoidal cross-sections and in all cases an expression of the form…”

“…Figure 2 shows that the agreement of the available experimental data with Equation 4 is good, with a reasonably small maximum residual error of approximately 1%, which is within the limits of the accuracy of the experimental measurements. (For a full review of these data the reader is directed to Dey (2002) and Sharifi (2009)). This level of agreement also indicates that the EDR technique is sufficiently accurate to be adopted as a simple method for estimating the discharge in channels with an end drop.…”