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Parameter Optimization and Process Calibration 223 Performance Evaluation In order to determine the performance of the GA calibration, the computed objective function of each child is compared with the TD’s objective function. The performance of the calibration process is evaluated by the degree of fitness (f(x)). In practice, f(x) is calculated by using an evaluation function (EF). Various EFs are discussed elsewhere. In this chapter, the simple least square approximation (1 dimension) is selected: ( ) ∑ ⎛ OOFi − COFi ⎟ ⎞ EF = f x = ⎜ ⎝ OOFi ⎠ where i = 1, … , n OOF = observed objective function COF = computed objective function As discussed in Chapter two, there is no standard method of determining the best EF and the selection is totally subjective. Simple least squares was used because of its long historical associations. Toleration of f(x) Tolerance is assigned to pause the automatic GA calibration method. In the previous chapter, 5% of true value is considered to be excellent for stream flow measurement. The tolerance is calculated based on this accuracy: 2 COF = (100% - 5%) × OOF = 0.95 OOF Substitute into the selected EF E. F. = f ( x) = ⎛ OOF − COF ⎜ ⎝ OOFi ⎞ ⎟ ⎠ 2 ⎛ OOF − 0.95OOF ⎜ ⎝ OOFi i i i i ∑ ⎜ ⎟ = ∑⎜ ⎟ = ∑ ⎞ ⎟ ⎠ 2 (0.05) 2 ∴ Tolerance = 2 ( 0.05) ⋅ n where n = number of calibration parameters The main purpose of the sensitivity-based GA calibration method is to minimize the error between the computed objective function and observed objective function for all rainfall events. Figures 14.9 and 14.10 show the calibration plot before and after using the preliminary GA calibration method, based on work done by Wan (2001).
224 Rules for Responsible <strong>Modeling</strong> Figure 14.9: Before Applying GA Calibration Method Figure 14.10: After Applying GA Calibration Method After only 7 cycles the calibrated parameters provide nearly the same result as the TD. Hence, the GA calibration method is evidently efficient. In order to
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