In this section, a quantitative assessment of the uncertainties in the prediction of the scour depth around piers with debris accumulation is presented using the EPR, MT, and GEP models. The uncertainty analysis is employed to the data set of 432 experimental measurements used in this study, which was used to derive the proposed models. The uncertainty analysis defines the individual prediction error as . The calculated prediction errors for the entire data set are used to calculate the mean and standard deviation of the prediction errors as and , respectively. A negative mean value demonstrates that the prediction model underestimated the observed values, and a positive value shows that the equation overestimated the observed values. Using the values of and S_{e}, a confidence band can be defined around the predicted values of an error using the Wilson score method without continuity correction (Newcombe 1998; Sattar 2014); the use of 1.96S_{e} yields an approximately 95% confidence band. The results of the uncertainty analysis, the mean prediction errors of the various models, the width of the uncertainty band, and the 95% prediction interval error are given in Table 7. The three proposed approaches have produced absolute mean prediction errors much less than those of the empirical equations. The proposed models showed approximately similar behavior, whereas empirical equations showed the opposite behavior. In the proposed models, the MT model demonstrates better behavior than the GEP and EPR models. The uncertainty band for the MT model ranged from −3.03 to +3.03. This range is smaller than that of the EPR and GEP models, which were and , respectively. Similarly, the lowest 95% confidence prediction error interval was observed for the MT model. The MT model had the lowest mean prediction error and the smallest uncertainty bands in comparison with other ones.

Table 7

Models . | Mean prediction error . | Width of uncertainty band . | 95% prediction error interval . |
---|---|---|---|

EPR | + 0.0306 | ± 3.1472 | −0.7185 to 0.9253 |

GEP | + 0.0305 | ± 3.0812 | −4.9626 to 1.7305 |

MT | + 0.0189 | ± 3.0282 | −4.8749 to 1.3591 |

Models . | Mean prediction error . | Width of uncertainty band . | 95% prediction error interval . |
---|---|---|---|

EPR | + 0.0306 | ± 3.1472 | −0.7185 to 0.9253 |

GEP | + 0.0305 | ± 3.0812 | −4.9626 to 1.7305 |

MT | + 0.0189 | ± 3.0282 | −4.8749 to 1.3591 |

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