One of the main causes of bridge collapse may be flood flow scour near piers. Several experimental and local field investigations were carried out to study scour depth. However, existing empirical equations do not commonly provide accurate scour prediction due to the complexity of the scour process. Physical and economic considerations often lead to bridge foundation constructs which included a pier column based on a pile cap supported by an array of piles. Piers with this configuration are referred to as complex piers. A few studies have been done on complex bridge pier scour depth estimation. Such efforts may be classified into theoretical and empirical equations. This paper investigates local scour around complex bridge piers by using harmony search algorithm under clear water conditions. Statistical indices such as the coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and bias were used to evaluate the performance of these methods. By designing laboratory tests, 82 experimental data points were measured by authors. Also 615 experimental data sets with the same measured experimental conditions were collected from published literature and used for optimization. The results show that the developed HS model can predict scour depth better than other equations according to statistical indices.

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Scour depth prediction is a vital issue in bridge pier design. Recently, good progress has been made in the development of artificial intelligence (AI) to predict scour depth around hydraulic structures base such as bridge piers. In this study, two hybrid intelligence models based on combination of group method of data handling (GMDH) with harmony search algorithm (HS) and shuffled complex evolution (SCE) have been developed to predict local scour depth around complex bridge piers using 82 laboratory data measured by authors and  615 data points from published literature. The results were compared to conventional GMDH models with two kinds of transfer functions called GMDH1 and GMDH2. Based upon the pile cap location, data points were divided into three categories. The performance of all utilized models was evaluated by the statistical criteria of R, RMSE, MAPE, BIAS, and SI. Performances of developed models were evaluated by experimental data points collected in laboratory experiments, together with commonly empirical equations. The results showed that GMDH2SCE was the superior model in terms of all statistical criteria in training when the pile cap was above the initial bed level and completely buried pile cap. For a partially-buried pile cap, GMDH1SCE offered the best performance. Among empirical equations, HEC-18 produced relatively good performances for different types of complex piers. This study recommends hybrid GMDH models, as powerful tools in complex bridge pier scour depth prediction.