Linear genetic programming to scour below submerged pipeline

Genetic programming (GP) has nowadays attracted the attention of researchers in the prediction of hydraulic data. This study presents Linear Genetic Programming (LGP), which is an extension to GP, as an alternative tool in the prediction of scour depth below a pipeline. The data sets of laboratory measurements were collected from published literature and were used to develop LGP models. The proposed LGP models were compared with adaptive neuro-fuzzy inference system (ANFIS) model results. The predictions of LGP were observed to be in good agreement with measured data, and quite better than ANFIS and regression-based equation of scour depth at submerged pipeline.     

Prediction of scour depth at piers with debris accumulation effects using linear genetic programming

Abstract

Exact evaluation of scour depth around piers under debris accumulation is crucial for the safe design of pier structures. Experimental studies on scouring around pier bridges with debris accumulation have been conducted to estimate the maximum scour depth using various empirical relationships. However, due to the oversimplification of a complex process, the proposed relationships have not always been able to accurately predict the pier scour depth. This research proposes linear genetic programming (LGP) approach as an extension of the genetic programming to predict the scour depth around bridge piers. Among the artificial intelligence techniques, LGP and locally weighted linear regression (LWLR) models have not been used to predict the scour depth at bridge piers. Literature experimental data were collected and used to develop the models. The performance of the LGP method was compared with gene-expression programming, LWLR, multilinear regression and empirical equations using rigorous statistical criteria. The correlation coefficient (R) and the root mean squared error (RMSE) were (R?=?0.962, RMSE =0.31) and (R?=?0.885, RMSE =0.542) for the LGP and LWLR, respectively. The results demonstrated the superiority of the LGP method for increasing the accuracy of the predicted scour depth in comparison with the other models.     

Estimation of pile group scour using adaptive neuro-fuzzy approach

An accurate estimation of scour depth around piles is important for coastal and ocean engineers involved in the design of marine structures. Owing to the complexity of the problem, most conventional approaches are often unable to provide sufficiently accurate results. In this paper, an alternative attempt is made herein to develop adaptive neuro-fuzzy inference system (ANFIS) models for predicting scour depth as well as scour width for a group of piles supporting a pier. The ANFIS model provides the system identification and interpretability of the fuzzy models and the learning capability of neural networks in a single system. Two combinations of input data were used in the analyses to predict scour depth: the first input combination involves dimensional parameters such as wave height, wave period, and water depth, while the second combination contains nondimensional numbers including the Reynolds number, the Keulegan–Carpenter number, the Shields parameter and the sediment number. The test results show that ANFIS performs better than the existing empirical formulae. The ANFIS predicts scour depth better when it is trained with the original (dimensional) rather than the nondimensional data. The depth of scour was predicted more accurately than its width. A sensitivity analysis showed that scour depth is governed mainly by the Keulegan–Carpenter number, and wave height has a greater influence on scour depth than the other independent parameters.     

New expression-based models to estimate scour depth at clear water conditions in rectangular channels

Scouring in the channel contractions occurs due to the flow concentration within them inducing excessive bed shear stress. This is a complex process, so it is difficult to describe it through a general empirical model, the present research work describes contemporary conceptual relationships to estimate the local scour depth under equilibrium and clear water conditions in rectangular channels. Incidentally, gene-expression programming (GEP), evolutionary polynomial regression (EPR), and model tree (MT)-based formulations were utilized to predict the scour depth at long contractions. The input variables comprising average flow velocity, critical threshold velocity of sediment movement, flow depth, median particle diameter, geometric standard deviation, and uncontracted and contracted channel widths were used to feed the applied models. The performances of the developed approach were compared with those calculated using existing scour prediction equations. The results showed that the developed MT approach in terms of linear relationships could predict the scour depth more precisely than GEP, EPR, and the traditional equations. What is more, dimensionless parameter of h₁/b₁ (ratio of upstream flow depth to uncontracted channel width) was determined as the most influential variable in predicting the scour depth in long contractions.     

Prediction of wave-induced scour depth under submarine pipelines using machine learning approach

The scour around submarine pipelines may influence their stability; therefore scour prediction is a very important issue in submarine pipeline design. Several investigations have been conducted to develop a relationship between wave-induced scour depth under pipelines and the governing parameters. However, existing formulas do not always yield accurate results due to the complexity of the scour phenomenon. Recently, machine learning approaches such as Artificial Neural Networks (ANNs) have been used to increase the accuracy of the scour depth prediction. Nevertheless, they are not as transparent and easy to use as conventional formulas. In this study, the wave-induced scour was studied in both clear water and live bed conditions using the M5’ model tree as a novel soft computing method. The M5’ model is more transparent and can provide understandable formulas. To develop the models, several dimensionless parameter, such as gap to diameter ratio, Keulegan-Carpenter number and Shields number were used. The results show that the M5’ models increase the accuracy of the scour prediction and that the Shields number is very important in the clear water condition. Overall, the results illustrate that the developed formulas could serve as a valuable tool for the prediction of wave-induced scour depth under both live bed and clear water conditions.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.     

Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (S_max/H₀) on the basis of the following variables: relative water depth at the toe of the breakwater (h_toe/L₀), Shields parameter (θ), non-breaking wave steepness (H₀/L₀), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.     

一种基于小波分解和模糊推理神经网络的潮位预测方法

潮位预测严重影响沿海区域,尤其是近海浅水沿岸地区居民的生产生活和涉海活动。谐波分析是长周期潮位预测的传统方法,但无法预测非周期性气象过程发生时的水位变化。与数据处理方法相结合,人工智能的方法通过拟合输入与输出数据的历史数值关系,能够有效预测高度非线性和非平稳的流模式,因而在时间序列数据预测领域得到了广泛的应用。本文结合自适应模糊推理系统（Adaptive Neuro-Fuzzy Inference System, ANFIS）和小波分解方法,利用水位异常和风切变分量作为输入数据,实现了一种综合的多时效潮位预测方法。文中测试了多种输入变量组合和小波-ANFIS（WANFIS）模型,并与人工神经网络（Artificial Neural Network, ANN）、小波-ANN（WANN）和ANFIS模型进行了预测结果对比。通过不同指数的误差分析来看,相比ANN模型,ANFIS模型能够更准确的预测潮位变化,小波分解对ANFIS预测精度有一定的提高,且模型中水位异常和风切变分量数据的加入比单一的潮位数据输入能取得更好的预测结果。     

Circular time-domain reflectometry system for monitoring bridge scour depth

Abstract

Sediment has a severe effect on bridge stability, and time-domain reflectometry (TDR) is a suitable method for assessing scour depth. This paper presents a fundamental study to demonstrate the suitability of a circular TDR system to enhance the resolution when monitoring scour depth with consideration of detailed local changes over a wide area around piers. A total of 32 electrodes are vertically installed on a cylinder pier around the circumference at ～7.36?mm intervals. Scour depth is investigated through small-scale laboratory experiments, where a measured waveform reflects the artificially constructed scour depth with high resolution (≈5?mm). Different scour types including circular, mushroom, elliptical, and irregular shapes are developed to verify the application of circular TDR, and shapes are predicted through the detailed local distribution. The influences of the reflected waveform according to water level change, temperature variation, and salinity effect are investigated as additional considerations, and the relative deviation of scour depth is analyzed. This study demonstrates that the proposed circular TDR system achieves better resolution than existing single TDR systems and may provide a better alternative technique for monitoring scour depth.     

GMDH to predict scour depth around a pier in cohesive soils

This study presents new application of group method of data handling (GMDH) to predict scour depth around a vertical pier in cohesive soils. Quadratic polynomial was used to develop GMDH network. Back propagation algorithm has been utilized to adjust weighting coefficients of GMDH polynomial thorough trial and error method. Parameters such as initial water content, shear strength, compaction of cohesive bed materials, clay content of cohesive soils, and flow conditions are main factors affecting cohesive scour. Performances of the GMDH network were compared with those obtained using several traditional equations. The results indicated that the proposed GMDH-BP has produced quite better scour depth prediction than those obtained using traditional equations. To assign the most significant parameter on scour process in cohesive soils, sensitivity analysis was performed for the GMDH-BP network and the results showed that clay percentage was the most effective parameter on scour depth. The error parameter for three classes of IWC and C_p showed that the GMDH-BP model yielded better scour prediction in ranges of IWC = 36.3–42.28% and C_p = 35–100%. In particular application, the GMDH network was proved very successful compared to traditional equations. The GMDH network was presented as a new soft computing technique for the scour depth prediction around bridge pier in cohesive bed materials.     

Scour below pipelines and around vertical piles in random waves

An approach by which the scour depth and scour width below a fixed pipeline and scour depth around a circular vertical pile in random waves can be derived is presented. Here, the scour depth formulas by Sumer and Fredsøe [ASCE J. Waterw., Port, Coastal Ocean Eng. 116 (1990) 307] for pipelines and Sumer et al. [ASCE J. Waterw., Port, Coastal Ocean Eng. 114 (1992) 599] for vertical piles as well as the scour width formula by Sumer and Fredsøe [The Mechanics of Scour in the Marine Environment, World Scientific, Singapore, 2002] for pipelines combined with describing the waves as a stationary Gaussian narrow-band random process are used to derive the cumulative distribution functions of the scour depths and width. Comparisons are made between the present approach and random wave scour data. Tentative approaches to related random wave scour cases are also suggested.     

泥沙突变理论在海底管线冲刷中应用

基于泥沙突变理论,针对海底管线冲刷下泥沙的运动特征,建立恒定流作用下的泥沙起动模式,确定希尔兹数、无量纲参数、冲刷坑深度之间相互作用的非线性方程,推导了恒定流作用下海底管线冲刷坑深度的预测公式。将相同条件下该公式的计算结果与前人的试验资料进行了对比,可发现尽管计算结果存在一定的误差,但也基本能满足对冲刷坑深度的预测和判断,从而证明了泥沙突变模型在预测海底管线冲刷坑深度中的适用性。     

Prediction of local scour around circular piles under waves using a novel artificial intelligence approach

Abstract

The scour phenomena around vertical piles in oceans and under waves may influence the structure stability. Therefore, accurately predicting the scour depth is an important task in the design of piles. Empirical approaches often do not provide the required accuracy compared with data mining methods for modeling such complex processes. The main objective of this study is to develop three data-driven methods, locally weighted linear regression (LWLR), support vector machine (SVR), and multivariate linear regression (MLR) to predict the scour depth around vertical piles due to waves in a sand bed. It is the first effort to develop the LWLR to predict scour depth around vertical piles. The models simulate the scour depth mainly based on Shields parameter, pile Reynolds number, grain Reynolds number, Keulegan–Carpenter number, and sediment number. 111 laboratory datasets, derived from several experimental studies, were used for the modeling. The results indicated that the LWLR provided highly accurate predictions of the scour depths around piles (R?=?0.939 and RMSE = 0.075). Overall, this study demonstrated that the LWLR can be used as a valuable tool to predict the wave-induced scour around piles.     

The effects of uniform and nonuniform pile spacing variations on local scour at pile groups

Pile groups are frequently used to support bridge decks. Scour in the vicinity of piles is the main cause for the bridges failure. In this research, to address the effects of uniform and nonuniform pile spacing on the equilibrium scour depth, laboratory experiments were carried out under steady clear-water conditions. For this purpose, scour depth produced by pile group with various pile spacing and arrangement was investigated using a laboratory flume. Flume bed was covered by uniform sediments with a median size of 0.9?mm and 0.2?m thickness. Flow discharge and velocity as well as scour depth were recorded in each experiment and the data were analyzed. The results showed that the pile spacing influences the local scour depth and with increase in uniform and transverse (perpendicular to the flow) spacing, the maximum scour depth was reduced. The pile spacing variation in line with the flow has a minor effect on scour depth. In addition, the pile spacing perpendicular to the flow was with the most influences on scour depth. The results of this research can be used by engineers to optimize the design of bridges.     

Clear water scour around a finite array of cylinders

This experimental study presents clear-water scour and deposition patterns around hexagonal arrays of circular cylinders in steady flow conditions. Understanding the scour processes around such configurations could facilitate the design of several hydraulic and marine engineering structures, such as bridge piers and piles. The flow alteration caused by the examined porous obstacles depends on the solid volume fraction of the obstacles and on the angle of attack of the incoming flow, due to the limited number of cylinders constituting the array. Flume experiments with erodible bed were carried out for four array densities (solid volume fractions: 0.14, 0.20, 0.32 and 0.56) under three different orientations (regular, angled and staggered configurations). The scour/deposition characteristics were obtained by means of laser scanner and the results were compared to solid cylinders of equal circumambient diameter. Different angles of attack of the incoming flow lead to different blockage ratios, which have direct impact on the scour characteristics and deposition patterns. The arrays with the higher solid volume fraction generated scour/deposition patterns similar to solid cylinder, while in the arrays with the lower solid volume fractions, local scour around the individual small cylinders became evident. Finally, considering that the load bearing capacity of a pier basically depends on the area of its cross-section, a comparison of the maximum induced scour depth and volume by the cylinder arrays and the solid cylinder with equal solid cross-sectional area is presented, in order to introduce an alternative pier configuration that induces less scour. The results showed that the array of cylinders could generate 27% less scour volume and 22% less scour depth compared to its single solid cylinder counterpart.     

基于调和分析法与ANFIS系统的综合潮汐预报模型

港口沿岸地区以及河流入海口等地区的精确潮汐预报对于各种海洋工程作业有着非常重要的意义。潮汐水位的变化受到众多复杂因素的影响,而且这些复杂的因素往往有着较强的实变性和非线性。为了进一步提高沿岸港口码头等水域的潮汐水位的预测精度,本文提出了一种基于调和分析模型与自适应神经模糊推理系统相结合的模块化潮汐水位预测模型;并采用相关分析确定整个预测模型的输入维数;模块化将潮汐分解为两部分：由天体引潮力形成的天文潮部分和由各种天气以及环境因素引起非天文潮部分。其中调和分析法用于天文潮部分的预测,ANFIS用于预测具有较强非线性的非文潮部分。模块化综合了两种方法的优势,即调和分析法能够实现长期、稳定的天文潮预报,ANFIS能够以较高的精度实现潮汐非线性拟合与预测。模型使用ANFIS模型和调和分析模型分别对潮汐的非天文潮和天文潮部分进行仿真预测,然后将两部分的预测结果综合形成最终的潮汐预测值。此外,本文选用三种不同的模糊规则生成方法（grid partition （GP）,fuzzy c-means （FCM） and sub-clustering （SC））生成完整的ANFIS系统,并使用实测数据进行验证用以选取最优的ANFIS预测模型。最后将最优的ANFIS模型与调和分析模型相结合进行潮汐水位的最终预报。仿真实验选用Fort Pulaski潮汐观测站的实测潮汐值数据进行预报的仿真实验,仿真结果验证了该模型的可行性与有效性并取得了良好的效果,具有较高的预报精度。     

桩柱周围海底冲刷深度计算及动力参数的选取

通过６０年代以来研究的桩柱周围海底冲刷深度计算模式的对比分析表明,我国学者王汝凯等人提出的“普遍冲刷深度”、“局部冲刷深度”和“总冲刷深度”的计算模式在科研和生产实践中是可行的,能给设计和施工提供科学的和有价值的参数。各种冲刷深度的计算模式如下：普遍冲刷深度ｌｇ（Ｓｕ０／ｎ＋０．０５）＝－０．６６３＋０．３６４９ｌｇα（１）局部冲刷深度ｌｇ（Ｓｕ１／ｈ）＝－１．２９３５＋０．１９１７ｌｇβ（２）总     

NF-GMDH-Based self-organized systems to predict bridge pier scour depth under debris flow effects

Existence of debris structures inevitably ascends the rate of scour process around bridge piers and flow area not only lead into remarkable deviation of flow but also increase the velocity around bridge piers. A myriad of experimental and field studies to understand effective parameters on the scour depth with debris effects were conducted. To reach permissible values of the scour depth for the practical uses, relationships extracted in previous investigations suffer from lack of generalization for experimental data ranges. In this way, neuro-fuzzy group method of data handling (NF-GMDH)-based self-organized models is applied to evaluate the pier scour depth. In this study, NF-GMDH network is implemented using evolutionary algorithms listed particle swarm optimization (PSO), gravitational search algorithm (GSA), and genetic algorithm (GA). In all, 243 experimental datasets including a wide range of input and output parameters to develop the proposed models were compiled from various literature. The efficiency of NF-GMDH networks for training and testing stages was perused. NF-GMDH-PSO model provided the scour depth with more precise predictions (root mean squared error (RMSE)?=?0.388 and scatter index (SI)?=?0.343) in comparison with NF-GMDH-GA (RMSE?=?0.402 and SI?=?0.361) and NF-GMDH-GSA (RMSE?=?0.456 and SI?=?0.407) networks. In addition, blockage ratio (ΔA) was taken into account as the most sumptuous parameter with utmost level of effectiveness using the sensitivity analysis.     

Scour below submarine pipelines under irregular wave attack

Submarine pipelines are widely used coastal structures, and scour around them can influence their stability. In this study, scour around rigid submarine pipelines under normal-incidence irregular wave attack on horizontal and (1/10) sloping beaches is studied. This paper presents experimental results concerning scour under irregular wave attack. Multiple regression analysis is used to develop models to predict the scour depth under pipelines under the influence of irregular wave attack. The representative wave parameters that characterize the irregular sea state that causes the same scour depth as regular wave attack were determined.     

Estimation of scour around submarine pipelines with Artificial Neural Network

The process of scour around submarine pipelines laid on mobile beds is complicated due to physical processes arising from the triple interaction of waves/currents, beds and pipelines. This paper presents Artificial Neural Network (ANN) models for predicting the scour depth beneath submarine pipelines for different storm conditions. The storm conditions are considered for both regular and irregular wave attacks. The developed models use the Feed Forward Back Propagation (FFBP) Artificial Neural Network (ANN) technique. The training, validation and testing data are selected from appropriate experimental data collected in this study. Various estimation models were developed using both deep water wave parameters and local wave parameters. Alternative ANN models with different inputs and neuron numbers were evaluated by determining the best models using a trial and error approach. The estimation results show good agreement with measurements.