Reliability and sensitivity analysis of robust learning machine in prediction of bank profile morphology of threshold sand rivers

Abstract This paper investigates how to achieve an equilibrium or stable state in a channel by taking into account widening and variations in its cross-section geometry dimensions. The current proposal is carried out by using an artificial intelligence technique, a Feed-Forward Neural Network (FFNN), which is trained by Extreme Learning Machine (ELM) algorithm to predict the banks profile morphology or shape profile characteristics of banks after stability. Moreover, the performance of proposed FFNN-ELM model is compared with eight famous previous traditional models and also a designed Non-Linear Regression (NLR). The analyses have been validated using a large number of experimental studies at different flow discharge rates. The results of ELM in comparison with NLR and traditional methods shows that the FFNN-ELM model has the best performance with lower error index values of Root Mean Squared Error (RMSE) equal to 5.6E-5 and Mean Absolute Relative Error (MARE) equal to 0.016, compared to NLR (RMSE = 2.2E-4 and MARE = 0.1225) and the most accurate traditional model which is related to Cao and Knight’s [15] model (RMSE = 0.119 and MARE = 0.1095). Therefore, the FFNN-ELM model proposed in this paper maintains a suitable computational efficiency, as second-degree polynomial, for its performance compared to NLR and previous traditional models in estimating shape profile of stable channels banks. Furthermore, the uncertainty of proposed FFNN-ELM is calculated by Monte-Carlo based simulation method to assess the reliability of model to predict bank profile shape. The uncertainty result shows the less uncertainty of the FFNN-ELM model in shape simulation with the percentage of observed data bracketed by 95 percentage prediction uncertainties (95PPU) equal to 81.35% and d-factor value equal to 1.26 in test stage. Furthermore, the sensitivity of FFNN-ELM model relative to input parameters (flow discharge, Q, and lateral distance from the centreline of the channel, x,) represents that in nearly all discharges, the sensitivity value is negative, indicates that by increasing the value of x parameter, the predicted value for the vertical level of the bank’s by model decreases. Moreover, by increasing the flow discharge, the sensitivity of the FFNN-ELM model to the two effective parameters of Q and x on the estimation of vertical level of the stable channels bank is increased.

[1]  B. Eaton,et al.  Rational regime model of alluvial channel morphology and response , 2004 .

[2]  Gregorio G. Vigilar,et al.  Hydraulic Geometry of Threshold Channels , 1992 .

[3]  Van Rijn,et al.  Sediment transport; Part I, Bed load transport , 1984 .

[5]  Hossein Bonakdari,et al.  Flow Variables Prediction Using Experimental, Computational Fluid Dynamic and Artificial Neural Network Models in a Sharp Bend , 2016 .

[6]  Cajo J. F. ter Braak,et al.  Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation , 2008 .

[7]  H. Bonakdari,et al.  Modelling Stable Alluvial River Profiles Using Back Propagation-Based Multilayer Neural Networks , 2019, Advances in Intelligent Systems and Computing.

[8]  Miguel A. Mariño,et al.  Stable Width of an Alluvial Channel , 1997 .

[9]  Javad Sadeghi,et al.  Investigation of the Influences of Track Superstructure Parameters on Ballasted Railway Track Design , 2015 .

[10]  Baihai Zhang,et al.  Verification and predicting temperature and humidity in a solar greenhouse based on convex bidirectional extreme learning machine algorithm , 2017, Neurocomputing.

[11]  Amir Hossein Zaji,et al.  Simulation of open channel bend characteristics using computational fluid dynamics and artificial neural networks , 2015 .

[12]  J. Frick,et al.  Can end-users' flood management decision making be improved by information about forecast uncertainty? , 2011 .

[13]  Bing Wu,et al.  Fault diagnosis on slipper abrasion of axial piston pump based on Extreme Learning Machine , 2018, Measurement.

[14]  A. Tahershamsi,et al.  An evaluation model of artificial neural network to predict stable width in gravel bed rivers , 2012, International Journal of Environmental Science and Technology.

[15]  Soichi Nishiyama,et al.  Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool. , 2007, Journal of environmental management.

[16]  Hossein Bonakdari,et al.  A method based on the Tsallis entropy for characterizing threshold channel bank profiles , 2019, Physica A: Statistical Mechanics and its Applications.

[17]  Amir Hossein Zaji,et al.  GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs , 2015 .

[18]  Saumen Maiti,et al.  Short term memory efficient pore pressure prediction via Bayesian neural networks at Bering Sea slope of IODP expedition 323 , 2019, Measurement.

[19]  Bahram Gharabaghi,et al.  Development of robust evolutionary polynomial regression network in the estimation of stable alluvial channel dimensions , 2020 .

[20]  Rommel M. Barbosa,et al.  Geographical recognition of Syrah wines by combining feature selection with Extreme Learning Machine , 2018 .

[21]  Léon Bottou,et al.  Large-Scale Machine Learning with Stochastic Gradient Descent , 2010, COMPSTAT.

[22]  Bahram Gharabaghi,et al.  Reliable method of determining stable threshold channel shape using experimental and gene expression programming techniques , 2019, Neural Computing and Applications.

[23]  Babak Nadjar Araabi,et al.  Uncertainty analysis of developed ANN and ANFIS models in prediction of carbon monoxide daily concentration , 2010 .

[24]  W. Ta,et al.  Channel deposition induced by bank erosion in response to decreased flows in the sand-banked reach of the upstream Yellow River , 2013 .

[25]  M. Ghorbani,et al.  A comparative study of artificial neural network (MLP, RBF) and support vector machine models for river flow prediction , 2016, Environmental Earth Sciences.

[26]  S. Cao,et al.  Entropy-based design approach of threshold alluvial channels , 1997 .

[27]  Mansour Talebizadeh,et al.  Uncertainty analysis for the forecast of lake level fluctuations using ensembles of ANN and ANFIS models , 2011, Expert Syst. Appl..

[28]  Bahram Gharabaghi,et al.  Uncertainty analysis of shear stress estimation in circular channels by Tsallis entropy , 2018, Physica A: Statistical Mechanics and its Applications.

[29]  Basant Yadav,et al.  A hybrid wavelet-support vector machine model for prediction of Lake water level fluctuations using hydro-meteorological data , 2017 .

[30]  Hossein Bonakdari,et al.  Comparative analysis of GMDH neural network based on genetic algorithm and particle swarm optimization in stable channel design , 2017, Appl. Math. Comput..

[31]  Bahram Gharabaghi,et al.  Predicting Breaking Wave Conditions Using Gene Expression Programming , 2017 .

[32]  S. Cao,et al.  Design for Hydraulic Geometry of Alluvial Channels , 1998 .

[33]  Shahaboddin Shamshirband,et al.  Extreme learning machine assessment for estimating sediment transport in open channels , 2016, Engineering with Computers.

[34]  Pijush Samui,et al.  Predicting stable alluvial channel profiles using emotional artificial neural networks , 2019, Appl. Soft Comput..

[35]  J. Pelletier,et al.  Self‐Affine Fractal Spatial and Temporal Variability of the San Pedro River, Southern Arizona , 2019, Journal of Geophysical Research: Earth Surface.

[37]  Amir Hossein Zaji,et al.  New radial basis function network method based on decision trees to predict flow variables in a curved channel , 2017, Neural Computing and Applications.

[38]  Narasimhan Sundararajan,et al.  Fully complex extreme learning machine , 2005, Neurocomputing.

[39]  Mahmud Güngör,et al.  Generalized Regression Neural Networks and Feed Forward Neural Networks for prediction of scour depth around bridge piers , 2009, Adv. Eng. Softw..

[40]  Erdem Erkan,et al.  A study on the effect of psychophysiological signal features on classification methods , 2017 .

[41]  D. W. Knight,et al.  GEOMETRY OF SELF-FORMED STRAIGHT THRESHOLD CHANNELS IN UNIFORM MATERIAL. , 1998 .

[42]  Guang-Bin Huang,et al.  Extreme learning machine: a new learning scheme of feedforward neural networks , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[43]  Peter M. Allen,et al.  DOWNSTREAM CHANNEL GEOMETRY FOR USE IN PLANNING‐LEVEL MODELS , 1994 .

[44]  Lyman S. Willardson,et al.  Parabolic Canal Design and Analysis , 1984 .

[45]  B. Buvaneswari,et al.  High performance hybrid cognitive framework for bio-facial signal fusion processing for the disease diagnosis , 2019, Measurement.

[46]  Hossein Bonakdari,et al.  A Highly Efficient Gene Expression Programming Model for Predicting the Discharge Coefficient in a Side Weir along a Trapezoidal Canal , 2017 .

[47]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.

[48]  Subhasish Dey.  Bank profile of threshold channels : A simplified approach , 2001 .

[49]  K. Cohen,et al.  Spatial and temporal variations in river terrace formation, preservation, and morphology in the Lower Meuse Valley, The Netherlands , 2018, Quaternary Research.

[50]  Amir Hossein Zaji,et al.  A comparison of artificial intelligence-based classification techniques in predicting flow variables in sharp curved channels , 2019, Engineering with Computers.

[51]  Hossein Bonakdari,et al.  Sediment transport modeling in rigid boundary open channels using generalize structure of group method of data handling , 2019, Journal of Hydrology.

[52]  Bahram Gharabaghi,et al.  Assessment of geomorphological bank evolution of the alluvial threshold rivers based on entropy concept parameters , 2019, Hydrological Sciences Journal.

[53]  Yanqing Zhang,et al.  A genetic algorithm-based method for feature subset selection , 2008, Soft Comput..

[54]  Bahram Gharabaghi,et al.  Uncertainty analysis of intelligent model of hybrid genetic algorithm and particle swarm optimization with ANFIS to predict threshold bank profile shape based on digital laser approach sensing , 2018, Measurement.

[55]  J Stebbings,et al.  THE SHAPES OF SELF-FORMED MODEL ALLUVIAL CHANNELS. , 1963 .

[56]  Guang-Bin Huang,et al.  Convex incremental extreme learning machine , 2007, Neurocomputing.

[57]  Zhu Mao,et al.  Uncertainty quantification framework for wavelet transformation of noise-contaminated signals , 2019, Measurement.

[58]  Amir Hossein Zaji,et al.  Design of modified structure multi-layer perceptron networks based on decision trees for the prediction of flow parameters in 90° open-channel bends , 2016 .

[59]  R. Noori,et al.  Uncertainty analysis of streamflow drought forecast using artificial neural networks and Monte‐Carlo simulation , 2014 .

[60]  Bahram Gharabaghi,et al.  Development of more accurate discharge coefficient prediction equations for rectangular side weirs using adaptive neuro-fuzzy inference system and generalized group method of data handling , 2018 .

[61]  R. Millar,et al.  Stable Width and Depth of Gravel-Bed Rivers with Cohesive Banks , 1998 .

[62]  Ali Jamali,et al.  Analyzing bank profile shape of alluvial stable channels using robust optimization and evolutionary ANFIS methods , 2019, Applied Water Science.

[63]  Hossein Bonakdari,et al.  Developing an expert group method of data handling system for predicting the geometry of a stable channel with a gravel bed , 2017 .

[64]  G. Parker.  Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river , 1978, Journal of Fluid Mechanics.

[65]  R. Derose,et al.  Variability and uncertainty in reach bankfull hydraulic geometry , 2008 .

[66]  Zhiqiang Deng,et al.  How Reliable Are ANN, ANFIS, and SVM Techniques for Predicting Longitudinal Dispersion Coefficient in Natural Rivers? , 2016 .

[67]  Shahaboddin Shamshirband,et al.  A combined support vector machine-wavelet transform model for prediction of sediment transport in sewer , 2016 .

[68]  Bahram Gharabaghi,et al.  A methodological approach of predicting threshold channel bank profile by multi-objective evolutionary optimization of ANFIS , 2018 .

[69]  Yiming Huang,et al.  Spectral diagnosis and defects prediction based on ELM during the GTAW of Al alloys , 2019, Measurement.

[70]  Amir Hossein Zaji,et al.  Improving the performance of multi-layer perceptron and radial basis function models with a decision tree model to predict flow variables in a sharp 90° bend , 2016, Appl. Soft Comput..

[71]  Gregorio G. Vigilar,et al.  Stable Channels with Mobile Bed: Formulation and Numerical Solution , 1997 .

[72]  Hossein Bonakdari,et al.  Design of an adaptive neuro-fuzzy computing technique for predicting flow variables in a 90° sharp bend , 2017 .

[73]  James E. Pizzuto,et al.  Numerical simulation of gravel river widening , 1990 .

[74]  Ahmed M. A. Sattar,et al.  Prediction of Organic Micropollutant Removal in Soil Aquifer Treatment System Using GEP , 2016 .

[75]  S. Operto,et al.  Fast full waveform inversion with source encoding and second-order optimization methods , 2015 .

[76]  Hossein Bonakdari,et al.  Experimental and Numerical Study on Velocity Fields and Water Surface Profile in a Strongly-Curved 90° Open Channel Bend , 2014 .

[77]  C. Thorne,et al.  Stable Channels with Mobile Gravel Beds , 1986 .

[78]  Benoît Frénay,et al.  Parameter-insensitive kernel in extreme learning for non-linear support vector regression , 2011, Neurocomputing.

[79]  Binu P. Chacko,et al.  Handwritten character recognition using wavelet energy and extreme learning machine , 2012, Int. J. Mach. Learn. Cybern..

[80]  O. Kisi,et al.  Predicting the geometry of regime rivers using M5 model tree, multivariate adaptive regression splines and least square support vector regression methods , 2018, International Journal of River Basin Management.

[81]  Hossein Bonakdari,et al.  Enhanced formulation of the probability principle based on maximum entropy to design the bank profile of channels in geomorphic threshold , 2019, Stochastic Environmental Research and Risk Assessment.

[82]  Anne-Johan Annema,et al.  Precision requirements for single-layer feedforward neural networks , 1994, Proceedings of the Fourth International Conference on Microelectronics for Neural Networks and Fuzzy Systems.

[83]  C. Jebaraj,et al.  Injection molding process optimization of a bi-aspheric lens using hybrid artificial neural networks (ANNs) and particle swarm optimization (PSO) , 2019, Measurement.

[84]  Brian P. Bledsoe,et al.  WIDTH OF STREAMS AND RIVERS IN RESPONSE TO VEGETATION, BANK MATERIAL, AND OTHER FACTORS 1 , 2004 .

[85]  P. Diplas.  Characteristics of Self‐Formed Straight Channels , 1990 .

[86]  Gregorio G. Vigilar,et al.  Stable Channels with Mobile Bed: Model Verification and Graphical Solution , 1998 .

[87]  Claudionor Ribeiro da Silva,et al.  Soil prediction using artificial neural networks and topographic attributes , 2013 .

[88]  H. Md. Azamathulla,et al.  Alternative neural networks to estimate the scour below spillways , 2008, Adv. Eng. Softw..

[89]  Bahram Gharabaghi,et al.  Closure to “An integrated framework of extreme learning machines for predicting scour at pile groups in clear water condition” by: I. Ebtehaj, H. Bonakdari, F. Moradi, B. Gharabaghi, Z. Sheikh Khozani , 2019, Coastal Engineering.

[90]  S. Darby,et al.  Computer program for stability analysis of steep, cohesive riverbanks. , 2000 .

[91]  K. Abbaspour,et al.  Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT , 2007 .

[92]  Saeed Reza Khodashenas.  Threshold gravel channels bank profile: a comparison among 13 models , 2016 .

[93]  Bahram Gharabaghi,et al.  An integrated framework of Extreme Learning Machines for predicting scour at pile groups in clear water condition , 2018 .

[94]  Guang-Bin Huang,et al.  Trends in extreme learning machines: A review , 2015, Neural Networks.

[95]  Basant Yadav,et al.  Discharge forecasting using an Online Sequential Extreme Learning Machine (OS-ELM) model: A case study in Neckar River, Germany , 2016 .

[96]  Syunsuke Ikeda,et al.  Self-Formed Straight Channels in Sandy Beds , 1981 .

[97]  Hossein Bonakdari,et al.  Evaluation of artificial neural network model and statistical analysis relationships to predict the stable channel width , 2016 .

[98]  G. Parker,et al.  Stable width and depth of straight gravel rivers with heterogeneous bed materials , 1988 .

[99]  A. Hasheminezhad,et al.  Seismic response of shallow foundations over liquefiable soils improved by deep soil mixing columns , 2019, Computers and Geotechnics.

[100]  Mohammad Ali Ghorbani,et al.  Uncertainty assessment of the multilayer perceptron (MLP) neural network model with implementation of the novel hybrid MLP-FFA method for prediction of biochemical oxygen demand and dissolved oxygen: a case study of Langat River , 2017, Environmental Earth Sciences.