Intelligent flow friction estimation

Nowadays, the Colebrook equation is used as a mostly accepted relation for the calculation of fluid flow friction factor. However, the Colebrook equation is implicit with respect to the friction factor (). In the present study, a noniterative approach using Artificial Neural Network (ANN) was developed to calculate the friction factor. To configure the ANN model, the input parameters of the Reynolds Number (Re) and the relative roughness of pipe () were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output layers with, 2, 50, and 1 neurons, respectively. This configuration was capable of predicting the values of friction factor in the Colebrook equation for any given values of the Reynolds number (Re) and the relative roughness () ranging between 5000 and 108 and between 10−7 and 0.1, respectively. The proposed ANN demonstrates the relative error up to 0.07% which had the high accuracy compared with the vast majority of the precise explicit approximations of the Colebrook equation

Accurate solutions of Colebrook-White’s friction factor formulae

Estimations of friction factor (Ff) in pipeline systems and fluid transport are essential ingredients in engineering fields and processes. In this paper explicit friction factor formulae (Fff) were proposed and evaluated with an aim of developing error free Fff. General Fff that relate Ff, Reynolds number (Re) and relative roughness (Rr) were proposed. Colebrook – White’s formula was used to compute different Ff for Re between 4 x 103 and 1.704 x 108, and Rr between 1.0 x 10-7 and 0.052 using Microsoft Excel Solver to fix the Fff. The fixed Fff were used to compute Ff for Re between 4 x 103 and 1.704 x 108 and Rr between 1.0 x 10-7 and 0.052. Accuracy of the fixed Fff was evaluated using relative error; model of selection (MSC) and Akaike Information Criterion (AIC) and compared with the previous Fff using Colebrook–White’s Ff as the reference. The study revealed that Ff estimated using the fixed Fff were the same as Ff estimated using Colebrook – White’s Fff. The fixed Fff provided the lowest relative error of (0.02 %; 0.06 % and 0.04 % ), the highest MSC (14.03; 12.42 and 13.07); and the lowest AIC (-73006; -64580 and -67982). The study concluded that modeling of Fff using numerical methods and Microsoft Excel Solver are better tools for estimating Ff in pipeline flow problems.Keywords: Friction factor, MSC; AIC; Reynolds number; Engineering Field; pipe flow, statistical method

Prediction of Water Level Fluctuations of Chahnimeh Reservoirs in Zabol Using ANN, ANFIS and Cuckoo Optimization Algorithm

Forecasting changes in level of the reservoir are important in Construction, design and estimate the volume of reservoirs and also in managing of supplying water. In this study, we have used different models such as Artificial Neutral Network (ANN), Adaptive Neuro Fuzzy Inference System (ANFIS) and Cuckoo Optimization Algorithm (COA) for forecasting fluctuations in water level of Chahnimeh reservoirs in south-east of Iran. For this purpose, we applied three most important variables in water levels of the reservoir including evaporation, wind speed and daily temperature average to prepare the best entering variables for models. In addition, none accuracy of error in estimation of hydrologic variables and none assurance of exiting models are the result of their sensitivity to the educational complex for teaching of models and also preliminary decoration before beginning general education has been estimated. After comparing exiting and confidence interval of the ANN and ANFIS has been found that the result of ANFIS model is better described than other model because it was more accurate and does have lesser assurance

Some explicit formulations of Colebrook-White friction factor considering accuracy vs. computational speed

The Colebrook–White formulation of the friction factor is implicit and requires some iterations to be solved given a correct initial search value and a target accuracy. Some new explicit formulations to efficiently calculate the Colebrook–White friction factor are presented herein. The aim of this investigation is twofold: (i) to preserve the accuracy of estimates while (ii) reducing the computational burden (i.e. speed). On the one hand, the computational effectiveness is important when the intensive calculation of the friction factor (e.g. large-size water distribution networks (WDN) in optimization problems, flooding software, etc.) is required together with its derivative. On the other hand, the accuracy of the developing formula should be realistically chosen considering the remaining uncertainties surrounding the model where the friction factor is used. In the following, three strategies for friction factor mapping are proposed which were achieved by using the Evolutionary Polynomial Regression (EPR). The result is the encapsulation of some pieces of the friction factor implicit formulae within pseudo-polynomial structures

Uncertainty quantification of granular computing‑neural network model for prediction of pollutant longitudinal dispersion coefficient in aquatic streams

Discharge of pollution loads into natural water systems remains a global challenge that threatens water and food supply, as well as endangering ecosystem services. Natural rehabilitation of contaminated streams is mainly influenced by the longitudinal dispersion coefficient, or the rate of longitudinal dispersion (Dx), a key parameter with large spatiotemporal fluctuations that characterizes pollution transport. The large uncertainty in estimation of Dx in streams limits the water quality assessment in natural streams and design of water quality enhancement strategies. This study develops an artificial intelligence-based predictive model, coupling granular computing and neural network models (GrC-ANN) to provide robust estimation of Dx and its uncertainty for a range of flow-geometric conditions with high spatiotemporal variability. Uncertainty analysis of Dx estimated from the proposed GrC-ANN model was performed by alteration of the training data used to tune the model. Modified bootstrap method was employed to generate different training patterns through resampling from a global database of tracer experiments in streams with 503 datapoints. Comparison between the Dx values estimated by GrC-ANN to those determined from tracer measurements shows the appropriateness and robustness of the proposed method in determining the rate of longitudinal dispersion. The GrC-ANN model with the narrowest bandwidth of estimated uncertainty (bandwidth-factor = 0.56) that brackets the highest percentage of true Dx data (i.e., 100%) is the best model to compute Dx in streams. Considering the significant inherent uncertainty reported in the previous Dx models, the GrC-ANN model developed in this study is shown to have a robust performance for evaluating pollutant mixing (Dx) in turbulent environmental flow systems

Prediction of flow and its resistance in compound open channel

Flooding situation in rivers is a complex phenomenon and affects the livelihood and economic condition of the region. This complex condition has long been identified and intensive research work has been carried out to find out its remedial solution. During flood, river overtops its banks and spreads to flood plains, called compound channel. It has been observed that the flow velocity in flood plain subsection is slower than the velocity of its course. Due to this difference in velocities between main channel and flood plain, a large shear layer produces.This large shear layer retains complex turbulent structures of different scales within it. These turbulent structures produce extra resistance to flow, which induces uncertainty in predictions of flow and its resistance. It has been also observed that, numerical turbulence models can be used to find the point to point information. Hence the analysis of turbulent structures is prevalent in this situation. Earlier, researchers have adopted various numerical, analytical and empirical models to analyze turbulent flow in compound channels, generally for low development length. Therefore, in this study an effort is made to analyze the turbulent structure by Large Eddy Simulation method (LES) to predict the flow and its resistance involved in it. The LES is carried out taking sufficient development length so that uniform turbulent flow is developed. The development length is incorporated in the computational domain. However, it is a fact that numerical simulation of compound channels with different hydraulic conditions are computationally very expensive and arduous. Therefore,this analysis is further done by using adaptive approaches such as Artificial Neural Network (ANN) and Artificial Neuro Fuzzy Inference System (ANFIS).These models are used to predict flow and its resistanceof a compound channel for different hydraulic conditions.All the proposed models are compared well with the standard modes previously developed.The proposed models are found to give better results compared to other models when applied to globa data sets

Water temperature prediction in a subtropical subalpine lake using soft computing techniques

Lake water temperature is one of the key parameters in determining the ecological conditions within a lake, as it influences both chemical and biological processes. Therefore, accurate prediction of water temperature is crucially important for lake management. In this paper, the performance of soft computing techniques including gene expression programming (GEP), which is a variant of genetic programming (GP), adaptive neuro fuzzy inference system (ANFIS) and artificial neural networks (ANNs) to predict hourly water temperature at a buoy station in the Yuan-Yang Lake (YYL) in north-central Taiwan at various measured depths was evaluated. To evaluate the performance of the soft computing techniques, three different statistical indicators were used, including the root mean squared error (RMSE), the mean absolute error (MAE), and the coefficient of correlation (R). Results showed that the GEP had the best performances among other studied methods in the prediction of hourly water temperature at 0, 2 and 3 meter depths below water surface, but there was a different trend in the 1 meter depth below water surface. In this depth, the ANN had better accuracy than the GEP and ANFIS. Despite the error (RMSE value) is smaller in ANN than GEP, there is an upper bound in scatter plot of ANN that imposes a constant value, which is not suitable for predictive purposes. As a conclusion, results from the current study demonstrated that GEP provided moderately reasonable trends for the prediction of hourly water temperature in different depths. ResumenLa temperatura del agua es uno de los parámetros básicos para determinar las condiciones ecológicas de un lago, ya que está influenciada por procesos químicos y biológicos. Además, la exactitud en la predicción de la temperatura del agua es esencial para el manejo del lago. En este artículo se evalúa el desempeño de técnicas de soft computing como la Programación de Expresiones de Genes (PEG), que es una variante de la Programación Genética (PG), el Sistema Neuro-fuzzy de Inferencia Adaptativa (Anfis, en inglés) y las Redes Neuronales Artificiales (RNA) para predecir la temperatura del agua en diferentes niveles de una estación flotante del lago Yuan-Yang (YYL), en el centro-norte de Taiwán. Se utilizaron tres indicadores estadísticos, el Error Cuadrático Medio (ECM), el Error Absoluto Medio (MAE, en inglés) y el Coeficiente de Correlación (R) para evaluar el desempeño de las técnicas de computación. Los resultados muestran que la PEG es más exacta en la predicción de la temperatura del agua entre 0,2 y 3 metros de profundidad. Sin embargo, se evidencia una tendencia diferente a partir del metro de profundidad. A esta distancia de la superficie, las RNA son más exactas que la PEG y el Anfis. Los resultados de este estudio probaron claramente la usabilidad del PEG y las RNA en la predicción de la temperatura del agua a diferentes profundidades

Three-dimensional hydrodynamic models coupled with GIS-based neuro-fuzzy classification for assessing environmental vulnerability of marine cage aquaculture

There is considerable opportunity to develop new modelling techniques within a Geographic Information Systems (GIS) framework for the development of sustainable marine cage culture. However, the spatial data sets are often uncertain and incomplete, therefore new spatial models employing “soft computing” methods such as fuzzy logic may be more suitable. The aim of this study is to develop a model using Neuro-fuzzy techniques in a 3D GIS (Arc View 3.2) to predict coastal environmental vulnerability for Atlantic salmon cage aquaculture. A 3D hydrodynamic model (3DMOHID) coupled to a particle-tracking model is applied to study the circulation patterns, dispersion processes and residence time in Mulroy Bay, Co. Donegal Ireland, an Irish fjard (shallow fjordic system), an area of restricted exchange, geometrically complicated with important aquaculture activities. The hydrodynamic model was calibrated and validated by comparison with sea surface and water flow measurements. The model provided spatial and temporal information on circulation, renewal time, helping to determine the influence of winds on circulation patterns and in particular the assessment of the hydrographic conditions with a strong influence on the management of fish cage culture. The particle-tracking model was used to study the transport and flushing processes. Instantaneous massive releases of particles from key boxes are modelled to analyse the ocean-fjord exchange characteristics and, by emulating discharge from finfish cages, to show the behaviour of waste in terms of water circulation and water exchange. In this study the results from the hydrodynamic model have been incorporated into GIS to provide an easy-to-use graphical user interface for 2D (maps), 3D and temporal visualization (animations), for interrogation of results. v Data on the physical environment and aquaculture suitability were derived from a 3- dimensional hydrodynamic model and GIS for incorporation into the final model framework and included mean and maximum current velocities, current flow quiescence time, water column stratification, sediment granulometry, particulate waste dispersion distance, oxygen depletion, water depth, coastal protection zones, and slope. The Neuro-fuzzy classification model NEFCLASS–J, was used to develop learning algorithms to create the structure (rule base) and the parameters (fuzzy sets) of a fuzzy classifier from a set of classified training data. A total of 42 training sites were sampled using stratified random sampling from the GIS raster data layers, and the vulnerability categories for each were manually classified into four categories based on the opinions of experts with field experience and specific knowledge of the environmental problems investigated. The final products, GIS/based Neuro Fuzzy maps were achieved by combining modeled and real environmental parameters relevant to marine fin fish Aquaculture. Environmental vulnerability models, based on Neuro-fuzzy techniques, showed sensitivity to the membership shapes of the fuzzy sets, the nature of the weightings applied to the model rules, and validation techniques used during the learning and validation process. The accuracy of the final classifier selected was R=85.71%, (estimated error value of ±16.5% from Cross Validation, N=10) with a Kappa coefficient of agreement of 81%. Unclassified cells in the whole spatial domain (of 1623 GIS cells) ranged from 0% to 24.18 %. A statistical comparison between vulnerability scores and a significant product of aquaculture waste (nitrogen concentrations in sediment under the salmon cages) showed that the final model gave a good correlation between predicted environmental vi vulnerability and sediment nitrogen levels, highlighting a number of areas with variable sensitivity to aquaculture. Further evaluation and analysis of the quality of the classification was achieved and the applicability of separability indexes was also studied. The inter-class separability estimations were performed on two different training data sets to assess the difficulty of the class separation problem under investigation. The Neuro-fuzzy classifier for a supervised and hard classification of coastal environmental vulnerability has demonstrated an ability to derive an accurate and reliable classification into areas of different levels of environmental vulnerability using a minimal number of training sets. The output will be an environmental spatial model for application in coastal areas intended to facilitate policy decision and to allow input into wider ranging spatial modelling projects, such as coastal zone management systems and effective environmental management of fish cage aquaculture

Effect of Channel Boundary Conditions in Predicting Hydraulic Jump Characteristics using an ANFIS-Based Approach

Hydraulic jump is a phenomenon which is used to dissipate the kinetic energy of the flow and prevent scour below overflow spillways, chutes and sluices. This paper applies adaptive neuro-fuzzy inference system (ANFIS) as a Meta model approach to estimate hydraulic jump characteristics in channels with different bed conditions (i.e. channels with different shapes and appurtenances). In hydraulic jump characteristics modeling, different input combinations were developed and tested using 1700 experimental data. The obtained results indicated that the applied method has high capability in modeling hydraulic jump characteristics. It was observed that the developed models for expanding channel with a block performed more successful than other channels. For rectangular channels, it was found that the basin with rough bed led to better predictions compared to the basin with a step. In the prediction of jump length, the superior performance was obtained for the model with input combinations of Froude number and the relative height of jump. From the sensitivity analysis, it was induced that, Fr1 (upstream Froude number) is the most significant parameter in modeling process. Also comparison between ANFIS and semi-empirical equations indicated the great performance of the ANFIS