Revisiting the Estimation of Colebrook Friction Factor: A Comparison between Artificial Intelligence Models and C-W based Explicit Equations

Niazkar, Majid

doi:10.1007/s12205-019-2217-1

Cited by 31 publications

(35 citation statements)

References 26 publications

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“…Instead of transcendental functions (logarithms, non-integer power) that are used in the classical approach, in this communication, we replace the logarithm with its Padé approximant and a simple rational function, which was found using artificial intelligence (symbolic regression), in order to minimize the error. Although the new rational approximation may seem unintelligible to human eyes, results of 2 million input pairs found by the quasi-Monte Carlo method [38] confirm that the relative error of this new approximation does not exceed 0.866%, which is acceptable for the empirical Colebrook law [44] (trade-off between model complexity and accuracy [45,46]). Consequently, numerical experiments on 2 million of quasi-Monte Carlo pairs indicates that the rational approximation presented here provides for Colebrook's flow friction model a useful combination of Padé approximants and artificial intelligence (symbolic regression).…”

Section: Discussionmentioning

confidence: 99%

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Praks

Brkić

2019

Mathematics

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The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Padé approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function.

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Section: Discussionmentioning

confidence: 99%

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Praks

Brkić

2019

Mathematics

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“…ANN is a well-documented AI model inspired by the framework of biological human neurons. It has been successfully applied to numerous problems in different fields [ 19 – 21 ]. In essence, it is a powerful tool for finding a relationship between input and output data.…”

Section: Methodsmentioning

confidence: 99%

Application of artificial neural networks to predict the COVID-19 outbreak

Niazkar

2020

glob health res policy

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Background Millions of people have been infected worldwide in the COVID-19 pandemic. In this study, we aim to propose fourteen prediction models based on artificial neural networks (ANN) to predict the COVID-19 outbreak for policy makers. Methods The ANN-based models were utilized to estimate the confirmed cases of COVID-19 in China, Japan, Singapore, Iran, Italy, South Africa and United States of America. These models exploit historical records of confirmed cases, while their main difference is the number of days that they assume to have impact on the estimation process. The COVID-19 data were divided into a train part and a test part. The former was used to train the ANN models, while the latter was utilized to compare the purposes. The data analysis shows not only significant fluctuations in the daily confirmed cases but also different ranges of total confirmed cases observed in the time interval considered. Results Based on the obtained results, the ANN-based model that takes into account the previous 14 days outperforms the other ones. This comparison reveals the importance of considering the maximum incubation period in predicting the COVID-19 outbreak. Comparing the ranges of determination coefficients indicates that the estimated results for Italy are the best one. Moreover, the predicted results for Iran achieved the ranges of [0.09, 0.15] and [0.21, 0.36] for the mean absolute relative errors and normalized root mean square errors, respectively, which were the best ranges obtained for these criteria among different countries. Conclusion Based on the achieved results, the ANN-based model that takes into account the previous fourteen days for prediction is suggested to predict daily confirmed cases, particularly in countries that have experienced the first peak of the COVID-19 outbreak. This study has not only proved the applicability of ANN-based model for prediction of the COVID-19 outbreak, but also showed that considering incubation period of SARS-COV-2 in prediction models may generate more accurate estimations.

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“…Further details on GP may be found in Koza [35] for interested readers. Discipulus [36] software, which has been used for implementing GP in many studies [23,[26][27], was applied in this research.…”

Section: Genetic Programmingmentioning

confidence: 99%

“…Later, this method has been implemented as one of bridge subroutine approaches in the ISIS package program [20]. Although explicit equations have been commonly used for estimating many variables in various water resources applications [21][22][23][24][25], they should be exploited only when their background assumption(s) and valid ranges are applicable. In this regard, the limitations of the available explicit equations for predicting backwater depth include (1) they were not developed by powerful algorithms and (2) their accuracy is not enough to be applied in professional software for analyzing rivers and designing of hydraulic structures.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, even though several AI models like ANN have been applied to estimate afflux for arched bridges, Genetic programming, which has been successfully used for solving other water-related problems [23,[26][27], has not utilized for this purpose. Since better bridge backwater estimation can yield to more sustainable and reliable schemes for bridge safety during flood events, not only developing new accuracy-improved explicit equations using powerful optimization algorithms but also applying other powerful data mining approaches are still required.…”

Section: Introductionmentioning

confidence: 99%

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Bridge backwater estimation: A Comparison between artificial intelligence models and explicit equations

2020

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Estimation of bridge backwater has been one of practical challenges in hydraulic engineering for decades. In this study, Genetic Programming (GP) has been applied for estimating bridge backwater for the first time based on the conducted literature review. Furthermore, two new explicit equations are developed for predicting bridge afflux using Genetic Algorithm (GA) and hybrid MHBMO-GRG algorithm. The performances of these models are compared with Artificial Neural Network (ANN) and several explicit equations available in the literature considering both laboratory and field data. Based on five considered performance evaluation criteria, the two new explicit equations outperform the ones available in the literature. Furthermore, GP and ANN achieve the 2 best results in favor of four out of five considered criteria for train and test data, respectively. To be more specific, ANN improves the MSE and R 2 values of the explicit equation developed using GA by 44% and 12% for the test data while GP enhances the corresponding values by 62% and 9% for the train data. Finally, the results demonstrate that not only artificial intelligence models considerably improve bridge afflux estimation than the explicit equations but also the suggested equations significantly improve the accuracy of the available explicit ones.

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Revisiting the Estimation of Colebrook Friction Factor: A Comparison between Artificial Intelligence Models and C-W based Explicit Equations

Cited by 31 publications

References 26 publications

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Application of artificial neural networks to predict the COVID-19 outbreak

Bridge backwater estimation: A Comparison between artificial intelligence models and explicit equations

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