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A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense

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ENGINEERING WITH COMPUTERS 2023年第1期39卷 505-515页

作者： Shloof, A. M. Senu, N. Ahmadian, A. Pakdaman, M. Salahshour, S. Univ Putra Malaysia Dept Math & Stat Serdang Selangor Malaysia Univ Putra Malaysia Inst Math Res Serdang Selangor Malaysia Al Zintan Univ Fac Sci Dept Math Alzintan Libya Mediterranea Univ Reggio Calabria Dept Law Econ & Human Sci Reggio Di Calabria Italy Near East Univ Dept Math Mersin 10 Nicosia Turkey Atmospher Sci & Meteorol Res Ctr ASMERC Climatol Res Inst CRI Mashhad Razavi Khorasan Iran Bahcesehir Univ Fac Engn & Nat Sci Istanbul Turkey

This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help explain a variety of real-world physical problems. The technique implemented in this paper converts the original differential equation into a minimization problem using a suggested truncated power series of the solution function. Next, answer to the problem is obtained via computing the parameters with highly precise neural network model. We can get a good approximate solution of FFDEs by combining the initial conditions with the ANNs performance. Examples are provided to portray the efficiency and applicability of this method. Comparison with similar existing approaches are also conducted to demonstrate the accuracy of the proposed approach.

关键词： Artificial neural network Fractal-fractional differential equations back-propagation learning algorithm New generalized Caputo fractal-fractional derivative

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A highly accurate artificial neural networks scheme for solving higher multi-order fractal-fractional differential equations based on generalized Caputo derivative

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2023年第19期124卷 4371-4404页

作者： Shloof, A. M. Ahmadian, A. Senu, N. Salahshour, Soheil Ibrahim, S. N. I. Pakdaman, M. Univ Putra Malaysia Dept Math & Stat Serdang Selangor Malaysia Al Zintan Univ Fac Sci Dept Math Zintan Libya Cent Queensland Univ Coll Engn & Aviat Sch Engn & Technol Rockhampton Australia Lebanese Amer Univ Dept Comp Sci & Math Beirut Lebanon Near East Univ Dept Math Nicosia Mersin Turkiye Univ Putra Malaysia Inst Math Res Serdang Selangor Malaysia Bahcesehir Univ Fac Engn & Nat Sci Istanbul Turkiye Atmospher Sci & Meteorol Res Ctr ASMERC Climatol Res Inst Mashhad Iran

Artificial neural networks have great potential for learning and stability in the face of tiny input data changes. As a result, artificial intelligence techniques and modeling tools have a growing variety of applications. To estimate a solution for fractal-fractional differential equations (FFDEs) of high-order linear (HOL) with variable coefficients, an iterative methodology based on a mix of a power series method and a neural network approach was applied in this study. In the algorithm's equation, an appropriate truncated series of the solution functions was replaced. To tackle the issue, this study uses a series expansion of an unidentified function, where this function is approximated using a neural architecture. Some examples were presented to illustrate the efficiency and usefulness of this technique to prove the concept's applicability. The proposed methodology was found to be very accurate when compared to other available traditional procedures. To determine the approximate solution to FFDEs-HOL, the suggested technique is simple, highly efficient, and resilient.

关键词： artificial neural network back-propagation learning algorithm generalized Caputo fractal-fractional derivative higher order fractal-fractional differential equations power series

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A new artificial neural network structure for solving high-order linear fractional differential equations

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2018年第3期95卷 528-539页

作者： Rostami, F. Jafarian, A. Islamic Azad Univ Dept Math Urmia Branch Orumiyeh Iran

Artificial neural networks afford great potential in learning and stability against small perturbations of input data. Using artificial intelligence techniques and modelling tools offers an ever-greater number of practical applications. In the present study, an iterative algorithm, which was based on the combination of a power series method and a neural network approach, was used to approximate a solution for high-order linear and ordinary differential equations. First, a suitable truncated series of the solution functions were substituted into the algorithm's equation. The problem considered here had a solution as a series expansion of an unknown function, and the proper implementation of an appropriate neural architecture led to an estimate of the unknown series coefficients. To prove the applicability of the concept, some illustrative examples were provided to demonstrate the precision and effectiveness of this method. Comparing the proposed methodology with other available traditional techniques showed that the present approach was highly accurate.

关键词： High-order fractional differential equation power-series method artificial neural network criterion function back-propagation learning algorithm

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A new method based on artificial neural networks for solving general nonlinear systems

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INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2018年第3期9卷 207-218页

作者： Abbasnejad, H. Jafarian, A. Islamic Azad Univ Urmia Branch Dept Math Orumiyeh Iran

Implementation of the amazing features of the human brain in an artificial system has long been considered. It seems that simulating the human nervous system is a recent development in applied mathematics and computer sciences. The objective of this research is to introduce an efficient iterative method based on artificial neural networks for numerically solving nonlinear algebraic systems of polynomial equations. The method first performs some simple algebraic manipulations to convert the origin system to an approximated unconstrained optimisation problem. Subsequently, the resulting nonlinear minimisation problem is solved iteratively using the neural networks approach. For this aim, a suitable five-layer feed-back neural architecture is formed and trained using a back-propagation supervised learning algorithm which is based on the gradient descent rule. Ultimately, some numerical examples with comparisons are given to demonstrate the high accuracy and the ease of implementation of the present technique over other classical methods.

关键词： nonlinear algebraic system artificial neural networks approach criterion function back-propagation learning algorithm

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Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2017年第1期10卷 470-480页

作者： Jafarian, Ahmad Rostami, Fariba Golmankhaneh, Alireza K. Baleanu, Dumitru Islamic Azad Univ Dept Math Urmia Branch Orumiyeh Iran Islamic Azad Univ Young Res & Elite Club Urmia Branch Orumiyeh Iran Cankaya Uni Dept Math TR-06530 Ankara Turkey Inst Space Sci POB MG-23 R-76900 Bucharest Romania

Indeed, interesting properties of artificial neural networks approach made this non-parametric model a powerful tool in solving various complicated mathematical problems. The current research attempts to produce an approximate polynomial solution for special type of fractional order Volterra integrodifferential equations. The present technique combines the neural networks approach with the power series method to introduce an efficient iterative technique. To do this, a multi-layer feed-forward neural architecture is depicted for constructing a power series of arbitrary degree. Combining the initial conditions with the resulted series gives us a suitable trial solution. Substituting this solution instead of the unknown function and employing the least mean square rule, converts the origin problem to an approximated unconstrained optimization problem. Subsequently, the resulting nonlinear minimization problem is solved iteratively using the neural networks approach. For this aim, a suitable three-layer feed-forward neural architecture is formed and trained using a back-propagation supervised learning algorithm which is based on the gradient descent rule. In other words, discretizing the differential domain with a classical rule produces some training rules. By importing these to designed architecture as input signals, the indicated learning algorithm can minimize the defined criterion function to achieve the solution series coefficients. Ultimately, the analysis is accompanied by two numerical examples to illustrate the ability of the method. Also, some comparisons are made between the present iterative approach and another traditional technique. The obtained results reveal that our method is very effective, and in these examples leads to the better approximations.

关键词： Fractional equation Power-series method Artificial neural networks approach Criterion function back-propagation learning algorithm

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New combinative method for solving one-dimensional fractional Bratu differential equation

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INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS 2017年第2期7卷 142-156页

作者： Jafarian, Ahmad Kulaii, Layla Islamic Azad Univ Urmia Branch Dept Math Orumiyeh Iran

Indeed, the special advantages of artificial neural networks in modelling and solving complex real-world phenomena, have made them powerful computational and mathematical tools in applied sciences and engineering. The main purpose of this paper is to derive an iterative method based on a combination of neural nets approach and power-series method for an approximate treatment of the fractional Bratu-type equations. Supposedly, the problem considered has a solution in terms of the series expansion of unknown function, the proper implementation of a suitable neural architecture leads to estimate the unknown series coefficients, systematically. So as to show practical applicability and robustness of this technique, Bratu's boundary value problem in one-dimensional planar is solved as numerical example. Achieved numerical and simulative results reveal that the method is very effective and powerful.

关键词： artificial neural network back-propagation learning algorithm criterion function fractional Bratu-type power-series polynomial problem

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Analysis of Crack Coalescence in Concrete Using Neural Networks

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STRENGTH OF MATERIALS 2016年第6期48卷 850-861页

作者： Haeri, H. Sarfarazi, V. Zhu, Z. Islamic Azad Univ Bafgh Branch Young Researchers & Elite Club Bafgh Iran Hamedan Univ Technol Dept Min Engn Hamadan Iran Sichuan Univ Coll Architecture & Environm Chengdu Peoples R China

Fractures in the forms of joints and microcracks are commonly found in concretes, and their failure mechanism strongly depends on the crack coalescence pattern between pre-existing flaws. The determination of the failure behavior of nonpersistent joints is an engineering problem that involves several parameters as mechanical properties of concrete, normal stress and the ratio of joint surface to total shear surface. The impact of these parameters on the crack coalescence is investigated through the use of computational tools called neural networks. A number of networks of threshold logic units were tested, with adjustable weights. The computational method for the training process was a back-propagation learning algorithm. In this paper, the input data for crack coalescence consists of values of geotechnical and geometrical parameters. As an output, the network estimates the crack type coalescence (i.e., mode I, mode II, or mixed mode I-II) that can be used for stability analysis of concrete structures. The performance of the network is measured and the results are compared to those obtained by means of the experimental method.

关键词： back-propagation learning algorithm crack coalescence bridge non-persistent joint

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Two-Temperature Neural Sensing Scheme

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IEEE SENSORS JOURNAL 2016年第23期16卷 8468-8476页

作者： Yeh, Bih-Chyun Chang Gung Univ Sch Elect & Comp Engn Dept Elect Engn Coll Engn Taoyuan 333 Taiwan

We propose the optical laser frequency neural sensing scheme and two-temperature neural sensing scheme to measure the optical laser frequency and two temperatures of the heat reservoirs. The optical laser frequency and two-temperature requirement conditions are imposed by one-to-one functional map between normalized transmission spectrum and optical laser frequency as well as one-to-two functional map between normalized transmission spectrum and two temperatures. The proposed schemes using the optical laser frequency neural sensing scheme and two-temperature neural sensing scheme learn the mapping relationships for both optical laser frequency and two temperatures with their corresponding normalized transmission spectra. The experimental results show that the optical laser frequency neural sensing scheme and two-temperature neural sensing scheme to measure the optical laser frequency and two temperatures to get the root-mean-square errors of 5.9 MHz, 0.009 degrees C, and 0.008 C degrees, respectively.

关键词： Feed-forward neural networks back-propagation learning algorithm fiber Bragg gratings frequency sensor temperature sensor

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Corroboration of NDT and deconvolution neural networks for pedestrian bridge health assessment

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NONDESTRUCTIVE TESTING AND EVALUATION 2015年第1期30卷 89-103页

作者： Kilic, Gokhan Unluturk, Mehmet S. Izmir Univ Econ Dept Civil Engn TR-35330 Izmir Turkey Izmir Univ Econ Dept Software Engn TR-35330 Izmir Turkey

This paper describes the specific application of the non-destructive testing methods of visual inspection and ground penetrating radar (GPR) to a pedestrian bridge in Izmir, Turkey. The paper concentrates on the implementation of a deconvolution neural network (DNN) which is a procedure that employs neural network algorithms. By introducing collected GPR data to the DNN, the existence and location of cracks, rebar and moisture ingress on pedestrian pathways can reliably be located, thus providing superior information on which decisions relating to the functionality and life expectancy of a structure can be formulated. This study will be of benefit to engineers in providing a detailed and dependable assessment of the current state of structures such as pedestrian bridges.

关键词： artificial neural network health monitoring and assessment pedestrian bridges ground penetrating radar back-propagation learning algorithm

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Performance evaluation of the neural networks for moisture detection using GPR

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NONDESTRUCTIVE TESTING AND EVALUATION 2014年第4期29卷 283-296页

作者： Kilic, Gokhan Unluturk, Mehmet S. Izmir Univ Econ Dept Civil Engn TR-35330 Izmir Turkey Izmir Univ Econ Dept Software Engn TR-35330 Izmir Turkey

Ground penetrating radar (GPR) is a highly researched area;however, despite this, there is a lack of knowledge about the well-known problem of moisture distorting the results of GPR surveys. This research analyses the results of a GPR survey on a Case Study Bridge structure in order to analyse this effect, specifically when checking for the positioning of rebar. The expected distortions of the GPR results due to the presence of moisture were indeed present, as further evidenced by subsequent destructive testing and velocity analysis. Furthermore, neural networks were also utilised to detect moisture ingress from the GPR raw data.

关键词： GPR and data processing bridge structures non-destructive moisture ingress neural networks back-propagation learning algorithm

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