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Mathematical simulation of flow toward drains is an important and indispensable stage in drainage design and management. Many related models have been developed, but most of them simulate the saturated flow toward drains without a due consideration of the unsaturated zone. In this study, the two dimensional differential equation governing saturated and unsaturated flow in porous media is numerically solved and water table variations between drains predicted. By introducing and linking a proper optimization model to the numerical one, saturated and unsaturated soil hydrodynamic parameters were estimated within the inverse problem technique context. Data for calibration and verification were provided through a conduction of laboratory experimentation. Other laboratory data were also employed for the proposed model evaluation. The results indicated that in addition to a prediction of the water table variations between drains, the inverse problem model can be employed to estimate the unsaturated soil hydrodynamic parameters with a high degree of precision.

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One of the interesting and practical problems in thermo-fluid sciences is referred to finding the shape of a boundary on which a specific distribution of pressure, temperature or heat flux is known. Because solving such problems using experimental, semi-experimental and analytical methods is time-consuming or even impossible in some practical situations, myriad numerical methods have been introduced to solve surface shape design (SSD) problems. In all the numerical algorithms, an initial guess is modified through a numerical process until the desirable distribution of the target variable is achieved. All the numerical algorithms use three computational tools, i.e. grid generator, flow solver and shape updater to solve an SSD problem. In most of numerical algorithms, not only the three mentioned tools work separately but the shape updater is also not derived from the governing equations. In this article, to solve SSD problems containing convection heat transfer, a new shape design algorithm called direct design method is presented in which grid generator, flow solver and shape updater work simultaneously and also the shape updater is directly derived from the governing equations. Some SSD problems containing convection heat transfer in which instead of the boundary shape the distribution of the heat flux is known are solved using the proposed algorithm. The obtained results show the capability of the method in solving SSD problems containing internal convection heat transfer.

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Damage detection of structures is an important issue for maintaining structural safety and integrity. In order to evaluate the condition of structures, many structural health monitoring (SHM) techniques have been proposed over the last decades. Major approaches of SHM are non-destructive in nature and are widely used for damage detection in engineering structures such as aerospace, civil and marine structures. The existence of damage in a structure may be traced by comparing the response of time-domain wave traveling in the structure at its present state with a base-line response. A difference from the base-line response is correlated to the damage location through estimation of time of arrival of the new peaks (scattered waves). Thus, by employing the wave based methods, presence of damage in a structure is detected by inspecting at the wave parameters affected by the damage. The wave parameters that are commonly used for damage detection are the parameters representing attenuation, reflection and mode conversion of waves due to damage. Although detection of flaws is extremely important for many industrial applications, current approaches are severely restricted to specific flaws, simple geometries and homogeneous materials. In addition, the computational burden is very large due to the inverse nature of the problems where one solves many forward and backward problems. For instance, conventional ultrasonic methods measure the time difference of returning waves reflected from a crack; however, for laminated composite plates, the ultrasonic wave would be partially reflected at the interface of two layers where no crack actually exists, and partially continues to propagate further where it eventually is reflected back by the true crack. Numerical methods employed in crack detection algorithms require the solution of inverse problems in which the spatial problem is often discretized in space using finite elements in association with an optimization scheme. The solution of these problems is not unique, and sometimes the optimization algorithm may converge to local minima which are not the real optimal solution. Moreover, they often require hundreds of iterations to converge considering the algorithm used in the process. On the other hand, an accurate detection of cracks requires the re-meshing of the finite element domain at each iteration of the optimization. This is a severe limitation to any numerical approach when the conventional finite element method is employed for crack modeling, as the re-meshing of a domain is often not a trivial task. This paper investigates crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with particle swarm optimization (PSO) algorithm. The XFEM is utilized to model the cracked structure as a forward problem, while the PSO is employed for finding crack location as an optimization scheme. The XFEM is a robust tool for analysis of structures having discontinuities without re-meshing. Therefore, it is an efficient tool for an iterative process. Also, the PSO is a well-known non-gradient based method which is suitable for this inverse problem. The problem is formulated such that the PSO algorithm searches crack coordinates in order to detect the existing crack by minimizing an error function based upon sensor measurements. This problem is a non-destructive evaluation of a structure. Three benchmark numerical examples are solved to demonstrate capability and accuracy of the XFEM and the PSO for crack detection of 2D domains.

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In this paper, the diffusion coefficient in a normal tissue and tumor are to be estimated by the method of inverse problems. At the beginning, distribution of drug (with the assumption of uniform and isentropic diffusion coefficient) in the tissue is considered as the direct problem. In the direct problem, the governing equation is the convection–diffusion, which is the generalized form of fick’s law. Here, a source and a sink are defined; the source as the rate of solute transport per unit volume from blood vessels into the interstitial space and the sink as the rate of solute transport per unit volume from the interstitial space into lymph vessels are added to this equation. To solve the direct problem, the finite difference method has been considered. Additionally, the diffusion coefficient of a normal tissue and tumor will be approximated by parameter estimation method of Levenberg-Marquardt. This method is based on minimizing the sum of squared errors which in the present study, considered error is the difference of the estimated concentration and the concentration measured by medical images (simulated numerically). Finally, the results obtained by Levenberg-Marquardt method have provided an acceptable estimation of diffusion coefficient in normal tissue and tumor.

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It is clear that, having a exact knowledge about the geometry and properties of the materials and the domain that engineering problems are involved are very important specially in structural health monitoring, geotechnical earthquake engineering and other related field in civil engineering; in many cases, it might be useful if a suitable inverse solution is applied in order to detect the characteristics of the problems domain.
The main purpose of this paper is to development of the hybrid finite element- finite difference method for solving inverse elastodynamic and elastostatic scattering problems and combining that with particle swarm optimization algorithm as a quantitative approach fo solving these types of the problems. This hybrid method has been used in order to preparing the forward solution of the problems and by defining a suitable cost function and minimizing that using PSO algorithm, various kind of inverse problems are solved.
In general, an inverse scattering problem can be solved using qualitative or quantitative approaches. In some branches of quantitative techniques, usually, a forward solution is required and then using heuristic algorithm, the goal will be achieved. In this study, a hybrid FE-FD method is used as forward solver (which has the flexibility of finite element method and low computational cost of finite difference method); so, the domain inside and outside of the inclusion will be dicretized using finite difference method and the boundaries near the inclusion will be discretized by finite element method, and in this condition, the solution will be more flexible near the scatterer. In each solution step, first the finite element will be solved and the results will be transferred to the finite difference code and when the result is prepared in it, again, the response of the problem will go to finite element region.
In this research, at first, a geometry and related location will be assumes, randomly and then regarding that, using an OpenSees program code, the boundaries of the inclusion will be discretized and using the MATLAB program the related to finite difference region is discretized, then the results from these two codes will go and back until the response goes converge. Then, the PSO code which is developed in MATLAB will qualify the results and evaluate the cost function (e.g., the cost function is defined by minimizing the the error between the displacement that is from the main model and the predicted model), and if the cost function is large, the PSO algorithm will propose the new location and/or geometry of the inclusion and again, the loop will be repeated until the cost function be near the zero and the solution procedure will be terminated.
In order to evaluate, the efficiency and accuracy of the proposed approach, several problems are solved, where this algorithm could find the location and geometry of the inclusions (e.g., regular and irregular inclusion), the non-homogeneity of the inclusion and also detecting the soil layers by both static and dynamic loading.; the results show a very good accuracy as well as efficiency of the proposed approach for solving inverse problems in bounded and smi-infinite domains.

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Identification of the thermal conductivity of a functionally graded material (FGM) is considered as an inverse heat conduction problem. ‎In this investigation, the measurements of the temperatures on the portion of the 2D body where heat flux is specified as the boundary ‎condition and/or the heat flux on the portion of the boundary where temperature is specified as the boundary condition are used as ‎additional data needed to identify the thermal conductivity of the FGM domain in an inverse procedure. The thermal conductivity is ‎approximated as a quadratic function of only one direction, and therefore three constant coefficients should be estimated simultaneously.‎‏ ‏The solution of the direct heat conduction problem for‏ ‏FGM domain is obtained using the boundary elements method (BEM).‎‏ ‏The ‎imperialist competitive algorithm (ICA) which is an evolutionary and meta-heuristic global optimization is used to identify the constants ‎in the thermal conductivity function of the quadratic FGM. An inverse computer code is developed which employs the boundary ‎temperature and heat flux measurements data obtained by solving the direct boundary elements code with known thermal conductivity. ‎To show the feasibility and effectiveness of the developed inverse code, a number of example problems are solved and results are ‎verified.‎

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One of the major issues in the industry is inhomogeneity depth profiling in the metallic structures before reaching them to the border of demolition. Fuzzy logic based methodologies, due to their ability to describe the complex issues with empirical nature such as non-destructive testing, are used for this purpose and usually provide acceptable results. But empirical rules and also extracted data from non-destructive testing methods mainly have high degree of uncertainty and therefore Classical fuzzy methods, which are based on exact membership grades and Type-I membership functions, are incapable to deal with them. Therefore, they cannot deal with noisy environments and also cannot represent a good performance for accurate depth estimation of unknown cracks. In this paper, to allocate uncertainty to rules and membership functions, the type-II fuzzy logic system is used to solve the inverse problem of crack profile depth estimation. Also Alternating Current Field Measurement (ACFM) signals are used to sizing the depth of crack profile. Then, experimental results of the proposed method are compared to the other state of the arts in the presence of different level of noise and different type of cracks. The results show the superiority of the proposed method to the other methods.

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In this paper, a numerical algorithm based inverse method is used to estimate effective diffusion coefficient by using experimental tracer distribution. The Algorithm uses factitious experimental data which are produced by adding noise to numerical data obtained from direct problem. A comprehensive model (Diffusion-Convection-Reaction) is used to derive PET tracer distribution in tumor tissue with microvasculature network. This model was used because of considering all transport phenomena in tissue. In this work to achieve accurate distribution of tracer in tumor tissue, convection diffusion reaction equation which is a PDE is implemented. The proposed tracer in this work is Fluorodeoxyglucose (18F). Solution of inverse problem for estimating effective Diffusion Coefficient is based on minimization of least squares norm. In this work Levenberg-Marquardt technique is applied. Solution of parameter estimation problem require calculation of sensitivity matrix which elements are sensitivity coefficients. Sensitivity coefficients shows differentiation of Tracer concentration with respect to Effective Diffusion coefficient variation is calculated using first derivation of concentration equation. The equations of concentration distribution and sensitivity coefficients are solved using Finite volume method. The results show that the numerical algorithm is able to estimate the effective diffusion coefficient in tissue.

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Detection of defects in the internal surfaces of pipes due to the inherent feature of these surfaces which is inaccessibility is always a troublesome process. In this study, a novel method has been designed for detection of defect locations on the internal surfaces of pipes and accurate estimation of defect geometrical parameters such as length and average material loss depth. The way that this method works is that a band heater is located on the external surface of the pipe in inspection segment, and specified heat flux is applied to this surface for a short time, and the temperature of these sensors located on rear of the band heater is measured during and after of applying thermal heat flux. The local temperature rise on the section of the external surface of the pipe indicates a defect on its internal surface. In this case, a defect with unknown parameters is supposed on the internal surface of the pipe, and by using the inverse heat conduction method, an iterative numerical simulation procedure continues until the unknown geometrical parameters of defects are estimated in a way to minimize the difference between the measured and simulated temperature in the location of sensors.

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There are many factors causing damages to a structure, including earthquakes, winds, environmental effects, etc. In order to repair a damaged structure, first its damage locations should be identified. Therefore, the damage identification of structures is considered as an important issue in civil engineering as well as mechanical engineering. Many methodologies have been devised for damage identification of structures, which are generally categorized to destructive and non-destructive cases. As a non-destructive damage identification approach, solving inverse problems for identifying the properties of a damaged structure is one of the popular methods which utilizes an optimization algorithm to minimize an error function in terms of measured strains or displacements. Since an iterative procedure with significant number of structural analyses should be carried out for the optimization process, an efficient numerical method should be employed to reduce the total computational cost. In this paper, the identification of hole in two-dimensional continuum structures is investigated with finite cell method and particle swarm optimization algorithm. The finite cell method is an efficient numerical method for solving the governing equations of continuum structures having geometrical complexity and/or discontinuities, which uses the concept of virtual domain method. The use of this concept makes the mesh generation easier such that the simple structured meshes can be utilized even for the curved boundaries of a structure, and hence mesh refinement is not necessary for the problems like damage detection. The finite cell method uses adaptive numerical integration for the cells including non-uniform material distribution. Accordingly, quadtree integration is utilized for the structural analysis using the finite cell method. Consequently, the computational time is significantly reduced. On the other hand, particle swarm optimization is a well-known meta-heuristic algorithm, and hence it does not require the gradient information of the problem. This population-based algorithm has been inspired by the social behaviour of animals such as fish schooling and birds flocking. The basis of this algorithm relies on the social influence and learning which enable individuals to preserve cognitive consistency. Thus, the exchange of ideas and interactions between individuals can lead them to solve optimization problems like damage detection. This study proposes the finite cell method and particle swarm optimization algorithm for damage detection of plate structures with single hole or multiple holes. As a non-gradient-based method, particle swarm optimization explores the search space to find the coordinates of the existing damage by minimizing an error function. This error function is evaluated by the strains or displacements calculated by the structural analysis utilizing the finite cell method. In order to evaluate the proposed methodology, numerical examples are provided to demonstrate the capability of finite cell method and particle swarm optimization algorithm in damage detection of two-dimensional structures. The first example considers the damage detection of a plate with a single hole, and it also considers the effects of mesh density. The second example employs a plate structure with three holes. The results demonstrate that the proposed methodology, with suitable computational efforts, can successfully be applied to damage detection of these structures.

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In this paper, solution of inverse problems in a plane linear elastic bodies are investigated. For this purpose, sampling method in frequency domain is introduced for cavity/crack detection in a structural element such as plate. This method is categorized as a qualitative approach to image the geometrical features of unknown targets. This goal is followed by partitioning the investigated region into an arbitrary grid of sampling points, in which a linear equation is solved. The main idea of the linear sampling method is to search for a superposition of differential displacement fields which matches with a prescribed radiating solution of the homogeneous governing equation in Ω(D), for each sampling point. Although this method has been used in the context of inverse problems such as acoustics, and electromagnetism, there is no specific attempt to apply this method to identification of crack/cavities in a structural component. This study emphasizes the implementation of the sampling method in the frequency domain using spectral finite element method. A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.

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