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1 – 10 of 987In this paper, the Cauchy-type problem for the Laplace equation was solved in the rectangular domain with the use of the Chebyshev polynomials. The purpose of this paper is to…
Abstract
Purpose
In this paper, the Cauchy-type problem for the Laplace equation was solved in the rectangular domain with the use of the Chebyshev polynomials. The purpose of this paper is to present an optimal choice of the regularization parameter for the inverse problem, which allows determining the stable distribution of temperature on one of the boundaries of the rectangle domain with the required accuracy.
Design/methodology/approach
The Cauchy-type problem is ill-posed numerically, therefore, it has been regularized with the use of the modified Tikhonov and Tikhonov–Philips regularization. The influence of the regularization parameter choice on the solution was investigated. To choose the regularization parameter, the Morozov principle, the minimum of energy integral criterion and the L-curve method were applied.
Findings
Numerical examples for the function with singularities outside the domain were solved in this paper. The values of results change significantly within the calculation domain. Next, results of the sought temperature distributions, obtained with the use of different methods of choosing the regularization parameter, were compared. Methods of choosing the regularization parameter were evaluated by the norm Nmax.
Practical implications
Calculation model described in this paper can be applied to determine temperature distribution on the boundary of the heated wall of, for instance, a boiler or a body of the turbine, that is, everywhere the temperature measurement is impossible to be performed on a part of the boundary.
Originality/value
The paper presents a new method for solving the inverse Cauchy problem with the use of the Chebyshev polynomials. The choice of the regularization parameter was analyzed to obtain a solution with the lowest possible sensitivity to input data disturbances.
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This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for…
Abstract
Purpose
This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for predicting the internal boundary conditions for thermal analysis of mechanical structure. A few examples of heat transfer systems are given to illustrate the applicability of the method and the challenges that must be addressed in solving the inverse problem.
Design/methodology/approach
In this paper, the thermal network method and the finite difference method are used to model the two-dimensional heat conduction inverse problem of the tube structure, and the heat balance equation is arranged into an explicit form for heat load prediction. To solve the matrix ill-conditioned problem in the process of solving the inverse problem, a Tikhonov regularization parameter selection method based on the inverse computation-contrast-adjustment-approach was proposed.
Findings
The applicability of the proposed method is illustrated by numerical examples for different dynamically varying heat source functions. It is proved that the method can predict dynamic heat source with different complexity.
Practical implications
The modeling calculation method described in this paper can be used to predict the boundary conditions for the inner wall of the heat transfer tube, where the temperature sensor cannot be placed.
Originality/value
This paper presents a general method for the direct prediction of heat sources or boundary conditions in mechanical structure. It can directly obtain the time-varying heat flux load and thtemperature field of the machine structure.
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Ziqiang Cui, Qi Wang, Qian Xue, Wenru Fan, Lingling Zhang, Zhang Cao, Benyuan Sun, Huaxiang Wang and Wuqiang Yang
Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost…
Abstract
Purpose
Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.
Design/methodology/approach
In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.
Findings
This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.
Originality/value
The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.
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Hua‐Peng Chen and Nenad Bicanic
The paper aims to identify both the location and severity of damage in complex framed buildings using limited noisy vibration measurements. The study aims to directly adopt…
Abstract
Purpose
The paper aims to identify both the location and severity of damage in complex framed buildings using limited noisy vibration measurements. The study aims to directly adopt incomplete measured mode shapes in structural damage identification and effectively reduce the influence of measurement errors on predictions of structural damage.
Design/methodology/approach
Damage indicators are properly chosen to reflect both the location and severity of damage in framed buildings at element level for braces and at critical point level for beams and columns. Basic equations for an iterative solution procedure are provided to be solved for the chosen damage indicators. The Tikhonov regularisation method incorporating the L‐curve criterion for determining the regularisation parameter is employed to produce stable and robust solutions for damage indicators.
Findings
The proposed method can correctly assess the quantification of structural damage at specific locations in complex framed buildings using only limited information on modal data measurements with errors, without requiring mode shape expansion techniques or model reduction processes.
Research limitations/implications
Further work may be needed to improve the accuracy of inverse predictions for very small structural damage from noisy measurements.
Practical implications
The paper includes implications for the development of reliable techniques for rapid and on‐line damage assessment and health monitoring of framed buildings.
Originality/value
The paper offers a practical approach and procedure for correctly detecting structural damage and assessing structural condition from limited noisy vibration measurements.
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Keywords
Adam Basílio, Fran Sérgio Lobato and Fábio de Oliveira Arouca
The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented…
Abstract
Purpose
The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented by partial differential equations associated with initial and boundary conditions. In general, the resolution of these problems requires using numerical techniques through discretization of boundary and internal points of the domain considered, implying a high computational cost. As an alternative to reducing computational costs, various approaches based on meshless (or meshfree) methods have been evaluated in the literature. In this contribution, the purpose of this paper is to formulate and solve direct and inverse problems applied to Laplace’s equation (steady state and bi-dimensional) considering different geometries and regularization techniques. For this purpose, the method of fundamental solutions is associated to Tikhonov regularization or the singular value decomposition method for solving the direct problem and the differential Evolution algorithm is considered as an optimization tool for solving the inverse problem. From the obtained results, it was observed that using a regularization technique is very important for obtaining a reliable solution. Concerning the inverse problem, it was concluded that the results obtained by the proposed methodology were considered satisfactory, as even with different levels of noise, good estimates for design variables in proposed inverse problems were obtained.
Design/methodology/approach
In this contribution, the method of fundamental solution is used to solve inverse problems considering the Laplace equation.
Findings
In general, the proposed methodology was able to solve inverse problems considering different geometries.
Originality/value
The association between the differential evolution algorithm and the method of fundamental solutions is the major contribution.
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Mohamed S. Gadala and Fuchang Xu
To develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.
Abstract
Purpose
To develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.
Design/methodology/approach
An inverse heat transfer analysis procedure is developed and implemented into a 2D finite element program. In this method, the least‐squares technique, sequential function specification and regularization are used. Simplifications in the sensitivity matrix calculation and iterative procedures are introduced. The triangular and impulse‐like profiles of heat fluxes simulating practical conditions of impingement water cooling are used to investigate the accuracy and stability of the proposed inverse procedure. The developed program is then used to determine the heat flux during impingement water cooling.
Findings
A hybrid procedure is developed in which inverse calculations are conducted with a computation window. This procedure may be used as a whole time domain method or become a periodically sequential or real sequential method by adjusting the sequential steps.
Originality/value
Parametric study and application show that the developed method is effective and reliable and that inverse analysis may obtain the heat flux with an acceptable level of accuracy.
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Seyed Reza Aali, Mohammad Reza Besmi and Mohammad Hosein Kazemi
The purpose of this paper is to study variation regularization with a positive sequence extraction-normalized least mean square (VRP-NLMS) algorithm for frequency estimation in a…
Abstract
Purpose
The purpose of this paper is to study variation regularization with a positive sequence extraction-normalized least mean square (VRP-NLMS) algorithm for frequency estimation in a three-phase electrical distribution system. A simulation test is provided to validate the performance and convergence rate of the proposed estimation algorithm.
Design/methodology/approach
Least mean square (LMS) algorithms for frequency estimation encounter problems when voltage contains unbalance, sags and harmonic distortion. The convergence rate of the LMS algorithm is sensitive to the adjustment of the step-size parameter used in the update equation. This paper proposes VRP-NLMS algorithm for frequency estimation in a power system. Regularization parameter is variable in the NLMS algorithm to adjust step-size parameter. Delayed signal cancellation (DSC) operator suppresses harmonics and negative sequence component of the voltage vector in a two-phase Î ± β plane. The DSC part is placed in front of the NLMS algorithm as a pre-filter and a positive sequence of the grid voltage is extracted.
Findings
By adapting of the step-size parameter, speed and accuracy of the LMS algorithm are improved. The DSC operator is augmented to the NLMS algorithm for more improvement of the performance of this adaptive filter. Simulation results validate that the proposed VRP-NLMS algorithm has a less misalignment of performance with more convergence rate.
Originality/value
This paper is a theoretical support to simulated system performance.
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Jinlong Dong, Luca Di Rienzo, Olivier Chadebec and Jianhua Wang
This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a…
Abstract
Purpose
This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker.
Design/methodology/approach
Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W2 in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W1 in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W1. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values.
Findings
With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W2 and using edge elements in space W1. When solving the inverse problem in space W1, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred.
Originality/value
The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.
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Yongxiu He, Weijun Tao, Aiying Dai, Lifang Yang, Rui Fang and Furong Li
The purpose of this paper is to use artificial intelligence to evaluate the risks of urban power network planning.
Abstract
Purpose
The purpose of this paper is to use artificial intelligence to evaluate the risks of urban power network planning.
Design/methodology/approach
A fuzzy Bayesian least squares support vector machine (LS_SVM) model is established in this paper, which can learn the risk information of urban power network planning through artificial intelligence and acquire expert knowledge for its risk evaluation. With the advantage of possessing learning analog simulation precision and speed, the proposed model can be effectively applied in conducting a risk evaluation of an urban network planning system. First, fuzzy theory is applied to quantify qualitative risk factors of the planning to determine the fuzzy comprehensive evaluation value of the risk factors. Then, Bayesian evidence framework is utilized in LS_SVM model parameter optimization to automatically adjust the LS_SVM regularization parameters and nuclear parameters to obtain the best parameter values. Based on this, a risk comprehensive evaluation of urban network planning based on artificial intelligence is established.
Findings
The fuzzy Bayesian LS_SVM model established in this paper is an effective artificial intelligence method for risk comprehensive evaluation in urban network planning through empirical study.
Originality/value
The paper breaks new ground in using artificial intelligence to evaluate urban power network planning risks.
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Keywords
Andrzej Frąckowiak and Michał Ciałkowski
This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer…
Abstract
Purpose
This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer coefficient and temperature on the outer boundary of the blade are known. On this basis, the temperature on inner surfaces of the blade (the walls of cooling channels) is determined.
Design/methodology/approach
Such posed inverse problem was solved using the finite element method in the domain of the discrete Fourier transform (DFT).
Findings
Calculations indicate that the regularization in the domain of the DFT enables obtaining a stable solution to the inverse problem. In the example under consideration, problems with reconstruction constant temperature, assumed on the outer boundary of the blade, in the vicinity of the trailing and leading edges occurred.
Originality/value
The application of DFT in connection with regularization is an original achievement presented in this study.
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