An image reconstruction algorithm based on the semiparametric model for electrical capacitance tomography

AbstractElectrical capacitance tomography (ECT) is considered as a promising tomography technology, and exactly reconstructing the original objects is highly desirable in real applications. In this paper, a generalized image reconstruction model that simultaneously considers the inaccurate property in the measured capacitance data and the linearization approximation error is presented. A generalized objective function, which has been developed using a combinational M-estimation and an extended stabilizing item, is proposed. The objective function unifies six estimation methods into a concise formula, where different estimation methods can be easily obtained by selecting different parameters. The homotopy method that integrates the beneficial advantages of the alternant iteration scheme is employed to solve the proposed objective function. Numerical simulations are implemented to evaluate the numerical performances and effectiveness of the proposed algorithm, and the numerical results reveal that the proposed algorithm is efficient and overcomes the numerical instability in the process of ECT image reconstruction. For the reconstructed objects in this paper, a dramatic improvement in accuracy and spatial resolution can be achieved, which indicates that the proposed algorithm is a promising candidate for solving ECT inverse problems

Particle swarm optimization with sequential niche technique for dynamic finite element model updating

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Frequency response-based damage identification by minimum constitutive relation error and sparse regularization

The objective of this paper is to provide a new damage identification method using frequency response data. In this approach, the inverse identification problem is treated as a nonlinear optimization problem whose objective function is just the constitutive relation error (CRE). To circumvent the ill-posedness of the inverse problem which is caused by use of the possibly insufficient data and enhance the robustness of the identification process, the sparse regularization is introduced where the ℓ1-norm regularization term is added to the original CRE function. In regard to the minimum solution of the sparse-regularized CRE objective function, the alternating minimization (AM) method is established. The attractive features of the present damage identification approach are: (a) while coping with the sparse regularization, a closed-form solution is obtained due to the decoupling of the CRE function with respect to the damage parameters and hence the sparse regularization term would introduce little computational complexity; (b) the sparse regularization parameters are directly determined by a simple threshold setting method; (c) no sensitivity analysis is involved herein. Numerical examples are conducted to verify the proposed approach and the results show that the sparse regularization obviously improves the accuracy and robustness for the identified damages

Combining genetic algorithm and Sinc-Galerkin method for solving an inverse diffusion problem

A numerical approach combining the use of a genetic algorithm with the solution of the Sinc-Galerkin method is proposed for the determination of an unknown time-dependent diffusivity a(t) in an inverse diffusion problem (IDP). At the beginning of the numerical algorithm, Sinc-Galerkin method is employed to solve the direct diffusion problem. The present approach is to rearrange the matrix forms of the governing equations. Then, the genetic algorithm is adopted to find the solution of IDP. The genetic algorithm used in this work is not a classical genetic algorithm. Instead, the application of the genetic algorithm to this discrete-time optimal control problem is called a real-valued genetic algorithm(RVGA). Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data. Results Show that a reasonable estimation can be obtained by combining the genetic algorithm and Sinc-Galerkin method within a CPU with clock speed 2.7 GHz.Publisher's Versio

Calibration and Rescaling Principles for Nonlinear Inverse Heat Conduction and Parameter Estimation Problems

This dissertation provides a systematic method for resolving nonlinear inverse heat conduction problems based on a calibration formulation and its accompanying principles. It is well-known that inverse heat conduction problems are ill-posed and hence subject to stability and uniqueness issues. Regularization methods are required to extract the best prediction based on a family of solutions. To date, most studies require sophisticated and combined numerical methods and regularization schemes for producing predictions. All thermophysical and geometrical properties must be provided in the simulations. The successful application of the numerical methods relies on the accuracy of the related system parameters as previously described. Due to the existence of uncertainties in the system parameters, these numerical methods possess bias of varying magnitudes. The calibration based approaches are proposed to minimize the systematic errors since system parameters are implicitly included in the mathematical formulation based on several calibration tests. To date, most calibration inverse studies have been based on the assumption of constant thermophysical properties. In contrast, this dissertation focuses on accounting for temperature-dependent thermophysical properties that produces a nonlinear heat equation. A novel rescaling principle is introduced for linearzing the system. This concept generates a mathematical framework similar to that of the linear formulation. Unlike the linear formulation, the present approach does require knowledge of thermophysical properties. However, all geometrical properties and sensor characterization are completely removed from the system. In this dissertation, a linear one-probe calibration method is first introduced as background. After that, the calibration method is generalized to the one-probe and two-probe, one-dimensional thermal system based on the assumption of temperature-dependent thermophysical properties. All previously proposed calibration equations are expressed in terms of a Volterra integral equation of the first kind for the unknown surface (net) heat flux and hence requires regularization owning to the ill-posed nature of first kind equations. A new strategy is proposed for determining the optimal regularization parameter that is independent of the applied regularization approach. As a final application, the described calibration principle is used for estimating unknown thermophysical properties above room temperature

Vertical Cracks Excited in Lock-in Vibrothermography Experiments: Identification of Open and Inhomogeneous Heat Fluxes

Lock-in vibrothermography has proven to be very useful to characterizing kissing cracks producing ideal, homogeneous, and compact heat sources. Here, we approach real situations by addressing the characterization of non-compact (strip-shaped) heat sources produced by open cracks and inhomogeneous fluxes. We propose combining lock-in vibrothermography data at several modulation frequencies in order to gather penetration and precision data. The approach consists in inverting surface temperature amplitude and phase data by means of a least-squares minimization algorithm without previous knowledge of the geometry of the heat source, only assuming knowledge of the vertical plane where it is confined. We propose a methodology to solve this illposed inverse problem by including in the objective function penalty terms based on the expected properties of the solution. These terms are described in a comprehensive and intuitive manner. Inversions of synthetic data show that the geometry of non-compact heat sources is identified correctly and that the contours are rounded due to the penalization. Inhomogeneous smoothly varying fluxes are also qualitatively retrieved, but steep variations of the flux are hard to recover. These findings are confirmed by inversions of experimental data taken on calibrated samples. The proposed methodology is capable of identifying heat sources generated in lock-in vibrothermography experiments. © 2022 by the authors. Licensee MDPI, Basel, Switzerland