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Restoring an image from its convolution with an unknown blur function is a well-known ill-posed problem in image processing. Many approaches have been proposed to solve the problem and they have shown to have good performance in identifying the blur function and restoring the original image. However, in actual implementation, various problems incurred due to the large data size and long computational time of these approaches are undesirable even with the current computing machines. In this paper, an efficient algorithm is proposed for blind image restoration based on the discrete periodic Radon transform (DPRT). With DPRT, the original two-dimensional blind image restoration problem is converted into one-dimensional ones, which greatly reduces the memory size and computational time required. Experimental results show that the resulting approach is faster in almost an order of magnitude as compared with the traditional approach, while the quality of the restored image is similar.

This article introduces and evaluates the piecewise polynomial truncated singular value decomposition algorithm toward an effective use for moving force identification. Suffering from numerical non-uniqueness and noise disturbance, the moving force identification is known to be associated with ill-posedness. An important method for solving this problem is the truncated singular value decomposition algorithm, but the truncated small singular values removed by truncated singular value decomposition may contain some useful information. The piecewise polynomial truncated singular value decomposition algorithm extracts the useful responses from truncated small singular values and superposes it into the solution of truncated singular value decomposition, which can be useful in moving force identification. In this article, a comprehensive numerical simulation is set up to evaluate piecewise polynomial truncated singular value decomposition, and compare this technique against truncated singular value decomposition and singular value decomposition. Numerically simulated data are processed to validate the novel method, which show that regularization matrix L and truncating point k are the two most important governing factors affecting identification accuracy and ill-posedness immunity of piecewise polynomial truncated singular value decomposition. [ABSTRACT FROM AUTHOR]

• A preconditioned least square QR-factorization approach is developed for moving force identification. • The regularization matrix L is introduced to improve the ill-posed problems. • The number of iterations j is introduced to avoid noise disturbance and ensure the robustness. • Preconditioned least square QR-factorization approach is validated through numerical simulation. This paper develops a novel method for moving force identification (MFI) called preconditioned least square QR-factorization (PLSQR) method. The algorithm seeks to reduce the impact of identification errors caused by unknown noise. The biaxial moving forces travel on a simply supported bridge at three different speeds is used to generate numerical simulations to assess the effectiveness and applicability of the algorithm. Results indicate that the method is more robust towards ill-posed problem and has higher identification precision than the conventional time domain method (TDM). In addition, the robustness and ill-posed immunity of PLSQR are directly affected by two kinds of regularization parameters, namely, number of iterations j and regularization matrix L. Compared with the standard form of least square QR-factorization (LSQR), i.e., the regularization matrix L being the identity matrix I n , the PLSQR with the optimal number of iterations j and regularization matrix L has many advantages on MFI and it is more suitable for field trials due to better adaptability with type of sensors and number of sensors. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodology for moving force identification (MFI) from the responses of bridge deck. Based on the existing time domain method (TDM), the MFI problem eventually becomes solving the linear algebraic equation in the form Ax = b . The vector b is usually contaminated by an unknown error e generating from measurement error, which often called the vector e as ‘‘noise’’. With the ill-posed problems that exist in the inverse problem, the identification force would be sensitive to the noise e . The proposed truncated generalized singular value decomposition method (TGSVD) aims at obtaining an acceptable solution and making the noise to be less sensitive to perturbations with the ill-posed problems. The illustrated results show that the TGSVD has many advantages such as higher precision, better adaptability and noise immunity compared with TDM. In addition, choosing a proper regularization matrix L and a truncation parameter k are very useful to improve the identification accuracy and to solve ill-posed problems when it is used to identify the moving force on bridge. [ABSTRACT FROM AUTHOR]

• A preconditioned range restricted GMRES algorithm is developed for MFI. • It has significant advantages in both of the identification efficiency and accuracy. • The accuracy of the new method is very high in highly inaccurate measurement cases. • The new method is verified by numerical simulations and experimental studies. Moving force identification (MFI) is a widely concerned inverse problem in structural dynamics and well-known as intrinsically existing ill-posedness. With the help of Arnoldi process and Krylov subspace method, the generalized minimal residual (GMRES) method can be improved to a range restricted generalized minimal residual (RRGMRES) method. Furthermore, by introducing the smoothing-norm preconditioning, a preconditioned range restricted generalized minimal residual (PRRGMRES) method is proposed to provide a stable solution to the ill-posed dynamic force identification problem. Simulations show that the novel method has significant improvement when compared to the classic time domain method and the RRGMRES method. In addition, to show the effectiveness and advantages of the proposed method, the PRRGMRES method is also compared with a newly-proposed regularization method named the preconditioned least square QR-factorization (PLSQR) method. Simulation results show that the PRRGMRES method has much better robustness and higher computational efficiency than the PLSQR method especially in dealing with highly inaccurate measurement cases. Finally, the accuracy and efficiency of the PRRGMRES method is verified by experimental studies. The PRRGMRES method has good performance in both overcoming ill-posed problems and improving computational efficiency, which should be of the highest priority in adoption for MFI. [ABSTRACT FROM AUTHOR]

• A method is proposed to indirectly measure displacements under dominant design loads by exerting several simple testing loads. • Proper testing loads can be quickly found and have far less loading points than design loads. • Proposed indirect method is more robust to resist measurement noise than traditional direct method. • Reason why proposed indirect method has better robustness is explained. Structural stiffness of a real tension structure may degrade due to many factors, so the stiffness monitoring is very important. If the displacements under the dominant design loads are obtained, the stiffness state of the real structure can be intuitively assessed by a deformation checking process. However, exerting design loads on a real structure is neither efficient nor economical, because they usually have too many loading points. A method is hence proposed to indirectly measure the displacements under the design loads by merely exerting several simple testing loads. By utilizing the linear combination of several contributing eigenvectors to express the displacements, the problem of measuring displacements is transformed to that of measuring combinational coefficients of these contributing eigenvectors. The relationship between the combinational coefficients of the mutual contributing eigenvector of the design load and the testing load is set up firstly, with two basic conditions established. To satisfy the basic conditions, a strategy to decompose the design load and an algorithm to find proper testing loads are suggested. The numerical example of a cable net with two typical design loads is finally analyzed. Results illustrate that the proposed indirect method is effective, with three simple testing loads (no more than 3 loading points) found to replace the two design loads (181 loading points) in the on-site static testing. Besides, the proposed indirect method is more robust to resist the influence of measurement noise than the traditional direct method. The reason why the proposed indirect method has better robustness is also discussed. [ABSTRACT FROM AUTHOR]