A Finite Element Mesh Regrouping Strategy-Based Hybrid Light Transport Model for Enhancing the Efficiency and Accuracy of XLCT

X-ray luminescence computed tomography (XLCT) is an emerging hybrid imaging modality in optical molecular imaging, which has attracted more attention and has been widely studied. In XLCT, the accuracy and operational efficiency of an optical transmission model play a decisive role in the rapid and accurate reconstruction of light sources. For simulation of optical transmission characteristics in XLCT, considering the limitations of the diffusion equation (DE) and the time and memory costs of simplified spherical harmonic approximation equation (SPN), a hybrid light transport model needs to be built. DE and SPN models are first-order and higher-order approximations of RTE, respectively. Due to the discontinuity of the regions using the DE and SPN models and the inconsistencies of the system matrix dimensions constructed by the two models in the solving process, the system matrix construction of a hybrid light transmission model is a problem to be solved. We provided a new finite element mesh regrouping strategy-based hybrid light transport model for XLCT. Firstly, based on the finite element mesh regrouping strategy, two separate meshes can be obtained. Thus, for DE and SPN models, the system matrixes and source weight matrixes can be calculated separately in two respective mesh systems. Meanwhile, some parallel computation strategy can be combined with finite element mesh regrouping strategy to further save the system matrix calculation time. Then, the two system matrixes with different dimensions were coupled though repeated nodes were processed according to the hybrid boundary conditions, the two meshes were combined into a regrouping mesh, and the hybrid optical transmission model was established. In addition, the proposed method can reduce the computational memory consumption than the previously proposed hybrid light transport model achieving good balance between computational accuracy and efficiency. The forward numerical simulation results showed that the proposed method had better transmission accuracy and achieved a balance between efficiency and accuracy. The reverse simulation results showed that the proposed method had superior location accuracy, morphological recovery capability, and image contrast capability in source reconstruction. In-vivo experiments verified the practicability and effectiveness of the proposed method.

A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block

Null-space methods have long been used to solve large sparse n × n symmetric saddle point systems of equations in which the (2, 2) block is zero. This paper focuses on the case where the (1, 1) block is ill conditioned or rank deficient and the k × k (2, 2) block is non zero and small (k ≪ n). Additionally, the (2, 1) block may be rank deficient. Such systems arise in a range of practical applications. A novel null-space approach is proposed that transforms the system matrix into a nicer symmetric saddle point matrix of order n that has a non zero (2, 2) block of order at most 2k and, importantly, the (1, 1) block is symmetric positive definite. Success of any null-space approach depends on constructing a suitable null-space basis. We propose methods for wide matrices having far fewer rows than columns with the aim of balancing stability of the transformed saddle point matrix with preserving sparsity in the (1, 1) block. Linear least squares problems that contain a small number of dense rows are an important motivation and are used to illustrate our ideas and to explore their potential for solving large-scale systems.

Synchronized Assessment of Bridge Structural Damage and Moving Force via Truncated Load Shape Function

Moving load and structural damage assessment has always been a crucial topic in bridge health monitoring, as it helps analyze the daily operating status of bridges and provides fundamental information for bridge safety evaluation. However, most studies and research consider these issues as two separate problems. In practice, unknown moving loads and damage usually coexist and influence the bridge vibration synergically. This paper proposes an innovative synchronized assessment method that determines structural damages and moving forces simultaneously. The method firstly improves the virtual distortion method, which shifts the structural damage into external virtual forces and hence transforms the damage assessment as well as the moving force identification to a multi-force reconstruction problem. Secondly, a truncated load shape function (TLSF) technique is developed to solve the forces in the time domain. As the technique smoothens the pulse function via a limited number of TLSF, the singularity and dimension of the system matrix in the force reconstruction is largely reduced. A continuous beam and a three-dimensional truss bridge are simulated as examples. Case studies show that the method can effectively identify various speeds and numbers of moving loads, as well as different levels of structural damages. The calculation efficiency and robustness to white noise are also impressive.

Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

Advanced non-dimensional dynamic influence function method considering the singularity of the system matrix for accurate eigenvalue analysis of membranes

An advanced non-dimensional dynamic influence function method (NDIF method) for highly accurate free vibration analysis of membranes with arbitrary shapes is proposed in this paper. The existing NDIF method has the weakness of not offering eigenvalues and eigenmodes in the low frequency range when the number of boundary nodes of an analyzed membrane is increased to obtain more accurate result. This paper reveals that the system matrix of the membrane becomes singular in the lower frequency range when the number of the nodes increases excessively. Based on this fact, it provides an efficient way to successfully overcome the weaknesses of the existing NDIF method and still maintain its accuracy. Finally, verification examples show the validity and accuracy of the advanced NDIF method proposed.

A new torsional vibration coupling model for transmission system in diesel generator

The coupling between the crankshaft and the camshaft is neglected before in fault diagnosis which may lead to incomplete fault information. In this paper, a new torsional coupling model of a diesel generator transmission system is proposed for fault diagnosis. The natural frequency and forced torsional vibration response of the model are obtained by the system matrix method and Newmark-β method. For the system without considering the lumped mass of camshafts, some key natural frequencies are lost. The vibration dynamics are compared for the transmission system with and without the new coupling model. And important frequency responses are missed in the spectrums of the forced torsional vibration without the new coupling model. Finally, the new coupling model is implemented in fault diagnosis and the cause of an unusual vibration fault is deduced in the simulation, which confirms the feasibility of the proposed model in fault diagnosis.

Combined method for correction interval systems of linear algebraic equations

The possibility of application of the interval analysis for data processing in the field of spectral analysis is considered. It is assumed that the data have interval uncertainty; therefore the problem of finding unknown concentrations is posed as a linear interval tolerance problem. The incompatibility of the interval system of linear algebraic equations is shown for the initial data using the apparatus of the recognizing functional. The relevance of the topic is due to the need for regularization of inconsistent interval systems of linear equations. The idea of S. P. Shary of a combined method for correcting a linear tolerance problem has been implemented. A new method for managing the solution by changing the linear algebraic equations interval system matrix elements radii has been developed. The research results can be used for example, to calculate the substance’s concentrations by measurement of the characteristic X-ray radiation.

Response-Only Parametric Estimation of Structural Systems Using a Modified Stochastic Subspace Identification Technique

The present paper is a study of output-only modal estimation based on the stochastic subspace identification technique (SSI) to avoid the restrictions of well-controlled laboratory conditions when performing experimental modal analysis and aims to develop the appropriate algorithms for ambient modal estimation. The conventional SSI technique, including two types of covariance-driven and data-driven algorithms, is employed for parametric identification of a system subjected to stationary white excitation. By introducing the procedure of solving the system matrix in SSI-COV in conjunction with SSI-DATA, the SSI technique can be efficiently performed without using the original large-dimension data matrix, through the singular value decomposition of the improved projection matrix. In addition, the computational efficiency of the SSI technique is also improved by extracting two predictive-state matrixes with recursive relationship from the same original predictive-state matrix, and then omitting the step of reevaluating the predictive-state matrix at the next-time moment. Numerical simulations and experimental verification illustrate and confirm that the present method can accurately implement modal estimation from stationary response data only.

Use of instrumental variables methods in trajectory measurements’ problems

Possibilities of theinstrumental variables method using to improve the matrix properties of algebraic equations system are shown in the article. The problem of trajectory measurements from a network of ground-based, no-demand measuring stations using GLONASS navigation satellites is considered. The need to increase information content of trajectory measurements is especially important for trajectory measurements in the southern hemisphere of the Earth with a small number of measuring stations. The numerical experiment results with the simulation modeling use of trajectory measurements of the navigation satellite movement from two and three request-free measuring stations with geometric constraints are presented. The possibility of the measurements’ information content increasing from such base stations using the instrumental variables method is shown. Comparison of an indicator of the trajectory measurements informativenessis made according to the degree of the matrix conditionality of the algebraic equations system being solved. Based on the numerical experiment results, it isconsidered thepossibility to increase the information content of trajectory measurements from a network of non-query measuring stations with geometric constraints, with the instrumental variables involvement in the method processing. A quantitative estimate of the increase in information content was obtained in the form of a decrease in the condition number of the system matrix being solved by more than one order of magnitude. In the future, the research is predicted on the possibility of the trajectory measurements informativeness increasing for various basic functions used as instrumental variables, and their effect on the geometric constraints reducing an uneven network of measuring stations.