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The application of statistical inversion theory provides a powerful approach for solving estimation problems including the ability for uncertainty quantification (UQ) by means of Markov chain Monte Carlo (MCMC) methods and Monte Carlo integration. This paper aims to analyze the application of a state reduction technique within different MCMC techniques to improve the computational efficiency and the tuning process of these algorithms.

A reduced state representation is constructed from a general prior distribution. For sampling the Metropolis Hastings (MH) Algorithm and the Gibbs sampler are used. Efficient proposal generation techniques and techniques for conditional sampling are proposed and evaluated for an exemplary inverse problem.

For the MH-algorithm, high acceptance rates can be obtained with a simple proposal kernel. For the Gibbs sampler, an efficient technique for conditional sampling was found. The state reduction scheme stabilizes the ill-posed inverse problem, allowing a solution without a dedicated prior distribution. The state reduction is suitable to represent general material distributions.

The state reduction scheme and the MCMC techniques can be applied in different imaging problems. The stabilizing nature of the state reduction improves the solution of ill-posed problems. The tuning of the MCMC methods is simplified.

The paper presents a method to improve the solution process of inverse problems within the Bayesian framework. The stabilization of the inverse problem due to the state reduction improves the solution. The approach simplifies the tuning of MCMC methods.

Inverse problems in electromagnetism, namely, the recovery of sources (currents or charges) or system data from measured effects, are usually ill-posed or, in the numerical formulation, ill-conditioned and require suitable regularization to provide meaningful results. To test new regularization methods, there is the need of benchmark problems, which numerical properties and solutions should be well known. Hence, this study aims to define a benchmark problem, suitable to test new regularization approaches and solves with different methods.

To assess reliability and performance of different solving strategies for inverse source problems, a benchmark problem of current synthesis is defined and solved by means of several regularization methods in a comparative way; subsequently, an approach in terms of an artificial neural network (ANN) is considered as a viable alternative to classical regularization schemes. The solution of the underlying forward problem is based on a finite element analysis.

The paper provides a very detailed analysis of the proposed inverse problem in terms of numerical properties of the lead field matrix. The solutions found by different regularization approaches and an ANN method are provided, showing the performance of the applied methods and the numerical issues of the benchmark problem.

The value of the paper is to provide the numerical characteristics and issues of the proposed benchmark problem in a comprehensive way, by means of a wide variety of regularization methods and an ANN approach.

This study aims to investigate the possible use of a deep neural network (DNN) as an inverse solver.

Different models based on DNNs are designed and proposed for the resolution of inverse electromagnetic problems either as fast solvers for the direct problem or as straightforward inverse problem solvers, with reference to the TEAM 25 benchmark problem for the sake of exemplification.

Using DNNs as straightforward inverse problem solvers has relevant advantages in terms of promptness but requires a careful treatment of the underlying problem ill-posedness.

This work is one of the first attempts to exploit DNNs for inverse problem resolution in low-frequency electromagnetism. Results on the TEAM 25 test problem show the potential effectiveness of the approach but also highlight the need for a careful choice of the training data set.

Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of electrical capacitance tomography. Two known computational bottlenecks are the assembly of the FE equation system as well as the computation of the Jacobian. Here, existing computation techniques like adjoint field approaches require additional simulations. This paper aims to present fast numerical techniques for the sensor simulation and computations with the Jacobian matrix.

For the FE equation system, a solution strategy based on Green’s functions is derived. Its relation to the solution of a standard FE formulation is discussed. A fast stiffness matrix assembly based on an eigenvector decomposition is shown. Based on the properties of the Green’s functions, Jacobian operations are derived, which allow the computation of matrix vector products with the Jacobian for free, i.e. no additional solves are required. This is demonstrated by a Broyden–Fletcher–Goldfarb–Shanno-based image reconstruction algorithm.

MATLAB-based time measurements of the new methods show a significant acceleration for all calculation steps compared to reference implementations with standard methods. E.g. for the Jacobian operations, improvement factors of well over 100 could be found.

The paper shows new methods for solving known computational tasks for solving inverse problems. A particular advantage is the coherent derivation and elaboration of the results. The approaches can also be applicable to other inverse problems.

The purpose of this paper is to propose a two-degrees-of-freedom wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism based on spring, in order to improve the robot’s athletic ability, load capacity and rigidity, and to ensure the coordination of multi-modal motion.

First, based on the rotation transformation matrix and closed-loop constraint equation of the parallel trunk joint mechanism, the mathematical model of its inverse position solution is constructed. Then, the Jacobian matrix of velocity and acceleration is derived by time derivative method. On this basis, the stiffness matrix of the parallel trunk joint mechanism is derived on the basis of the principle of virtual work and combined with the deformation effect of the rope driving pair and the spring elastic restraint pair. Then, the eigenvalue distribution of the stiffness matrix and the global stiffness performance index are used as the stiffness evaluation index of the mechanism. In addition, the performance index of athletic dexterity is analyzed. Finally, the distribution map of kinematic dexterity and stiffness is drawn in the workspace by numerical simulation, and the influence of the introduced spring on the stiffness distribution of the parallel trunk joint mechanism is compared and analyzed. It is concluded that the stiffness in the specific direction of the parallel trunk joint mechanism can be improved, and the stiffness distribution can be improved by adjusting the spring elastic structure parameters of the rope-driven branch chain.

Studies have shown that the wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism based on spring has a great kinematic dexterity, load-carrying capacity and stiffness performance.

The soft-mixed structure is not mature, and there are few new materials for the soft-mixed mixture; the rope and the rigid structure are driven together with a large amount of friction and hindrance factors, etc.

It ensures that the multi-motion mode hexapod mobile robot can meet the requirement of sufficient different stiffness for different motion postures through the parallel trunk joint mechanism, and it ensures that the multi-motion mode hexapod mobile robot in multi-motion mode can meet the performance requirement of global stiffness change at different pose points of different motion postures through the parallel trunk joint mechanism.

The trunk structure is a very critical mechanism for animals. Animals in the movement to achieve smooth climbing, overturning and other different postures, such as centipede, starfish, giant salamander and other multi-legged animals, not only rely on the unique leg mechanism, but also must have a unique trunk joint mechanism. Based on the cooperation of these two mechanisms, the animal can achieve a stable, flexible and flexible variety of motion characteristics. Therefore, the trunk joint mechanism has an important significance for the coordinated movement of the whole body of the multi-sport mode mobile robot (Huang Hu-lin, 2016).

In this paper, based on the idea of combining rigid parallel mechanism with wire-driven mechanism, a trunk mechanism is designed, which is composed of four spring-based wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism in series. Its spring-based wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism can make the multi-motion mode mobile robot have better load capacity, mobility and stiffness performance (Qi-zhi et al., 2018; Cong-hao et al., 2018), thus improving the environmental adaptability and reliability of the multi-motion mode mobile robot.

The operating wagon records were produced from distinct railway information systems, which resulted in the wagon routing record with the same oriental destination (OD) was different. This phenomenon has brought considerable difficulties to the railway wagon flow forecast. Some were because of poor data quality, which misled the actual prediction, while others were because of the existence of another actual wagon routings. This paper aims at finding all the wagon routing locus patterns from the history records, and thus puts forward an intelligent recognition method for the actual routing locus pattern of railway wagon flow based on SST algorithm.

Based on the big data of railway wagon flow records, the routing metadata model is constructed, and the historical data and real-time data are fused to improve the reliability of the path forecast results in the work of railway wagon flow forecast. Based on the division of spatial characteristics and the reduction of dimension in the distributary station, the improved Simhash algorithm is used to calculate the routing fingerprint. Combined with Squared Error Adjacency Matrix Clustering algorithm and Tarjan algorithm, the fingerprint similarity is calculated, the spatial characteristics are clustering and identified, the routing locus mode is formed and then the intelligent recognition of the actual wagon flow routing locus is realized.

This paper puts forward a more realistic method of railway wagon routing pattern recognition algorithm. The problem of traditional railway wagon routing planning is converted into the routing locus pattern recognition problem, and the wagon routing pattern of all OD streams is excavated from the historical data results. The analysis is carried out from three aspects: routing metadata, routing locus fingerprint and routing locus pattern. Then, the intelligent recognition SST-based algorithm of railway wagon routing locus pattern is proposed, which combines the history data and instant data to improve the reliability of the wagon routing selection result. Finally, railway wagon routing locus could be found out accurately, and the case study tests the validity of the algorithm.

Before the forecasting work of railway wagon flow, it needs to know how many kinds of wagon routing locus exist in a certain OD. Mining all the OD routing locus patterns from the railway wagon operating records is helpful to forecast the future routing combined with the wagon characteristics. The work of this paper is the basis of the railway wagon routing forecast.

As the basis of the railway wagon routing forecast, this research not only improves the accuracy and efficiency for the railway wagon routing forecast but also provides the further support of decision-making for the railway freight transportation organization.

This paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator.

When a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method.

Simulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits.

Currently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking.

Through a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time.

Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Fast iterative algorithms for designing birefringent filters with any specified spectral response are proposed. From the Jones formalism, we derive two polynomials representing the transmitted and rejected response of the filter, respectively. Once the coefficients of the filters are obtained, the orientation angle of each birefringent section and the phase shift introduced by each compensator can be determined by an iterative algorithm that gives an efficient solution to the birefringent filter design problem. Afterward, some design examples are presented to demonstrate the effectiveness of the proposed approach. In comparison with results reported in the literature, this approach provides the best performance in terms of accuracy and time complexity.