Dynamic Modeling and State Estimation of Cable-Conduit Actuation During Interaction With Nonpassive Environments

A frequency method was proposed to analyze cable tension from measured natural frequencies according to cable tension monitoring of acable stayed bridge during construction. Xinzao Pearl River Grand Bridge was chosen as an example. A geometrical calculation simulation model was established to compare measured cable tension to theoretical cable tension during construction. This paper introduces several cable tension test methods. The principle and theoretical derivations under certain conditions, the method of which fundamental vibration frequency is deduced by dominating vibration frequency, the influence of boundary conditions, bending stiffness, and cable sag on the frequency method testing, and the practical application of frequency method were discussed. A spatial finite element model was established based on finite element software MIDAS. The application of the forward-analysis iterative method was considered to analyze the cable tension during construction. Then the cable tension test method and analysis principle were explored. Finally, it was shown that measured cable tension based on the frequency method was accurate. The measured value is approximately equal to the theoretical value. The experimental error was within the permitted range. The accuracy and reliability of the frequency method was effectively confirmed. The cable tension test for the similar bridges during construction was compatibly applied.

This paper is devoted to develop a robust numerical method to solve a system of complementarity problems arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differential equations (PDEs). We then introduce a fitted finite volume method for the spatial discretization along with a fully implicit time stepping scheme for the PDEs, which results in a system of nonlinear algebraic equations. We show that this scheme is consistent, stable and monotone, hence convergent. To solve the system of nonlinear equations effectively, an iterative solution method is established. The convergence of the solution method is shown. Numerical tests are performed to examine the convergence rate and verify the effectiveness and robustness of the new numerical scheme.

This paper develops a general method for solving reservoir simulation equations, which is based upon an implicit finite difference formulation of the partial differential equations of compositional thermal simulation, permitting the simulation of nearly all enhanced oil recovery techniques. The general method is used to derive 10 solution schemes, which include the well-known IMPES, Simultaneous Solution (SS), and Sequential Solution (SEQ) methods as sub-cases. The novelty of the general method lies in showing the interrelations of these methods, and also affording the possibility of deriving still other methods. The theoretical development of the general method is given in detail, and the special methods are derived in reference to the reservoir problems for which they were employed. The starting point is a system of nonlinear finite difference equations, typical of compositional thermal simulation. Newtonian iteration then leads to a system of equations. The partitioning of the left-hand side (containing the unknown vector) in a particular manner permits the derivation of 10 solution approaches, which are identified in detail. The proposed general method bridges the gap in the development of the reported solution methods, and also points to several new approaches. The procedure described can be utilized for a variety of simulation problems, with fully implicit source-sink terms (including heat loss, thermal cracking, etc.), for both the standard and multipoint difference schemes in multi dimensions.

CANM, a program for numerical solution of a system of nonlinear equations using the continuous analog of Newton's method

In the maintenance of cable structures, such as cable-stayed bridges, cable safety is assessed based on the cable tension. In Japan, the cable tension is generally estimated from the cable’s natural frequencies using the higher-order vibration method. In recent years, dampers have been installed onto cables to suppress aerodynamic vibrations. Because the damper changes the cable’s natural frequencies, the damper is removed to measure the natural frequencies and estimate the cable tension without a damper, and the damper is then reinstalled. To avoid damper removal and reinstallation, the authors previously proposed Method 2F for estimating the tension of a cable with a damper from the natural frequencies without removing the damper. Because the tension estimation error of the higher-order vibration method for a cable without a damper has been reported as 5%, the authors set the target tension estimation error within 5%. However, the tension estimation error of Method 2F exceeded 5% in the experimental verification. Furthermore, although Method 2F estimates the tension and bending stiffness of the cable and the damper parameters simultaneously from the natural frequencies, the accuracy of the bending stiffness and damper parameters is unsatisfactory. In this paper, the new Method 2FM is proposed to estimate the tension and bending stiffness of the cable and damper parameters using the natural frequencies and two-point mode shapes. With the addition of mode shapes, Method 2FM attempts to improve the accuracy of estimating the tension and other parameters. The validity of Method 2FM was confirmed by numerical simulations and experiments. The numerical verification confirmed that Method 2FM is superior to Method 2F in estimating the cable tension and damper parameters. The experimental verification confirmed that the tension estimation accuracy of Method 2FM is higher than that of Method 2F, and the estimation error is lower than 5%. However, the damper parameters estimated by Method 2FM are different to the design values. The reason for this is the modeling error of the damper, as found by conducting an element test on the damper.

Element-by-element iterative solution methods have been shown to be effective for solving large, sparse linear systems of equations with a positive definite stiffness matrix. In this paper the iterative method GMRES will be described. This solution method is also suited for solving nonsymmetric systems of equations. As acceleration technique an element-by-element preconditioner has been employed. Attention is focused mainly on the convergence behaviour of the method. The calculations described in this paper have been performed with the finite element package DIANA.

In literature, it has been reported that the convergence of some preconditioned stationary iterative methods using certain type upper triangular matrices as preconditioners are faster than the basic iterative methods. In this paper, a new preconditioned iterative method for the numerical solution of linear systems has been introduced, and the convergence analysis of the proposed method and an existing one have been done. Some numerical examples have also been given, which show the effectiveness of both of the methods.

97/04852 Coal pulsating combustion model: Xu, W. Ranshao Kexue Yu Jishu., 1996, 2, (3), 260–269. (In Chinese)

98/03268 Reopening of pulverized coal injection in blast furnace after a pause

99/00738 On the combustion of heat pump with solar steam turbine

99/00035 ESR study of the macromolecular structure of copper-porphyrin-labeled coal

The paper deals with a numerical algorithm to reduce the overall system of integral equations describing the heat transfer process at any geometrically complex area (both twodimensional and three-dimensional), to the iterative solution of a system of independent onedimensional integral equations. This approach has been called "string method" and has been used to solve a number of applications, including the problem of the detonation wave front for the calculation of heat loads in pulse detonation engines. In this approach "the strings" are a set of limited segments parallel to the coordinate axes, into which the whole solving area is divided (similar to the way the strings are arranged in a tennis racket). Unlike other grid methods where often for finding solutions, the values of the desired function in the region located around a specific central point here in each iteration step is determined by the solution throughout the length of the one-dimensional "string", which connects the two end points and set them values and determine the temperature distribution along all the strings in the first step of an iterative procedure.

Cable tension force is one of the most important structural parameters to monitor in cable-stayed bridges. For example, cable tension needs to be monitored during construction and maintenance to ensure the bridge is not overloaded. To economically monitor tension forces, this study proposes the use of an automated wireless tension force estimation system (WFTES) developed solely for cable force estimation. The design of the WFTES system can be divided into two parts: low-cost hardware and automated software. The low-cost hardware consists of an integrated platform containing a wireless sensing unit constructed from commercial off-the-shelf components, a low-cost commercial MEMS accelerometer, and a signal conditioning board for signal amplification and filtering. With respect to the automated software, a vibration-based algorithm using estimated modal parameters and information on the cable sag and bending stiffness is embedded into the wireless sensing unit. Since modal parameters are inputs to the algorithm, additional algorithms are necessary to extract modal features from measured cable accelerations. To validate the proposed WFTES, a scaled-down cable model was constructed in the laboratory using steel rope wire. The wire was exposed to broad-band excitations while the WFTES recorded the cable response and embedded algorithms interrogated the measured acceleration to estimate tension force. The results reveal the embedded algorithms properly identify the lower natural frequencies of the cable and make accurate estimates of cable tension. This paper concludes with a summary of the salient research findings and suggestions for future work.

In this paper, first, we use the Rich type iterative method for numerical solution of nonlinear fuzzy Fredholm integral equation. The main structure of this method is based on the Richardson iterative method and trapezoidal quadrature formula for Numerical solution of nonlinear fuzzy integral equations. Convergence, error analysis and numerical stability of the proposed method are also discussed.

The article is devoted to the analysis of methods for solving systems of multivalued logical equations by iteration methods. Iterative methods for solving such systems of equations are a mathematical description of the main process of functional-logical simulation, which is used at the stage of designing digital systems for objects control to verify the correctness of the design. Consideration of multi-valued values of logical signals at the outputs of blocks and elements of digital systems is explained by the fact that in some cases, to analyze the correctness of time relationships when simulating the hardware of digital systems, a several valued representation of logical signals is used, as well as that recently, logical elements are being developed that implement four or more valued logic. Based on the analysis of the structure of the system of logical equations used in digital hardware simulation, using graph and logical models, an analysis is made of the existence of solutions and their number. Iterative methods of a simple and generalized iteration are analyzed, a relationship is shown between the number of solutions of the system of equations and its graph representation, which reflects a given circuit of connecting elements of the hardware of a digital control system. For the generalized iteration method, options with a different structure of the iteration trace are considered, in particular, it is shown that, with a certain structure of the iteration trace, the generalized iteration turns into a simple iteration or Seidel iteration. It is shown that the generalized iteration most adequately describes the process of simulating the switching of logical signals in a simulated circuit of digital control systems hardware. The correspondence between various options of functional-logical simulation of digital systems and the used methods of iterative solution of systems of logical equations is shown.