Identification and Defect Detection of Continuous Dynamic Systems

2006 ◽  
Author(s):  
A. Siami ◽  
M. Farid
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Defect Detection ◽  
Equations Of Motion ◽  
Continuous System ◽  
Least Square Method ◽  
Least Square ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Continuous Dynamic

This paper presents a systematic and efficient algorithm using a coupled finite element - finite difference - least square method for identification and defect detection of continuous system using dynamic response of such systems. First the governing partial differential equations of motion of continuous systems such as beams are reduced to a set of ordinary differential equations in time domain using finite elements. Then finite difference method is used to convert these equations into a set of algebraic equations. This set of equations is considered as a set of equality constraints of an optimization problem in which the objective function is the summation of the squares of differences between measured data at specific points and the predicted data obtained by the solution of the governing system of differential of equations. This method has been successfully applied to find mechanical properties of aforementioned systems in an iterative procedure.

scholarly journals Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting

2020 ◽  
Vol 7 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Bolat Duissenbekov ◽  
Abduhalyk Tokmuratov ◽  
Nurlan Zhangabay ◽  
Zhenis Orazbayev ◽  
Baisbay Yerimbetov ◽  
...  
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Difference Equations ◽  
Constant Load ◽  
Time Interval ◽  
Test Case ◽  
Algebraic Equations ◽  
Nonlinear Properties ◽  
Finite Difference Equations ◽  
Concrete Shells

AbstractThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.

scholarly journals Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

2021 ◽  
Vol 5 (4) ◽  
pp. 167
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Umar Nazir ◽  
Poom Kumam ◽  
Muhammad Sohail
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Comparison Study ◽  
Nano Fluid ◽  
Complicated Geometry ◽  
Maple Code

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

Identification of Nonlinear Systems by Haar Wavelet

2004 ◽  
Author(s):  
Shy-Leh Chen ◽  
Keng-Chu Ho
Keyword(s):  
Nonlinear Systems ◽  
Least Square Method ◽  
Haar Wavelet ◽  
State Equation ◽  
Least Square ◽  
Algebraic Equations ◽  
Function Form ◽  
Unknown Parameters ◽  
Complete Orthogonal Basis ◽  
Unknown System

This study addresses the identification of autonomous nonlinear systems. It is assumed that the function form in the nonlinear system is known, leaving some unknown parameters to be estimated. It is also assumed that the free responses of the system can be measured. Since Haar wavelets can form a complete orthogonal basis for the appropriate function space, they are used to expand all signals. In doing so, the state equation can be transformed into a set of algebraic equations in unknown parameters. The technique of Kronecker product is utilized to simplify the expressions of the associated algebraic equations. Together with the least square method, the unknown system parameters are estimated. Several simulation examples verify the analysis.

Defect detection of nickel plated punched steel strip based on improved least square method

Optik ◽  
2020 ◽  
Vol 206 ◽  
pp. 164331
Author(s):  
Binfang Cao ◽  
Jianqi Li ◽  
Chengfa Liu ◽  
Lingjie Qin
Keyword(s):  
Defect Detection ◽  
Steel Strip ◽  
Least Square Method ◽  
Least Square

Modeling Impacts Between a Continuous System and a Rigid Obstacle Using Coefficient of Restitution

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Chandrika P. Vyasarayani ◽  
John McPhee ◽  
Stephen Birkett
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Continuous System ◽  
Coefficient Of Restitution ◽  
Continuous Systems ◽  
Rigid Obstacle ◽  
Unit Impulse ◽  
Before And After ◽  
System Equations ◽  
The Impact

In this work, we discuss the limitations of the existing collocation-based coefficient of restitution method for simulating impacts in continuous systems. We propose a new method for modeling the impact dynamics of continuous systems based on the unit impulse response. The developed method allows one to relate modal velocity initial conditions before and after impact without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. We also compare the results obtained by unit impulse-based coefficient of restitution method with a penalty approach.

Least Square Inversed Analysis of Soil Parameter for Foundation with Two-Order Gradient Theoretic Method

2011 ◽  
Vol 243-249 ◽  
pp. 2294-2299 ◽  
Author(s):  
Yao Feng Xie
Keyword(s):  
Differential Equations ◽  
Error Function ◽  
Least Square Method ◽  
Least Square ◽  
Gradient Theory ◽  
Mechanical Theory ◽  
Soil Parameter ◽  
True Value ◽  
Initial Soil ◽  
Calculation Results

Combined with two-order gradient theory, the least square inversed analysis of the soil parameter for the foundation is studied and put forward in detail. After the mechanical theory for the plate on the foundation is introduced, the controlling differential equations of the plate on the foundation which is subjected to vertical loads are deduced. Through utilizing Fourier transformative theory, the corresponding solutions to the plate on the foundation are gained. Linear algebra controlling equations for the plate are achieved which leads to solve the original differential equations more easily. The least square error function for the soil parameter on the plate is established and applied with the two-order gradient method. The inversed steps on the least square error function for the soil parameter are listed. The calculation results verify the conclusions that the soil parameter of the foundation can be efficiently inversed by applying the least square theory. When different initial soil parameter is set, the iterative computations can be convergent to the true value of the soil parameter. And this least square method can also be applied for the problem of inversed analysis of parameters for other foundation models.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

scholarly journals Calculation of ICG kinetics by two simultaneous differential equations and non-linear least square method.

Kanzo ◽  
1988 ◽  
Vol 29 (10) ◽  
pp. 1368-1373
Author(s):  
Yutaka SAGAWA ◽  
Toshiko YOSHIKATA ◽  
Nagaki SHIMADA ◽  
Motonobu SUGIMOTO
Keyword(s):  
Differential Equations ◽  
Least Square Method ◽  
Least Square ◽  
Non Linear ◽  
Linear Least Square

Solitary waves of the RLW equation via least squares method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ozlem Ersoy Hepson ◽  
Idris Dag ◽  
Bülent Saka ◽  
Buket Ay
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Spline Functions ◽  
Algebraic Equations ◽  
B Spline ◽  
B Splines ◽  
Rlw Equation ◽  
Set Up

Abstract Integration using least squares method in space and Crank–Nicolson approach in time is managed to set up an algorithm to solve the RLW equation numerically. Trial functions in the least square method consist of a combination of the quartic B-spline functions. Integration of the RLW equation gives a system of algebraic equations. The solutions consisting of a combination of the quartic B-splines are given for some initial and boundary value problems of RLW equation.

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