A non‐linear inverse vibration problem of estimating the time‐dependent stiffness coefficients by conjugate gradient method

Abstract

SUMMARYAn iterative regularization method, i.e. the conjugate gradient method (CGM) is applied to an inverse non-linear force vibration problem to estimate the unknown time-dependent sti ness coe cients (or spring constants) in a damped system by using the measured system displacement. It is assumed that no prior information is available on the functional form of the unknown sti ness coe cients in the present study, thus, it is classiÿed as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact displacement measurements. The numerical simulations are performed to test the validity of the present algorithm by using di erent types of sti ness coe cients and measurement errors. Results show that an excellent estimation on the time-dependent spring constants can be obtained with any arbitrary initial guesses within a couple of seconds of CPU time at Pentium III-500 MHz PC.

An Inverse Vibration Problem Solved by an Artificial Neural Network

“…From the values presented in Table 4, it can be noticed that the stiffness estimations are strongly affected by the quality of the experimental data. However, the estimation results obtained when the experimental data are corrupted by a 1% noise are similar to that presented in [9]. The worst estimation has been achieved considering discontinuous stiffness coefficients functions.…”

“…In all cases, the training phase was stopped with 5 × 10 4 epoches. Best results were obtained using ANN-2, see Inverse solutions obtained are similar to those presented by C. H. Huang [9]. However, after training process, ANN's are much faster than the variational approach, additionally, ANN's are intrinsicly parallel algorithms.…”

“…In this work a MLP Neural Network is employed to solve the same problem presented in [9], a 2-DOF dynamical system. The following parameters have been used in the forward problem, given by system (2.1)-(2.2): M 1 = 1.0 and M 2 = 3.0; C 1 (t) = 8.0 and C 2 (t) = 5.0; f 1 (t) = 50.0 and f 2 (t) = 60.0; and initial conditions x(0) = 0 andẋ(0) = 0.…”

“…These methods are usually classified under different categories, such as frequency and time domain methods, and deterministic and stochastic approaches [3]. Among the deterministic approaches the Conjugate Gradient method with the Adjoint Equation has been successfully used for different damaged lumped parameter systems [9,8,4]. Among the stochastic methods, the use of the artificial neural networks (ANN), which has already been used successfully in thermal sciences [12], has also been presented as a satisfactory choice to deal with the damage identification problem [5,13,14,2].…”

An Inverse Vibration Problem Solved by an Artificial Neural Network

“…The stiffness estimation problem has already been solved employing others methods [8,9,4]. In this work a MLP Neural Network is employed to solve the same problem presented in [9], a 2-DOF dynamical system.…”