K. Shankar

PARAMETRIC IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS USING COMBINED LEVENBERG–MARQUARDT AND GENETIC ALGORITHM

This technical note presents the parametric identification of multi-degree-of-freedom nonlinear dynamic systems in the time domain using a combination of Levenberg–Marquardt (LM) method and Genetic Algorithm (GA). Here the crucial initial values to the LM algorithm are supplied by GA with a small population size. Two nonlinear systems are studied, the complex one having two nonlinear spring-damper pairs. The springs have cubic nonlinearity (Duffing oscillator) and dampers have quadratic nonlinearity. The effects of noise in the acceleration measurements and sensitivity analysis are also studied. The performance of combined GA and LM method is compared with pure LM and pure GA in terms of solution time, accuracy and number of iterations, and convergence and great improvement is observed. This method is found to be suitable for the identification of complex nonlinear systems, where the repeated solution of the numerically difficult equations over many generations requires enormous computational effort.

Joint damage identification using Improved Radial Basis Function (IRBF) networks in frequency and time domain

In this paper, a novel two-stage Improved Radial Basis Function (IRBF) neural network technique is proposed to predict the joint damage of a fifty member frame structure with semi-rigid connections in both frequency and time domain. The effective input patterns as normalized design signature indices (NDSIs) in frequency domain and acceleration responses in time domain are simulated numerically from finite element analysis (FEA) by considering different levels of damage severity using Latin hypercube sampling (LHS) technique. The conventional RBF network is used in the first stage of IRBF network and in the second stage reduced search space moving technique is employed for accurate prediction with less than 3% error. The numerical simulation of the substructural joint damage identification of a fifty member frame structure with and without addition of 5% Gaussian random noise to the input patterns is presented and compared with conventional CPN-BPN hybrid method. The two-stage IRBF method is found to be superior in accuracy to conventional hybrid methods as well as to conventional RBF method. An important benefit of the proposed novel IRBF method is the significant reduction in the computational time with good accuracy of joint damage identification.

Improved Complex-valued Radial Basis Function (ICRBF) neural networks on multiple crack identification

Absolute mean percentage error (AMPE) of single crack and multiple crack identification using different RBF networks. A two-stage ICRBF neural network is developed for multiple crack identification.Conventional CRBF neural network is used in the first stage of ICRBF.Reduced search space moving technique is used in the second stage of ICRBF.Crack location and depth are identified using frequency domain vibration signals.ICRBF is more efficient followed by IRBF, CRBF, RBF and MLP neural networks. This paper introduces a new class of neural networks in complex space called Complex-valued Radial Basis Function (CRBF) neural networks and also an improved version of CRBF called Improved Complex-valued Radial Basis Function (ICRBF) neural networks. They are used for multiple crack identification in a cantilever beam in the frequency domain. The novelty of the paper is that, these complex-valued neural networks are first applied on inverse problems (damage identification) which come under the category of function approximation. The conventional CRBF network was used in the first stage of ICRBF network and in the second stage a reduced search space moving technique was employed for accurate crack identification. The effectiveness of proposed ICRBF neural network was studied first on a single crack identification problem and then applied to a more challenging problem of multiple crack identification in a cantilever beam with zero noise as well as 5% noise polluted signals. The results proved that, the proposed ICRBF and real-valued Improved RBF (IRBF) neural networks have identified the single and multiple cracks with less than 1% absolute mean percentage error as compared to conventional CRBF and RBF neural networks, mainly because of their second stage reduced search space moving technique. It appears that IRBF neural network is a good compromise considering all factors like accuracy, simplicity and computational effort.

Structural Damage Identification Using Improved RBF Neural Networks in Frequency Domain

This paper presents a novel two stage improved Radial basis function (RBF) neural network for the damage identification of multimember structures in the frequency domain. The improvement of the proposed RBF network is carried out in two stages, viz. (i) first stage damage prediction by conventional RBF network trained with effective input-output patterns and (ii) in the second stage, minimization of the prediction error below the predefined error tolerance (3%) by training the network with patterns from reduced search space located after the first stage prediction. The network effective input patterns are fractional frequency change ratios (FFCs) and damage signature indices (DSIs), and the corresponding output patterns are stiffness values or damage severity of the structure at different damage levels. A Latin hypercube search (LHS) technique is used for finding the effective input-output patterns from the search space to improve the training efficiency. The numerical simulation of structural damage identification for two multimember structures; a six-storey steel structure and a nine-member frame structure, are evaluated with and without addition of 5% random noise to the input patterns using the proposed network. The novel improved RBF network is shown to be a good damage identification strategy for multiple member structures compared to conventional RBF and existing hybrid methods in terms of accuracy and computational effort.

Parametric Identification of Structures with Nonlinearities Using Global and Substructure Approaches in the Time Domain

This paper presents further research on the parametric identification of structures with non-linearities in stiffness and damping properties. Parametric identification is carried out using acceleration responses in the time domain and is useful for structural health monitoring. Cubic nonlinearities in springs and quadratic nonlinearities in dampers are considered. Structural parametric identification is modeled as an inverse problem, based on minimizing the difference between measured responses and calculated responses from a mathematical model. The results of both global and substructural identification approaches are compared. The substructural approach allows us to identify a smaller domain while ignoring external parameters, resulting in a reduced model, but on the other hand the formulation is more complex. Genetic algorithms (GA) are used for filtering the unknown parameter values from within a given range. Simple real coded GA as well as a superior hybrid version obtained by combining with the Levenberg-Marquardt (LM) have been studied. Several numerical examples, including variations of a 10 DOF non-linear lumped mass system and a 12 member truss with several non-linear tuned mass dampers have been studied. The effect of measurement noise have been considered. The substructural method is shown to be superior overall in terms of speed, accuracy and economy (number of sensors) although the global identification approach implemented in conjunction with hybrid GA performs well in some cases.

Application of RBF neural network in prediction of particle damping parameters from experimental data

Particle damping is one of the recent passive damping methods and its relevance in space structural applications is increasing. This paper presents the novel application of a radial basis function (RBF) neural network to accurately predict the modal damping ratio of a particle damping system using system input parameters such as particle size, particle density, packing ratio, and their effect at different modes of vibration. The prediction of particle damping using the RBF neural network is studied in comparison with the back propagation neural (BPN) network on an aluminum alloy beam structure with extensive experimental tests. The prediction accuracy of the RBF neural network is significant with 9.83% error compared to 12.22% obtained by the BPN network for a best case. Limited experiments were also carried out on a mild steel beam to study and compare the trends predicted in earlier studies. The relationships obtained by the proposed method readily provide useful guidelines in the design of particle dampers for space applications. The RBF neural network provides superior accuracy with reduced computational effort.

Experimental investigation of particle damper-based vibration suppression in printed circuit board for spacecraft applications

One of the effective methods of passive vibration suppression is through the application of particle damping technique. This paper discusses the novel application of particle damper capsule to suppress the vibration of a Printed Circuit Board (PCB) and study the relationships between the vibration responses and the input force amplitude for various particle damper parameters such as Particle Size (PS), Particle Density (PD) and Packing Ratio (PR). Several experiments were carried out with different combinations of particle damper parameters for the estimation of vibration responses in the PCB for the primary modes of vibration. Based on these, the factors which affect the vibration responses are studied in detail for the chosen combination of system parameters. Also, the relationships between the response and the applied force for various PS, PR, PD and response locations are obtained and they are used to arrive at the design guidelines for the particle damper suitable for spacecraft electronic packages. The vibration suppression of PCB under random vibration environment is performed to demonstrate the effectiveness of the designed particle damper.

Damage Identification of Multimember Structure using Improved Neural Networks

A novel two stage Improved Radial Basis Function (IRBF) neural network for the damage identification of a multimember structure in the frequency domain is presented. The improvement of the proposed IRBF network is carried out in two stages. Conventional RBF network is used in the first stage for preliminary damage prediction and in the second stage reduced search space moving technique is used to minimize the prediction error. The network is trained with fractional frequency change ratios (FFCs) and damage signature indices (DSIs) as effective input patterns and the corresponding damage severity values as output patterns. The patterns are searched at different damage levels by Latin hypercube sampling (LHS) technique. The performance of the novel IRBF method is compared with the conventional RBF and Genetic algorithm (GA) methods and it is found to be a good multiple member damage identification strategy in terms of accuracy and precision with less computational effort.

Parametric Estimation Of Nonlinear 3D Of System Using Genetic Algorithm In Time Domain

This paper mainly concentrates on the procedural technique to identify the system parameters of multi degrees of freedom nonlinear system using Genetic Algorithm (GA) in time domain. Conventional optimization techniques are mainly calculus based, and often fails in search for global optimum. In this paper estimation has been done using continuous Genetic Algorithm (GA). In parametric estimation the difference between experimental acceleration and acceleration estimated by GA is minimized by updating the parameters. A three degrees of freedom (3-DOF) system with two pairs of non-linear spring and damper (Van der Pol–Duffing oscillator) is considered. Both hardening and softening type of nonlinear springs are considered and corresponding parameters are estimated. The system is excited by known harmonic forces at each mass to ensure enough excitation. Different combinations of hardening and softening nonlinear springs, nonlinear dampers, and single and two nonlinear springs are solved in the present study. The percentage of error in estimation of parameters is less than 5%. Perturbation analysis has been done to study the sensitivity of parameters on output. genetic algorithm, non-linear damper, hardening softening nonlinear springs, perturbation analysis