Sidney Bruce Shiki

On the application of discrete-time Volterra series for the damage detection problem in initially nonlinear systems

Nonlinearities in the dynamical behavior of mechanical systems can degrade the performance of damage detection features based on a linearity assumption. In this article, a discrete Volterra model is used to monitor the prediction error of a reference model representing the healthy structure. This kind of model can separate the linear and nonlinear components of the response of a system. This property of the model is used to compare the consequences of assuming a nonlinear model during the nonlinear regime of a magneto-elastic system. Hypothesis tests are then employed to detect variations in the statistical properties of the damage features. After these analyses, conclusions are made about the application of Volterra series in damage detection.

Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinearprocedures are not used currently in practical applications due to the complexity and difficulty forimplementation of such techniques. Therefore, the development of techniques that consider the nonlinearbehavior of structures for damage detection is a research of major importance since nonlineardynamical effects can be erroneously treated as damage in the structure by classical metrics. Thispaper proposes the discrete-time Volterra series for modeling the nonlinear convolution between theinput and output signals in a benchmark nonlinear system. The prediction error of the model in anunknown structural condition is compared with the values of the reference structure in healthy conditionfor evaluating the method of damage detection. Since the Volterra series separate the responseof the system in linear and nonlinear contributions, these indexes are used to show the importanceof considering the nonlinear behavior of the structure. The paper concludes pointing out the mainadvantages and drawbacks of this damage detection methodology.

UPDATING OF A NONLINEAR FINITE ELEMENT MODEL USING DISCRETE-TIME VOLTERRA SERIES

IN THIS STUDY, THE DISCRETE-TIME VOLTERRA SERIES ARE USED TO UPDATE PARAMETERS IN A NONLINEAR FINITE ELEMENT MODEL. THE MAIN IDEA OF THE VOLTERRA SERIES IS TO DESCRIBE THE DISCRETE-TIME OUTPUT OF A NONLINEAR SYSTEM USING MULTIDIMENSIONAL CONVOLUTIONS BETWEEN THE VOLTERRA KERNELS REPRESENTED IN A KAUTZ ORTHOGONAL BASIS AND THE EXCITATIONS. A METRIC BASED ON THE RESIDUE BETWEEN THE EXPERIMENTAL AND THE NUMERICAL VOLTERRA KERNELS IS USED TO IDENTIFY THE PARAMETERS OF THE NUMERICAL MODEL. FIRST, THE IDENTIFICATION OF THE LINEAR PARAMETERS IS PERFORMED USING A METRIC BASED ONLY ON THE FIRST ORDER VOLTERRA KERNELS. THEN THE NONLINEAR PARAMETERS ARE IDENTIFIED THROUGH A METRIC BASED ON THE HIGHER-ORDER KERNELS. THE ORIGINALITY OF THIS NONLINEAR UPDATING METHOD STEMS FROM THE DECOUPLING OF LINEAR AND NONLINEAR PARAMETERS AND THE USE OF GLOBAL NONLINEAR MODEL. IN ORDER TO PUT IN LIGHT THE APPLICABILITY OF THIS TECHNIQUE, THIS WORK FOCUS ON THE IDENTIFICATION OF THE PARAMETERS IN A NONLINEAR FINITE ELEMENT MODEL OF A BEAM THAT WAS PRELOADED BY COMPRESSION MECHANISM. THIS WORK SHOWS THAT THE UPDATED NUMERICAL MODEL WAS ABLE TO REPRESENT THE BEHAVIOUR OBSERVED IN THE EXPERIMENTAL MEASUREMENTS.

Evaluation of damage indexes for structural health monitoring in nonlinear mechanical systems based on Volterra series

Nonlinear behavior can be important for the monitoring of the structural state of mechanical systems since it can be mistakenly classified as a damage in the systems. However, nonlinear tools are still not consolidated and need further research for applications in mechanical system. Discrete-time Volterra series is an interesting mathematical framework to deal with nonlinear dynamics. It is a clear generalization of the linear convolution for weakly nonlinear systems. In the present work two different damage indicators are proposed based on Volterra models by considering linear and nonlinear contributions of the total response. The goal is to evaluate these indicators using an experimental test rig where the damages are simulated and considering the nonlinear regime of motion. The main advantages and drawbacks of the proposed methodology are highlighted in the final remarks.