Effect of Parametric Uncertainties on the Effectiveness of Discrete Piezoelectric Spatial Modal Filters

Abstract

Modal filters may be obtained by a weighted sum of the signals of an array of sensors distributed on the host structure. However, the effect of parametric uncertainties on the effectiveness of the modal filter has received little attention. This work presents some numerical and experimental results on the effect of uncertainties of sensor array spatial distribution and weighting coefficients on the modal filtering effectiveness. For that, a free rectangular plate with twelve bonded piezoelectric sensors is considered. The spatial distribution of the array of piezoelectric sensors was optimized in a previous work to improve the effectiveness and frequency range of a set of modal filters. An experimental implementation of the modal filters was performed through a voltage divider and summing amplifier circuits and used to validate the performance of the modal filters. From numerical and experimental analysis, it was noticed, however, that the effectiveness of the modal filters are quite sensitive to the array spatial distribution and weighting coefficients. First, the effect of uncertainties of the array spatial distribution on the output of the modal filters was analyzed numerically using a finite element model. In this case, the main challenge was the cost of function evaluation and, thus, focus was put on solutions for the parameters sampling and approximations using response surface methods. Then, the effect of uncertainties of the weighting coefficients was evaluated using stochastic modeling combined with the measurement of individual responses of piezoelectric sensors. Confidence intervals for the modal filters output were evaluated and compared to experimental results with satisfactory results.

Semi-modal active vibration control of plates using discrete piezoelectric modal filters

“…This work extends previous ones in which modal filters based on optimally located arrays of piezoelectric sensors applied to a free-free rectangular plate were designed [21] and experimentally validated with satisfactory results [22]. In the present work, the modal filters outputs are used for feedback vibration control.…”

“…The effect of uncertainties of weighting coefficients on the quality of the implemented spatial modal filter was presented in a recent work [22].…”

Diseño de filtros modales considerando el posicionamiento óptimo de los acelerómetros

“…Su metodología utiliza un enfoque similar a Preumont et al [3], en tanto al abordaje del diseño a partir de la discretización del dominio frecuencial de respuestas teóricas. En un trabajo posterior, Trindade y Pagani Jr. [7] presentan resultados numéricos y experimentales del impacto de las incertidumbres en la posición de los sensores y las ganancias del filtro en el desempeño de este último. Continuando con esta línea de trabajo, Shigueoka and Trindade [8], aborda la determinación de la configuración adecuada de posiciones de los sensores a partir de un dominio continuo de posiciones candidatas.…”

Otimização de filtros modais espaciais usando redes de sensores aplicados ao controle de vibrações de estruturas do tipo viga e placa

“…Mais tarde, foi realizada uma análise do efeito que desvios no posicionamento das pastilhas piezoelétricas e nos valores do ganho de cada sensor teriam na FRF do filtro modal (TRINDADE et al, 2013). Conforme comentado no trabalho, quando a otimização escolhe o posicionamento dos sensores para aumentar a banda de frequência do filtro modal, há uma tendência de que a sensitividade a desvios no posicionamento também aumente.…”

“…Esses dois casos acabam por ter uma indesejável consequência. Erros presentes no vetor b são consideravelmente ampliados no cálculo dos ganhos α j do filtro modal quando a matriz é mal condicionada, o que seria desejável evitar, pois uma análise do efeito de incertezas em filtros modais aplicados uma placa mostrou que desvios nos ganhos α j dos sensores afetam mais o desempenho do filtro modal do que desvios no posicionamento ξ j dos sensores (TRINDADE et al, 2013).…”