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In this paper, a multi-frequency MEMS acoustic emission (AE) sensor is designed, characterized, and tested. The sensor includes sixteen individual resonators tuned in the range of 100 kHz to 700 kHz. The resonator frequencies are selected to form constructive interference when they are connected in parallel to increase the signal-to-noise ratio. Each resonator is comprised of a membrane that forms the mass and four beams that provide stiffness. The membrane size is kept the same for each resonator to have approximately the same sensitivity per frequency. The influence of spring elements on the resonant frequency and the sensitivity is numerically demonstrated. The sensor is manufactured using MEMSCAP PiezoMUMPs. The characterization experiments show a slight shift in the resonant frequency of individual resonators compared to the design values. The MEMS sensor is packaged using a custom-designed printed circuit board to improve the signal-to-noise ratio. The sensor performance is compared with a conventional AE sensor. The sensitivity and frequency bandwidth of the MEMS AE device is brought to a comparable level to bulky AE sensors. 

Growth curve models (GCMs), with their ability to directly investigate within-subject change over time and between-subject differences in change for longitudinal data, are widely used in social and behavioral sciences. While GCMs are typically studied with the normal distribution assumption, empirical data often violate the normality assumption in applications. Failure to account for the deviation from normality in data distribution may lead to unreliable model estimation and misleading statistical inferences. A robust GCM based on conditional medians was recently proposed and outperformed traditional growth curve modeling when outliers are present resulting in nonnormality. However, this robust approach was shown to perform less satisfactorily when leverage observations existed. In this work, we propose a robust double medians growth curve modeling approach (DOME GCM) to thoroughly disentangle the influence of data contamination on model estimation and inferences, where two conditional medians are employed for the distributions of the within-subject measurement errors and of random effects, respectively. Model estimation and inferences are conducted in the Bayesian framework, and Laplace distributions are used to convert the optimization problem of median estimation into a problem of obtaining the maximum likelihood estimator for a transformed model. A Monte Carlo simulation study has been conducted to evaluate the numerical performance of the proposed approach, and showed that the proposed approach yields more accurate and efficient parameter estimates when data contain outliers or leverage observations. The application of the developed robust approach is illustrated using a real dataset from the Virginia Cognitive Aging Project to study the change of memory ability. 

Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non‐normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project.