Wilkins Aquino

Optimal experimental design provides a way of determining a-priori the best locations at which to place accelerometers in vibrations analysis experiments. However, in practice, sensors often fail during experimentation due high mechanical accelerations. There have been limited works exploring the use of robust OED in the context of vibrations analysis, where design spaces (i.e. candidate sensor locations and orientations) are high-dimensional and the finite-element models are expensive to compute. Therefore, this work considers the application of more general robust OED formulations to such a structural dynamics problem. We employ a relaxation-based approach that enables the use of efficient gradient-based optimization. Furthermore, we leverage a binary-inducing penalty during optimization to provide a binary sensor design as an alternative to leveraging post-optimization rounding heuristics. We consider performance metrics based on the log-determinant of the parameter covariance as well those based on parameter and prediction mean-squared errors. We find that although robust and classical designs are similar for the structural dynamics problem of interest, robust designs outperform classical designs on average over relevant failure scenarios of interest.

Optimal experimental design provides a way of determining a-priori the best locations at which to place accelerometers in vibrations analysis experiments. However, in practice, sensors often fail during experimentation due high mechanical accelerations. There have been limited works exploring the use of robust OED in the context of vibrations analysis, where design spaces (i.e. candidate sensor locations and orientations) are high-dimensional and the finite-element models are expensive to compute. Therefore, this work considers the application of more general robust OED formulations to such a structural dynamics problem. We employ a relaxation-based approach that enables the use of efficient gradient-based optimization. Furthermore, we leverage a binary-inducing penalty during optimization to provide a binary sensor design as an alternative to leveraging post-optimization rounding heuristics. We consider performance metrics based on the log-determinant of the parameter covariance as well those based on parameter and prediction mean-squared errors. We find that although robust and classical designs are similar for the structural dynamics problem of interest, robust designs outperform classical designs on average over relevant failure scenarios of interest.

Ultrasound shear wave elastography is a medical imaging technique where mechanical properties (e.g., shear modulus) of soft tissue are imaged with the goal of diagnosing disease. However, different sources of noise or error often lead to poor images that exacerbate uncertainty of medical diagnosis based on these techniques. Sources of uncertainty include scatterer positions and strengths (e.g., emanating from the cellular structure of tissue), other surrounding tissue not included in the image, and electronic noise, among others. In this work, we are developing Optimal Experimental Design (OED) techniques based on the simulation of the ultrasound imaging process and particle tracking to identify controls that maximize the quality of elastography images. Specifically, we propose a general formulation for OED where the observation error depends on both uncertain quantities and the variables to be inferred (e.g., shear moduli). Furthermore, we pose a nonlinear OED problem where the main design variables are the angles used in plane wave compounding for ultrasound motion tracking of propagating shear waves. The goal of the OED problem is to find the number and values of compounding angles that minimize bias and variance in the estimated shear modulus image. We will demonstrate our approach through various numerical examples.

Detection and identification of nonlinearity is a task of high importance for structural dynamics.On the one hand, identifying nonlinearity in a structure would allow one to build more accurate models of the structure.On the other hand, detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage within the structure.Common damage cases which cause nonlinear behaviour are breathing cracks and points where some material may have reached its plastic region.Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour.In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest.The data-driven model selected for the current application is a neural network.The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data.The neural network is trained to predict the accelerations of the structure for a time-instant using as input accelerations of previous time-instants, i.e. one-step-ahead predictions.Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated.Given that the structure is linear, the distribution of the aforementioned gradients should be unimodal and quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal.To test the above assumption, data from an experimental structure are considered.The structure is tested under different scenarios, some of which are linear and some of which are nonlinear.More specifically, the nonlinearity is introduced as a column-bumper nonlinearity, aimed at simulating the effects of a breathing crack and at different levels, i.e. different values of the initial gap between the bumper and the column.Following the proposed method, the statistics of the distributions of the gradients for the different scenarios can indeed be used to identify cases where nonlinearity is present.Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for lower values of the initial column-bumper gap, i.e. for "more nonlinear" scenarios.

Abstract Acoustic gravimetric biosensors attract attention due to their simplicity, robustness, and low cost. However, a prevailing challenge in these sensors is dissipation which manifests in a low quality factor ( Q -factor), which limits their sensitivity and accuracy. To mitigate dissipation of acoustic sensors in liquid environments we introduce an innovative approach in which we combine microfluidic channels with gravimetric sensors. To implement this novel paradigm we chose the quartz crystal microbalance (QCM) as our model system, owing to its wide applicability in biosensing and the relevance of its operating principles to other types of acoustic sensors. We postulate that the crucial determinant for enhancing performance lies in the ratio between the width of the microfluidic channels and the wavelength of the pressure wave generated by the oscillating channel side walls driven by the QCM. Our hypothesis is supported by finite element analysis (FEA) and dimensional studies, which revealed two key factors that affect device performance: (1) the ratio of the channel width to the pressure wavelength ( $$W/{\lambda }_{{\rm {p}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) and (2) the ratio of the channel height to the shear evanescent wavelength ( $$H/{\lambda }_{{\rm {s}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). To validate our hypothesis, we fabricated a microfluidic QCM (µ-QCM) and demonstrated a remarkable 10-fold improvement in its dissipation when compared to conventional QCM. The novel microfluidic approach offers several additional advantages, such as direct data interpretation, reduced volume requirement for sample liquids, and simplified temperature control, augmenting the sensor’s overall performance. By fostering increased sensitivity, accuracy, and ease of operation, our novel paradigm unlocks new possibilities for advancing gravimetric technologies, potentially for biosensing applications.

This paper presents a numerical framework for designing diffuse fields in rooms of any shape and size, driven at arbitrary frequencies. That is, we aim at overcoming the Schroeder frequency limit for generating diffuse fields in an enclosed space. We formulate the problem as a Tikhonov regularized inverse problem and propose a low-rank approximation of the spatial correlation that results in significant computational gains. Our approximation is applicable to arbitrary sets of target points and allows us to produce an optimal design at a computational cost that grows only linearly with the (potentially large) number of target points. We demonstrate the feasibility of our approach through numerical examples where we approximate diffuse fields at frequencies well below the Schroeder limit.

Abstract We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This assumption is difficult to justify in many inverse problems, where the specification of the data generation process is not obvious. We adopt a Gibbs posterior framework that directly posits a regularized variational problem on the space of probability distributions of the parameter. We propose a novel model comparison framework that evaluates the optimality of a given loss based on its ‘predictive performance’. We provide cross-validation procedures to calibrate the regularization parameter of the variational objective and compare multiple loss functions. Some novel theoretical properties of Gibbs posteriors are also presented. We illustrate the utility of our framework via a simulated example, motivated by dispersion-based wave models used to characterize arterial vessels in ultrasound vibrometry.

of the U.

Goal: Develop a general sensor placement framework for different systems (e.g.structures, heat conduction, etc.)