“Elastography” refers to the procedure of using ultrasound to image tissue deformation. Images showing tissue deformation are sensitive to distributions of tissue mechanical properties. The mechanical properties themselves may be quantified by solving an inverse elasticity problem. An iterative approach to solving the inverse problem can be formulated by repeated solutions of the forward problem. That is, the shear modulus distribution sought is that which predicts a displacement field most consistent with the measured displacement field. Here we show that given plane displacement measurements for plane stress elasticity, the continuous elastic equilibrium equation uniquely determines the modulus distribution. On the other hand, we shall also demonstrate that the discrete elasticity equations from standard FEM discretization does not, even at the limit of infinite mesh refinement. We diagnose the problem as an underenforcement of the elasticity equations. With this knowledge, we have been able to design new forward elasticity FEM formulations that provide provably convergent forward and inverse elasticity solutions.
Monitoring of impurity gases in spent nuclear fuel (SNF) canisters is a novel structural health monitoring (SHM) approach for SNF in dry storage. The SNF canisters are sealed containers that do not facilitate visual access to the inside. Acoustic sensing can be deployed by taking advantage of the pathways unobstructed by internal hardware. Although the ultrasonic time-of-flight (TOF) measurement can provide valuable information, it is limited in its ability to discern the concentration of more than one impurity gas. In this case, deep learning algorithms, particularly Convolutional Neural Networks (CNNs), offer a promising solution. In this study, CNN-based probabilistic deep learning models were implemented to detect and quantify impurity gases in helium. An experimental platform was established to simulate canister conditions, and ultrasonic test data were collected. The presence of argon and air in helium at concentrations ranging from 0% to 1.2% at increments of 0.05% was considered. The multi-layer perceptron (MLP), decision tree (DT), and logistic regression (LR) classifiers achieved high accuracies when distinguishing pure helium from helium with impurities. CNN with dropout layers and CNN using maximum likelihood estimation showed similar performance, indicating their ability to capture uncertainties. The ensemble CNN model exhibited improved predictions and the ability to balance individual gas concentration by integrating 1D and 2D-CNN models. These findings contribute probabilistic deep learning solutions for impurity gas detection and analysis within SNF canisters, thus ensuring safe storage and management of SNFs.
This study examines the performance of the ducted rotor in hover and edgewise flight conditions. The flow over a three-dimensional model of a ducted rotor was simulated using the Spalart-Allmaras RANS model implemented in a stabilized finite element method. A sliding mesh was used to conveniently account for the large-scale motion associated with rotor revolutions. The simulation results were analyzed to understand the flow physics and quantify the contributions of the rotor and various sections of the duct interior surfaces on the total aerodynamic forces (thrust, drag and side force) and moments (pitching and rolling). In edgewise flight, freestream flow separates off the front of the duct inlet causing a region of recirculating flow and upwash in the rotor plane. The upwash region biases rotor thrust production to the front of the disk. The swirl velocity further biases the region of flow separation over the inlet and upwash at the front of the rotor towards the retreating side of the disk. The shift of thrust production on the rotor and duct towards the front produces a strong nose up pitching moment on the ducted rotor. The rear of the diffuser is a significant contributor to the total drag, this force as incudes a nose down pitch moment which partially negates the moment from the duct inlet. The rotor is the primary source of vertical vibratory forces as well as vibratory pitching and rolling moments. The small tip clearance of the rotor causes a local interaction between the blade tip and duct that is the dominant contributor to in-plane vibratory forces on the ducted rotor.
