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We present a predictive runtime monitoring technique for estimating future vehicle positions and the probability of collisions with obstacles. Vehicle dynamics model how the position and velocity change over time as a function of external inputs. They are commonly described by discrete-time stochastic models. Whereas positions and velocities can be measured, the inputs (steering and throttle) are not directly measurable in these models. In our paper, we apply Bayesian inference techniques for real-time estimation, given prior distribution over the unknowns and noisy state measurements. Next, we pre-compute the set-valued reachability analysis to approximate future positions of a vehicle. The pre-computed reachability sets are combined with the posterior probabilities computed through Bayesian estimation to provided a predictive verification framework that can be used to detect impending collisions with obstacles. Our approach is evaluated using the coordinated-turn vehicle model for a UAV using on-board measurement data obtained from a flight test of a Talon UAV. We also compare the results with sampling-based approaches. We find that precomputed reachability analysis can provide accurate warnings up to 6 seconds in advance and the accuracy of the warnings improve as the time horizon is narrowed from 6 to 2 seconds. The approach also outperforms sampling in terms of on-board computation cost and accuracy measures.

In three-dimensional (3D) medical ultrasound imaging with two-dimensional (2D) arrays, sparse 2D arrays have been studied to reduce the number of active channels. Among them, sparse 2D arrays with regular or uniform arrangements of elements have advantages of low side lobe energy and uniform field responses over the entire field of view. This paper presents two uniform sparse array models: sparse rectangular arrays (SRAs) on a rectangular grid and sparse spiral arrays (SSAs) on a sunflower grid. Both arrays can be easily implemented on the commercially available or the custom-made arrays. To suppress the overall grating lobe levels, the transmit (Tx) and receive (Rx) array pairs of both the array models are designed not to have grating lobes at the same locations in the Tx/Rx beam patterns, for which the theoretical design rules are also proposed. Computer simulation results indicate that the proposed array pairs for both the SRAs and the SSAs achieve peak grating lobe levels below &ndash, 40 dB using about a quarter of the number of elements in the dense rectangular array while maintaining similar beam widths to that of the dense array pair.

3D ultrasound imaging with 2D transducer arrays of large number of elements suffers from high hardware and computational complexity. In order to reduce the number of active channels, various sparse 2D array designs were presented. However, the proposed designs so far have either irregular element distribution that cannot guarantee uniformity among the scan lines or lack of analysis. In this study, a generalized sparse rectangular array (SRA) is presented, and a design rule that avoids common grating lobes of the transmit and receive SRA pairs is derived by analyzing the beam patterns. The continuous wave (CW) and pulsed wave responses of the SRA pairs are simulated to verify the proposed design rule.

We propose a predictive runtime monitoring approach for linear systems with stochastic disturbances. The goal of the monitor is to decide if there exists a possible sequence of control inputs over a given time horizon to ensure that a safety property is maintained with a sufficiently high probability. We derive an efficient algorithm for performing the predictive monitoring in real time, specifically for linear time invariant (LTI) systems driven by stochastic disturbances. The algorithm implicitly defines a control envelope set such that if the current control input to the system lies in this set, there exists a future strategy over a time horizon consisting of the next N steps to guarantee the safety property of interest. As a result, the proposed monitor is oblivious of the actual controller, and therefore, applicable even in the presence of complex control systems including highly adaptive controllers. Furthermore, we apply our proposed approach to monitor whether a UAV will respect a “geofence” defined by a geographical region over which the vehicle may operate. To achieve this, we construct a data-driven linear model of the UAVs dynamics, while carefully modeling the uncertainties due to wind, GPS errors and modeling errors as time-varying disturbances. Using realistic data obtained from flight tests, we demonstrate the advantages and drawbacks of the predictive monitoring approach.

Accurate predictions of the amount of harvestable energy available from ambient vibrations are important for design of energy harvesters and for their integration in specific applications. This need has motivated the development of many mathematical models for piezoelectric energy harvesters (PEHs). Existing models, however, require material and geometric PEH data that are often incorrect and/or unavailable. As a more accurate and practical means to meet this need, we propose an energy conversion model of a cantilevered PEH that requires only geometric data and modal parameters that can be directly measured using a standard vibration test. The newly proposed model facilitates calculation of the maximum output power and thus enables visualization of the harvestable energy from the target vibrating structure. Prediction accuracy of the proposed model was confirmed in our study through finite element analysis and experimental results. Practical use of the proposed energy conversion model was demonstrated by applying it to a cooling fan unit of a boiler facility in a power plant.

The modern advances in wireless technology and low-power electronics has brought a variety of wireless sensors in market recently; however, the limited lifespan and high replacement cost of batteries make it difficult to fully utilize performance of wireless sensors. Energy harvesting (EH) technology that harvests electrical energy from the ambient vibration energy has been emerged as an ultimate solution to prolong the battery life or eliminate the need of batteries for wireless sensors. Energy harvesting (EH) skin is one of the EH devices that generates electrical energy from the vibrating skin structure with an additional thin piezoelectric layer as one embodiment. As long as the power level of EH skin does not far exceed required one of wireless sensors, the key design consideration must be reliable power generation through the life of wireless sensors regardless of uncertainty and/or variation in material property, boundary condition, excitation etc. This paper presents a framework of statistical model calibration to develop a stochastic computer model for robust and reliable EH skin design. The framework consists of two different hierarchical levels: (1) bottom-level calibration with mechanical response and (2) top-level calibration with electrical response. Cantilever-type energy harvesters are used to demonstrate the statistical calibration framework. The statistical calibration employs uncertainty propagation analysis, optimization and likelihood metric to obtain unknown model variables such as compliance (s11), piezoelectric strain coefficient (d31) and permittivity (e33). With a computer model after model calibration, the EH skin was designed to generate maximum power and the probability density function (PDF) of predicted power is calculated and verified by experiments. Finally, a prototype of the EH skin was manufactured and demonstrated to operate wireless temperature sensors for structural health monitoring and/or building automation. It is conclude that the EH skin can generates enough power to operate many wireless sensors for building automation, smart plant and/or structural health monitoring.