High-rate systems are defined as physical systems that undergo large perturbations, often exceeding 100 g’s, over very short durations, often less than 100 milliseconds. Examples include blast mitigation mechanisms and advanced weaponry. The use of control feedback to empower high-rate systems requires the capability to estimate system states of interest in the realm of microseconds. However, due to the dynamics of these high-rate systems being highly nonlinear and nonstationary, it is challenging to predict their behavior using conventional state estimation methods. To address this issue, we conduct a study that explores the integration of topological data analysis (TDA) and recurrent neural network (RNN) to improve predictive capabilities for high-rate systems. Here, TDA features are used as the input to a machine learning algorithm to determine the state of a high-rate system. We conduct practical evaluations using laboratory datasets from experiments in the dynamic reproduction of projectiles in ballistic environments for advanced research (DROPBEAR), focusing on localizing fast-changing boundary conditions on a cantilever beam. The study demonstrates the ability of the method to classify and predict a system’s fundamental frequencies. This approach helps understand the structure of the underlying high-rate dynamics, leading to improved accuracy and precision in state estimation and prediction.
KEYWORDS: Field programmable gate arrays, Sampling rates, Vibration, Signal to noise ratio, Structural dynamics, Data acquisition, Windows, Manufacturing, Control systems, Computation time
High-rate time series forecasting has applications in the domain of high-rate structural health monitoring and control. Hypersonic vehicles and space infrastructure are examples of structural systems that would benefit from time series forecasting on temporal data, including oscillations of control surfaces or structural response to an impact. This paper reports on the development of a software-hardware methodology for the deterministic and low-latency time series forecasting of structural vibrations. The proposed methodology is a software-hardware co-design of a fast Fourier transform (FFT) approach to time series forecasting. The FFT-based technique is implemented in a variable-length sequence configuration. The data is first de-trended, after which the time series data is translated to the frequency domain, and frequency, amplitude, and phase measurements are acquired. Next, a subset of frequency components is collected, translated back to the time domain, recombined, and the data's trend is recovered. Finally, the recombined signals are propagated into the future to the chosen forecasting horizon. The developed methodology achieves fully deterministic timing by being implemented on a Field Programmable Gate Array (FPGA). The developed methodology is experimentally validated on a Kintex-7 70T FPGA using structural vibration data obtained from a test structure with varying levels of nonstationarities. Results demonstrate that the system is capable of forecasting time series data 1 millisecond into the future. Four data acquisition sampling rates from 128 to 25600 S/s are investigated and compared. Results show that for the current hardware (Kintex-7 70T), only data sampled at 512 S/s is viable for real-time time series forecasting with a total system latency of 39.05 μs in restoring signal. In totality, this research showed that for the considered FFT-based time series algorithm the fine-tuning of hyperparameters for a specific sampling rate means that the usefulness of the algorithm is limited to a signal that does not shift considerably from the frequency information of the original signal. FPGA resource utilization, timing constraints of various aspects of the methodology, and the algorithm accuracy and limitations concerning different data are discussed.
KEYWORDS: Field programmable gate arrays, Clocks, Neurons, Signal to noise ratio, Structural health monitoring, Sensors, Detection and tracking algorithms, Data acquisition, Damage detection, Algorithm development
Hard real-time time-series forecasting of temporal signals has applications in the field of structural health monitoring and control. Particularly for structures experiencing high-rate dynamics, examples of such structures include hypersonic vehicles and space infrastructure. This work reports on the development of a coupled softwarehardware algorithm for deterministic and low-latency online time-series forecasting of structural vibrations that is capable of learning over nonstationary events and adjusting its forecasted signal following an event. The proposed algorithm uses an ensemble of multi-layer perceptrons trained offline on experimental and simulated data relevant to the structure. A dynamic attention layer is then used to selectively scale the outputs of the individual models to obtain a unified forecasted signal over the considered prediction horizon. The scalar values of the dynamic attention layer are continuously updated by quantifying the error between the signal’s measured value and its previously predicted value. Deterministic timing of the proposed algorithm is achieved through its deployment on a field programmable gate array. The performance of the proposed algorithm is validated on experimental data taken on a test structure. Results demonstrate that a total system latency of 25.76 µs can be achieved on a Kintex-7 70T FPGA with sufficient accuracy for the considered system.
High-rate dynamic systems are defined as systems that undergo large levels of acceleration, often over 100g, over short durations, typically less than 100 ms. Examples of such systems include active blast mitigation mechanisms, adaptive air bag deployment, and hypersonic systems. Their dynamics is uniquely characterized by 1) large uncertainties in the external loads; 2) high levels of nonstationarities and heavy disturbances; and 3) unmodeled dynamics generated from changes in system configurations. High-rate structural health monitoring (HRSHM) is concerned with the development of sub-millisecond state estimation capabilities in order to facilitate the future implementation of decision systems to improve the safety and operation of high-rate systems.
High-rate dynamic systems undergo events of amplitudes greater than 100 gs in a span of less than 100 ms. The unique characteristics of high-rate dynamic systems include 1) large uncertainties in the external loads, 2) high levels of non-stationarity and heavy disturbances, and 3) unmolded dynamics generated from changes in the system configurations. This paper presents a deep learning algorithm consisting of an ensemble of long short-term memory (LSTM) cells used to conduct high-rate state estimation. The ensemble of LSTMs receives and transforms the signal into inputs of different time resolutions. Each input vector correlates to an LSTM cell which predicts the signal in real-time and produces feature vectors. The feature vectors are then processed through an attention layer and dense layer to predict the physical features of the system. Here, we study the temporal evolution of the attention layer weights to conduct state estimation, while the LSTM cells are attempting to conduct measurement predictions. We study the performance of the algorithm on experimental data generated by DROPBEAR, a dedicated testbed for high-rate structural health monitoring research. State estimation consists of estimating, in real-time, the location of a cart that moves along a beam. Results show that the attention layer weights can be used to estimate the cart location but that the beam requires impact excitations to accelerate the convergence of the algorithm.
Recent advances in sensing are empowering the deployment of inexpensive dense sensor networks (DSNs) to conduct structural health monitoring (SHM) on large-scale structural and mechanical systems. There is a need to develop methodologies to facilitate the validation of these DSNs. Such methodologies could yield better designs of DSNs, enabling faster and more accurate monitoring of states for enhancing SHM. This paper investigates a model-assisted approach to validate a DSN of strain gauges under uncertainty. First, an approximate physical representation of the system, termed the physics-driven surrogate, is created based on the sensor network configuration. The representation consists of a state-space model, coupled with an adaptive mechanism based on sliding mode theory, to update the stiffness matrix to best match the measured responses, assuming knowledge of the mass matrix and damping parameters. Second, the physics-driven surrogate model is used to conduct a series of numerical simulations to map damages of interest to relevant features extracted from the synthetic signals that integrate uncertainties propagating through the physical representation. The capacity of the algorithm at detecting and localizing damages is quantified through probability of detection (POD) maps. It follows that such POD maps provide a direct quantification of the DSNs’ capability at conducting its SHM task. The proposed approach is demonstrated using numerical simulations on a cantilevered plate elastically restrained at the root equipped with strain gauges, where the damage of interest is a change in the root’s bending rigidity.
In this paper a piezoelectric energy harvester for scavenging wasted vibration energy inside a vehicle tire is designed and its performance is experimentally verified. Piezoelectric type energy harvesters can be used to collect vibrational energy and power such systems, but they need to be carefully designed to address power generation and durability performances. In this study, we address a reliability based design optimization (RBDO) approach to design the harvester that considers the uncertainty in dimensional tolerances and material properties, to be compared to the traditional deterministic design optimization (DDO). Both designs are manufactured for the experimental evaluation to demonstrate the merits of RBDO design over DDO.
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