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In high-rate structural health monitoring, it is crucial to quickly and accurately assess the current state of a component under dynamic loads. State information is needed to make informed decisions about timely interventions to prevent damage and extend the structure’s life. In previous studies, a dynamic reproduction of projectiles in ballistic environments (DROPBEAR) testbed was used to evaluate the accuracy of state estimation techniques through dynamic analysis. This paper extends previous research by incorporating the local eigenvalue modification procedure (LEMP) and data fusion techniques to create a more robust state estimate using optimal sampling methodologies. The process of estimating the state involves taking a measured frequency response of the structure, proposing frequency response profiles, and accepting the most similar profile as the new mean for the position estimate distribution. Utilizing LEMP allows for a faster approximation of the proposed model with linear time complexity, making it suitable for 2D or sequential damage cases. The current study focuses on two proposed sampling methodology refinements: distilling the selection of candidate test models from the position distribution and applying a Kalman filter after the distribution update to find the mean. Both refinements were effective in improving the position estimate and the structural state accuracy, as shown by the time response assurance criterion and the signal-to-noise ratio with up to 17% improvement. These two metrics demonstrate the benefits of incorporating data fusion techniques into the high-rate state identification process. 

Systems experiencing high-rate dynamic events, termed high-rate systems, typically undergo accelerations of amplitudes higher than 100 g-force in less than 10 ms. Examples include adaptive airbag deployment systems, hypersonic vehicles, and active blast mitigation systems. Given their critical functions, accurate and fast modeling tools are necessary for ensuring the target performance. However, the unique characteristics of these systems, which consist of (1) large uncertainties in the external loads, (2) high levels of non-stationarities and heavy disturbances, and (3) unmodeled dynamics generated from changes in system configurations, in combination with the fast-changing environments, limit the applicability of physical modeling tools. In this paper, a deep learning algorithm is used to model high-rate systems and predict their response measurements. It consists of an ensemble of short-sequence long short-term memory (LSTM) cells which are concurrently trained. To empower multi-step ahead predictions, a multi-rate sampler is designed to individually select the input space of each LSTM cell based on local dynamics extracted using the embedding theorem. The proposed algorithm is validated on experimental data obtained from a high-rate system. Results showed that the use of the multi-rate sampler yields better feature extraction from non-stationary time series compared with a more heuristic method, resulting in significant improvement in step ahead prediction accuracy and horizon. The lean and efficient architecture of the algorithm results in an average computing time of 25 μμs, which is below the maximum prediction horizon, therefore demonstrating the algorithm’s promise in real-time high-rate applications. 

Many structures are subjected to varying forces, moving boundaries, and other dynamic conditions. Whether part of a vehicle, building, or active energy mitigation device, data on such changes can represent useful knowledge, but also presents challenges in its collection and analysis. In systems where changes occur rapidly, assessment of the system’s state within a useful time span is required to enable an appropriate response before the system’s state changes further. Rapid state estimation is especially important but poses unique difficulties.

In determining the state of a structural system subjected to high-rate dynamic changes, measuring the frequency response is one method that can be used to draw inferences, provided the system is adequately understood and defined. The work presented here is the result of an investigation into methods to determine the frequency response, and thus state, of a structure subjected to high-rate boundary changes in real-time.

In order to facilitate development, the Air Force Research Laboratory created the DROPBEAR, a testbed with an oscillating beam subjected to a continuously variable boundary condition. One end of the beam is held by a stationary fixed support, while a pinned support is able to move along the beam’s length. The free end of the beam structure is instrumented with acceleration, velocity, and position sensors measuring the beam’s vertical axis. Direct position measurement of the pin location is also taken to provide a reference for comparison with numerical models.

This work presents a numerical investigation into methods for extracting the frequency response of a structure in real-time. An FFT based method with a rolling window is used to track the frequency of a data set generated to represent the range of the DROPBEAR, and is run with multiple window lengths. The frequency precision and latency of the FFT method is analyzed in each configuration. A specialized frequency extraction technique, Delayed Comparison Error Minimization, is implemented with parameters optimized for the frequency range of interest. The performance metrics of latency and precision are analyzed and compared to the baseline rolling FFT method results, and applicability is discussed.

 

Real-time model updating of active structures subject to unmodeled high-rate dynamic events require structural model updates on the timescale of 2 ms or less. Examples of active structures subjected to unmodeled high-rate dynamic events include hypersonic vehicles, active blast mitigation, and orbital infrastructure. Due to the unmodeled nature of the events of interest, the real-time model updating algorithm should circumvent any model pre-calculations. In this work, we present a methodology that updates the finite element analysis (FEA) model of a structure experiencing varying dynamics through online measurements. The algorithm is demonstrated for a testbed, comprised of a cantilever beam and a roller that serves as movable support. The structure’s state is updated (i.e. the position of the moving roller) by continuously updating the associated FEA model through an online adaptive meshing and search algorithm. The structure’s state is continuously estimated by comparing the measured signals with FEA models. New FEA models are built based on the enhanced estimate of the structure’s state through adaptive meshing for modal analysis and adaptive search space for the FEA model selection. The proposed methodology is verified experimentally in real-time using the testbed. It is demonstrated that the adaptive features can achieve accurate state estimations within the required 2 ms timescale.