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.
Development of a real-time solver for the local eigenvalue modification procedure
Real-time model updating for active structures experiencing high-rate dynamic events such as; hypersonic vehicles, active blast mitigation, and ballistic packages require that continuous changes in the structure’s state be updated on a timescale of 1 ms or less. This requires the development of real-time model updating techniques capable of tracking the structure’s state. The Local Eigenvalue Modification Procedure (LEMP) is a structural dynamic modification procedure that converts the computationally intensive global eigenvalue problem used in modal analysis into a set of second-order equations that are more readily handled. Implementation of LEMP for tracking a structure’s state results in secular equations that must be solved to obtain the modified eigenvalues of the structure’s state. In this work, the roots of the secular equations are solved iteratively using a divide and conquer approach, leading to faster root convergence. The present study reports on developing a real-time computing module to perform LEMP in the context of real-time model updating with a stringent timing constraint of 1 ms or less. In this preliminary work, LEMP is applied to tracking the condition of a numerical cantilever beam structure, which depicts changes in a structure’s state as a change in the roller position. A discussion of variations in timing results and accuracy are discussed.
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- Award ID(s):
- 1956071
- NSF-PAR ID:
- 10340294
- Editor(s):
- Zonta, Daniele; Su, Zhongqing; Glisic, Branko
- Date Published:
- Journal Name:
- SPIE Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2022
- Page Range / eLocation ID:
- 51
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
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.more » « less
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null (Ed.)Structural health monitoring of complex structures is often limited by restricted accessibility to locations of interest within the structure and availability of operational loads. In this work, a novel output-only virtual sensing scheme is proposed. This scheme involves the implementation of the modal expansion in an augmented Kalman filter. Performance of the proposed scheme is compared with two existing methods. Method 1 relies on a finite element model updating, batch data processing, and modal expansion (MUME) procedure. Method 2 employs a recursive sequential estimation algorithm, which feeds a substructure model of the instrumented system into an Augmented Kalman Filter (AKF). The new scheme referred to as Method 3 (ME-AKF), implements strain estimates generated via Modal Expansion into an AKF as virtual measurements. To demonstrate the applicability of the aforementioned methods, a rollercoaster connection was instrumented with accelerometers, strain rosettes, and an optical sensor. A comparison of estimated dynamic strain response at unmeasured locations using three alternative schemes is presented. Although acceleration measurements are used indirectly for model updating, the response-only methods presented in this research use only measurements from strain rosettes for strain history predictions and require no prior knowledge of input forces. Predicted strains using all methods are shown to sufficiently predict the measured strain time histories from a control location and lie within a 95% confidence interval calculated based on modal expansion equations. In addition, the proposed ME-AKF method shows improvement in strain predictions at unmeasured locations without the necessity of batch data processing. The proposed scheme shows high potential for real-time dynamic estimation of the strain and stress state of complex structures at unmeasured locations.more » « less
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null (Ed.)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.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1117/12.2613208
