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1. Progress Towards Data-Driven High-Rate Structural State Estimation on Edge Computing Devices

   https://doi.org/10.1115/detc2022-90118  

   Satme, Joud; Coble, Daniel; Priddy, Braden; Downey, Austin R.; Bakos, Jason D.; Comert, Gurcan (August 2022, 34th Conference on Mechanical Vibration and Sound (VIB))

   Abstract Structures operating in high-rate dynamic environments, such as hypersonic vehicles, orbital space infrastructure, and blast mitigation systems, require microsecond (μs) decision-making. Advances in real-time sensing, edge-computing, and high-bandwidth computer memory are enabling emerging technologies such as High-rate structural health monitoring (HR-SHM) to become more feasible. Due to the time restrictions such systems operate under, a target of 1 millisecond (ms) from event detection to decision-making is set at the goal to enable HR-SHM. With minimizing latency in mind, a data-driven method that relies on time-series measurements processed in real-time to infer the state of the structure is investigated in this preliminary work. A methodology for deploying LSTM-based state estimators for structures using subsampled time-series vibration data is presented. The proposed estimator is deployed to an embedded real-time device and the achieved accuracy along with system timing are discussed. The proposed approach has shown potential for high-rate state estimation as it provides sufficient accuracy for the considered structure while a time-step of 2.5 ms is achieved. The Contributions of this work are twofold: 1) a framework for deploying LSTM models in real-time for high-rate state estimation, 2) an experimental validation of LSTMs running on a real-time computing system. 

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2. Multi-Time Resolution Ensemble LSTMs for Enhanced Feature Extraction in High-Rate Time Series

   https://doi.org/10.3390/s21061954  

   Barzegar, Vahid; Laflamme, Simon; Hu, Chao; Dodson, Jacob (March 2021, Sensors)

   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. 

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3. Deterministic and low-latency time-series forecasting of nonstationary signals

   https://doi.org/10.1117/12.2629025  

   Chowdhury, Puja; Barzegar, Vahid; Satme, Joud; Downey, Austin; Laflamme, Simon; Bakos, Jason D.; Hu, Chao (April 2022, Active and Passive Smart Structures and Integrated Systems XVI. SPIE, Apr. 2022)

   Han, Jae-Hung; Shahab, Shima; Yang, Jinkyu (Ed.)

   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. 

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4. Development of a real-time solver for the local eigenvalue modification procedure

   https://doi.org/10.1117/12.2613208  

   Ogunniyi, Emmanuel; Downey, Austin R.; Bakos, Jason (April 2022, SPIE Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2022)

   Zonta, Daniele; Su, Zhongqing; Glisic, Branko (Ed.)

   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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5. tspDB: Time Series Predict DB

   Agarwal, Anish and (January 2021, Proceedings of Machine Learning Research)

   A major bottleneck of the current Machine Learning (ML) workflow is the time consuming, error prone engineering required to get data from a datastore or a database (DB) to the point an ML algorithm can be applied to it. This is further exacerbated since ML algorithms are now trained on large volumes of data, yet we need predictions in real-time, especially in a variety of time-series applications such as finance and real-time control systems. Hence, we explore the feasibility of directly integrating prediction functionality on top of a data store or DB. Such a system ideally: (i) provides an intuitive prediction query interface which alleviates the unwieldy data engineering; (ii) provides state-of-the-art statistical accuracy while ensuring incremental model update, low model training time and low latency for making predictions. As the main contribution we explicitly instantiate a proof-of-concept, tspDB which directly integrates with PostgreSQL. We rigorously test tspDB’s statistical and computational performance against the state-of-the-art time series algorithms, including a Long-Short-Term-Memory (LSTM) neural network and DeepAR (industry standard deep learning library by Amazon). Statistically, on standard time series benchmarks, tspDB outperforms LSTM and DeepAR with 1.1-1.3x higher relative accuracy. Computationally, tspDB is 59-62x and 94-95x faster compared to LSTM and DeepAR in terms of median ML model training time and prediction query latency, respectively. Further, compared to PostgreSQL’s bulk insert time and its SELECT query latency, tspDB is slower only by 1.3x and 2.6x respectively. That is, tspDB is a real-time prediction system in that its model training / prediction query time is similar to just inserting, reading data from a DB. As an algorithmic contribution, we introduce an incremental multivariate matrix factorization based time series method, which tspDB is built off. We show this method also allows one to produce reliable prediction intervals by accurately estimating the time-varying variance of a time series, thereby addressing an important problem in time series analysis. 

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