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1. 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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2. Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models

   Biwei Huang, Kun Zhang ( January 2019 , Proceedings of the 36th International Conference on Machine Learning)

   In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify the causal structure, and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the time-varying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods. 

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3. Functional time series forecasting: Functional singular spectrum analysis approaches

   https://doi.org/10.1002/sta4.621  

   Trinka, Jordan ; Haghbin, Hossein ; Lin Shang, Han ; Maadooliat, Mehdi ( October 2023 , Stat)

   We introduce two novel nonparametric forecasting methods designed for functional time series (FTS), namely, functional singular spectrum analysis (FSSA) recurrent and vector forecasting. Our algorithms rely on extracted signals obtained from the FSSA method and innovative recurrence relations to make predictions. These techniques are model‐free, capable of predicting nonstationary FTS and utilize a computational approach for parameter selection. We also employ a bootstrap algorithm to assess the goodness‐of‐prediction. Through comprehensive evaluations on both simulated and real‐world climate data, we showcase the effectiveness of our techniques compared to various parametric and nonparametric approaches for forecasting nonstationary stochastic processes. Furthermore, we have implemented these methods in theRfssaR package and developed a shiny web application for interactive exploration of the results.

    

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4. Few-shot Time-Series Forecasting with Application for Vehicular Traffic Flow

   https://doi.org/10.1109/IRI54793.2022.00018  

   Tran, Victor ; Panangadan, Anand ( August 2022 , Information Reuse and Integration for Data Science (IRI), 2022 IEEE 23rd International Conference on)

   Few-shot machine learning attempts to predict outputs given only a very small number of training examples. The key idea behind most few-shot learning approaches is to pre-train the model with a large number of instances from a different but related class of data, classes for which a large number of instances are available for training. Few-shot learning has been most successfully demonstrated for classification problems using Siamese deep learning neural networks. Few-shot learning is less extensively applied to time-series forecasting. Few-shot forecasting is the task of predicting future values of a time-series even when only a small set of historic time-series is available. Few-shot forecasting has applications in domains where a long history of data is not available. This work describes deep neural network architectures for few-shot forecasting. All the architectures use a Siamese twin network approach to learn a difference function between pairs of time-series, rather than directly forecasting based on historical data as seen in traditional forecasting models. The networks are built using Long short-term memory units (LSTM). During forecasting, a model is able to forecast time-series types that were never seen in the training data by using the few available instances of the new time-series type as reference inputs. The proposed architectures are evaluated on Vehicular traffic data collected in California from the Caltrans Performance Measurement System (PeMS). The models were trained with traffic flow data collected at specific locations and then are evaluated by predicting traffic at different locations at different time horizons (0 to 12 hours). The Mean Absolute Error (MAE) was used as the evaluation metric and also as the loss function for training. The proposed architectures show lower prediction error than a baseline nearest neighbor forecast model. The prediction error increases at longer time horizons. 

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5. Optimization of Rapid State Estimation in Structures Subjected to High-Rate Boundary Change

   https://doi.org/10.1115/SMASIS2020-2306  

   Scheppegrell, James ; Moura, Adriane G. ; Dodson, Jacob ; Downey, Austin ( September 2020 , ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems)

   null (Ed.)

   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.

    

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