Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising

Abstract

A new dynamic mode decomposition (DMD) method is introduced for simultaneous online system identification and denoising in conjunction with the adoption of an extended Kalman filter algorithm\color{black}. The present paper explains the extended-Kalman-filter-based DMD (EKFDMD) algorithm and illustrates that EKFDMD requires significant numerical resources for many-degree-of-freedom (many-DoF) problems and that the combination with truncated proper orthogonal decomposition (trPOD) helps us to apply the EKFDMD algorithm to many-DoF problems. The numerical experiments of the present study illustrate that EKFDMD can estimate eigenvalues from a noisy dataset with a few DoFs better than or as well as the existing algorithms, whereas EKFDMD can also denoise the original dataset online. In particular, EKFDMD performs better than existing algorithms for the case in which system noise is present. The EKFDMD with trPOD can be successfully applied to many-DoF problems, including a fluid-problem example, and the results reveal the superior performance of system identification and denoising. Note that these superior results are obtained despite being an online procedure.

References in corpus (7)

• On Dynamic Mode Decomposition: Theory and Applications
• Sparsity-promoting dynamic mode decomposition
• Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
• Dynamic mode decomposition using a Kalman filter for parameter estimation
• Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising
• Preconditioned dynamic mode decomposition and mode selection algorithms for large datasets using incremental proper orthogonal decomposition
• Online dynamic mode decomposition for time-varying systems

Cited by in corpus (13)

• Determinant-based Fast Greedy Sensor Selection Algorithm
• Dynamic mode decomposition using a Kalman filter for parameter estimation
• Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising
• Data-Driven Approach for Noise Reduction in Pressure-Sensitive Paint Data Based on Modal Expansion and Time-Series Data at Optimally Placed Points
• Data-driven Vector-measurement-sensor Selection based on Greedy Algorithm
• Quantitative Evaluation of a Linear Reduced-order Model based on Particle-image-velocimetry Data of Separated Flow Field around Airfoil
• Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model
• Proof-of-concept Study of Sparse Processing Particle Image Velocimetry for Real Time Flow Observation
• Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data
• Combining Dynamic Mode Decomposition with Ensemble Kalman Filtering for Tracking and Forecasting
• Variational Mode Decomposition-Based Nonstationary Coherent Structure Analysis for Spatiotemporal Data
• Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis
• Triple decomposition and sparse representation for noisy pressure-sensitive paint data