POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

Zhang, Zhongqiang; Yang, Xiu; Lin, Guang

doi:10.3390/math4020026

Cited by 14 publications

(17 citation statements)

References 31 publications

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“…In the oceanography and atmospheric sciences, the EOF analysis has been widely used to determine the best locations for placing observation points to measure parameters of interest such as tides, sea temperatures, or winds (e.g., Yang et al, ; Yildirim et al, ; Zhang et al, ). However, in their applications, the EOF‐based approach was applied to oceanic and atmospheric state variables that possess a noticeable periodicity.…”

Section: Initialization By the Eofmentioning

confidence: 99%

Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake

Mulia

Gusman

Satake

2017

Geophysical Research Letters

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Recently, there are numerous tsunami observation networks deployed in several major tsunamigenic regions. However, guidance on where to optimally place the measurement devices is limited. This study presents a methodological approach to select strategic observation locations for the purpose of tsunami source characterizations, particularly in terms of the fault slip distribution. Initially, we identify favorable locations and determine the initial number of observations. These locations are selected based on extrema of empirical orthogonal function (EOF) spatial modes. To further improve the accuracy, we apply an optimization algorithm called a mesh adaptive direct search to remove redundant measurement locations from the EOF-generated points. We test the proposed approach using multiple hypothetical tsunami sources around the Nankai Trough, Japan. The results suggest that the optimized observation points can produce more accurate fault slip estimates with considerably less number of observations compared to the existing tsunami observation networks.

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Section: Initialization By the Eofmentioning

confidence: 99%

Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake

Mulia

Gusman

Satake

2017

Geophysical Research Letters

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“…e center manifold order reduction method is a local order reduction method based on the center manifold theory [13,[23][24][25][26][27].…”

Section: Center Manifold Order Reduction Methodsmentioning

confidence: 99%

“…e POD method is an order reduction method suitable to process large and complex structures quickly and efficiently [2,23,24]. e POD method has been widely studied and applied by many scholars in recent years.…”

Section: Introductionmentioning

confidence: 99%

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

Zhang

et al. 2021

Shock and Vibration

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The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

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“…In the EOF analysis, spatiotemporal variations of any variables of interest can be represented in the modal domain, and most of the energy in natural phenomena are typically contained in large‐scale modes. Such an analysis has been proven effective to measure relative energy of system dynamics existing in particular modes (Yang et al, ; Yildirim et al, ; Zhang et al, ). In tsunami events, such modes are often controlled by the source (Mulia, Gusman, et al, ; Mulia, Inazu, et al, ; Tang et al, ), which is critical to be quantified in order to both accurately characterize the inducing source and estimate the tsunami impacts (Titov et al, ).…”

Section: Methodsmentioning

confidence: 99%

An Optimized Array Configuration of Tsunami Observation Network Off Southern Java, Indonesia

et al. 2019

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Historical records have proven that the southern coasts of Java, Indonesia, are prone to tsunamis. The existing tsunami observing system using bottom pressure gauges, also known as tsunameters, composes a global network but is too sparse for regional tsunami forecasts. The nearest tsunameter to Indonesia is located approximately 500‐km offshore, which is not very useful for the area, particularly for a tsunami source in eastern part of the Sunda megathrust. Here we propose a methodology to optimally place offshore tsunameters with the main consideration of operational costs, which is proportional to the number of observation points. We use a stochastic slip model of earthquakes with Mw 8.8–9.2 to generate multiple tsunami source realizations representing possible future events in the region. Based on the sources, we then identify a potential zone where an early tsunami detection is feasible. Furthermore, empirical orthogonal functions derived from tsunami simulations are used to determine the initial locations for tsunameter placement inside the specified zone. Finally, we apply an optimization scheme to improve the initial locations that facilitates both tsunami forecasts and source characterizations through a tsunami waveform inversion analysis. Our result indicates that six tsunameters are sufficient to efficiently cover the major seismogenic region in the study area.

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POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

Cited by 14 publications

References 31 publications

Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake

Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

An Optimized Array Configuration of Tsunami Observation Network Off Southern Java, Indonesia

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