Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Optimal arrangement of sensors to predict vibration and soundradiation of underwater structures based on compressive sensing theory
Lei Xiong, Meixia Chen, Wenkai Dong

School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology
Wuhan, Hubei, China

ABSTRACTabove researches mainly focused on reorganization of modal matrix,however, neglected the sparsity of vibration modal parameters.

For underwater structures, vibration and sound radiation are closely
related to the sound invisibility. In engineering, these can get througharranging some sensors on the surface of structure. Combined with thecompressive sensing theory, this paper presents a method for the optimalarrangement of sensors. Then, a process for predicting vibration andsound is formed based on the data from these sensors. The optimal sensor
arrangement method reduces the number of sensors and maintains theaccuracy of prediction results.

With the rapid development of data science, Compressed Sensing(CS)have attracted a wide range of attention from researchers of computer
graphics and signal analysis. Optimizing the arrangement of sensors
from data sparsity has rarely been studied. Taking advantage of thesparsity of modal parameters, such as modal participation coefficients, amethod for optimizing sensor locations based on CS is presented in thispaper.

KEY WORDS: Structure vibration; Sound radiation; Compressive

COMPRESSIVE SENSING THEORYsensing; Cylinder shell; Optimal sensor arrangement

Compressed Sensing is a signal capture and recovery scheme proposedby Candes(2005) and Donoho(2006). It breaks the limits of traditional
Shannon sampling theory and has received considerable attention.
However, its weakness is that the terminal data is greatly reduced andsparse which could not guarantee the reliability and stability ofreconstructed signal. Therefore, Compressed Sensing needs to pay
attention to the following three key steps.

INTRODUCTION

Many researches elaborated the basic principle of vibration noise
prediction and applied them to engineering(Liu and Maury, 2016; Zhang
et al., 2016; Van Hauwermeiren et al., 2021; X. Zhao, 2005 and Rongfu
Mao, 2017). In practice, misplaced sensors lead to problems such as
distorted data and lack of observation value which decrease the ability toSignal Sparse Expression
forecast vibration noise. About sensor optimal placement, Kammer(1991)
firstly presented the Effective Independence(EI) method to optimize theSparse signals are essential for compressive sensing process. Assuming
Fisher information matrix by using the vibration modal matrix of thethat there is a signal v(v∈RN), it satisfies:
structure so that the modal vectors of interest are linearly independentand thereby determine the number and location of sensors. Since then,
v0 =K
(1)
numerous scholars have improved and expanded on the Effective
where, * 0 means 0-norm of a vector, K indicates the degree of signal
Independence method in different directions. Carne(1995) mentionedthat Modal Assurance Criterion(MAC) can to evaluate the square of thesparsity. If K meets specific some criteria, it’s easy to recover real signal
cosine between the modal vectors. Requiring all the non-diagonal
from sparse data. Yet, majority of initial signals are not sparse, namely,elements of the MAC matrix to be relatively small, a set of sensors which
K=N. In this case, through finding an appropriate sparse base matrix
will be a good design for vector correspondence can be determined. InΨ(Shi, Liu and Gao,2009), v still can express as:addition, genetic algorithms(GA) have been successfully applied toN
sensor optimization arrangement. Yan(2002) defined the sum of the =vs=Ψ s, Ψ ∈ R N × N(2)n •Ψ nn =1
eigenvalue of the correlative matrix of control input energy from sensors
In this formula, v is a N-dimensional initial signal, Ψ is a N×N
as objective function and optimized the sensor location and number in adimensional sparse basis, and s is the coordinate of v under the column
space truss. Brunt(2010) applied the genetic algorithm to a simply
space of Ψ. By equation 2, the non-sparse signal v is converted into a
supported flexible plate using a similar objective function. Yuan(2009)
sparse signal s.
combined the EI method and MAC to overcome the drawbacks of MAC
and ensured the good linear independence of the modal vectors. The∑1008