For underwater structures, vibration and sound radiation are closely related to the sound invisibility. In engineering, these can get through arranging some sensors on the surface of structure. Combined with the compressive sensing theory, this paper presents a method for the optimal arrangement of sensors. Then, a process for predicting vibration and sound is formed based on the data from these sensors. The optimal sensor arrangement method reduces the number of sensors and maintains the accuracy of prediction results.
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 to forecast vibration noise. About sensor optimal placement, Kammer(1991) firstly presented the Effective Independence(EI) method to optimize the Fisher information matrix by using the vibration modal matrix of the structure so that the modal vectors of interest are linearly independent and thereby determine the number and location of sensors. Since then, numerous scholars have improved and expanded on the Effective Independence method in different directions. Carne(1995) mentioned that Modal Assurance Criterion(MAC) can to evaluate the square of the cosine between the modal vectors. Requiring all the non-diagonal elements of the MAC matrix to be relatively small, a set of sensors which will be a good design for vector correspondence can be determined. In addition, genetic algorithms(GA) have been successfully applied to sensor optimization arrangement. Yan(2002) defined the sum of the eigenvalue of the correlative matrix of control input energy from sensors as objective function and optimized the sensor location and number in a space truss. Brunt(2010) applied the genetic algorithm to a simply supported flexible plate using a similar objective function. Yuan(2009) combined the EI method and MAC to overcome the drawbacks of MAC and ensured the good linear independence of the modal vectors. The above researches mainly focused on reorganization of modal matrix, however, neglected the sparsity of vibration modal parameters.
