## 1 Introduction
In the studies of [20; 21; 22; 23; 24], scholars designed a series of basis functions of ARMs using the radiated sound power matrix and completed the calculation of ARMs and the reconstruction of the sound field. [PERSON] and [PERSON] et al. introduced ESM into the application of ARM and conquered the difficulty of solving the radiation sound impedance on the vibrating bodies [25; 26]. The theory of ARM is widely used in the nearfield acoustic holography (NAH), source localization, and sound field reconstruction. [PERSON], [PERSON], and [PERSON] et al. have proven that the expansion coefficients of the orthogonal bases may have high sparsity when combining ARM with ESM [27; 28; 29]. Based on the theory of compressed sensing (CS), the sound field reconstruction of structural sound source can be accomplished with sparse measurement points. [PERSON], [PERSON], and [PERSON] et al. discussed the optimization methods of measurement systems based on ARM and found that, with non-uniform distribution of measurement points, the accuracy of sound reconstruction could be higher [30; 31; 32]. However, all the above studies were carried out in the free field. The studies in the non-free-field deserve more attention. With the maturity of the sound field separation technology (SFS), the sound reconstruction and prediction in the non-free-field are more convenient. In the NAH theory based on ESM, several methods could be applied to separate the real sources from the disturbed sources such as the double-layer sound pressure measurement method, double-layer particle velocity measurement method, and single-layer sound pressure-particle velocity measurement method. In fact, in the non-free-field, the strengths of real sources could also be obtained with SFS based on the structural vibration [1; 33]. Thus, the discussion about the optimization of measurement system in non-free-field could be completed. In this paper, two methods based on the theory of ARM are proposed to predict the sound radiation of an elastic structure with finite submerge depth. SFS is used to construct the ARMs accurately when the reflection sounds have a significant influence on the structural vibration. Generally, the measurement point arrangement should change as the existence of the reflection sounds changes the details of SVM. Regretfully, the quantity of measurement points still is limited by the Nyquist sampling rule. However, according to the good convergence of ARM, the quantity of measurement points could be invariant and further reduced. In spite of this, the ill-condition problem of the sensing matrices may lead to large prediction errors and should be avoided. With the help of EFI, the measurement point arrangement could be optimized by reducing the condition numbers of the sensing matrices and the accuracy of prediction could be improved. Furthermore, some other factors such as the frequency, the signal-noise ratio (SNR), and the submerged depth, which may affect the prediction accuracy, are analyzed in the paper. When the submerged depth is large enough, the process of prediction could be simplified with a 'quick case' because the effect of reflection sounds on the structural vibration could be neglected. In order to illustrate the paper more clearly, a flowchart is given out as Figure 1.  
In Section 2, the theoretical bases of the prediction methods such as ESM, CMESM, and VR-ESM will be presented. The method of SFS will also be introduced to apply for the sound prediction in the half-space. Then, in Section 3, some numerical simulations will be carried out to manifest the efficiency of CMESM and VR-ESM. The results of ESM are regarded as the references to highlight the advantages of CMESM and VR-ESM to enhance the sparsity of the measurement system. Meanwhile, the necessity of EFI to optimize the measurement system will be confirmed. In Section 4, some factors that could affect the  
Figure 1: The flowchart illustrating the methodology of the paper.