## 5 Conclusions and Prospects  
In this paper, two methods of predicting the sound field of submerged structure with sparse measurement points are proposed. It has been proven that the method could be applied for a structure located in the half-space. With some simulations, several significant conclusions could be obtained as below:  
1. When arranging measurement points on the surface of the source, the traditional method based on the SVM should at least obey the Nyquist sampling rule. In other words, the quantity of measurement points mainly depends on the highest order of the vibration modes in every direction. When the reflection boundary exists and is quite close to the structure, the details of SVM may change and the measurement point arrangement should change at some special frequencies. However, to compute the exact detail of SVM is computationally costly, especially when the size of the structure is large, the shape of the structure is irregular, the coupling effect of reflection sounds could not be neglected, and so on. Therefore, the measurement point arrangement based on SVM could hardly be regarded as the optimal arrangement. 2. With the theory of ARM, the quantity of measurement points could be much smaller than for the SVM, as the sound field could be expressed well with only few ARMs. However, the ill-condition problem of the sensing matrices affects the prediction accuracy. Though arranging measurement points uniformly is easy and convenient in engineering, it could hardly be regarded as the optimal arrangement as the ill-condition problem could be severe to reinforce prediction errors. Adding more points to the measurement set could improve the prediction accuracy as well as increase the computation. Therefore, with a fixed quantity of measurement points, the arrangement should be optimized to avoid the ill-condition problem of the sensing matrices. With the optimization of the EFI, the condition number of the sensing matrix is limited and the stability and accuracy of prediction could be guaranteed. 3. Some factors that may affect the prediction accuracy are also analyzed in this paper, such as the truncation number of ARMs \(L1\), SNR, computer frequency \(f_{0}\), and the submerged depth \(h_{U}\). Some conclusions could be given as below:  
* The proposed method could be well applied for different frequencies. However, the arrangement of measurement points could have a significant influence on the prediction result. It is still necessary to manage the arrangement with EFI to reduce the prediction errors. * The prediction accuracy could be satisfying when the SNR is high enough. When the ARM truncation number is either excessively small or excessively big, the prediction errors are remarkable. Thus, the optimal truncation number of ARMs should be selected appropriately according to the prediction errors at the test points. * When the submerged depth is quite small such that the structural vibration is obviously affected by the reflection sounds, it is necessary to use SFS to maintain the accuracy of the prediction result. However, when the submerged depth is large enough, the dipole matrix for the free field could be used to construct the ARMs and the prediction results could also be accurate. The benefit is that not only the computation is reduced, the stability of the prediction is also reinforced. Though there was no experimental result in this paper because it is difficult for the researchers to acquire satisfying experimental conditions in the laboratory, the method of carrying out experimental research could still be designed as in the following steps:  
* Choose an appropriate experimental environment. To simulate a structure with finite submerged depth, the experiment should be carried out in open water to avoid the effect of reflection sounds from the horizontal direction. Meanwhile, the depth of the water should be enough large that the reflection sounds from the bottom could be neglected.