## 1 Introduction  
In marine engineering, floating raft systems are widely used in kinds of ships, warships, submarines and other related structures, equipment, and facilities [1]. Usually, vibration isolators are installed to collect the raft system and base. On the one hand, they could protect the machines and devices installed on the rafts from sudden external shocks under certain circumstances. On the other hand, and more importantly, the floating raft is a key technique for vibration and noise control. The vibration and noise control are vital for submarines. Normally, a submarine has a circle hull and a relatively long body and the raft system is installed inside compactly. Figure 1 gives a schematic diagram of a floating raft system installed in a submarine [1]. Many vibration isolators are needed between the floating raft structures and supporting base in all directions, along with the hull circle. There are kinds of vibration isolator types, like airbags, also known as gasbags, which are commonly employed due to their large bearing capacity and good vibration isolation performance [2]. As technology advances,especially at present when anti-submarine technology keeps improving, the underwater quieting performance of submarines has been unprecedentedly challenging [3]. Therefore, any aspects negatively affecting the concealment ability should be considered and avoided. Many factors show a great impact on the vibration and noise control performance, such as the isolator type and its installed station. The good installation status of floating raft isolation systems is very important in reducing vibrations and noises which would affect, both directly and prominently, the overall performance. Figure 2 gives an installation schematic diagram of a vibration isolator in the horizontal direction. In the installation area, two metal plates, i.e., the upper backing plate and the lower backing plate in the schematic, are fine machined. This helps get a relatively correct distance between the two plates. For the installing process of big vibration isolators, ideally, it is best to make the vibration isolator height exactly equal to the distance between the base and the surface to be supported. However, the isolators usually could not match the spacing between the base and the distance. When there is a difference between the isolator height and the distance, it is necessary to install adjusting shims [4], which means the sizes of the shims need be obtained. The common way to ascertain the thickness of the shim for the isolator is to manually measure the spacing between the mounting surfaces and then subtract the isolator height. Since the isolator height is usually known, the mounting space needs to be measured. The traditional technique of measuring the installation space is to use tools like micrometers and vernier calipers, which have many drawbacks. When measuring, operators usually use a vernier caliper, setting it vertical to the mounting plates and ensuring the  
Figure 1: The schematic diagram of vibration isolators for floating rafts in submarines. Figure 2: The installation of a vibration isolator between rafts and supporting base. two measuring jaws are in contact with the two surfaces. The displacement could then be read and recorded. And the basic dimensions of the shims could be obtained. Afterwards, an initial shim would be manufactured for preinstallation. And the shim will be adjusted several times until a satisfying shim shape is reached. Many problems may show up in the manual measuring processes. Firstly, the measurement accuracy cannot be guaranteed, so that the adjustment shims may be made with large errors, which affects the installation of the rafts and equipment. Secondly, since there are only a few sampling points available during the measurement for adjustment shims, the reconstruction of shim mounting surface is only usually determined by three measured points. In this case, the mounting surfaces of the shims and the rafts may not be in contact effectively.