# Prediction Research on Irregularly Cavited Components Volume Based on Gray Correlation and PSO-SVM
## 2 Preliminary  
By applying the ideal-gas equation-of-state, a volume-measurement device for irregularly cavited components using micro-compressed air was designed. The principle of volume measurement for irregularly cavited components is shown in Figure 1. During detection, the irregularly cavitied components to be detected were filled with air at normal temperature and pressure, and after sealing the air inlet, the precision cylindrical-compression-rod was driven by a servo motor, and extended into the interior of the irregularly cavitied components to be tested for a certain length, in order to micro-compress the air inside the cavity. The mass of the fixed group of gas in the cavity before and after micro-compression remained constant. By measuring the pressure and temperature of the air in the irregular cavity before and after micro-compression, and the volume of the compression-rod extending into the cavity, the cavity volume of the irregularly cavited components to be measured can be obtained, following the ideal-gas equation-of- state, which can be written as follows:  
\[PV=Z\text{m}RT \tag{1}\]  
where \(P\) is the gas pressure, the unit of gas pressure is the pascal (Pa), \(V\) is the volume, the unit of volume is milliliter (mL), \(Z\) is the compression coefficient (dimension is 1), m is the mass (mol), \(T\) is the absolute temperature, the unit of temperature is the kelvin (K), and \(R\) is the gas constant (\(R\) = 8.31 J/(mol\(\cdot\)K)).  
However, the detection accuracy of the volume of irregularly cavited components obtained by the above method was still low. Through experiments and analysis of past detection methods, it was found that there were many influencing factors when using this method to detect the volume of irregularly cavited components. In addition to the pressure and temperature in the cavity to be measured, environmental factors such as air-equilibrium time after micro-compression, ambient atmospheric-pressure and humidity will also lead to some deviations in the equation-of-state for gas, which will have a certain impact on the accuracy and stability of volume detection of irregularly cavited components. To attack these problems mentioned above, a volume-prediction model of irregularly -cavitied components based on gray correlation and particle-swarm-optimization support vector machine was proposed in this paper. Firstly, gray correlation analysis was used, and then several key factors related to the volume of irregularly cavitied components in the process of volume measurement using micro-compressed air were extracted, so as to reduce the dimensions to be considered in modeling. Then, using the support vector machine to train the extracted detection-values of important factors, a volume-prediction model of irregularly cavitied components was established simultaneously. In order to obtain a solution to the precision requirements of SVM calculation and modeling which may have problems caused by parameter errors, the research used the particle-swarm algorithm to optimize SVM parameters. The prediction accuracy of SVM was reduced, and the convergence speed of SVM was increased, the volume-prediction value of irregularly cavited components was obtained, and fast and accurate volume-measurement of irregularly cavited components was realized.