# A Novel Optimization Layout Method for Clamps in a Pipeline System
## 1 Introduction  
The aviation hydraulic pipeline system is connected to the hydraulic pump and other components to provide power for the elevator, rudder, undercarriage and other parts of the aircraft, and thus plays an important role on aircraft safety. Because of the lightweight requirements of the system, a large number of flexible clamps are used in the aviation hydraulic pipeline system, in which the support is weak, leading to serious coupling vibration and complicated vibration problems. When the frequency of external vibration is close to natural frequency of the pipeline system, structural resonance occurs, which might cause failures of the hydraulic pipeline system. Therefore, the investigation of the pipeline system vibration and its control has great value in engineering application. Scholars have verified the effectiveness of various methods on the vibration control from the theoretical and experimental aspects [1; 2; 3; 4; 5; 6]. According to mechanisms, these methods can be classified as follows:  
1. Active control of the pipe directly to reduce the vibration;
2. Use damping materials between the hydraulic pipeline and the foundation to suppress the vibration transmission;
3. Control the fluid pulsation in the pipeline to reduce the vibration of the excitation source;
4. Adjust the number, position and layout of the supports in the system to change the dynamic characteristics of the system. The implementation of active control requires space and energy input, making it more difficult to be applied in aero hydraulic pipeline systems. Due to the extremely small space and the complicated layout of pipes on aircraft, it is often unrealistic to set up a large damping device. In addition, due to the large temperature fluctuation of aero hydraulic pipeline system, the service life of the damping material is greatly limited. Pulsation attenuators tend to increase the mass of the system and can only reduce the vibration caused by fluid. This means that the first three methods have their limitations in aero applications. By adjusting the number and layout of pipeline supports, changing the dynamic characteristics of the system to reduce the vibration is at present the most commonly used, most convenient, and most economical method. For many years, the arrangement of the clamps in the aero hydraulic pipeline systems was determined empirically according to the prototype. The number, position, and orientation of the clamps were mainly depended on the on-site experience of workers, while standards and norms are lack. Reasonable layout parameters can improve the dynamic characteristics of the pipeline system, avoiding the resonance, reducing the vibration amplitude and ensuring the reliable operation of the hydraulic system, which is of great significance to the safety of aircrafts [7]. Therefore, it is necessary to optimize the clamp layout by systematic and standardized methods to ensure the safe operation of the system. Genetic algorithm (GA) is a kind of randomized search method that learns from evolution of biology. It was first proposed by Professor [PERSON] in the United States in 1975 [8]. With inherent implicit parallelism and global optimization ability, the genetic algorithm has been applied in many fields [9; 10; 11; 12; 13] and showed good convergence. Among them, some scholars [9] combined BP (back-propagation) neural network [14] with GA. The neural network is relatively studied in theory and performance. Scholars [15; 16; 17; 18] used neural network to make prediction and some of them [17; 18] then input the predicted data into different algorithms to get optimal results. These works showed the strong nonlinear mapping capability, high efficiency, and flexible structure of neural network. Focusing on the multi-support, long-span characteristics of the aviation hydraulic pipeline system, a typical clamp-supported Z-tube system was selected as the object. First, the sensitivity analysis method [19; 20; 21; 22] was used to analyze the influence of the clamps position on the output.