# Shape Optimization of the Streamlined Train Head for Reducing Aerodynamic Resistance and Noise
## 1 Introduction  
High-speed trains have attracted worldwide attention because of their advantages, such as rapid speed, riding comfort, running safety and reliability. However, the operation of high-speed trains also brings considerable problems to the environment, railway construction and locomotive manufacturing industry. The dynamic environment of regular trains is primarily mechanical action, while that of high-speed trains is primarily aerodynamic action. The interaction between trains and the air flow will become more significant with the increase of the cruising speed, resulting in a series of aerodynamic problems, such as aerodynamic resistance, aerodynamic noise, passing pressure wave, tunnel compression wave and expansion wave, crosswind stability [1; 2; 3; 4], etc. The aerodynamic resistance of a train is found to be proportional to the square of velocity, and the aerodynamic noise proportional to the sixth power of velocity. This is an objective law that cannot be avoided by any form of ground transportation. If the velocity reaches 300 km/h, the aerodynamic resistance accounts for more than 75% of the total resistance of a high-speed train [5]. Meanwhile, aerodynamic noise has also become the main noise source [6]. Aerodynamic resistance and aerodynamic noise, which are closely related to energy consumption and environmental protection, have become the main factors affecting the improvement of train speed. In the past decades, numerous investigations have been conducted to reduce the aerodynamic resistance or reduce the aerodynamic noise. Geometric modifications of train shape are the most effective methods to optimize aerodynamic performance. [PERSON] designed some bottom deflectors around the bogie cabin for the purpose of reducing the aerodynamic resistance [7]. [PERSON] set up a train model with bionic round pits to investigate the effects of non-smooth surface on the aerodynamic resistance reduction [8]. [PERSON] proposed two side skirts so as to maximize resistance reduction, and the wind tunnel tests demonstrate that the drag coefficient was reduced by at least 5% [9]. As to the reduction of aerodynamic noise, [PERSON] established an effective method for calculating aerodynamic noise of a train and designed local structures to reduce the aerodynamic noise [10]. [PERSON] investigated the aerodynamic noise of the pantograph of a train and found that the main noise source of pantograph was distributed in the pan-head [11]. [PERSON] investigated the influence of pantograph cavity on the aerodynamic noise of a train as well as the flow around the train, and found that the pantograph cavity configuration could reduce the noise of pantograph [12]. Although these studies provide effective methods and suggestions for the resistance reduction or noise reduction of high-speed trains, the designs in these studies are essentially optimum seeking methods. In this method, some conceptual configurations are first drawn up, then compared and selected through experiments and/or simulations, and finally improved according to the operating conditions. This optimum seeking method relies too much on engineering experience, and the final design is usually not optimal. To resolve this, a direct optimization method is developed. The optimization design variables are obtained through parametric modeling of train shape, which can be automatically updated by the optimization algorithm, so as to obtain the optimal train shape. [PERSON] established a parametric model of the train nose and obtained the optimal train nose shape with the lowest aerodynamic resistance through genetic algorithms [13]. [PERSON] optimized the train shape based on the Kriging model with the goal of reducing the resistance and lift [14]. [PERSON] considered aerodynamic resistance and lift as optimization objectives and used partial differential equation (PDE) parametric modeling to optimize the train shape [15].