# Analysis of Wind Speed Characteristics Along a High-Speed Railway
## 1 Introduction  
Since the early twenty-first century, high-speed railway (HSR) systems have developed rapidly and play a crucial role in advancing social and economic conditions [1]. Ensuring path safety in HSRs has become a primary focus of research. One significant factor that threatens HSR safety is strong wind [2]. If the instantaneous wind speed reaches the critical overturning threshold, a high-speed train could overturn within 1-2 s, resulting in severe financial losses and potential fatalities. The world's HSR nations place high value on and implement robust wind defense measures for their railways. In order to make short-term forecasts of peak wind speeds two minutes in advance, Deutsche Bahn developed the \"Nowcasting\" automatic short-term wind speed forecasting system [3]. France has developed the capability to predict wind speeds within a four-minute timeframe, while China currently issues alarms only after detecting strong winds [4]. Strong gusts cause a train to slow down or stop, necessitating adherence to a \"10 min rule\" before removing cautionary measures and resuming regular operations. Japan has similarly implemented a wind speed driving guideline, referred to asthe \"30 min rule,\" which is comparable to the one used in China. Japan has also developed a \"strong wind warning system\" that provides a 10 min advance warning and allows for forecast cancellation [5]. Without upgrades and advancements, these preventive measures continue to rely on forecasting technologies that are over a decade old. HSR, being faster and more susceptible to wind than conventional trains, requires higher standards for wind prediction accuracy. The forecasting time horizon and the forecasting method are two fundamental criteria for the early classification of wind speed forecasting models. Wind speed forecasts are broken down into four categories based on the forecast time range: very short-term (a few seconds to 30 min ahead), short-term (30 min to 6 hours ahead), medium-term (6 h to 1 day ahead), and long-term (over 1 day ahead). In general, the forecast accuracy is higher the shorter the forecast horizon [6]. The four categories below can be determined by the forecasting method [7; 8; 9]: (1) physical models, (2) statistical models, (3) machine learning models, and (4) hybrid models. The physical model is composed of discrete conservation equations for mass, momentum, and energy in the atmosphere and is mostly based on numerical weather prediction (NWP) [10; 11]. NWP predicts wind speed by resolving intricate mathematical models using meteorological information like temperature, pressure, surface roughness, and obstacles [12]. By identifying the relationship between observed historical data and anticipated future data, statistical models can create forecast data [13]. When the model's training sequence adheres to the assumptions of the statistical model, common statistical techniques like autoregressive moving average (ARMA) [14], autoregressive integrated moving average (ARIMA) [15], fractional ARIMA (f-ARIMA) [16], and vector autoregressive (VAR) [17] can achieve outstanding predictive performance. As a result, the historical properties of the series have a significant impact on the forecasting effectiveness of statistical methods. In practice, it is frequently challenging to manage the noise, nonlinearity, instability, fluctuation, and other features of the original time series, which leaves the model with little modeling data and reduces its predictive power [18]. Machine learning models include multilayer perceptron (MLP) [19], backpropagation neural networks (BPNN) [20], support vector machine (SVM) [21], fuzzy logic [22], extreme learning machines (ELM) [23], and deep neural models such as convolutional neural network (CNN) [24], long short-memory (LSTM) network [25], and transformer [26]. These models have strong data fault tolerance and can establish the relationship between input and output data.