# Machine Learning Based Design of Railway Prestressed Concrete Sleepers
###### Abstract  
The state-of-the-art design methods for railway prestressed concrete sleepers are currently based on the quasi-static stresses resulting from a simplification of dynamic wheel loads, and subsequently the quasi-static responses of concrete sleepers. This method has been widely used in practices to overcome the complexity of dynamic analysis and testing. A single load factor (or called dynamic impact factor) for a partial safety-factored design (or k factors for the test criteria) is commonly used to crudely account for dynamic train-track interactions over different levels of track irregularities. The dynamic impact factors for either design or testing are usually obtained from either (i) railway infrastructure managers (i.e., in EN 13230), or (ii) prescribed standardised factors (i.e., AS 1085.14, AREMA Chapter 30, JSA--JIS E 1201). The existing design concepts for prestressed concrete sleepers using either (i) an allowable stress design or (ii) the limit state design method require many iterations for calculations and optimisations. The design process to achieve optimal products suitable for track, operational, and environmental parameters is, thus, very time-consuming. On this ground, this study investigates the potential capability of machine learning (ML) to learn from large amounts of design data sets and then to facilitate the design and capacity prediction of railway prestressed concrete sleepers. Three ML algorithms are developed, namely deep learning, Bayesian Neural Network, and random forest. Through a combination of hand-calculated design data, industry design data, and experimental investigations in compliance with EN 13230, over 3000 sets of design data have been collected. These data sets are used to assimilate a comprehensive database for machine learning. Four indicators, namely mean squared error (MSE), root-mean-square error (RMSE), mean absolute error (MAE), and R\({}^{2}\) are used to benchmark the accuracy and precision of machine learning models. Our results reveal that the random forest algorithm offers the best performance. The values of MSE, RMSE, MAE, and R\({}^{2}\) are 0.54, 0.74, 0.25, and 0.99, respectively. Note that the Bayesian neural network also performs very well. In contrast, the deep learning algorithm performs worse than the others. The insight demonstrates machine learning's capability to aid in the design of railway prestressed concrete sleepers, to satisfy both serviceability and ultimate limit states  
machine learning; railway construction; design; prestressed concrete sleepers +
Footnote †: journal: Applied Sciences  
play a key role in enhancing lateral track stability and maintaining the rail gauge. From the advent of the railway to the present, the vast majority of materials for railway sleepers are wood, concrete, and steel. In 1943, the first prestressed concrete sleepers were put into use, which demonstrates the advantages of large longitudinal, transverse resistance, and long service life [1]. An example of concrete sleepers reaching their end of life can be shown in Figure 1. Note that prestressed concrete sleepers are the most common type of railway sleepers in use globally [2]. It is estimated that as of 2013, the global investment in railway infrastructures accounted for a third of the total investment in the railway market, about USD 70 billion [3]. The design and manufacture of concrete sleepers has become one of the most critical and fundamental processes for enabling railway infrastructure construction work. In Europe, limit state design standards (on the basis of a performance-based design concept) can be referred to for railway concrete sleepers design such as BS EN 13230-2 [4] and UIC 713: 1 ED 2004 [5]. For the design procedure, service life should be carefully considered because it can affect the performance requirements significantly.