Abstract
Track foundation stiffness (also referred as the track modulus) is one of the main parameters that affect the track performance, and thus, quantifying its magnitudes and variations along the track is widely accepted as a method for evaluating the track condition. In recent decades, the train-mounted vertical track deflection measurement system developed at the University of Nebraska–Lincoln (known as the MRail system) appears as a promising tool to assess track structures over long distances. Numerical methods with different levels of complexity have been proposed to simulate the MRail deflection measurements. These simulations facilitated the investigation and quantification of the relationship between the vertical deflections and the track modulus. In our previous study, finite element models (FEMs) with a stochastically varying track modulus were used for the simulation of the deflection measurements, and the relationships between the statistical properties of the track modulus and deflections were quantified over different track section lengths using curve-fitting approaches. The shortcoming is that decreasing the track section length resulted in a lower accuracy of estimations. In this study, the datasets from the same FEMs are used for the investigations, and the relationship between the measured deflection and track modulus averages and standard deviations are quantified using artificial neural networks (ANNs). Different approaches available for training the ANNs using FEM datasets are discussed. It is shown that the estimation accuracy can be significantly increased by using ANNs, especially when the estimations of track modulus and its variations are required over short track section lengths, ANNs result in more accurate estimations compared to the use of equations from curve-fitting approaches. Results also show that ANNs are effective for the estimations of track modulus even when the noisy datasets are used for training the ANNs.
Highlights
It is widely accepted that a track modulus, and its variations, are indicators of subgrade conditions [1,2,3,4,5]
The estimated track modulus average is compared with the track modulus inputted initially into the finite element models (FEMs) to generate Yrel data
The effectiveness of the proposed network is measured based on three parameters: the coefficient of determination (R2), the root mean square error (RMSE), and the mean absolute percentage error (MAPE) [39]
Summary
It is widely accepted that a track modulus, and its variations, are indicators of subgrade conditions [1,2,3,4,5]. Trackside measurement techniques are used to measure the rail deflection at specific locations under specified static loads or moving loads [9] These techniques provide accurate estimations of track stiffness, they are laborious and time-consuming, especially when multi-point measurements are required. Comprehensive analysis is typically needed to investigate the relationship between deflection measurements from on-train systems and track modulus [16,17]. In addition to the experimental studies, different numerical models have been used to investigate the relationship between track modulus and Yrel data, and numerical approaches have been proposed to estimate the track modulus from Yrel [21,26]. Feedforward neural networks are proposed as a function approximation technique to estimate the track modulus average (UAve) and standard deviation (USD) from Yrel data. The accuracy of the track modulus estimations using these ANNs is investigated using R2, RMSE and MAPE
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