Energy-efficient train speed profile optimization problem in urban rail transit systems has attracted much attention in recent years because of the requirement of reducing operation cost and protecting the environment. Traditional methods on this problem mainly focused on formulating kinematical equations to derive the speed profile and calculate the energy consumption, which caused the possible errors due to some assumptions used in the empirical equations. To fill this gap, according to the actual speed and energy data collected from the real-world urban rail system, this paper proposes a data-driven model and integrated heuristic algorithm based on machine learning to determine the optimal speed profile with minimum energy consumption. Firstly, a data-driven optimization model (DDOM) is proposed to describe the relationship between energy consumption and discrete speed profile processed from actual data. Then, two typical machine learning algorithms, random forest regression (RFR) algorithm and support vector machine regression (SVR) algorithm, are used to identify the importance degree of velocity in the different positions of profile and calculate the traction energy consumption. Results show that the calculation average error is less than 0.1 kwh, and the energy consumption can be reduced by about 2.84% in a case study of Beijing Changping Line.

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Since the commodity and financial attributes of crude oil will have a long-term or short-term impact on crude oil prices, we propose a de-dimension machine learning model approach to forecast the international crude oil prices. First, we use principal component analysis (PCA), multidimensional scale (MDS), and locally linear embedding (LLE) methods to reduce the dimensions of the data. Then, based on the recurrent neural network (RNN) and long-term and short-term memory (LSTM) models, we build eight models for predicting the future and spot prices of international crude oil. From the analysis and comparison of the prediction results, we find that reducing the dimension of the data can improve the accuracy of the model and the applicability of RNN and LSTM models. In addition, the LLE-RNN/LSTM models can most successfully capture the nonlinear characteristics of crude oil prices. When the moving window size is twenty, that is, when crude oil price data are lagging by almost a month, each model can minimize its error, and the LLE-RNN /LSTM models have the best robustness.