Two-dimensional transient cycle decomposition and reduction (CDR) for data driven nonlinear dynamic system modelling

Transient test cycles are an essential part of the development of both on and off-highway vehicles and machines. These cycles are used to test and validate the dynamic operation and performance of systems, and they also form part of regulations such as Real-world Driving Emissions (RDE). A common approach to generating a transient cycle is to replicate recorded real-world transient operation. However, the dynamics of transient operation can vary significantly based on factors such as the operating environment, the use case, the user, and the type of vehicle or machine. The feasible duration of a transient test cycle is also often limited by development time and cost. Therefore, there is a need for a method to synthesize transient test cycles from real-world data in order to replicate a wide range of feasible dynamic operation in the shortest possible time. This paper proposes an innovative transient Cycle Decomposition and Reduction (CDR) method that generates a shortened representative driving cycle in speed-torque two-dimensional space. The steps include identifying micro-trajectories using critical points (e.g. minimum torque), identifying features of micro-trajectories, grouping similar micro-trajectories using k-means clustering and Gaussian process models, and using Markov chain models to efficiently splice together the micro-transients to form a new reduced cycle. The method is flexible and can be used to generate reduced transient cycles for both on-road and off-road applications. The proposed CDR method is demonstrated by using it to perturb a system and collect data for the identification of nonlinear dynamic system models. A 30-minute transient cycle is reduced to a 200-second representative cycle, which is used to train a Neuro-Fuzzy NOx emission model. The results show that this model can accurately predict NOx emissions behaviour over the original transient cycle. The proposed CDR method is easy to expand to higher dimensions and can be applied in a wide range of applications. Additionally, the information extracted during the process has useful physical meaning and can be further utilised, for example in driving pattern recognition, vehicle diagnosis, and autonomous vehicles.