Modelling of driving cycles including time-varying features of road slope, vehicle mass and traffic congestionDoctoral thesis (in Croatian), Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Croatia,, 2022
Plug-in Hybrid Electric Vehicles (PHEV) represent a key enabling technology to make the transport system more efficient, cleaner, quieter, and less dependent on oil reserves. Since driving cycles are related to driving conditions and driver behaviour, they are crucial for estimating energy consumption and pollutant emissions, and they are widely used in designing and parameterising the structure of PHEV powertrain and its control strategy. Nowadays, various studies related to PHEVs, as well as other vehicle types, are usually based on certification driving cycles, which do not take into account realistic driving conditions including road slope, but are rather based on “artificially” generated vehicle velocity-time profiles. However, for the purposes of designing and testing a vehicle control system, realistic driving cycles should be used, which reflect the actual driving behavior and road conditions. In this sense, the main aim of this thesis is focused on the synthesis and validation of realistic driving cycles represented by vehicle velocity, acceleration and road slope time profiles, which are derived from recorded GPS vehicle tracking data. The thesis first establishes a stochastic model of driving cycles based on Markov chains, which includes combinations of discrete values of vehicle velocity, vehicle acceleration, road slope and road slope time derivative as Markov states. For this purpose, a rich set of driving cycles of city buses operating in the city of Dubrovnik has been collected. By random sampling of a multidimensional transition probability matrix (TPM), a large set of synthetic driving cycles is generated. To reduce the memory requirement while improving computational efficiency, the implementation of TPM in the form of a sparse matrix based on a dictionary of keys (DOK) is proposed. In addition, including of passengers' mass into driving cycle synthesis process is considered based on vehicle stopping events. Traffic congestion is taken into account through the formation of separate TPMs for each traffic congestion category, which is carried out through clustering of recorded driving cycles based on established traffic congestion criteria. For the purpose of synthetic driving cycles validation, a dedicated neural network (NN) is proposed, which predicts the vehicle fuel consumption for a given driving cycle. The NN approach is based on driving cycle time series input data arranged in a form of fixed‐dimension histogram of counted discrete values of vehicle velocity, acceleration, and road slope. In support of validation of synthetic driving cycles, a rich set of statistical features from the time and frequency domains are considered, including unique indicators of cross-correlation of vehicle velocity, vehicle acceleration, and road slope. The significance of each nominated statistical feature and its impact on fuel consumption is analyzed by using a linear regression analysis and Least Absolute Shrinkage and Selection Operator (LASSO) feature selection method. For unambiguous, single-criteria validation of synthetic driving cycles with respect to recorded driving cycles, a reduced-order LASSO regression model is proposed that takes only a few most significant statistical features as inputs and gives fuel consumption as output. The driving cycle validation method based on multiple criteria is also examined as a potential further improvement. The proposed validation approaches are based on minimizing the deviation of statistical features of synthetic driving cycles from the mean/expected values of recorded driving cycles. Finally, the thesis proposes deterministic and stochastic models for predicting vehicle velocity on receding time horizon, and accordingly driving cycle features relevant for model predictive control of PHEV. Predictive models are based on a feedforward multilayer neural networks, which are trained by using the data on current vehicle position, current vehicle velocity or velocity history, time of day, and weekday, and as an output give sequence of vehicle velocities on the receding time horizon. The accuracy of vehicle velocity prediction is demonstrated on a separate set of recorded driving cycles. The main aim of the thesis is to propose a systematic procedure of multi-dimensional driving cycle synthesis, which utilizes driving data recorded using a vehicle telemetry tracking system and at the end results in a minimum number of representative synthetic driving cycles for a wide range of driving conditions. The thesis is organized in eight chapters, whose content is summarized in what follows. Chapter 1, „Introduction“ outlines the motivation for the conducted research, presents the literature overview, and provides the main hypothesis and an overview of the thesis. Chapter 2, „Recording, pre-processing and analysis of driving cycles“ describes the procedure of driving data recording by utilizing GPS/GPRS vehicle tracking devices for the case of a city bus fleet. Pre-processing of recorded driving data is carried out in terms of extracting driving cycles defined by recorded data between end stations of a certain route, filtering of driving cycles with respect to various criteria, reconstruction of precise road slope profiles using regression method based on Gaussian processes, and categorization of driving cycles in accordance to a traffic congestion index. A comprehensive analysis of interdependence of vehicle velocity, acceleration, road slope, and passengers mass is performed to determine whether the synthesis of driving cycles should be carried out jointly with respect to velocity, acceleration, road slope and passengers mass' states or the road slope and passengers' mass can be modeled independently of velocity and acceleration. Chapter 3, „Synthesis of multidimensional driving cycles“ proposes a method for synthesis of multidimensional driving cycles based on Markov chains. Different ways of realizing the transition probability matrix (TPM) are considered along with related implementation aspects, including computational efficiency analysis. It is proposed to adopt a stochastic driving cycle model represented by an 8D TPM using vehicle velocity, acceleration, road slope, and road slope time derivative states, and based on this model a rich set of synthetic driving cycles is generated. An independent, vehicle stopping event-based synthesis method of passengers’ mass profiles is also proposed. Traffic congestion is considered through the formation of separate TPMs for three levels of congestion (light, medium, and heavy). The chapter concludes with a preliminary analysis of validity of the generated synthetic driving cycles, based on a comparison of distributions of characteristic statistical features between synthetic and recorded driving cycles. Chapter 4, „Regression model for predicting fuel consumption“ establishes a regression model for predicting fuel consumption based on appropriately formed input features of synthetic driving cycles and corresponding neural network (NN). The emphasis is on including a road slope feature when designing the model inputs to improve prediction accuracy. The proposed regression models are trained, validated, and tested on an augmented dataset of combined driving cycles, which are derived through random addition of recorded microcycles whose length corresponds to resolution of fuel consumption measurement. A comparative analysis of fuel consumption prediction accuracy is performed between NN and simpler, linear-in-parameter polynomial regression models, for the case with included and excluded road slope information. In addition, several methods for fine-tuning of NN models are conducted and described in detail, which are related to dimensionality reduction, finding the most appropriate architecture, determining the optimal learning rate, and regularizing the NN. Although the proposed regression model for predicting fuel consumption can be applied to various transport-related studies, in this thesis it is used for determining the fuel consumption related to a set of synthetic driving cycles generated in third chapter for the purpose of their validation. Chapter 5, „Multi-criteria validation of driving cycles“ deals with validation of multidimensional synthetic driving cycles generated in the third chapter. A rich set of driving cycle-related statistical features are nominated to describe different driving patterns, which in addition to general statistical indices includes frequency domain ones and cross-correlation of vehicle speed, vehicle acceleration and road slope features. A comparative analysis of the characteristic statistical features calculated for each recorded and synthetic driving cycle is performed to verify that the distributions of the statistical features for the synthetic driving cycles resembles well those obtained for the recorded driving cycles. For the needs of unambiguous validation of driving cycles, several lumped indicators of driving cycle representativeness are derived, which are based on consolidation of individual statistical features or similarity index between two vectors/matrices used to model driving cycles. The selection of the most appropriate representativeness indicator for the final validation of driving cycles is carried out based on correlation analysis in relation to fuel consumption deviation from the mean value of concatenated recorded driving cycles. Finally, a multi-criteria validation procedure is proposed, which highlights and analyzes several most representative driving cycles from the Pareto frontier of lumped representativeness indicators. Chapter 6, „Feature selection-supported validation of driving cycles“ deals with feature selection techniques based on linear regression analysis and least absolute shrinkage and selection operator (LASSO), which serves to determine the relevance of each nominated statistical feature. The competitiveness of the fuel consumption prediction accuracy of linear and LASSO regression models of reduced order is examined in relation to baseline neural network model established in the fourth chapter. The procedure of extracting representative synthetic driving cycles based on LASSO-predicted fuel consumption is presented and compared with the Euclidean distance lumped indicator-based approach. To further improve the process of unambiguous validation of synthetic driving cycles, a dual-criterion validation method based on both Euclidean distance and LASSO-predicted fuel consumption is examined, as well. Chapter 7, „Prediction of driving cycle features“ first describes the process of data preparation for learning, validation, and testing of a vehicle velocity prediction models. Next, static stochastic and deterministic deep feedforward neural network prediction models are proposed, where the former predicts the vehicle velocity distribution along the route, while the latter predicts the vehicle velocity profile on receding time horizon. A comprehensive analysis of the prediction accuracy of the developed predictive models is performed based on test dataset and considering different forecast quality indicators. Deterministic model is additionally examined in terms of influence of each input variable candidates (current vehicle position, current velocity or history of vehicle velocities, time of day, and weekday), velocity history length, and prediction horizon length on the accuracy of vehicle velocity profile prediction. Finally, a dynamic stochastic model is proposed, which combines the properties of both previously developed predictive models, in terms of predicting expectations and standard deviations of velocity patterns on the receding time horizon. Chapter 8, „Conclusion“ outlines the main results, guidelines for future research, and the following major contributions of the doctoral thesis: 1) Driving cycle model based on Markov chains, which in addition to vehicle velocity and acceleration as the Markov states accounts for the road slope, vehicle mass, and traffic congestion features; 2) Validation of driving cycle model based on recorded fuel consumption data and fuel consumption predictions obtained by using a neural network parameterized based on the driving cycle model features; 3) Stochastic model for predicting driving cycle statistical features meant to be applied in stochastic model predictive control of PHEV.