ADVANCED MODELING AND OPTIMIZATION FOR VIRTUAL CALIBRATION OF INTERNAL COMBUSTION ENGINES

Due to the high complexity of modern internal combustion engines and powertrain systems, the proper calibration of the electronic control unit’s (ECU) parameters has a strong impact on project targets like fuel consumption, emissions and drivability, as well as development costs and project duration. Simulation methods representing the system behavior with a model can support the calibration process considerably. However, standard physics-based models are often not able to describe all effects with sufficient accuracy, or the effort to set up a detailed model is too high. Physics-based models can also have a high computational demand, so that their simulation is not real-time capable. More suited for ECU calibration are data-driven models, combined with Design of Experiment (DoE). The system to be calibrated is identified with few specific test bench or vehicle measurements. From these measurements, a mathematical regression model is built. This paper describes recently developed machine learning methods based on Gaussian processes. In contrast to polynomial models or neural network regression, Gaussian processes are able to model strongly nonlinear systems with high accuracy, and are robust against measurement noise and outliers. No expert knowledge is required for their practical application, all model parameters are determined automatically by probabilistic principles. The data-driven model replaces the real engine or vehicle in the calibration process, and combined with optimization methods, the best set of ECU parameters with respect to the project targets is identified. The short response time of Gaussian process models further enables their use in real-time environments, e.g. Hardware-in-the-Loop (HiL) test systems or even directly on the ECU. This paper shows the application of the datadriven approach in the calibration process on several examples. Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Advanced Modeling and Optimization for Virtual Calibration of Internal Combustion Engines Page 2 of 9 INTRODUCTION The process of calibrating the parameters of the engine’s electronic control unit (ECU) has a strong impact on project targets like fuel consumption, emissions, drivability, as well as development costs. One major challenge is the increasing number of engine parameters, which must be optimized over the entire engine operating range, in order to provide the best compromise between conflicting targets. Figure 1 shows a typical set of inputs and outputs considered during base calibration of a modern direct injection gasoline engine. Each new engine parameter leads to a multiplication of the measurement effort, if classical calibration methods are applied. Simulation methods that represent the system behavior by a model can support the calibration process considerably. Figure 2 shows the different phases of a standard calibration process, from the base calibration at the engine test bench to the test Figure 1: Typical parameter and optimization targets of a modern gasoline engine. Figure 2: Different phases of the calibration process for a gasoline engine. Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Advanced Modeling and Optimization for Virtual Calibration of Internal Combustion Engines Page 3 of 9 and validation of the entire calibration. In each phase, the calibration engineer struggles with new challenges, leading to a very high measurement effort and an extensive use of prototypes, i.e. engines and complete vehicles. Appropriate simulation methods, where the relevant system behavior is represented by a model, can reduce the calibration effort and demand for real prototypes significantly. An essential prerequisite for the practical application is that the models have to provide a very high accuracy and can be configured with relatively low measurement and time effort. This excludes in most cases the use of physicsbased models. More suitable are data-driven models combined with a Design of Experiment (DoE). DESIGN OF EXPERIMENT AND DATADRIVEN MODELING The basic idea of DoE is to characterize an unknown system, e.g. an internal combustion engine, by a data-driven mathematical model using a matching test plan to minimize the measurement effort. Compared to a full factorial test plan, the number of required measurements can be reduced by orders of magnitudes with a proper DoE, especially for high dimensional identification problems. The determination of the calibration parameters is done based on a trained model and the use of mathematical optimization algorithms. The overall process is depicted in Figure 3. The first applications of data-driven modeling and DoE in ECU calibration started more than a decade ago [1]. The combination of DoE with modern test bench automation methods allows a fast and simultaneous variation of all parameters, which further increases the efficiency [2]. The key element of the entire DoE process is the mathematical model. Often, polynomials or neural networks are used [3], but both types have significant disadvantages which limit their use in the calibration process. Polynomials are easy to understand and available in many commercial tools. The major drawback is that only a very simple system behavior can be described. Polynomials are also sensitive to single measurement errors, which can deteriorate the model if not detected as outliers. Alternatively, neural networks are theoretically able to describe any complex system behavior, but often require high expertise for the model configuration and additional validation data to avoid model over fitting. As a consequence of the listed drawbacks, DoE methods were only applied by a few experts in the past and limited to a small number of use cases. A new approach is the use of machine learning methods based on Gaussian processes. From a complete set of basis functions, a Bayesian approach determines automatically the set of functions which represents the training data with highest probability [4]. The function set is characterized by so-called hyperparameters: signal noise, signal strength, and a length scale for each input dimension D which describes the rate of Figure 3: Overview of the DoE process from the test plan to the optimization of the system outputs. Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Advanced Modeling and Optimization for Virtual Calibration of Internal Combustion Engines Page 4 of 9 change of the output over the respective input. The hyperparameters are determined automatically from the training data based on maximum likelihood optimization. The final formula for the prediction of an output y depending on the inputs x1, x2, . , xD can be reduced to a summation of overlapping Gaussian kernel functions [5], see Figure 4. N represents the number of training data points, Qi is a combination of the signal noise and signal strength hyperparamters for data point i, lj is the length scale hyperparameter, and Xi,j stands for the position of the training data in the input space. This regression model allows a precise description of complex and highly nonlinear systems without over fitting. A one-dimensional example is given in Figure 5. The training data points for the output (y-axis) show a strong nonlinear behavior with respect to the input (x-axis) including some measurement noise. The upper half of Figure 5 shows the attempt to describe the input-output relationship with a polynomial model, which fails in fitting the data properly even with a high model order of 5. The lower half shows the model fit based on the Gaussian process approach. Here, the true relationship is described very well without fitting the noise in the data. Additionally, a locally resolved model variance can be derived from the Gaussian process algorithm [5]. This can be used to indicate a level of model uncertainty, which increases in areas with insufficiently provided training data points. Based on this, a recommendation for a valid model range can be derived. If the model variance exceeds a certain threshold, the model prediction can be classified as unreliable, as shown with the grey line in Figure 5. These areas can then be excluded from the subsequent calibration optimization. Also, this information can be used to define and collect new measurements to improve the model quality. The available information regarding model accuracy and validity is important for the use in series ECU calibration and for user acceptance. These highly flexible and accurate Gaussian process models enable an easy generation of global engine models for the entire operating range and all relevant calibration parameters. In contrast to the often used two-stage approach [6], engine speed and load can be included as a normal input variables. The modeling process is done in a few minutes on a standard PC, even for complex problems with more than ten input dimensions and thousands of training data points. Since the model accuracy depends mainly on the local density of the training data in the input space, an equal distribution of the data points is desired. This is provided best by a space filling DoE test plan such as a Sobol sequence [7]. Figure 4: Formula of the Gaussian process model for predicting an output y. Figure 5: Modeling of a complex one-dimensional relationship with a polynomial model of 5 order (upper half) and the Gaussian process algorithm (lower half). The dashed lines indicate the model variance. Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Advanced Modeling and Optimization for Virtual Calibration of Internal Combustion Engines Page 5 of 9 GAUSSIAN PROCESS MODELING AND ITS APPLICATION IN ECU CALIBRATION The capability of building easily very precise data-driven models, e.g. of a global engine, enables the use of model-based methods for a broad range of calibrati