Application of the Gaussian Process Regression Method Based on a Combined Kernel Function in Engine Performance Prediction

Abstract

At present, regression modeling methods fail to achieve higher simulation accuracy, which limits the application of simulation technology in more fields such as virtual calibration and hardware-in-the-loop real-time simulation in automotive industry. After fully considering the abruptness and complexity of engine predictions, a Gaussian process regression modeling method based on a combined kernel function is proposed and verified in this study for engine torque, emission, and temperature predictions. The comparison results with linear regression, decision tree, support vector machine (abbreviated as SVM), neural network, and other Gaussian regression methods show that the Gaussian regression method based on the combined kernel function proposed in this study can achieve higher prediction accuracy. Fitting results show that the R 2 value of engine torque and exhaust gas temperature after the engine turbo (abbreviated as T4) prediction model reaches 1.00, and the R 2 value of the nitrogen oxide (abbreviated as NOx) prediction model reaches 0.9999. The model generalization ability verification test results show that for a totally new world harmonized transient cycle data, the R 2 value of engine torque prediction is 0.9993, the R 2 value of exhaust gas temperature is 0.995, and the R 2 value of NOx emission prediction result is 0.9962. The results of model generalization ability verification show that the model can achieve high prediction accuracy for performance prediction, temperature prediction, and emission prediction under steady-state and transient operating conditions.

Increasing transparency in machine learning through bootstrap simulation and shapely additive explanations

“…Two studies may find vastly different results in the predictive accuracy of machine-learning methods even if they use near identical models, covariates, and model summary statistics just due to the choice of the train-test sets (which are determined strictly by random number generation) [ 32 , 35 , 36 , 48 , 49 ]. As a result, this study highlights the importance of utilizing multiple different train and test sets when executing machine-learning for prediction of clinical outcomes to accurately represent the variance that is present just in the choice of selection of train and test sets [ 16 , 18 , 50 ]. This will accurately characterize the accuracy of the model and allow for better replications of the study.…”

“…Depending on which training set is present, a covariate can be twice as important to the final result of the model. This result highlights the need for multiple different “seeds” to be set prior to model training when splitting the training and test sets in order to avoid potential training-set biases and to have the model at least be representative of the cohort it is being trained and tested on (if not representative of the population the cohort is a sample of) [ 16 , 30 , 53 ]. Similar to the model accuracy statistics, this also highlights the difficulty in replication of results in machine-learning models from study to study [ 1 , 54 , 55 ].…”

“…However, the increase in ML algorithms compared to traditional parametric methods comes at a significant cost: interpretability [11][12][13][14][15]. Linear regression and logistic regression have clear interpretable output that have been widely studied [16][17][18]. Machine-learning algorithms are often noninterpretable, leading to their reputation as a "black box" algorithm [10,[19][20][21].…”

A misfire-integrated Gaussian process (MInt-GP) emulator for energy-assisted compression ignition (EACI) engines with varying cetane number jet fuels

“…Machine Learning (ML)-based surrogate modeling of internal combustion engines (ICE) has been widely used for a broad range of applications. 25–29 Data-driven ML approaches, in particular, are popular for building ICE surrogate models; such approaches include neural networks (NN), 30–45 Support Vector Machines (SVM), 46–49 Gaussian Processes (GPs, 50–60 also known as kriging 61 ), and other learning models. 62–68 In surrogate modeling applications with limited training runs from expensive simulators, GPs (and its recent non-stationary extensions) have several key advantages over alternate deep learning models.…”

“…This necessitates the development of more robust ML models which can function well under high variability in inputs and operating conditions, while also not placing a large demand on experimental training data. Shi et al 56 developed a GP-based engine surrogate model using a combined kernel function (trained using experimental data), which was able to accurately predict the engine torque, NOx emissions, and exhaust gas temperature of a diesel engine, and showed better prediction accuracy than other methods such as decision trees, NNs and SVMs. Pan et al 72 used a GP model trained with experimental data to perform engine calibration on fuel consumption, soot emission and NOx emission; they found that this GP-based model performed better than polynomial models and NNs.…”