A Study on Statistical Modeling with Gaussian Process Prediction

In recent years, higher performance base models for vehicles and engines have been required to efficiently and accurately conduct Model Based Development(MBD) or HILS. Therefore, it is needed to create more precise models for torque and engine speed control in vehicle developments. There are a lot of statistical ways to create prediction models, such as linear and non-linear regressions. For this study, we used prediction function from data sets which are defined as normal distributions and the Gaussian process. Here is an example of our investigation. There is a data set extracted from an unknown distribution. The Gaussian process is a methodology to predict the response variable y(new) from the given new input vector X-new and learned data. We decided to use this process experimentally for our investigation because it could illustrate linearity and non-linearity of data sets even when the Kernel function was used. However, we mainly investigated how we could obtain and utilize input output information and predicted models through the Gaussian process. It is essential to utilize the information when the process is used to actual models, such as the above mentioned engines. We investigated if it was possible to replace physical models with statistical ones by conducting simulation with the Gaussian process model. For making useful observations on predicted model in this study, such as output of predict model via statistical models. Our primary purpose of this study was how to input data in simulation software in order to obtain highly accurate prediction models. We previously believed that the Gaussian process was a perfect methodology. In order to create prediction models as targeted, we must consider how to provide input data to prediction software and which input data should be used. This paper reports the best way to utilize the Gaussian process model for next development tool.