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A study on statistical modeling with Gaussian process prediction

机译：高斯过程预测的统计建模研究

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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 from the given new input vector x and learned data. We decided to use this process experimentally for our investigation because it could illustrate linearity and nonlinearity 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.
机译：近年来，为了高效，准确地进行基于模型的开发（MBD）或HILS，需要用于车辆和发动机的高性能基础模型。因此，需要为车辆开发中的扭矩和发动机转速控制创建更精确的模型。创建预测模型的统计方法有很多，例如线性回归和非线性回归。在本研究中，我们使用了来自定义为正态分布和高斯过程的数据集的预测函数。这是我们调查的一个例子。有一个从未知分布中提取的数据集。高斯过程是一种根据给定的新输入向量x和学习到的数据预测响应变量y的方法。我们决定将这一过程实验性地用于我们的研究，因为即使使用Kernel函数，它也可以说明数据集的线性和非线性。但是，我们主要研究了如何通过高斯过程获得和利用输入输出信息和预测模型。当过程用于实际模型（例如上述引擎）时，利用信息至关重要。我们调查了是否有可能通过用高斯过程模型进行仿真来用统计模型代替物理模型。为了在本研究中对预测模型进行有益的观察，例如通过统计模型输出预测模型。这项研究的主要目的是如何在仿真软件中输入数据，以获得高度准确的预测模型。我们以前认为高斯过程是一种完美的方法。为了创建针对性的预测模型，我们必须考虑如何向预测软件提供输入数据以及应使用哪些输入数据。本文报告了将高斯过程模型用于下一个开发工具的最佳方法。

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