Application of Stochastic Regression for the Configuration of Microrotary Swaging Processes
Table 1
Regression and learning methods included in the μ-ProPlAn software prototype.
Method
Description
Linear regression
As fundamental multivariate regression function, µ-ProPlAn offers the option to perform a simple linear regression on the provided data. As a result, a function of the form is determined. Thereby, the least squares method is applied to minimize the distance between the regression model and the original data points. Additionally, μ-ProPlAn offers additional functionality to linearize, for example, exponential or logarithmic data to enable linear regressions.
Polynomial regression
In case of univariate cause-effect relations, a polynomial regression can be conducted to achieve functions of the form . This method again uses the least squares method.
In contrast to the methods above, tree- or rule-based approaches do not result in a single analytic function. In general, they divide the search space into smaller segments, for which a regression can be performed. Usually, both methods use linear regressions for each segment.
Locally weighted linear regression (LWL) (e.g., [9])
LWL constitutes an abstract prediction model, which performs a locally weighted linear regression each time a prediction is requested. Thereby, a kernel function is used to weight adjacent data points and finally a linear regression is performed. This method particularly excels in interpolating missing data in between available data points.
A support vector machine is usually used as classifier. Thereby, it learns a model, which separates a set of data points in one or more classes, maximizing the distance between each data point and the classification curve. The same method can be used for regression, particularly if the provided data contains strong variances.
Neuronal networks
A neural network usually consists of a number of layers, each containing a defined number of nodes. The nodes of each layer are interconnected. During the supervised training of the network, these connections’ weights are adapted to recreate the desired output on the last layer. Thereby, the quality of the prediction strongly depends on a suitable network structure (i.e., number of layers/nodes, selected activation functions, etc.)
