Support vector machines: Their use in geotechnical engineering as illustrated using seismic liquefaction data

Empirical models based on known or measured sample data are often used to develop solutions to problems in which the underlying first principles are not well defined and it is not possible to define a concise relationship between the variables, or the problem is too complicated to be described mathematically. Increasingly, various modern learning algorithms such as neural networks are being considered to develop models that essentially map a dependency between the inputs and outputs from known data patterns. This study looks at a fairly new pattern recognition tool known as support vector machines (SVM) that can be used for solving classification-type problems. There are two main ideas underlying the SVM for discriminant-type problems. The first is an optimum linear separating hyperplane (decision surface) that separates the data patterns. The second main idea is the use of kernel functions (dot product of two vectors) to apply mapping to the original nonlinear data patterns, such that the data becomes linearly separable in a high-dimensional feature space. An overview of the SVM is first presented followed by an illustration of its use to assess seismic liquefaction data. The SVM model was trained and tested on a relatively large data set comprising 226 field records of liquefaction performance and cone penetration test measurements. The overall classification success rate for the entire data set is 98%. (c) 2007 Elsevier Ltd. All rights reserved.