Extended least squares support vector machine with applications to fault diagnosis of aircraft engine

Recently, a robust least squares support vector machine (R-LSSVM) was proposed, but its computational complexity is very high compared with the traditional least squares support vector machine (LSSVM). To reduce R-LSSVM's computational complexity, an improved version, i.e., extended LSSVM (E-LSSVM), is developed in this paper. E-LSSVM and R-LSSVM are equivalent in terms of the generalization performance, but the former needs lower computational complexity than the latter. It is proved that the traditional LSSVM is a special case of E-LSSVM, and based on this fact, we know that the bias in the traditional LSSVM owns manifest physical meaning, i.e., the mean of the modeling error. To solve the mathematical model of E-LSSVM, two algorithms, DE-LSSVM (dual E-LSSVM) and PE-LSSVM (primal E-LSSVM), are proposed from dual and primal spaces, respectively. Even competing against the traditional LSSVM, DE-LSSVM takes the edge in term of the training time. In addition, the sparse problem and cross validation of DE-LSSVM are discussed as well. To verify the effectiveness and soundness of the proposed DE-LSSVM and PE-LSSVM, experiments on regression and classification problems are investigated. To be more important, DE-LSSM and PE-LSSVM are successfully applied to the fault diagnosis of aircraft engine, showing that they are eligible for potential techniques of the fault diagnosis of aircraft engine.