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This paper aims to enhance the reliability of self-validating multifunctional sensors.

An effective fault detection, isolation and data recovery (FDIR) strategy by using kernel principal component analysis (KPCA) coupled with gray bootstrap and fault reconstruction methods.

The proposed FDIR strategy is able to the address fault detection, isolation and data recovery problem of self-validating multifunctional sensors efficiently.

A KPCA-based model which can overcome the limitation of existing linear-based models is used to achieve the fault detection task. By using gray bootstrap method, the position of all faulty sensitive units can be calculated even under the multiple faults situation. A reconstruction-based contribution method is adopted to evaluate the amplitudes of the fault signals, and the fault-free output of the faulty sensitive units can be used to replace the fault output.

This study aims to accurately evaluate the influence of various error intervals on the performance of the wiper.

The wiper structural system is decomposed into classical four-link planar for kinematics analysis, and it was modeled respectively by using interval method, universal grey number theory and enumeration approach depending on the nature of uncertainty.

The universal grey number theory is a viable methodology for the accurate analysis of uncertain structural system.

(1) The model of uncertain wiper structural system is established. (2) Universal grey number theory and new parameters are adopted to analyze the presence of uncertain wiper structural system. (3) Comparative analysis of response quantities is obtained by interval method, universal grey number theory and enumeration method.

To solve the problem of simulation evaluation with small samples, a fresh approach of grey estimation is presented based on classical statistical theory and grey system theory. The purpose of this paper is to make full use of the difference of data distribution and avoid the marginal data being ignored.

Based upon the grey distribution characteristics of small sample data, the definition about a new concept of grey relational similarity measure comes into being. At the same time, the concept of sample weight is proposed according to the grey relational similarity measure. Based on the new definition of grey weight, the grey point estimation and grey confidence interval are studied. Then the improved Bootstrap resampling is designed by uniform distribution and randomness as an important supplement of the grey estimation. In addition, the accuracy of grey bilateral and unilateral confidence intervals is introduced by using the new grey relational similarity measure approach.

The new small sample evaluation method can realize the effective expansion and enrichment of data and avoid the excessive concentration of data. This method is an organic fusion of grey estimation and improved Bootstrap method. Several examples are used to demonstrate the feasibility and validity of the proposed methods to illustrate the credibility of some simulation data, which has no need to know the probability distribution of small samples.

This research has completed the combination of grey estimation and improved Bootstrap, which makes more reasonable use of the value of different data than the unimproved method.