Singular value decomposition (SVD) is an effective method used in bearing fault diagnosis. Ideally two important problems should be solved in any diagnosis: one is how to decide the dimension embedding of the trajectory matrix (TM); the other is how to select the singular value (SV) representing the intrinsic information of the bearing condition. In order to solve such problems, this study proposed an effective method to find the optimal TM and SV and perform fault signal filtering based on false nearest neighbors (FNN) and statistical information criteria. First of all, the embedded dimension of the trajectory matrix is determined with the FNN according to the chaos theory. Then the trajectory matrix is subjected to SVD, which is helpful to acquire all the combinations of SV and decomposed signals. According to the similarities of the signal changed back and signal in normal state based on statistical information criteria, the SV representing fault signal can be obtained. The spectrum envelope demodulation method can be used to perform effective analysis on the fault. The effectiveness of the proposed method is verified with simulation signals and low-speed bearing fault signals, and compared with the published SVD-based method and Fast Kurtogram diagnosis method.

Multivariate statistical process control is the continuation and development of unitary statistical process control. Most multivariate statistical quality control charts are usually used (in manufacturing and service industries) to determine whether a process is performing as intended or if there are some unnatural causes of variation upon an overall statistics. Once the control chart detects out-of-control signals, one difficulty encountered with multivariate control charts is the interpretation of an out-of-control signal. That is, we have to determine whether one or more or a combination of variables is responsible for the abnormal signal. A novel approach for diagnosing the out-of-control signals in the multivariate process is described in this paper. The proposed methodology uses the optimized support vector machines (support vector machine classification based on genetic algorithm) to recognize set of subclasses of multivariate abnormal patters, identify the responsible variable(s) on the occurrence of abnormal pattern. Multiple sets of experiments are used to verify this model. The performance of the proposed approach demonstrates that this model can accurately classify the source(s) of out-of-control signal and even outperforms the conventional multivariate control scheme.

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In qualitative multiple criteria decision making (MCDM) process, dealing with complex linguistic evaluations and modeling interaction phenomena among criteria are two important issues. The purpose of this study is to introduce two Choquet integral operators for HFLTSs to tackle interactions among criteria and then implement these operators to a well-known MCDM method, namely, the MULTIMOORA (multi-objective optimization by ratio analysis plus the full multiplicative form). Firstly, we introduce new operations for HFLTSs based on some linguistic scale functions. Then, we define two hesitant fuzzy linguistic Choquet integral operators and propose a novel score function for hesitant fuzzy linguistic elements. Afterwards, we improve the HFL-MULTIMOORA method to handle the hesitant fuzzy linguistic MCDM problems in which the criteria are interdependent. Finally, an illustration regarding the human resource development at Sichuan University is shown to verify the applicability and validity of the proposed method.

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