Gaussian Mixture Model Based Classification Revisited: Application to the Bearing Fault Classification

Abstract

Condition monitoring and fault detection are nowadays popular topic. Different loads, enviroments etc. affect the components and systems differently and can induce the fault and faulty behaviour. Most of the approaches for the fault detection rely on the use of the good classification method. Gaussian mixture model based classification are stable and versatile methods which can be applied to a wide range of classification tasks. The main task is the estimation of the parameters in the Gaussian mixture model. Those can be estimated with various techniques. Therefore, the Gaussian mixture model based classification have different variants which can vary in performance. To test the performance of the Gaussian mixture model based classification variants and general usefulness of the Gaussian mixture model based classification for the fault detection, we have opted to use the bearing fault classification problem. Additionally, comparisons with other widely used non-parametric classification methods are made, such as support vector machines and neural networks. The performance of each classification method is evaluated by multiple repeated k-fold cross validation. From the results obtained, Gaussian mixture model based classification methods are shown to be competitive and efficient methods and usable in the field of fault detection and condition monitoring. Highlights• Gaussian-mixture-model-based classification was applied to the bearing-fault classification. • To discriminate the faulty from non-faulty bearings only simple statistics from vibrational data was used. • Two different datasets, the Case Western Rice University dataset and Bearing vibration data collected under time-varying rotational speed conditions dataset are used. • The Gaussian-mixture-model-based classification method showed to be a competitive and efficient method.

Optimizing the Estimation of a Histogram-Bin Width—Application to the Multivariate Mixture-Model Estimation

“…Nonetheless, we used only the lower-dimensional settings to demonstrate the usefulness of our proposals due to the fact that both the histogram and Gaussian mixture-model parameters are not suitable for a higher-dimensional setting without any special care. For that reason we left the question open to be researched in the future, and because said parameters can be used for high dimensional classification datasets; e.g., for image classification or condition monitoring [11]. Although we have only used the Gaussian mixture model as our reference mixture-model parameter estimation problem, the proposal can be extended to various non-Gaussian models; e.g., copula-based models [39].…”

“…Nonetheless, obtaining a non overlapping grid with no gaps using other polytopes is not an easy job; hence, hyper-rectangles are the most preferred option. However, if used, the counting method remains the same; i.e., Equations (8) and (11) are unchanged; only the definition of operation y ∈ V j in Equation 10is changed due to the different definition of the jth bin volume V j .…”

“…, v d } can be inexpensively estimated, it could it result in improvements in the performance of the parameter estimation . It is clear that the estimation of the histogram-bin width h, as described above, can be translated into an estimation of the histogram's number of bins v. In the following explanations we will refer to the different number of bins v as different binning v and the histogram estimation for the binning v is the problem of estimating the frequency k j for each bin j, as defined in Equation (11). The problem of estimating the optimum binning v can thus be formulated as the following constrained-integer optimization problem max H(v),…”

“…It is clear that different binning v should produce different results for H(v), even though it is not obvious from the definition in Equation (22). Different binning v leads to different frequencies k j (Y), if we recall Equation (11), and additionally, a different number of bins V, ultimately giving different values to the ∑ V j=1 log Γ(k j (Y) + 1/2) term in Equation (22). Nonetheless, as the number of bins V increases (with the increase in the marginal number of bins v i , the bin width shrinks h i → 0), it will lead to the state where each populated bin contains only one observation, k j (Y) = 1 ∀j ∈ {1, .…”

“…Although it is always good to check multiple possible solutions, this can bring a lot of unwanted overhead in terms of the computational time. In some specific cases the amount of time available, or, simply, the amount we want to invest, is limited, whereas the need for high accuracy is always a requirement [11].…”