Fault diagnosis of non-Gaussian process based on FKICA

https://doi.org/10.1016/j.jfranklin.2016.11.012Get rights and content

Highlights

  • A new KICA algorithm is proposed based on fault-related kernel independent component analysis (FKICA).

  • Compared to conventional principal component analysis, the data space is decomposed into four subspaces.

  • According to the fault-related kernel independent component analysis algorithm, the fault diagnosis approach is proposed.

Abstract

Recent approaches to independent component analysis (ICA) have introduced kernel function to obtain highly accurate solutions, particularly where classical linear methods experience difficulty in non-Gaussian process monitoring. These approaches are developed based on the statistics with normal data. However in some industry processes, certain fault data can be pre-separated from the normal data manually. In order to utilize this part of data, fault-related kernel independent component analysis (FKICA) is put forward as an improved algorithm of KICA in this paper. FKICA can make full use of the historical fault data by decomposing the data space into four subspaces and make the algorithm more sensitive to certain fault. The proposed methods are applied to monitoring of fused magnesia furnace smelting process. The experiment results show that the proposed methods are more sensitive to the known faults.

Introduction

Recently, multivariate statistical process monitoring (MSPM) has been intensively researched. Particularly, principal component analysis (PCA) and partial least squares (PLS) which are widely applied in the industrial processes have been important approaches for monitoring of the process performance [1], [2], [3], [4], [5], [14], [22], and some improved methods, such as kernel principal component analysis (KPCA) and kernel partial least squares (KPLS) have achieved great success in process monitoring and fault diagnosis [15], [18], [20], [23].

The kernel principal component analysis (KPCA) mentioned above is used to solve the modeling problem in principal component subspace (PCS) and residual subspace (RS), and has effectively carried on the fault detection and fault alarm [27]. But KPCA method is only calculated according to the observation data of covariance matrix in signal data processing, namely the second order statistical property. It does not take the high order statistical properties of signal data into account, so after transformation, there still exists between the data of higher-order redundant information. Further, the traditional process monitoring methods based on principal component analysis require that process data satisfies independent identically distribution and multivariate normal distribution assumption. And the assumption is often difficult to satisfy in most practical industrial process [10].

Some modified algorithms are proposed in recent years [6], [7], [8], [9]. A new structure of preprocessing-modeling-postprocessing is proposed, within which modified orthogonal projections to latent structures (MOPLS) method is developed to improve the performance of quality-related fault detection [12]. In some researches, advantages of some popular multivariate statistical monitoring method are merged. The principal component regression method (PCR), the partial least squares regression method (PLSR) and the modified partial least squares regression method (MPLSR) are merged with respective advantages to increase the prediction accuracy [11].

In fact, most industrial processes data not only contain Gaussian distribution, but also may contain sub-Gaussian, super-Gaussian and non-Gaussian distribution; independent component analysis (ICA) and its related improved algorithm can effectively extract information from a variety of complex industrial distribution data and model the industry process [21]. As an extension of PCA, ICA focuses on high order statistical properties among data. It makes the components not only unrelated, but also statistically independent as possible after transformation. The basic idea is that assuming measured signal in the process is composed of some of the independent source signals, noises and interference signal superposition mixed together. And then, according to certain standards (mainly information theory criterion) we can estimate the source signals from the measured signal. The advantages of this method is mainly reflected on two points: first, compared with principal component analysis, independent component analysis method can process data mixed by various source signals which are independent with each other, can better describe the behavior of the process; Second, the independent component analysis method can effectively process non-Gaussian distribution on the processing of data [34]. Therefore, ICA can more fully reveal the essence of between data structure. Because of this, the ICA achieves important breakthrough in many aspects compared with the traditional method and is increasingly becoming a potential analysis tool in signal processing [13].

However, ICA-based linear projection is also inadequate to represent the data with a non-linear structure [30]. Some algorithms facing non-linear system are proposed, a novel particle filtering technique named sequential evolutionary filter (SEF) is proposed to estimate state in nonlinear system [31]. Kernel based non-linear algorithm has also been researched recently. Non-linear process monitoring technique based on kernel independent component analysis (KICA) was proposed [32,33]. KICA consists of two steps: KPCA (kernel centering, kernel whitening) and an iterative procedure of the modified ICA. Therefore, KICA can be thought as performing ICA in the whitened kernel space generated from KPCA. The main non-linearity of process data is captured by KPCA and the additional ICA procedure gives statistically independent components from the observed data. But determining the optimal number of independent components in the kernel space and identifying which variable causes the process were not taken into account (Table 1).

Industry process such as the magnesia production contains a lot of nonlinear characteristic. The fused magnesia furnace is one of the main equipment for the producing of fused magnesia, which is a kind of mine heat electric arc furnace. With the development of melting technology, fused magnesia furnace has been widely developed in magnesia industry. Overall, equipment of fused magnesia furnace includes transformer, circuit short net, electrode lifting gear, electrode, furnace shell, etc. The control room which appears beside furnace controls electrode lifting and falling. Furnace shell is commonly rounded and slightly tapered. For the convenience of pulling off furnace shell from molten pile, a ring is welded in the furnace shell wall. The mobile car is equipped below furnace, so that after melting, the furnace occupied with molten pile can be moved to destination for cooling. The fused magnesia furnace diagram is shown in Fig. 2.

Particularly, noises caused by the electric arc are related with the frequency and electric current.But during the spreading of noises, some non-linear characteristics are introduced. Due to the nonlinear characteristic, traditional linear ICA method cannot detect faults accurately, So in our paper, we apply the kernel independent component analysis (KICA) in magnesia production process, which maps the input data into high dimensional space to eliminate the non-linear feature and makes the data linear separable.

In some cases, workers with experiences can distinguish normal data from some known fault data, which means the training data set can be pre-separated into normal training data set and fault-related training data set. In order to utilize workers’ experiences we proposed the fault-related kernel independent analysis (FKICA) method by utilizing the separated data sets. Experiment results show that, model established with FKICA are more sensitive with the known fault.

The rest of this paper is organized as follows. The basic principles of KICA are introduced in Section 2. Monitoring process use FKICA is proposed in Section 3. The simulation results and analysis are shown in Section 4 and the conclusions are gained in Section 5.

Section snippets

The basic principles of KICA

In this section, the basic principles of KICA are introduced. Firstly, in order to capture the nonlinearity of the observed data, it is mapped the into a feature space where the data has a more-linear structure.Φ:RmF(featurespace)

Secondly, the modified linear ICA is applied in this feature space and the independent components of data are extracted. Before applying ICA we have to remove the correlation with the whitening algorithm, “kernel tricks” is utilized to extract whitened PCs in

Offline modeling of fault-related kernel independent component analysis

Based on the above analysis, we proposed the fault-related kernel independent analysis (FKICA). In traditional KICA based monitoring methods, the original feature space is made up of the principal subspace and residual subspace. The corresponding subspaces are further divided into fault-related parts and fault-unrelated parts, namely four monitoring subspace which contains fault related principal component subspace (FRPCS), fault unrelated principal component subspace (FUPCS), fault related

The simulation and analysis of fused magnesia furnace smelting process

The fused magnesia furnace is a kind of melting furnace. Its heat source is electric arc. It can well smelt magnesia by concentrating heat. The fused magnesia furnace produces high temperature to complete melting process by use arc produced under high current. Due to reasons such as electrode lifter failure, the distance between fused magnesia furnace wall and electrode is too close to make furnace temperature anomalies, which result in Furnace leakage. This will lead to great threat of

Conclusion

For process monitoring problems with nonlinear, non-Gaussian characteristics, from the aspect of the fault-related and unrelated, a fault-related kernel independent component analysis method (FKICA) is proposed in this paper and used in industrial process monitoring. Traditionally, original feature space is made up of principal subspace and residual subspace. In our method, the corresponding subspaces are further divided into four monitoring subspace. Fault related data set is utilized to

Acknowledgement

This work is supported by China׳s National 973 program (2009CB320600 and 2009CB320604) and NSF in China (61325015 and 61273163).

References (26)

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