Shock and Vibration

Volume 2017 (2017), Article ID 1524840, 13 pages

https://doi.org/10.1155/2017/1524840

## An Enhanced Factor Analysis of Performance Degradation Assessment on Slurry Pump Impellers

Smart Engineering Asset Management Laboratory (SEAM), Department of Systems Engineering & Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong

Correspondence should be addressed to Peter W. Tse

Received 25 July 2016; Accepted 13 December 2016; Published 4 January 2017

Academic Editor: Mickaël Lallart

Copyright © 2017 Shilong Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Slurry pumps, such as oil sand pumps, are widely used in industry to convert electrical energy to slurry potential and kinetic energy. Because of adverse working conditions, slurry pump impellers are prone to suffer wear, which may result in slurry pump breakdowns. To prevent any unexpected breakdowns, slurry pump impeller performance degradation assessment should be immediately conducted to monitor the current health condition and to ensure the safety and reliability of slurry pumps. In this paper, to provide an alternative to the impeller health indicator, an enhanced factor analysis based impeller indicator (EFABII) is proposed. Firstly, a low-pass filter is employed to improve the signal to noise ratios of slurry pump vibration signals. Secondly, redundant statistical features are extracted from the filtered vibration signals. To reduce the redundancy of the statistic features, the enhanced factor analysis is performed to generate new statistical features. Moreover, the statistic features can be automatically grouped and developed a new indicator called EFABII. Data collected from industrial oil sand pumps are used to validate the effectiveness of the proposed method. The results show that the proposed method is able to track the current health condition of slurry pump impellers.

#### 1. Introduction

Slurry pumps, such as oil sand pumps, are widely used in industry to convert electrical energy to slurry potential and kinetic energy. Slurry pumps work under adverse conditions, so their impellers are prone to suffer wear, resulting in breakdown. Therefore, fault diagnosis and prognosis of slurry pump impellers are major concerns. Recent research has classified different slurry pump impeller health conditions. Qu and Zuo [1] proposed a data cleaning algorithm, based on support vector machines and random subsampling validation, to classify and identify different impeller health conditions. A modified neighborhood rough set model was proposed by Zhao et al. [2] to select useful features for the identification of different impeller health conditions. They found that the modified model can produce higher prediction accuracies than the original neighborhood rough set model. In addition to fault diagnoses of slurry pump impellers, prognostic studies of slurry pumps have also been carried out. These prognostic works can be broadly divided into two steps [3]. The first is to assess performance degradation, and the second is to estimate the remaining useful life of the pumps. In this study, only the performance degradation assessment of slurry pump impellers is investigated.

Performance degradation assessment tracks the health conditions of components and systems. A number of typical examples show how different methods have been developed for performance degradation assessment. Zhao et al. [4] used half and full spectra, fuzzy preference based on rough sets, and principle component analysis (PCA) to develop a new indicator for impeller damage to pumps. The results illustrate that the indicator is capable of monitoring the health status of pump impellers monotonically. Miao et al. [5] used hidden Markov Models to propose a novel probability health description index to monitor gear health conditions. Based on the discrete wavelet transform, Wang et al. [6] developed a health indictor known as the frequency spectrum growth index (FSGI) for the evaluation of gear health conditions. Wang et al. [7] went on to fuse different statistical features, describing the gear health conditions using support vector data descriptions. Miao et al. [8] combined comblet filtering and an exponentially weighted moving average method, to develop a health conditions indicator (HCI) for bearing degradation assessment. Lei et al. [9] proposed two diagnostic parameters to track the health conditions of planetary gearboxes, in terms of the statistical characteristics of planetary gearbox vibration signals in the domains of both time and frequency. Based on the industrial run to alert slurry pump data, Tse and Wang [3, 10] also designed a specific moving average wear degradation index and an impeller health indicator, to assess slurry pump impeller degradation. The impeller health indicator is constructed by using the PCA of the statistical features extracted from the slurry pump vibration signals. Therefore, it is vital that performance degradation assessment extracts and develops an effective health condition indicator from raw signals.

The slurry pump original vibration signals are part of a high dimensional data set. Moreover, the common statistical indicators for monitoring the degradation were not effective in tracking the health conditions of the slurry pumps. To minimize the computational burden and to discover an effective indicator for monitoring the degradation of the slurry pump, methods such as feature clustering are used. Feature clustering, such as PCA and independent component analysis, are widely used to investigate the correlation of selected attributes and to reduce the dimension of the feature space. For example, Tse and Wang [11] applied the PCA method to construct a health indicator to monitor the health evolution of an impeller. Chang et al. [12] used the PCA combined with a support vector machine to extract the first principal feature associated with the operating mine system gearbox. The PCA algorithm was found to be effective in removing redundancy and reducing the dimensionalities of the feature space. Harmouche et al. [13, 14] proposed a fault detection approach using the PCA, based on probability distribution, which can successfully detect incipient faults that are undetectable by traditional methods. Lee et al. [15] used a modified independent component analysis algorithm to extract important independent components from a multivariate statistical data set, which was applied to fault diagnosis in a wastewater treatment process. However, the abovementioned methods cannot ensure that the representation of the whole content of the original variable data is preserved and are not able to cluster features into a single new effective indicator when assessing slurry pump impeller degradation. Therefore, the traditional statistical method of factor analysis (FA), based on the indicators extracted from the slurry pump vibration data, is proposed in this paper. FA [16] is a widely used statistical tool in different fields, such as economics [17], business [18], psychology [19], social sciences [20, 21], and medicine [22, 23]. However, it is rarely applied to fault diagnosis and prognosis of complex mechanics system, particularly feature extraction and selection. Apley and Shi [24] proposed a creative FA, which can extract diagnostic features from a large volume of automated in-process measurement data. Zhang et al. [25] studied a novel fault FA scheme, which can reduce the influence on fault detection of the relay protection’s wrong action device. Kuravsky et al. [26] proposed a wavelet-based confirmatory FA for monitoring the damage accumulation factors responsible for the evolution of technical and other systems. In sum, the FA has been proven effective in combining potential latent variables, covering the whole content of the original variables, similar to the PCA. Compared to the PCA, which focuses on the ranking and selection of the components, the FA could classify, group, and remove the redundancy of the data information. The calculation process of the FA is more complicated than the PCA method, with an extra step, known as factor rotation. This kind of grouping function could increase the efficiency of the new indicator, developed through FA, in the evaluation of the degradation of the slurry pump impellers. In addition, the FA measures underlying factors, in which the identification of such underlying factors simplifies the understanding and description of the complex original variables and also reduces the number of factors. In other words, the FA algorithm can be taken as a data-reduction technique, as it reduces a large number of correlated variables to a smaller set of factors that reflect the original variables. In this study, combining the FA with a low-pass moving average filter is proposed and used to track the health conditions of a slurry pump, with less dimensions and a more effective new health indicator.

A low-pass filter is applied to the slurry pump vibration signals. To provide an alternative to the impeller health indicator, an enhanced factor analysis based impeller indicator (EFABII) is proposed in this study. The procedures of the proposed method are similar to those reported in our previous publication. The major difference is that the FA can be used to reduce the dimensionality of the statistical features. In addition, it can also be used to categorize the statistical features. Therefore, the relationship between different statistical features can be clearly identified.

The rest of the paper is organized as follows. In Section 2, the FA is reviewed and discussed. A method used for slurry pump impeller performance degradation assessment is proposed in Section 3. In Section 4, industrial data are used to validate the effectiveness of the proposed method. Conclusions are drawn in Section 5.

#### 2. Factor Analysis Principle

Factor analysis [27, 28] is a method that uses a lower number of new variables, known as common factors, to describe the variability of the observed and correlated variables. The observed variables are therefore the linear combinations of the new factors and errors. The FA is generally divided into four steps: calculation of correlation matrix for all variables; factor extraction; factor rotation; establishment of latent factors. Based on the FA principles, an enhanced factor analysis method was proposed in this paper.

Suppose that are observed and correlated variables. The FA aims to solve the following mathematical problem. The matrix form of the FA equation is derived as follows [27]:where is the vector of the observed variables; is the mean vector of the observed variables; is the factor loadings of a constant -by- matrix; is a vector of independent and standardized common factors which is the unobservable latent variable; is a vector of specific factors which cannot be included by those common factors; is the number of the original features and is equal to 18 in this paper, and is the observed variables.

Here, the vectors and must satisfy the following requirements [27]:

In addition, because the common factor and specific factor are irrelevant, then

Common factor accounts for the correlation among the variables. The larger the coefficient of each common factor , the more explained the content between that common factor and that corresponding variable. The specific factor explains the remaining variance and the error of that variable. As aforementioned, the factor loading is here referred to as the correlation. Factor loading is the correlation coefficient between the th variables and the th common factor. It reflects the relative importance of the th variables and the th common factor. The closer to 1 its absolute value is, the higher relative degree it has. The factor loadings equation can be obtained from

From (2), the variance of can be deduced, which is as follows [28]:

Then, the total variance of is

Therefore, the commonality is the sum square of the coefficients or factor loadings of the common factors. The common variance reflects the explained extent of the common factor to the total variance of the variables. The larger is, the higher the correlation between that kind of factor and its variables is.

The establishment of the enhanced FA model identifies the common factors and classifies the variables but more importantly enables the meaning of every common factor to be studied, and further analysis can be carried out. The original variables are considered as a linear combination of common factors through this model. To acquire a better result through the enhanced FA model, the factor-loading matrix should be rotated. The common factors can then explain the original variables specifically and precisely. The methods of factor rotation can be divided into orthogonal and oblique. Therefore, to simplify the rotation of the factor-loading matrix, the polarized squared value of each column and row of the factor-loading matrix should be set up close to 0 or 1 [16, 27–29]. For the method described in this study, “Equimax” is chosen as the rotation method, as this is a compromise between polarizing the rows’ and columns’ factor matrix.

The last step of the enhanced FA model is to acquire the factor scores. These can be used to conduct further studies, such as regression or the evaluation of sample classification analysis.

According to (1) and (4), the factor scores function can be written as follows:

The coefficients of the factors should be first deduced so each of the factor scores can then be obtained.

#### 3. The Proposed Method for Impeller Performance Degradation Assessment

In this study, a new statistics impeller health indicator is developed for describing the degradation performance assessment of slurry pumps. This new health indicator is built according to our previous studies [3, 7, 10]. The vibration measurement data were collected from the application of the smart asset management system (SAMS) software developed by the Smart Engineering Asset Management Lab. The data acquisition instruments included a National Instrument (NI) DAQ 9172 and a DAQ module NI 9234. Four accelerometers were installed in four different positions on the slurry pumps, to monitor the various working conditions. The data measurements were recorded using a number series from 1 to 1101 to identify their source. The recording period was three months and the sampling rate was 51,200 Hz. Vibration data solely from channel 3 were used in this study. The details of the steps for processing the data are as follows.

Suppose is the original vibration data of the slurry pump, and let denote the total number of measurement files and , and define . is equal to 51,200, which is the sampling rate of the measurement files.

A low-pass filter with a cut-off frequency of 110 Hz was applied to process the slurry pump original vibration data . Nine statistical features in the time domain and their corresponding frequencies were then extracted from the processed vibration signals . Normalization was conducted before applying the FA.

The original feature matrices in time and frequency domains are, respectively, constructed as where represents the features in time domain and represents the features in frequency domain. The subscript represents low-pass filtering. The following equations for the nine statistical features were extracted from signals in time and frequency domains after the low-pass filter was initially applied to process raw vibration data ( represents the processed vibration data in temporal and spectral domains).(1)Mean:(2)Standard deviation (STD):(3)Root mean square: (4)Skewness:(5)Kurtosis:(6)Crest factor:(7)Clearance factor:(8)Shape factor:(9)Impulse factor:

These features are used to construct a new feature matrix:

The new feature matrix is then normalized according to

A moving average process is used for each column of the new matrix from (20):

Through (21), a new matrix is generated for the study of the EFA based impeller indicator. Then the enhanced factor analysis based impeller indicator (EFABII) can be calculated by combining the result from (21) and (7). The details of the calculation procedures are summarized in Figure 1.