Investigation on enhanced mathematical morphological operators for bearing fault feature extraction

doi:10.1016/j.isatra.2021.07.027

ISA Transactions

Volume 126, July 2022, Pages 440-459

https://doi.org/10.1016/j.isatra.2021.07.027 Get rights and content

Highlights

•
The concept of GCMO is proposed for the design of new morphological operators.
•
Three specific GCMOs based on the product, convolution and cross-correlation operations are proposed.
•
Several new compound morphological operators are proposed for impulse feature extraction.
•
The morphological cross-correlation operators exhibit better performance in bearing fault feature extraction.

Abstract

Morphological filtering has been extensively applied to rotating machinery diagnostics, whereas traditional morphological operators cannot effectively extract fault-triggered transient impulse components from noisy mechanical vibration signal. In this paper, a framework of generalized compound morphological operator (GCMO) is presented to enhance the extraction ability of impulsive fault features. Further, several new compound morphological operators are developed for transient impulse extraction by introducing the product, convolution, and cross-correlation operations into the GCMO framework. In addition, a novel strategy for selecting the structural element length is proposed to optimize the repetitive impulse feature extraction of the compound morphological operators. The fault feature extraction performance of the developed compound morphological operators is investigated and validated on the simulation signals and measured railway bearing vibration signals, and compared with the combined morphological operators and five existing feature extraction methods. The results demonstrate that the morphological cross-correlation operators are more efficient in repetitive fault impulse feature extraction and bearing fault diagnosis than the combined morphological operators and the comparison methods.

Introduction

Rotating machinery equipment holds a considerable proportion in modern transportation and industrial production. An unexpected failure in mechanical components may lead to prolonged machine downtime or serious human injury, hence causing huge economic losses. Thus, fault diagnosis and prediction of rotating machinery equipment are of great importance to ensure operation safety and improve economic benefits [1], [2]. Currently, vibration analysis is an approach often utilized in the fault detection of rotating machinery [3]. Nevertheless, the repetitive transient impulses triggered by faulty components in rotating machinery equipment are usually hidden by the measured vibration signals. Consequently, transient impulse feature extraction has become a crucial prerequisite for accurate fault detection of rotating machinery equipment [4], [5].

Many signal processing-based approaches have been presented to excavate repetitive impulses of vibration signals for rotating machinery fault diagnosis [6], [7], such as blind deconvolution [8], [9], envelope analysis [10], [11], decomposition-based methods [12], [13], [14], [15], and morphological filtering [16], [17]. Among these methods, the minimum entropy deconvolution (MED) [8] and fast kurtogram [10] are two popular filtering methods for impulse feature recovery in rotating machinery diagnostics. Morphological filtering is a typical nonlinear signal processing approach derived from the set theory. In this technique, the impulsive features in the signal can be excavated by interacting with a specified structural element (SE) [18]. Compared with the MED and fast kurtogram methods, morphological filtering is a non-iterative method and does not need to decompose the spectral frequency band. The morphological operator is the key to extract the repetitive impulse components hidden in a noisy signal. The basic morphological operators can only recover the negative or positive impulses from the analyzed signals and have been proved to exhibit low-pass filtering characteristics [19]. In contrast, the combined morphological operators constructed by the arithmetic operations of basic morphological

operators can enhance the bidirectional impulse features and can be divided into two categories. The first category is the gradient operators, which are obtained from the difference of two basic morphological operators with complementary effects, mainly including the gradient of dilation and erosion (GDE) operator [20], the gradient of closing and opening (GCO) operator [21], [22], and the gradient of closing–opening and opening–closing (GCOOC) operator [23]. It has been proven that these morphological gradient operators exhibit the characteristics of a high-pass filter and are often used to enhance the impulsive features associated with rotating machinery faults [19]. The recent developments of morphological gradient operators can be found in [24], [25]. Another category is the average-hat operators obtained by subtracting the arithmetic average of two basic morphological operators with complementary effects from the signal, mainly containing the average-hat of dilation and erosion (AHDE) operator [26], the average-hat of closing and opening (AHCO) operator [27], and the average-hat of closing–opening and opening–closing (AHCOOC) operator [19], [28]. The morphological average-hat operators possess the properties of high-pass filtering and deliver better impulse extraction performance than the morphological average operators. Although these combined morphological operators have been extensively utilized in the fault identification of different rotating machinery components, they are insufficient in extracting fault impulse features from noisy mechanical vibration signals.

In recent years, several compound morphological operators have been constructed from the composite of two different combined morphological operators [29], [30], [31], [32], [33]. Based on the product operation, the morphology gradient product operator (MGPO) [29]–the product of GCO and GCOOC, and the morphology hat product operator (MHPO) [30]–the product of AHCO and AHCOOC, were proposed to enhance the extraction capability of fault impulse features. More recently, a morphology gradient convolution operator (MGCO) [32]–the convolution of GCO and GCOOC, was used to disclose impulsive bearing damage symptoms. The MGCO inherits the transient impulse extraction capability of the two morphological gradient operators and possesses the denoising characteristics of the convolution operator. In addition, the morphology gradient cross-correlation operator (MGCCO) [33]–the cross-correlation between the GCO and GCOOC, was applied to eliminate the excessive interference noise in the vibration signals and recover the repetitive transient impulses. Although the above-mentioned compound morphological operators can exhibit a stronger capability in reducing interference noises and extracting repetitive transient impulses than the combined morphological operators, they are only composed of a few combined morphological operators (i.e., GCO, GCOOC, AHCO, and AHCOOC) and may not be suitable for various vibration signal analysis. Moreover, the performance of compound morphological operators constructed through other morphological operators has not been thoroughly investigated.

In this paper, the concept of the generalized compound morphological operator (GCMO) is proposed and several new compound morphological operators are proposed for impulse feature extraction by using three specific mathematical operations. The simulation signals and measured bearing experimental signals are employed to investigate and verify the effect of typical compound morphological operators in impulse feature extraction. The main contributions and novelties of this study are described as follows:

(1) A framework of GCMO is proposed to design new morphological operators for fault impulse extraction, and several new compound morphological operators are developed by introducing the product, convolution, and cross-correlation operations into the GCMO.

(2) A novel strategy for selecting the SE length is proposed to optimize the repetitive impulse extraction of the compound morphological operators. The performance of the combinations of the SE length selection strategy and typical compound morphological operators is investigated and compared using simulations and railway axle-box bearing experiments, and compared with the combined morphological operators and five existing feature extraction methods.

(3) The advantages and limitations of typical compound morphological operators in fault impulse feature extraction are summarized, and the guidance for the use of compound morphological operators in bearing failure detection is presented.

The structure of the remaining of this work is as follows. Section 2 concisely introduces the reported morphological operators for impulse feature extraction. In Section 3, the concept of GCMO and several new compound morphological operators are proposed. Section 4 introduces the implementation framework of compound morphological operators for rotating machinery fault detection. In Sections 5 Simulation analysis, 6 Experimental results, simulation signals and measured railway bearing vibration data are analyzed to confirm the efficacy of the compound morphological operators, respectively, and their performance is contrasted with five existing approaches. In Section 7, the main conclusions of this research work are summarized.

Section snippets

Primary morphological operators

The advanced morphological operators are constructed by two fundamental morphological operators, namely, erosion and dilation. Supposing $f (n)$ is a time-domain discrete signal with length $N$ and $g (m)$ is a specific SE with length $M$ . The morphological erosion and dilation operators are, respectively, defined as follows [18]: $(f Θ g) (n) = min_{m} [f (n + m) - g (m)]$ $(f \oplus g) (n) = max_{m} [f (n - m) + g (m)]$ where symbols $Θ$ and $\oplus$ denote the erosion and dilation operators, respectively; $m = 0, 1, 2, \dots, M - 1$ , $n = 0, 1, 2, \dots, N - 1$ , and $M \leq N$ .

The closing and opening

Definitions of generalized compound morphological operators

Given the design of new compound morphological operators, the GCMO is formulated as: $G C M O (n) = operation (M O_{1} (n), M O_{2} (n))$ where $operation (M O_{1} (n), M O_{2} (n))$ represents a generalized mathematical operation between two different morphological operators $M O_{1} (n)$ and $M O_{2} (n)$ , $n = 0, 1, \dots, N - 1$ , and $N$ denotes the length of the signals.

Good filtering performance can be achieved if the mathematical operations and morphological operators selected to construct the compound morphological operators satisfy the following conditions as

Application framework

The SE has an essential impact on the filtering capability of morphological operators. The SE is determined by its shape, length, and height. Among the different SEs, the flat SE has a simple structure (i.e., zero height and single length parameter) [34] and can maintain the main morphological characteristics of the signal [35]. Thus, the flat SE is utilized in this study. The calculation time and noise elimination effect can be balanced by reasonably selecting the SE length. In [21], [36], a

Simulated signal and results

The performance of the compound morphological operators in repetitive transient impulse extraction can be demonstrated by simulation signals. Based on the numerical model in [3], [15], [40], the bearing fault simulation signal is formulated as: $x (t) = x_{1} (t) + x_{2} (t) + x_{3} (t) + n (t)$ $x_{1} (t) = \sum_{j = 1}^{97} e^{- 1000 \cdot (t - j / 97 - ɛ_{j})} sin [2 π \cdot 2000 \cdot (t - j / 97 - ɛ_{j})]$ $x_{2} (t) = 0.2 \cdot sin (2 π \cdot 10 \cdot t + π / 6) + 0.2 \cdot sin (2 π \cdot 20 \cdot t - π / 3)$ $x_{3} (t) = \sum_{r = 1}^{3} B_{r} \cdot e^{- 800 \cdot (t - τ_{r})} sin [2 π \cdot 3500 \cdot (t - τ_{r})]$ where $x_{1} (t)$ signifies the periodic impulses triggered by the local damage on bearing component, and the impulse

Experimental results

In this section, three vibration acceleration data sets from the railway rolling bearing test bench are analyzed to testify the efficiency of the compound morphological operators in extracting repetitive impulse features.

The test platform is mainly composed of the driving device, loading device, and wheelset mounted with axle-box bearings, as displayed in Fig. 13(a). An axle-box bearing with outer race damage and an axle-box bearing with rolling element damage were tested respectively at a

Discussion and conclusions

In this paper, a framework of GCMO was proposed for designing new morphological operators for enhancing impulse feature extraction. Further, eighteen compound morphological operators are developed by introducing the product, convolution, and cross-correlation operations into the GCMO, and a novel strategy is proposed to identify an optimal SE length for compound morphological operators. The performance of eighteen compound morphological operators is investigated and compared using simulation

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the Autonomous Research Subject of State Key Laboratory of Traction Power, Southwest Jiaotong University, China (No. 2020TPL-T08, No. 2021TPL-T11) and Fundamental Research Funds for the Central Universities of China (No. 2682021CX090, No. 2682021CG003). The authors thank the editors and reviewers for their valuable suggestions.

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Practice articleInvestigation on enhanced mathematical morphological operators for bearing fault feature extraction

Highlights

Abstract

Introduction

Section snippets

Primary morphological operators

Definitions of generalized compound morphological operators

Application framework

Simulated signal and results

Experimental results

Discussion and conclusions

Declaration of Competing Interest

Acknowledgments

Mech Syst Signal Process

Measurement

J Sound Vib

ISA Trans

Mech Syst Signal Process

Tribol Int

Geoexploration

Mech Syst Signal Process

Mech Syst Signal Process

Mech Syst Signal Process

Mech Syst Signal Process

Mech Syst Signal Process

ISA Trans

Mech Syst Signal Process

J Sound Vib

ISA Trans

Mech Syst Signal Process

Mech Syst Signal Process

Mech Syst Signal Process

ISA Trans

Mech Syst Signal Process

Measurement

J Sound Vib

Practice article
Investigation on enhanced mathematical morphological operators for bearing fault feature extraction