To enhance the accuracy of gear fault identification under variable speed conditions, this paper proposes a method combining Adaptive Time-Varying Comb Filter (ATVCF) and Improved Arithmetic Optimization Algorithm (IAOA) optimized Stacked Denoising Autoencoder (SDAE). The ATVCF preprocessing is utilized for noise reduction in gear vibration signals, preserving effective signals while filtering out noise components. To address the shortcomings of the Arithmetic Optimization Algorithm (AOA) in global search and local exploitation, an improved version, IAOA, is introduced. This improvement includes the incorporation of a cosine regulatory factor to enhance the global search capability and local optimization ability of the mathematical optimizer acceleration function (MOA) within the algorithm. Additionally, a Random Opposite-based Learning strategy (ROBL) is introduced to increase the population diversity of the algorithm, thereby enhancing its search capability. Furthermore, the parameter optimization of the IAOA-SDAE model ensures the fault identification accuracy and stability of the model. The analysis of variable speed gear vibration test data verifies the effectiveness and superiority of the proposed method in intelligent fault identification of variable speed gears.
1. Introduction
Gearboxes are crucial variable-speed and transmission components in wind turbines. Gears operate under variable speed conditions for extended periods and in harsh environments, making them prone to failures such as tooth surface wear, tooth root cracks, and tooth breakage. Compared to constant speed conditions, gear fault characteristics under variable speeds vary with changes in rotational speed, thus making fault identification more challenging.
Based on the complexity of the model and the scale of data processed, common intelligent gear fault identification methods can be divided into two categories: shallow learning-based and deep learning-based intelligent fault diagnosis methods. Among them, deep learning-based intelligent fault diagnosis methods, with deep learning as the core, can adaptively extract fault features and fit complex mapping relationships by constructing suitable deep learning models, effectively improving the accuracy of fault identification. These methods have thus been widely applied in the field of fault diagnosis . Common deep learning methods include Deep Belief Networks (DBNs), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Autoencoders (AEs). As an unsupervised data dimension compression and data feature representation method, AE possesses strong generalization capabilities and is therefore widely used in dimensionality reduction and anomaly detection.
Stacked Denoising Autoencoders (SDAEs), a type of AE, have further enhanced fault feature extraction capabilities by incorporating noise into the input to train the model, making it more robust in noise reduction and feature extraction. Arithmetic Optimization Algorithm (AOA) , a newly proposed meta-heuristic optimization algorithm based on the distribution characteristics of arithmetic operators, exhibits strong convergence, robustness, and high precision. However, it is sensitive to initial values, converges slowly, easily falls into local optimal solutions, and lacks sufficient search and optimization capabilities. Many scholars have conducted extensive research on improving the optimization performance of AOA, achieving certain results in increasing convergence speed , enhancing algorithm robustness , and avoiding premature convergence. However, research on global search and local exploitation capabilities is insufficient, leading to poor optimization results.
Noise in signals significantly affects fault identification accuracy. Vibration signals acquired using vibration acceleration sensors are complex and have low signal-to-noise ratios (SNRs). Therefore, vibration signals require preprocessing for noise reduction. Commonly used noise reduction methods include wavelet threshold denoising Empirical Mode Decomposition (EMD) , and Variational Mode Decomposition (VMD). Wavelet threshold denoising has high requirements for signal stationarity, and threshold selection significantly impacts the results. EMD-derived modes suffer from inherent degradation issues and high computational complexity. VMD results are greatly influenced by initial conditions. Moreover, these noise reduction methods are not designed for variable speed conditions and their signal decomposition capabilities significantly decrease when rotational speed varies greatly.
Adaptive Time-Varying Filtering (ATVF) is a time-varying filtering method designed for variable speed conditions. It adapts filter parameters based on the time-varying characteristics of signal frequencies, demonstrating good signal analysis adaptability. However, the filter bandwidth of this method needs to be preset and cannot precisely focus on the filtering of gear mesh frequencies and their sidebands.
Therefore, this paper introduces comb filtering into ATVF to propose ATVCF. In summary, for intelligent fault diagnosis of gears under variable speeds, this paper proposes a variable speed gear intelligent fault diagnosis method based on ATVCF and IAOA-optimized SDAE. This method first performs noise reduction through ATVCF, then utilizes IAOA to optimize the structural parameters of SDAE, and adopts the Random Opposite-based Learning strategy (ROBL) to enhance the search capability of IAOA, avoiding local optimality. The effectiveness and superiority of the proposed method are verified through analysis of gear test data under variable speeds.
2. Literature Review
2.1 Gear Fault Diagnosis
Gearboxes, as critical transmission components in mechanical systems, play a vital role in converting and transmitting torque and speed. Due to their complex operating environments and long-term operation under variable loads and speeds, gears are prone to various faults. Therefore, gear fault diagnosis is crucial for ensuring the stable operation of mechanical systems and preventing potential accidents.
Gear fault diagnosis methods can be broadly classified into two categories: model-based methods and data-driven methods. Model-based methods rely on establishing precise mathematical models of gear dynamics and fault mechanisms to predict and diagnose faults. However, due to the complexity and nonlinearity of gear systems, accurate modeling is challenging. Data-driven methods, on the other hand, rely on collected vibration, sound, and other signals to extract fault features and diagnose faults using data analysis and machine learning techniques.
In recent years, with the rapid development of artificial intelligence and data analysis technologies, intelligent fault diagnosis methods based on deep learning have received increasing attention. These methods can automatically extract fault features from data, adaptively fit complex mapping relationships, and effectively improve fault identification accuracy.
2.2 Deep Learning for Fault Diagnosis
Deep learning, as a branch of machine learning, has achieved remarkable results in image recognition, speech recognition, and other fields. Its application in fault diagnosis has also become a research hotspot.
Common deep learning methods used in fault diagnosis include Deep Belief Networks (DBNs), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Autoencoders (AEs). These methods can automatically extract fault features from vibration signals and other data, achieving high-accuracy fault identification.
Among them, Autoencoders (AEs) are unsupervised learning algorithms that can reduce data dimensionality and express data features. They have strong generalization capabilities and are widely used in dimensionality reduction and anomaly detection. Stacked Denoising Autoencoders (SDAEs) further enhance fault feature extraction capabilities by incorporating noise into the input to train the model, making it more robust in noise reduction and feature extraction.
2.3 Arithmetic Optimization Algorithm (AOA)
Arithmetic Optimization Algorithm (AOA) is a newly proposed meta-heuristic optimization algorithm based on the distribution characteristics of arithmetic operators. It simulates the arithmetic operations of multiplication, division, addition, and subtraction in the natural world to search for optimal solutions.
AOA has strong convergence, robustness, and high precision. However, it is sensitive to initial values, converges slowly, easily falls into local optimal solutions, and lacks sufficient search and optimization capabilities. Therefore, many scholars have conducted research on improving the optimization performance of AOA.
3. Methodology
3.1 Adaptive Time-Varying Comb Filter (ATVCF)
Adaptive Time-Varying Comb Filter (ATVCF) combines the filtering ideas of comb filtering and time-varying filtering, making it suitable for extracting gear fault vibration signals under variable speeds. The center frequency and bandwidth of its filters adaptively change with the variation of vibration signal frequencies.
Comb filters can be constructed using various methods, such as Morlet wavelets, harmonic wavelets, and Fourier kernel functions. Since the Fourier kernel function has an amplitude of 1 within the passband, allowing signal components within the passband to pass losslessly, it is used in the construction of comb filters.
The time-frequency characteristics of the ATVCF filter are shown in Figure 1. As the gear’s rotational speed changes, the center frequency and bandwidth of the ATVCF filter adaptively adjust to filter out noise components and retain effective signals.
3.2 Improved Arithmetic Optimization Algorithm (IAOA)
To address the shortcomings of the Arithmetic Optimization Algorithm (AOA) in global search and local exploitation, this paper proposes an Improved Arithmetic Optimization Algorithm (IAOA). The improvements include:
- Cosine Regulatory Factor: Introducing a cosine regulatory factor to enhance the global search capability and local optimization ability of the mathematical optimizer acceleration function (MOA) within the algorithm.
- Random Opposite-based Learning strategy (ROBL): Increasing the population diversity of the algorithm to enhance its search capability by introducing ROBL.
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