Nowadays, renewable energy has been emerging as the major source of energy and is driven by its aggressive expansion and falling costs. Most of the renewable energy sources involve turbines and their operation and maintenance are vital and a difficult task. Condition monitoring and fault diagnosis have seen remarkable and revolutionary up-gradation in approaches, practices and technology during the last decade. Turbines mostly do use a rotating type of machinery and analysis of those signals has been challenging to localize the defect. This paper proposes a new hybrid model wherein multiple swarm intelligence models have been evaluated to optimize the conventional Long Short-Term Memory (LSTM) model in classifying the faults from the vibration signals data acquired from the gearbox. This helps to analyze the performance and behavioral patterns of the system more effectively and efficiently which helps to suggest for replacement of the unit with higher precision. The results have demonstrated that the proposed hybrid modeling approach is effective in classifying the faults of the gearbox from the time series data and achieve higher diagnostic accuracy in comparison to the conventional LSTM methods.
Fault diagnosis has a significance in identifying the degrading parts of the rotating machinery and replacement of the same well before a total breakdown to reduce the downtime. Especially in wind turbines, gears, shafts, blades and rolling bearings play a vital role that is widely used in the transmission of power. Any failures within them would introduce unexpected and unwarranted breakdown time, expensive maintenance, loss in production and delayed distribution of power. Hence, it is necessary to identify and predict such faults during the Operation and Maintenance (O&M) at early stages itself and increase the production of power to prevent power disruptions and catastrophic failures.
Condition monitoring facilitates collecting the health information of the machinery through different methods such as vibration, acoustic and thermal imaging analysis. Earlier, the methodology adopted was through the processing of signals to derive deeper insights into different spectra such as time and frequency. The transition of Artificial Intelligence (AI) has been extensively investigated in the rotating machinery devices with versatile machine learning and deep neural network models. AI-led to relate the spectral insights in identifying the defects, further seeking more insights to categorize, to forecast the Remaining Useful Life (RUL) of the machinery components, and to replace the required ones.
Few research studies state how the traditional Convolution Neural Network (CNN) model has effective in the fault diagnosis for the classification of faults based on vibration analysis, by learning the features acquired from rolling bearings [
New emerging methods in condition monitoring arise, to improve the reliability of gearboxes apart from the regular signal processing and applying machine learning models to categorize the faults accordingly. In recent years, Deep Neural Networks such as CNN and LSTM have widely been used to classify the faults and as well predict the RUL of the machinery too. These neural networks, used for classification of faults were Deep-Belief Network, Deep-Boltzmann Machines, Restricted Boltzmann Machines and Auto-Encoders [
Wavelet analysis integrated with CNN model [
This paper has been organized as follows: Section 2 states the recent related research works regarding gearbox fault classification. Section 3 details the proposed hybrid LSTM gearbox fault diagnosis method along with the optimization techniques utilized for the classification of faults. In Section 4, the evaluated results of the custom hybrid model have been tabulated with metrics and later discussed the comparison of the proposed hybrid method with conventional LSTM methods. Finally, the conclusions followed by the references have been presented.
Some of the recent existing methodologies proposed for gearbox fault classification have been reviewed in this section.
Chen et al. [
Merainani et al. [
Liu et al. [
Malik et al. [
Medina et al. [
Johnson et al. [
One of the researchers, (Tang et al. [
Liu et al. [
The existing literature has used different approaches in evaluating the gearbox fault diagnosis. Moreover, several kinds of research exist applying the vanilla deep learning models with few having in-depth customization. Hence, proposed herewith a novel approach by fine-tuning the parameters and activation functions of the conventional LSTM recurrent neural network model.
This novel approach constitutes of hybrid LSTM based model wherein optimization has been applied with swarm intelligence algorithms. Detailed evaluations and comparison of the results are performed using a gearbox condition monitoring data set to classify the faults accordingly. This article highlights the following:
Proposal of a custom hybrid LSTM model with swarm intelligence for fault diagnosis of gearbox.
In-depth analysis on a restricted subset of gearbox data with hybrid LSTM on 10 different load conditions.
Evaluation on different LSTM activation function, i.e., Sigmoid, hyperbolic tangent (tanh), Rectified Linear Unit (ReLU); optimized with Particle Swarm Optimization (PSO), Firefly Algorithm (FA), Cuckoo Search Optimization (CSO), and Ant Colony Optimization (ACO) algorithms in combination with specified LSTM activation functions.
Observations of each group of optimization and activation functions on all different 10 loads for the classification of faults.
Tabulation of performance metrics such as accuracy, precision, recall, specificity, sensitivity, F-Score, weight, bias and activation functions such as default sigmoid, hyperbolic tangent, and ReLU activation functions along with its customized parameters.
This proposed hybrid fault diagnosis methodology explains the approach of how the swarm intelligence algorithms have been combined with LSTM network model to classify the faults of gearbox. The proposed gearbox fault diagnosis method applying Hybrid-LSTM network model comprises of four steps and is illustrated in
Long Short-Term Memory (LSTM) network is one of the variants of recurrent neural network. This has been widely applied on time series datasets recently and has been proven as a highly efficient learning neural network model among others.
An LSTM network enables to input sequence data into a network and make predictions based on the individual time steps of the sequence data. For conventional or default activation functions like sigmoid and tan h functions, the gradients decrease quickly with training error propagating to forward layers. The activation functions for sigmoid and hyperbolic tangent and its differential functions are formulated as in
Recently, the ReLU activation function gained tremendous recognition, especially in the last few years. This is because its gradient will not decrease with the independent variables increasing. Hence, the network with ReLU activation function can overcome the vanishing of the gradient. The ReLU and its differential functions are mathematically formulated in the
A five-layer LSTM customized neural network is implemented with one sequence input layer, one bi-directional LSTM layer other than the default LSTM layer for standardization, one fully connected layer, one softmax layer and one output layer for classification. Each LSTM unit has an input gate, the forget gate, and the output gate along with the memory unit that is being read and updated periodically [
wherein
In this research, few of the swarm intelligence algorithms Particle Swarm, Firefly, Cuckoo Search, and Ant Colony in combination with specified custom LSTM activation functions (in multiple combinations as well) by replacing their regular activation functions, i.e., Sigmoid, hyperbolic tangent and ReLU have been discussed and evaluated herewith. Using the parameters achieved by the respective equations mentioned below (13,14,15,16) each for different customized activation functions, defining the layered network and the network is trained, validated, tested and executed for 5 epochs.
This optimization method commonly recognized as PSO [
This optimization technique is derived from one of the bird’s species known as Cuckoo following their strategy of laying eggs in the nests of different other bird species [
Firefly Algorithm (FA) proposed here is based on the behavior of fireflies employing flashing signals to interact with light emitted by another brighter partner moving towards it. The attraction is commensurate to the brightness, i.e., both increase as their distance decreases [
The behavior of ants moving randomly by laying their pheromone and searing for an optimal path commonly recognized as Ant Colony Optimization. The advantage of ACO is that it shows prior success in evolving general RNNs for time series data prediction [
In this section, two fault conditional cases such as the healthy tooth and broken tooth have been considered with the gearbox fault diagnosis dataset [
This open source gearbox fault diagnosis dataset comprises of the vibration dataset recorded by using Spectra Quest’s Gearbox Fault Diagnostics Simulator. Dataset has been recorded with the help of 4 vibration sensors placed in four different directions. Additionally, the dataset has been observed under variation of loads at a frequency of 30 Hz from ‘0’ to ‘90’ percent with two different scenarios: 1) Healthy condition and 2) Broken Tooth Condition.
Initially, the gearbox fault diagnosis dataset is converted to time series data to perform LSTM classification. The evaluation has been performed considering restricted data available in the dataset. To classify the two health conditions of the gearbox data, 70% samples have been employed to train the proposed hybrid network and the rest have been used for testing. That is for this work; Training and Testing dataset are of the order
The proposed hybrid LSTM network has been trained on different conventional activation functions sigmoid, hyperbolic tangent (tanh) and ReLU. Additionally, this training has also been extended to other proposed customized activation functions such as sigmoid PSO, sigmoid Cuckoo, sigmoid FA, and sigmoid ACO; tanh PSO, tanh Cuckoo, tanh FA, and tanh ACO; ReLU PSO, ReLU Cuckoo, ReLU FA and ReLU ACO. The results have been evaluated for load, weight and bias values on a gearbox vibration data acquired at different loads 0, 10, 20, 30, 40, 50, 60 70, 80 and 90. The accuracy of each has been computed and best of the results were obtained taking into consideration every state of load. Especially, the best results were achieved with load 10 and 40. The results observed have been tabulated in
S. No. | Activation Function | Load | Bias | Weight | Accuracy |
---|---|---|---|---|---|
1 | ReLU | 0 | 0.2500 | –0.0016 | 0.6250 |
2 | Sigmoid-PSO | 0.2502 | –0.0019 | 0.6250 | |
3 | Sigmoid-Cuckoo | 0.2503 | –0.0035 | 0.7500 | |
4 | Sigmoid-Firefly | 0.2502 | 0.0017 | 0.6250 | |
5 | Sigmoid-ACO | 0.2502 | 0.0002 | 0.5000 | |
6 | ReLU-PSO | 0.2500 | 0.0005 | 0.6250 | |
7 | ReLU-Cuckoo | 0.2504 | –0.0023 | 0.6250 | |
8 | ReLU-Firefly | 0.2504 | 0.0006 | 0.6250 | |
9 | ReLU-ACO | 0.2500 | 0.0005 | 0.1250 | |
10 | tanh-PSO | 0.2503 | –0.00268 | 0.6250 | |
11 | tanh-Cuckoo | 0.2500 | 0.0015 | 0.5000 | |
12 | tanh-Firefly | 0.2504 | 0.0022 | 0.6250 | |
13 | tanh-ACO | 0.2506 | 0.0014 | 0.7500 | |
1 | ReLU | 10 | 0.2502 | 0.0005 | 0.6250 |
2 | Sigmoid-PSO | 2.50E-01 | –2.92E-03 | 0.8750 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | –7.90E-04 | 0.5000 | |
4 | Sigmoid-Firefly | 2.50E-01 | 6.06E-04 | 0.5000 | |
5 | Sigmoid-ACO | 2.50E-01 | –2.83E-03 | 0.5000 | |
6 | ReLU-PSO | 2.50E-01 | –3.03E-03 | 0.5000 | |
7 | ReLU-Cuckoo | 2.50E-01 | 6.81E-04 | 0.2500 | |
8 | ReLU-Firefly | 2.50E-01 | –4.26E-03 | 0.5000 | |
9 | ReLU-ACO | 2.50E-01 | 1.08E-03 | 0.7500 | |
10 | tanh-PSO | 0.2500 | –0.0023 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | –7.58E-05 | 0.3750 | |
12 | tanh-Firefly | 2.50E-01 | 9.34E-04 | 0.5000 | |
13 | tanh-ACO | 2.50E-01 | 1.66E-03 | 0.5000 | |
1 | ReLU | 20 | 0.2501 | –0.0019 | 0.6250 |
2 | Sigmoid-PSO | 2.50E-01 | –1.33E-03 | 0.6250 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | 2.21E-03 | 0.6250 | |
4 | Sigmoid-Firefly | 2.50E-01 | –1.52E-05 | 0.7500 | |
5 | Sigmoid-ACO | 2.50E-01 | –1.33E-03 | 0.6250 | |
6 | ReLU-PSO | 2.50E-01 | 1.79E-03 | 0.5000 | |
7 | ReLU-Cuckoo | 2.50E-01 | –1.49E-03 | 0.3750 | |
8 | ReLU-Firefly | 2.50E-01 | 1.32E-05 | 0.5000 | |
9 | ReLU-ACO | 2.50E-01 | –9.22E-04 | 0.7500 | |
10 | tanh-PSO | 2.50E-01 | 0.0027 | 0.7500 | |
11 | tanh-Cuckoo | 2.50E-01 | –1.64E-04 | 0.6250 | |
12 | tanh-Firefly | 2.50E-01 | –2.17E-03 | 0.7500 | |
13 | tanh-ACO | 2.50E-01 | 1.08E-03 | 0.5000 | |
1 | ReLU | 30 | 0.2499 | –0.0038 | 0.5000 |
2 | Sigmoid-PSO | 2.50E-01 | 7.58E-04 | 0.5000 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | –1.74E-03 | 0.1250 | |
4 | Sigmoid-Firefly | 2.50E-01 | 2.83E-03 | 0.5000 | |
5 | Sigmoid-ACO | 2.50E-01 | 1.58E-03 | 0.6250 | |
6 | ReLU-PSO | 2.50E-01 | –3.03E-03 | 0.5000 | |
7 | ReLU-Cuckoo | 2.50E-01 | –3.20E-03 | 0.5000 | |
8 | ReLU-Firefly | 2.50E-01 | 1.35e-03 | 0.6250 | |
9 | ReLU-ACO | 2.50E-01 | 2.68E-03 | 0.7500 | |
10 | tanh-PSO | 2.50E-01 | –2.07E-03 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | –1.35E-03 | 0.3750 | |
12 | tanh-Firefly | 2.50E-01 | –9.23E-04 | 0.5000 | |
13 | tanh-ACO | 2.50E-01 | 4.30E-04 | 0.6250 | |
1 | ReLU | 40 | 0.2498 | –0.0019 | 0.5000 |
2 | Sigmoid-PSO | 2.50E-01 | –5.22E-04 | 0.5000 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | –2.25E-03 | 0.5000 | |
4 | Sigmoid-Firefly | 2.50E-01 | –1.61E-04 | 0.7500 | |
5 | Sigmoid-ACO | 2.50E-01 | –1.46E-03 | 0.6250 | |
6 | ReLU-PSO | 0.2502 | –5.30014 | 0.7500 | |
7 | ReLU-Cuckoo | 2.50E-01 | 2.64E-03 | 0.8750 | |
8 | ReLU-Firefly | 2.50E-01 | 1.97e-03 | 0.7500 | |
9 | ReLU-ACO | 2.50E-01 | 7.12E-04 | 0.7500 | |
10 | tanh-PSO | 2.50E-01 | 1.54E-03 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | –1.35E-03 | 0.7500 | |
12 | tanh-Firefly | 2.50E-01 | –2.82E-03 | 0.6250 | |
13 | tanh-ACO | 2.50E-01 | 1.35E-03 | 0.7500 | |
1 | ReLU | 50 | 2.51E-01 | 1.00E-04 | 0.3750 |
2 | Sigmoid-PSO | 2.50E-01 | 1.52E-04 | 0.5000 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | 3.61E-04 | 0.6250 | |
4 | Sigmoid-Firefly | 2.50E-01 | 1.17E-03 | 0.3750 | |
5 | Sigmoid-ACO | 2.50E-01 | –1.78E-03 | 0.2500 | |
6 | ReLU-PSO | 2.50E-01 | –4.84E-04 | 0.2500 | |
7 | ReLU-Cuckoo | 2.50E-01 | 3.53E-03 | 0.6250 | |
8 | ReLU-Firefly | 2.50E-01 | 6.33E-04 | 0.5000 | |
9 | ReLU-ACO | 2.50E-01 | 4.54E-04 | 0.3750 | |
10 | tanh-PSO | 2.50E-01 | 3.36E-03 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | –1.15E-03 | 0.3750 | |
12 | tanh-Firefly | 2.50E-01 | –4.92E-04 | 0.6250 | |
13 | tanh-ACO | 2.50E-01 | –2.35E-03 | 0.2500 | |
1 | ReLU | 60 | 2.50E-01 | –3.54E-03 | 0.6250 |
2 | Sigmoid-PSO | 2.50E-01 | –2.31E-03 | 0.6250 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | 2.28E-03 | 0.6250 | |
4 | Sigmoid-Firefly | 2.50E-01 | –1.46E-04 | 0.3750 | |
5 | Sigmoid-ACO | 2.50E-01 | –3.14E-03 | 0.1250 | |
6 | ReLU-PSO | 2.50E-01 | –1.30E-03 | 0.5000 | |
7 | ReLU-Cuckoo | 2.50E-01 | –1.64E-04 | 0.7500 | |
8 | ReLU-Firefly | 2.50E-01 | 1.05E-04 | 0.7500 | |
9 | ReLU-ACO | 2.50E-01 | –1.23E-03 | 0.5000 | |
10 | tanh-PSO | 2.50E-01 | –1.20E-04 | 0.7500 | |
11 | tanh-Cuckoo | 2.50E-01 | –1.17E-03 | 0.7500 | |
12 | tanh-Firefly | 2.50E-01 | 1.18E-03 | 0.5000 | |
13 | tanh-ACO | 2.50E-01 | –2.02E-04 | 0.5000 | |
1 | ReLU | 70 | 2.50E-01 | –233E-03 | 0.5000 |
2 | Sigmoid-PSO | 2.50E-01 | 1.51E-04 | 0.3750 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | 7.72E-04 | 0.5000 | |
4 | Sigmoid-Firefly | 2.50E-01 | –1.91E-03 | 0.3750 | |
5 | Sigmoid-ACO | 2.50E-01 | 2.56E-03 | 0.2500 | |
6 | ReLU-PSO | 2.51E-01 | 1.26E-03 | 0.6250 | |
7 | ReLU-Cuckoo | 2.50E-01 | 2.91E-03 | 0.5000 | |
8 | ReLU-Firefly | 2.50E-01 | 1.95E-03 | 0.5000 | |
9 | ReLU-ACO | 2.50E-01 | 9.59E-09 | 0.6250 | |
10 | tanh-PSO | 2.51E-01 | 2.79E-03 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | –8.82E-04 | 0.6250 | |
12 | tanh-Firefly | 2.50E-01 | 1.73E-04 | 0.7500 | |
13 | tanh-ACO | 2.50E-01 | –9.11E-04 | 0.5000 | |
1 | ReLU | 80 | 2.51E-01 | 1.27E-03 | 0.3750 |
2 | Sigmoid-PSO | 2.51E-01 | 8.56E-04 | 0.5000 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | –4.33E-03 | 0.7500 | |
4 | Sigmoid-Firefly | 2.50E-01 | 2.47E-04 | 0.5000 | |
5 | Sigmoid-ACO | 2.50E-01 | 3.64E-04 | 0.1250 | |
6 | ReLU-PSO | 2.50E-01 | 5.32E-03 | 0.5000 | |
7 | ReLU-Cuckoo | 2.50E-01 | 4.40E-04 | 0.5000 | |
8 | ReLU-Firefly | 2.50E-01 | 1.95E-03 | 0.5000 | |
9 | ReLU-ACO | 2.50E-01 | –1.59E-03 | 0.3750 | |
10 | tanh-PSO | 2.50E-01 | 1.99E-03 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | 1.12E-03 | 0.5000 | |
12 | tanh-Firefly | 2.50E-01 | –2.38E+00 | 0.7500 | |
13 | tanh-ACO | 2.251E-01 | 5.57E-04 | 0.5000 | |
1 | ReLU | 90 | 2.50E-01 | –2.47E-03 | 0.6250 |
2 | Sigmoid-PSO | 2.50E-01 | 1.36E-03 | 0.5000 | |
3 | Sigmoid-Cuckoo | 2.50E-01 | 1.14E-03 | 0.3750 | |
4 | Sigmoid-Firefly | 2.50E-01 | –2.81E-03 | 0.5000 | |
5 | Sigmoid-ACO | 2.51E-01 | 1.06E-03 | 0.2500 | |
6 | ReLU-PSO | 2.50E-01 | 5.32E-03 | 0.5000 | |
7 | ReLU-Cuckoo | 2.50E-01 | –1.63E-03 | 0.3750 | |
8 | ReLU-Firefly | 2.50E-01 | –1.58E-03 | 0.6250 | |
9 | ReLU-ACO | 2.50E-01 | –1.42E-03 | 0.5000 | |
10 | tanh-PSO | 2.50E-01 | 6.20E-04 | 0.5000 | |
11 | tanh-Cuckoo | 2.50E-01 | 8.72E-04 | 0.5000 | |
12 | tanh-Firefly | 2.50E-01 | –1.70E-03 | 0.6250 | |
13 | tanh-ACO | 2.50E-01 | 8.56E-04 | 0.2500 |
Further, the performance of the gearbox classification is examined by using various performance parameters that presents the predicted and expected/actual classifications. The result of classifying is predicted into two categories such as healthy and broken tooth conditions.
Few of the performance parameters considered here like Accuracy, true positive rate (Sensitivity), false positive rate (Specificity), Precision, and F-Score. A higher value of ‘True Positive’ detection is enviable for vigorous gearbox classification. Accuracy is formulated as the percentage of the number of faults classified correctly versus total faults as in
where True Positives (TP) is the number of faults classified as faults, True Negatives (TN) is the number of normal classified as normal, False Positives (FP) is the number of normal classified as faults and False Negatives (FN) is the number of faults classified as normal.
Load | Customized Activation | Execution time | Specificity | Sensitivity | Precision | Recall | F-score |
---|---|---|---|---|---|---|---|
0 | ReLU | 3 m 19 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 |
Sigmoid-PSO | 3 m 18 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
Sigmoid-Cuckoo | 3 m 19 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
Sigmoid-Firefly | 3 m 22 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
Sigmoid-ACO | 3 m 18 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
ReLU-PSO | 3 m 20 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
ReLU-Cuckoo | 3 m 20 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
ReLU-Firefly | 3 m 21 s | 0.5000 | 0.7500 | 0.6000 | 0.7500 | 0.6661 | |
ReLU-ACO | 3 m 31 s | 0.2500 | 0 | 0 | 0 | 0 | |
tanh-PSO | 3 m 14 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
tanh-Cuckoo | 3 m 21 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
tanh-Firefly | 3 m 17 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
tanh-ACO | 3 m 17 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
10 | ReLU | 3 m 23 s | 0.7500 | 0.5000 | 0.6667 | 0.5000 | 0.5714 |
Sigmoid-PSO | 3 m 10 s | 0.7500 | 1 | 0.8000 | 1 | 0.8889 | |
Sigmoid-Cuckoo | 3 m 6 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
Sigmoid-Firefly | 2 m 53 s | 1 | 0 | – | 0 | 0 | |
Sigmoid-ACO | 3 m 13 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
ReLU-PSO | 2 m 58 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
ReLU-Cuckoo | 3 m 8 s | 0.2500 | 0.2500 | 0.2500 | 0.2500 | 0.2500 | |
ReLU-Firefly | 3 m 9 s | 1 | 0 | – | 0 | 0 | |
ReLU-ACO | 3 m 1 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
tanh-PSO | 2 m 48 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
tanh-Cuckoo | 3 m 1 s | 0.7500 | 0 | 0 | 0 | 0 | |
tanh-Firefly | 2 m 55 s | 1 | 0 | – | 0 | 0 | |
tanh-ACO | 3 m 36 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
20 | ReLU | 3 m 34 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 |
Sigmoid-PSO | 2 m 45 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
Sigmoid-Cuckoo | 3 m 5 s | 0.5000 | 0.7500 | 0.6000 | 0.7500 | 0.6667 | |
Sigmoid-Firefly | 3 m 2 s | 1 | 0.5000 | 1 | 0.5000 | 0.6667 | |
Sigmoid-ACO | 3 m 4 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
ReLU-PSO | 3 m 3 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
ReLU-Cuckoo | 3 m 3 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
ReLU-Firefly | 2 m 55 s | 0 | 1 | 0.5000 | 0.6667 | ||
ReLU-ACO | 3 m 0 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
tanh-PSO | 2 m 47 s | 1 | 0.5000 | 1 | 0.5000 | 0.6667 | |
tanh-Cuckoo | 3 m 10 s | 0.7500 | 0.5000 | 0.6667 | 0.5000 | 0.5714 | |
tanh-Firefly | 3 m 16 s | 1 | 0 | 1 | 0 | 0.6667 | |
tanh-ACO | 3 m 18 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
30 | ReLU | 3 m 24 s | 1 | 0 | – | 0 | 0 |
Sigmoid-PSO | 3 m 1 s | 0 | 1 | 0 | 1 | 0.6667 | |
Sigmoid-Cuckoo | 3 m 2 s | 0.2500 | 0 | 0 | 0 | 0 | |
Sigmoid-Firefly | 2 m 48 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
Sigmoid-ACO | 2 m 55 s | 0.5000 | 0.7500 | 0.6000 | 0.7500 | 0.6667 | |
ReLU-PSO | 3 m 1 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
ReLU-Cuckoo | 3 m 12 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
ReLU-Firefly | 2 m 55 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
ReLU-ACO | 3 m 5 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
tanh-PSO | 2 m 57 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
tanh-Cuckoo | 3 m 3 s | 0.7500 | 0 | 0 | 0 | 0 | |
tanh-Firefly | 2 m 54 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
tanh-ACO | 2 m 56 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
40 | ReLU | 3 m 21 s | 0 | 1 | 0.5000 | 1 | 0.6667 |
Sigmoid-PSO | 3 m 18 s | 1 | 0 | – | 0 | 0 | |
Sigmoid-Cuckoo | 3 m 6 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
Sigmoid-Firefly | 2 m 50 s | 1 | 0.5000 | 1 | 0.5000 | 0.6667 | |
Sigmoid-ACO | 3 m 6 s | 0.5000 | 0.7500 | 0.6000 | 0.7500 | 0.6667 | |
ReLU-PSO | 3 m 1 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
ReLU-Cuckoo | 3 m 4 s | 1 | 0.7500 | 1 | 0.7500 | 0.8751 | |
ReLU-Firefly | 2 m 49 s | 1 | 0.5000 | 1 | 0.5000 | 0.6667 | |
ReLU-ACO | 3 m 8 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
tanh-PSO | 3 m 1 s | 1 | 0 | – | 0 | 0 | |
tanh-Cuckoo | 2 m 53 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
tanh-Firefly | 3 m 1 s | 1 | 0 | 1 | 0.2500 | 0.4000 | |
tanh-ACO | 2 m 56 s | 1 | 0.5000 | 1 | 0.5000 | 0.6667 | |
50 | ReLU | 3 m 22 s | 0.2500 | 0.5000 | 0.4000 | 0.5000 | 0.4444 |
Sigmoid-PSO | 3 m 12 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
Sigmoid-Cuckoo | 3 m 3 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
Sigmoid-Firefly | 2 m 49 s | 0.2500 | 0.5000 | 0.4000 | 0.5000 | 0.4444 | |
Sigmoid-ACO | 2 m 55 s | 0.2500 | 0.2500 | 0.2500 | 0.2500 | 0.2500 | |
ReLU-PSO | 3 m 6 s | 0.5000 | 0 | 0 | 0 | 0 | |
ReLU-Cuckoo | 3 m 15 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
ReLU-Firefly | 2 m 57 s | 1 | 0 | – | 0 | 0 | |
ReLU-ACO | 3 m 2 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
tanh-PSO | 2 m 39 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
tanh-Cuckoo | 3 m 1 s | 0 | 0.7500 | 0.4286 | 0.7500 | 0.5455 | |
tanh-Firefly | 2 m 58 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
tanh-ACO | 3 m 1 s | 0.5000 | 0 | 0 | 0 | 0 | |
60 | ReLU | 3 m 14 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 |
Sigmoid-PSO | 3 m 8 s | 0.7500 | 0.5000 | 0.6667 | 0.5000 | 0.5714 | |
Sigmoid-Cuckoo | 3 m 4 s | 0.5000 | 0.7500 | 0.6000 | 0.7500 | 0.6667 | |
Sigmoid-Firefly | 3 m 2 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
Sigmoid-ACO | 3 m 4 s | 0.2500 | 0 | 0 | 0 | 0 | |
ReLU-PSO | 3 m 1 s | 1 | 0 | – | 0 | 0 | |
ReLU-Cuckoo | 3 m 4 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
ReLU-Firefly | 2 m 55 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
ReLU-ACO | 2 m 55 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
tanh-PSO | 3 m 19 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
tanh-Cuckoo | 3 m 3 s | 0.7500 | 0.7500 | 0.7500 | 0.7500 | 0.7500 | |
tanh-Firefly | 2 m 56 s | 1 | 0 | – | 0 | 0 | |
tanh-ACO | 2 m 55 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
70 | ReLU | 3 m 22 s | 0 | 1 | 0.5000 | 1 | 0.6667 |
Sigmoid-PSO | 3 m 12 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
Sigmoid-Cuckoo | 2 m 57 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
Sigmoid-Firefly | 3 m 9 s | 0.2500 | 0.5000 | 0.4000 | 0.5000 | 0.4444 | |
Sigmoid-ACO | 2 m 57 s | 0.2500 | 0 | 0 | 0 | 0 | |
ReLU-PSO | 3 m 6 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
ReLU-Cuckoo | 2 m 53 s | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | |
ReLU-Firefly | 2 m 46 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
ReLU-ACO | 3 m 5 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
tanh-PSO | 3 m 4 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
tanh-Cuckoo | 2 m 57 s | 0.2500 | 1 | 0.5714 | 1 | 0.7273 | |
tanh-Firefly | 2 m 59 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
tanh-ACO | 3 m 0 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
80 | ReLU | 3 m 15 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 |
Sigmoid-PSO | 3 m 1 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
Sigmoid-Cuckoo | 3 m 4 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
Sigmoid-Firefly | 3 m 3 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
Sigmoid-ACO | 3 m 10 s | 0.2500 | 0 | 0 | 0 | 0 | |
ReLU-PSO | 2 m 49 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
ReLU-Cuckoo | 3 m 11 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
ReLU-Firefly | 2 m 51 s | 1 | 0 | – | 0 | 0 | |
ReLU-ACO | 2 m 50 s | 0.7500 | 0 | 0 | 0 | 0 | |
tanh-PSO | 2 m 59 s | 0.2500 | 0.7500 | 0.5000 | 0.7500 | 0.6000 | |
tanh-Cuckoo | 3 m 8 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
tanh-Firefly | 3 m 3 s | 0.5000 | 1 | 0.6667 | 1 | 0.8000 | |
tanh-ACO | 2 m 59 s | 0.7500 | 0.2500 | 0.5000 | 0.2500 | 0.3333 | |
90 | ReLU | 3 m 14 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 |
Sigmoid-PSO | 3 m 4 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
Sigmoid-Cuckoo | 3 m 1 s | 0.5000 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
Sigmoid-Firefly | 3 m 10 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
Sigmoid-ACO | 3 m 4 s | 0.2500 | 0.2500 | 0.2500 | 0.2500 | 0.2500 | |
ReLU-PSO | 3 m 12 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
ReLU-Cuckoo | 3 m 5 s | 0.7500 | 0 | 0 | 0 | 0 | |
ReLU-Firefly | 3 m 14 s | 1 | 0.2500 | 1 | 0.2500 | 0.4000 | |
ReLU-ACO | 3 m 2 s | 0.7500 | 0.2500 | 0.3333 | 0.2500 | 0.2857 | |
tanh-PSO | 3 m 7 s | 0 | 1 | 0.5000 | 1 | 0.6667 | |
tanh-Cuckoo | 3 m 4 s | 1 | 0 | – | 0 | 0 | |
tanh-Firefly | 3 m 0 s | 0.2500 | 1 | 0 | 1 | 0.7273 | |
tanh-ACO | 3 m 14 s | 0.5000 | 0 | 0 | 0 | 0 |
The proposed hybrid LSTM network is compared with conventional LSTM network with parameters such as bias, weight, execution time, accuracy, precision and recall.
Load | Activation functions | Bias | Weight | Accuracy | Execution time | Precision | Recall |
---|---|---|---|---|---|---|---|
0 | Sigmoid | 0.2525 | 9.3737 | 0.6250 | 3m 20sec | 0.5714 | 1 |
Tan-h | 0.25039 | −0.00018 | 0.6250 | 4m 3s | 0.6000 | 0.7500 | |
10 | Sigmoid | 0.2503 | 0.0018 | 0.5000 | 3m 25s | 0.5000 | 1 |
Tan-h | 0.2505 | −0.0006 | 0.7750 | 3m 25s | 0.3333 | 0.2500 | |
20 | Sigmoid | 0.2508 | 0.0023 | 0.2500 | 3m 19s | 0.3333 | 0.5000 |
Tan-h | 0.2503 | −0.0031 | 0.5000 | 3m 24s | 0.5000 | 0.5000 | |
30 | Sigmoid | 0.2508 | −0.0023 | 0.6250 | 3m 17s | 0.6667 | 0.5000 |
Tan-h | 0.2505 | −0.005 | 0.6250 | 3m 29s | 0.6000 | 0.7500 | |
40 | Sigmoid | 2.51E-01 | 3.12E-04 | 0.5000 | 3m 28s | – | 0 |
Tan-h | 0.2506 | −0.0001 | 0.5000 | 3m 29s | – | 0 | |
50 | Sigmoid | 2.50E-01 | 3.27E-04 | 0.5000 | 3m 21s | 0.5000 | 1 |
Tan-h | 2.51E-01 | −1.59E-03 | 0.5000 | 3m 39s | 0.5000 | 0.2500 | |
60 | Sigmoid | 2.51E-01 | −2.29E-03 | 0.6250 | 3m 23s | 0.6667 | 0.5000 |
Tan-h | 2.51E-01 | 1.96E-03 | 0.6250 | 3m 38s | 0.6000 | 0.7500 | |
70 | Sigmoid | 2.50E-01 | 7.78E-04 | 0.5000 | 3m 25s | 0.5000 | 0.5000 |
Tan-h | 2.51E-01 | 1.52E-03 | 0.5000 | 3m 32s | 0.5000 | 0.5000 | |
80 | Sigmoid | 2.50E-01 | −7.89E-03 | 0.6250 | 3m 21s | 1 | 0.2500 |
Tan-h | 2.50E-01 | −3.38E-04 | 0.2500 | 3m 32s | 0.2500 | 0.2500 | |
90 | Sigmoid | 2.51E-01 | 2.98E-03 | 0.2500 | 3m 25s | 0.3333 | 0.5000 |
Tan-h | 2.51E-01 | 1.34E-03 | 0.5000 | 3m 32s | 0.5000 | 0.2500 |
The comparison results for accuracy measurement for proposed hybrid network and conventional network are also illustrated in
In this study, the proposed hybrid LSTM network model along with different swarm intelligence algorithms has been evaluated for the fault diagnosis of the gearbox. In order, to address the challenges of over-fitting and enhancing the performance of conventional LSTM with a tiny training set, swarm intelligence optimization algorithms such as PSO, Cuckoo, Firefly and ACO along with ReLU activation function have been considered. From the evaluated results highest accuracy of 87.5% has been achieved with both Sigmoid-PSO and ReLU-Cuckoo customized activation functions. The results highlight that the proposed method would achieve higher accuracy in condition monitoring of gears for fault diagnosis. Comparative studies have also indicated that results of hybridization optimized with swarm intelligence are superior to the conventional LSTM model.
The authors would like to acknowledge the Artificial Intelligence and Data Analytics (AIDA) Laboratory, CCIS, Prince Sultan University, Riyadh, Saudi Arabia for the support.