Optimized ELM based on Whale Optimization Algorithm for gearbox diagnosis

Extreme learning machine (ELM) is a fast and quick learning algorithm with better generalization performance. However, the randomness of input weight and hidden layer bias may affect the overall performance of ELM. This paper proposed a new approach to determine the optimized values of input weight and hidden layer bias for ELM using whale optimization algorithm (WOA), which we call WOA-ELM. An online gearbox vibration signals is used in this study. Empirical mode decomposition (EMD) and complementary mode decomposition (CEEMD) are used to decompose the signals into sub-signals known as intrinsic mode functions (IMFs). Then, statistical features are extracted from selected IMFs. WOA-ELM is used for classification of healthy and faulty condition of gearbox. The result shows that WOA-ELM provide better classification result as compared with conventional ELM. Therefore, this study provide a new diagnosis approach for gearbox application.


Introduction
Gearbox diagnosis study is one of the most important research study as gearbox is a crucial engineering unit in many industry. The study also help to ensure the functionality and reliability of gearbox applications and avoiding failures [1,2]. Advancement of technology has make the diagnosis approach has been improved from time to time. Nowadays, diagnosis based on frequency spectrum is no longer efficient as it may lead to inaccurate result which can lead to machine breakdown and catastrophic failure [3,4].
Automated diagnosis approach is known as a recent trend for diagnosis study. Basically, it consists of signal processing, features extraction, features selection and machine learning algorithm. A lots of research using automated diagnosis approach has been proposed recently in many areas of study [5][6][7][8].
Extreme learning machine (ELM) is a technique to train single-hidden layer feedforward neural network (SLFN) that has been proposed by Huang, Zhu and Siew in 2006 [9]. ELM has gained a lots of attention from many researcher since then. It has been applied in many area of study such as rotating machinery application [10][11][12], air quality forecasting [13], electric load forecasting [14], machining [15], etc. By comparing with conventional neural network, ELM provide thousands of time faster learning, better generalization and simple model [9]. Basically, ELM assign the input weight and hidden layer bias randomly. This make the algorithm less effective which subject to the given values [16]. Also, it also effect the ELM performance and provide unstable ELM output [17]. This paper aim to propose an approach to determine the optimized value of input weight and hidden layer bias by using whale optimization algorithm (WOA), so called as WOA-ELM. WOA is a new meta-heuristic method proposed by Mirjalili and Lewis in 2016 inspired by whale feeding behaviour of humpback whales [18]. According to Mirjalili and Lewis, WOA provide better performance as compared with PSO, GSA, GA, etc. as it has been tested with 29 mathematical benchmark and 6 structural design problem [18]. This method also has been successfully applied in many field such as machinery diagnosis [19,20], brain tumour [21], and breast cancer and tumour [22,23].
The rest of this paper is organized as follow. Section 2 presented the algorithm theory of ELM and WOA-ELM. Section 3 presented the WOA-ELM diagnosis approach and feature extraction using EMD and CEEMD. Section 4 draw the conclusion of the study. Figure 1. SLFN structural design.

Extreme learning machine (ELM)
The ELM was developed precisely only for handling SLFN structural design. Figure 1 shows the structure of SLFN where is the input data array, is the input weight, is the hidden layer bias, is the output weight and is the output layer array. The annotation present as follows: where , , and are the input number, hidden neuron and output neuron. For computation ease, it has been observed that the weight and bias are placed together in the same matrix.
In ELM, input weight is initialized randomly by sampling the values in the sense of uniform distribution between -1 and 1 and it is not change throughout the training phase. Analytical process of maintaining the universal approximation capability of SLFNs allow the construction of matrix [9]. Then, hidden neurons feature map ( ) is computed as follows: where (. ) is the activation function, = (1, … , ) and is the number of samples in training dataset. Then, solve linear system using simple generalized inverse operation in order to compute , as follow: Where † is the Moore-Penrose generalized inverse of . The Moore-Penrose solution is a least-square solution for a general linear system. Hence, it enable the ELM to achieve small training error, small norm of the weight and better generalization performance. Also, it does not stuck in local minima as the gradient descent-based learning methods [9]. The pseudocode of ELM algorithm presented as follow: Step 1: Function ELM_train ( , , , , ).

Step 2:
Input: A training set { , }, number of hidden neurons , the input weight, , and hidden layer bias .
Step 3: If and are empty, then initialize and randomly between [-1, 1] and end.

Parameter optimization using WOA-ELM
As mentioned, initialize the input weight, and hidden layer bias, will influence classification result. Optimization using meta-heuristic algorithm is one of the approach in order to determine the optimized value of and . In this study, a new and nature-inspired metaheuristic method known as WOA is used with ELM to determine its parameter. Number of hidden neuron, is also one of parameter for ELM. It do not has specific rule in determining the value but it also influence the classification result. Hence, there are three ELM parameters will be optimized in this study which are , , and .
WOA was inspired by humpback whale hunting behaviour, also known as bubble-net hunting strategy [18]. This hunting strategy mainly consists of search of prey, encircling prey and bubble-net feeding manoeuvre. The complete description of each strategy is elaborated fully in reference [18].The pseudocode of WOA algorithm presented as follow: Step 1: Initialize the whales population ( = 1,2, … , ) Step 2: Calculate the fitness of each search agent, * is the best search agent.  20 3 The complete algorithm for parameter optimization using WOA-ELM shown in Figure 2. All three parameter has interval value set from [0,1] for and and [1,200] for . The number of iteration is set to 100 with search agent number is set to 150. For ELM, "rbf" activation function is used. For objective function of WOA, the average classification accuracy of training and testing is used as described in Equation (4)

Signal processing and feature extraction
As mentioned earlier, an online gearbox vibration signals downloaded from Acoustic and Vibration Database provided by Eric Bechhoefer are used [24]. The signals consists of healthy and faulty signal condition. The sampling rate for the signals is 97 656 Hz and it was recorded for 6 seconds. The signals was taken using accelerometer sensor in radial direction. Generally, gearbox vibration signals always subject to high noise contamination which make the extraction of features directly is not efficient [25]. Hence, empirical mode decomposition (EMD) and complementary ensemble empirical mode decomposition (CEEMD) have been used. These signal decomposition method at some extend has the capability to remove some noise from the vibration signals [26].
At first, all the vibration signals will be decomposed into sets of IMFs using EMD and CEEMD. Then, the statistical features listed in Table 1 are extracted from the combination of selected IMFs. The IMF was selected based on correlation criterion [27]. Then, the statistical features divided into training and testing dataset for classification. WOA is used to determine the optimized , , and value for ELM algorithm. Full procedure of WOA-ELM for gearbox diagnosis shown in Figure 3.

Statistical parameter Equation
Crest factor

Margin factor
The statistical features then divided into training and testing dataset. For ELM, all the features value need to be normalized within 0 to 1. Hence, the normalization of   20 3 features are based on Equation (5). The distribution of these dataset summarized in Table 2.
where is a normalized features, is statistical features, , is the maximum statistical feature value and is a constant for normalization which has been set to 1.3. Figure 4-11 shows the distribution of statistical features for EMD and CEEMD.

, , and optimization using WOA-ELM
The value of , , and will be optimized based on WOA-ELM. As mentioned above, the iteration is set to 100 and no of search agent is set to 150. The value of , , and are set to its specific interval [0,1] for and and [1,200] for . Figure 12 and 13 shows the optimization fitness convergence curve result for EMD and CEEMD.  and need to be expand into matrix. Hence, the optimized value will be acted as a middle value for the matrix where all the value will be uniformly random within specific range of . It been described as Equation (6) and (7) below.
The value also expand into matrix by using the same concept, described in Equation (8) and (9):

Classification based on WOA-ELM
By using the matrix and with , the classification is done. For running the ELM, it has been run for 30 times in order to avoid tweak problem and get a stable classification accuracy. A comparison between gearbox diagnosis result between WOA-ELM and conventional ELM have been studied. For conventional ELM, the and are set in random and default way and is set to 8 which is equivalent to the number of statistical features used. Its shows that the proposed WOA-ELM method are able to improve the classification accuracy which means tuning an optimized value for , , and are very important. Figure 14 shows the training accuracy, Figure 15 shows the testing accuracy and Figure 16 shows the average accuracy of training and testing. Based on the result, the proposed WOA-ELM is able to improve the accuracy performance by 6% to 8% as compared with conventional ELM.

Conclusions
This paper present the parameter optimization using WOA for determine the optimized input weight, bias and number of hidden neurons for ELM algorithm, based on MATLAB platform. The proposed method has been applied to the gearbox diagnosis study. An online gearbox vibration signals are used in this study. EMD and CEEMD method have been used for signal processing and features extraction procedure. A comparison has been presented between proposed WOA-ELM methods with conventional ELM method in this paper. The diagnosis accuracy shows that WOA-ELM provide better accuracy as compared with conventional ELM where the input  20 3 weight and bias is set to random value and hidden neuron is set equivalent to the number of features extracted. Therefore, applying WOA-ELM for gearbox diagnosis can improve the failure efficiency. For future study, the proposed WOA-ELM will be applied in other rotating machinery applications such as bearing, shaft and belt to verify the superiority of this method in machinery diagnosis study.