Bed as follows: (1) Initialize the population of whales and define theBed as follows: (1)
Bed as follows: (1) Initialize the population of whales and define the
Bed as follows: (1) Initialize the population of whales and define the parameters of WOA approach. Particularly, set the population size N = 50, maximum number of iterations T = 200 (i.e., epoch limits). On account of VME involves two crucial parameters to become optimized, so the position of each whale is expressed by a vector X i = [, f d ], exactly where is definitely the penalty issue of VME, f d denotes the initial mode center-frequency of VME and meets f d = d /2. The upper and lower bound of the vector X i ML-SA1 TRP Channel respectively is set as [200, 10,000] and [ f s /100, f s /2], where f s may be the sampling frequency on the raw bearing vibration signal. (2) Calculate the fitness worth of every single whales and identify the present optimal position of whales. In this step, inspired by signal-to-noise ratio (SNR) [36] and fault function ratio (FFR) [37], a new and productive sensitive index hailed as signal characteristic frequency-to-noise ratio (SCFNR) is regarded as the fitness worth to guide the parameter optimization procedure of VME, and also the SCFNR index is calculated by A( f ci )M MSCFNR(i ) = ten logi =1 N(12)j =A( f j ) – A( f ci )i =where f ci suggests the i-th fault characteristic frequency of Hilbert envelope spectrum on the extracted mode components ud , A( f ci ), i = 1, 2, , M denotes the amplitude of Hilbert envelope spectrum from the original bearing vibration signal at the i-th fault characteristic frequency, A( f j ), j = 1, 2, , N represents the amplitude of Hilbert envelope spectrum of your original bearing vibration signal in the j-th frequency f, N and M will be the quantity of all frequencies and fault characteristic frequencies of Hilbert envelope spectrum of the original bearing vibration signal, respectively. The bigger SCFNR value represents theEntropy 2021, 23,6 ofbetter feature extraction ability of VME. That is certainly, parameter optimization process of VME is often understood as the procedure of maximizing the fitness value (SCFNR). Hence, the objective function of parameter optimization procedure of VME can be defined as follows: argmaxSCFNRi i =(, f d ) (13) s.t. [200, 10000] and f [ f /100, f /2] s s dEntropy 2021, 23, x FOR PEER Assessment ferentwhere SCFNRi denotes the SCFNR value from the extracted mode elements beneath difcombination parameters i = (, f d ), f s represents the sampling frequency of 6 of 30 the original bearing vibration signal.Figure 1. Figure 1. The flowchart WOA to optimize optimize the parameters of VME. The flowchart of working with of applying WOA to the parameters of VME.(three)(1) Initialize thethe stop situation, update the parameters a, A, C, l and p beneath every Before reaching population of whales and define the parameters of WOA technique. Specifically, 0.5, the position updating = 50, maximum number of iterations T = 200 (i.e., iteration. If p set the population size N pattern with the shrinking encircling mechanism of epoch adopted. Otherwise, the position key parameters with the spiral model the position whales is limits). Resulting from VME requires twoupdating pattern to become optimized, so of whales is adopted. That is expressed by a vector X i = [ , fshrinking encircling mechanism or of of every whale is, the probability of picking the d ] , exactly where is definitely the penalty factor the spiral model to update the position of whales is the C2 Ceramide supplier identical. Concretely, if p= 0.five . The VME, f d denotes the initial mode center-frequency of VME and meets f d d 2 and | A| 1, update the position on the currenti whale according to Equation (14). If p 0.five, upper and reduced bound from the whale X respectively is set.