Ied into an discrete emission matrix. This HMMR classic paper are rewritten as follows: HMMR model, where the running-in phase is really a cubic spline Gaussian regression model, – as well as the steady phase is really a linear = (, A,regression1model, as shown by Equation (28). Gaussian U1 , U2 , , 2) (29)Machines 2021, 9,Figure 12. Unscaled Dynasore Inhibitor damage tracking in healthful stage. Figure 12. Unscaled damage tracking in healthier stage.18 ofFinally, in line with the maximum likelihood estimation algorithm, the model paramT eters could be obtained asEt U j j jL L ; et-;e log p – ; e = tlog p bjt ; Z t P Z S t eS t =e ;U log p S 1 ;T p S t |S tN 1 t ;TA v , N eT; U T 2, two t = log p[S(1); ] pt[S2(t)|S(t -q 11 ; A] Nt et ; US(t) , S tS(t) S t) 1 St =TSjN et ; U jTv j ,Q T T q q2 j 2 q(28) (30) (30)where Uj would be the regression coefficient with the the Ref. [38], Equation (30) could be solved by Based on the method proposed in (l 1) -dimensional lth order function under In line with the system proposed in the Ref. [38], Equation (30) might be solved by expectation aximization (EM) jp ]T is definitely the regression inputshown in Figure below the algorithm. Its results are (i.e., time input) 13, where the jth hidden state. j [1, t j t j2 the expectation aximization,(EM)talgorithm. Its final results are shown in Figure 13, where the service state wholesome bearing is automatically divided into the initial a single standthe hidden state of theN (0, 1) would be the Gaussian distribution with in to the initial running-in jth service state. of thehealthy bearing is automatically divided zero imply and running-in phase plus the steady operating phase. The finish of your initial running-in phase–that is, the phase and the steady operating phase. The end in the initial running-in phase–that is, the ard deviation, of j the the typical deviation of your be finally model below the theoretical is steady operation phase–will be finally regarded because the jth hidden starting point on the steady operation phase–willregression regarded because the theoretical starting point point h11 in Equation parameters for the HMMR model in this paper arethe PSW datafolpoint h in Equation (25). 10b shows the standardized result of rewritten as in state. Thus, the (25). Figure 10b shows the standardized outcome on the PSW information in Figure 10a obtained by the above system. Figure 10a obtained by the above approach. lows:, A, U 1, U 2 ,(29)Lastly, as outlined by the maximum likelihood estimation algorithm, the model parameters might be obtained asFigure 13. Healthy stage segmentation of Bearing 1-1. Figure 13. Healthful stage segmentation of Bearing 1-1.Figure 1 illustrates the crack length within the spall location to represent the harm degree Figure 1 illustrates the crack length inside the spall region to represent the damage degree of a precise broken bearing. A number of spall regions are also shown in Figure 1 and are of a distinct broken bearing. Many spall areas are also shown in Figure 1 and are represented because the ONPG Formula identifier `’ in Table two. Damage related standardized PSW worth is given within the very same column of Table 2, with each other with RMS and kurtosis. Compared using the standard RMS and kurtosis, an clear optimistic correlation might be observed among the standardized PSW worth plus the crack length.Machines 2021, 9,17 ofrepresented as the identifier `’ in Table two. Damage related standardized PSW value is offered within the very same column of Table 2, together with RMS and kurtosis. Compared using the standard RMS and kurtosis, an apparent positive correlation c.