PSI - Issue 17

Andra Gabriela Stancu et al. / Procedia Structural Integrity 17 (2019) 238–245 A. G. Stancu et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Baseline convergence

By setting up the signature set S, the condition of the system can be established by evaluating the statistical impact of new system states to the historical state sets. To achieve this, the convergence algorithm is implemented. To evaluate the statistical impact of the current state S n on the previous state {S 1 , S 2 , … S n-1 }, firstly the mean value of the state set is defined as: | >1 = ∑ =1 = 1 ∑ =1 [ 1 2 ⋮ ] = [ ( 1 : ), ( 2 : ), ( : )] (2) Where μ n is a matrix of size N x 1. N is the number of types of P, and E is the expectation operator. Therefore, the statistical difference D of two consecutive sets of data, namely {S 1 , S 2 , … S n-1 } and {S 1 , S 2 , … S n } can be estimated by applying the method below: ( , −1 ) = 100% × √ 1 ∑ =1 (1 − ( 1 : ) ( 1 : −1 )) ) 2 (3) Converges when: ( , −1 ) <= Convergence rate (4) In practice, it is beneficial to collect as many relevant parameters as possible. However, their magnitude is generally expressed on different scales. Simply amalgamate them will cause the parameters with higher magnitude to dominante. To produce an overall indicator, reasonably considering the impact of all parameters, the deviation of each parameters in μ n is evaluated in % . Equation 3 describes the distance between two sets of observations in N-dimension. As the observation number n is continuously growing, it is anticipated that D will decrease in an exponential trend, until it converges at n = c. A convergence criterion is used for the evaluation of the signature sets and the parameters contained. If increasing the number of signature sets does not have any sensible effect on the calculated D after a certain n = c, then it is considered that signature set {S 1 , S 2 , … S c } can be seen as a baseline condition Base , containing c observations each with N types of parameters, i.e.: Base = {S 1 , S 2 , … S c }, where c meets the convergence criteria (5) The convergence criterion must be carefully chosen, as it affects the monitoring process. It should guarantee a practically achievable convergence time (which does not take too long to satisfy) and avoids D converging too quickly, failing to capture the baseline condition. Theoretically, c should be determined as the minimum number that satisfies the criteria, since a high value of c will result in subtle defects in the signatures being averaged out. The convergence criteria depends on how complex the machinery monitored is. Generally, it is considered that a recording time of at least 20 times the slowest rotating shaft speed should make a meaningful processing data length [3]. Therefore, the convergence rate should be selected so that it allows at least these amount of data to be recorded for one measurement, and a rule of thumb based on practical experience demands the rate to be 5% - 10%.

2.3. Similarity analysis

The Base condition established in section 2.2 is used in identifying potential defects at later stages of operation. The subsequent conditions, i.e. signature sets, measured are defined in a similar manner and containing an identical number of observations to the Base condition, to be sensibly compared.