OPTIMIZATION OF FAULT DIAGNOSIS IN HELICOPTER HEALTH AND USA(52)

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Several methods exist for non-linear optimization problems, two of them being evolutionary optimization and Trust Region. Evolutionary optimiza-tion is inspired by the process of natural selection. Trust Region is a tradi-tional steepest descent method.
All methods presented here attempt to minimize square sum r., unless otherwise stated. The two former methods need model order to be decided in advance, while the remaining ones are capable of estimating this parameter. All methods were tested using a synthetically generated dataset.
Evolutionary Optimization with Pre-De.ned Order (EO)
This methods uses evolutionary optimization (Sec. A.4.2)
to adjust the sig-moid parameters given a prede.ned function order, with the aim to minimize sum square r.. As the function order is .xed, there is no danger of "over .t-ting". The method was tested using an elite ratio of 0.1. Of the remaining individuals, the crossover fraction was set to 0.8 and mutation fraction the remaining 0.2. Initial range for dcd and the a(dk) parameters were set to the range of i. All p(dk) parameters had their initial range set to the range of t, and the qd (k) parameters where given the static initial range from 0 to 10. A population size of 200 individuals where evaluated over 200 generations with the end result shown in .gure 6.17.
Orders was set to 3.

For the example dataset, the approximation has one miss-placed step and a signi.cant bias toward the end of the dataset. In general, this method works well. The main drawbacks is that it does not determine order, and convergence is slow due to a poorly chosen initial condition.
Trust Region with Pre-De.ned Order (TR)
This method was tested using convergence of the solution to the approximate function as stopping criteria. The dcd parameter was given the initial value
(k)(k)
equal to μi, while the ad and qd parameters were set to 0 and 1 respectively. Each sigmoid’s position, p(dk), was set so that the sigmoids were uniformly distributed across t. Final
results
are
shown
in
.gure
6.18.
Orders was set to 3.

This method performs reasonably well on the example dataset. The main

6.4. SIGMOID PROGRESSION ANALYSIS
objection to this method is execution speed, as robust evolutionary optimiza-tion requires a large number of evaluations of the object function. Further, this method is incapable of determining model order.
Residual Spectrum Validation (RSV)
In the context of HUMS data analysis, it would be su.cient to analyze the last 200 -300 .ight hours of an aircraft to assess the condition of the drive-train. For an indicator series of this duration, more than three or four transition would be extremely unlikely. Consequently, good results can be obtained using a .xed model order. Still it would be desirable to automati-cally determine the optimal model order, with the optimal order being one which balances the power spectrum of r.while at the same time minimizes model order.
　
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