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The two initial methods require order to be determined in advance. Al-though, in an industrial setting, such a requirement can be met by using a reasonable order given the length of the data set, it is also desirable to have a more autonomous solution. Further, the evolutionary algorithm is not well suited for high order models.
The spectral validation method produces good results when used as a wrapping around Trust Region. An objection to this algorithm is execution time, as it re-estimates the model each time order is incremented, thus requir-

6.4. SIGMOID PROGRESSION ANALYSIS
ing substantial execution time for high order models. This could probably be amended by using the .nal results from the last optimization as initial condition when model order is incremented, simply adding a sigmoid in the region where model error is largest. Such improvements have however not been further explored in this study.
Iteratively evolutionary estimation was an attempt to estimate a complex function using a reduced parameter space, by estimating one segment at a time. The method is still slow, and lacks accuracy because it does not solve the global optimization problem.
Trust Region with initial guess given by band-limited derivation is clearly the best method for the problem at hand, as the initial position is very close to the optimal solution. This means that convergence is quick, and that the initial position is closer to the global optimum than any local optimums.
6.4.3 Trend Analysis
Given a d.which is optimized to closely approximate d, the parameters con-trolling d.constitutes a compact form representation of d.. By analyzing this compact form representation, it is possible to understand the behavior of d., and the d which it approximates. The traversal through states associated with mechanical degradation is however manifested as changes in the value of c not d. It is thus necessary to separate the contribution from .b and c.in d.. As already explained, a step change constitutes a change in b while a trend constitutes a change in c. In the progression pattern referred to as normal, both b and c are static.
(k)(k)(k)
From this information, the key properties ar , ad and qd are extracted. The two latter parameters hold the information necessary to identify what type of transition is being approximated by a sigmoid, and consequently the behavior of b and c within the region covered by the sigmoid. The former parameter holds the information necessary to understand the progression of the indicator scatter level.
In order to separate c and b, the qd (k) metric is tested against a threshold Tq. If a qd (k) value overshoots this threshold, transition k is considered to be part of b. Inversely, if a qd (k) value is inferior to Tq, transition k is considered to be part of c. After the transition has been sorted, .b and c.are constructed from their respective sigmoids, giving the full 4-way decomposition(Fig. 6.22).
In order to detect changes in the condition of the underlying asset, .uctuations in the value of c and the gain of w must be monitored. This is done by computing the time derivative of c.(Fig. 6.22)
　
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