6.2 Progression Analysis
As explained in chapter 3.3.1, the gear vibration signatures are given by the matrices A and B in
equations
3.2,
3.3
and
3.4
[30].
From
this
understanding
of vibration signatures, gear condition estimation is transformed into a sys-tem identi.cation problem. Each condition a given gear can exhibit has its set of values for A and B. Thus, by estimating these matrices, it is possible to uncover the corresponding condition. Although this equation set is underde-termined, making an unambiguous estimation impossible, it is fairly straight forward to specify a set of condition indicators capturing the essence of A and B. Consequently, the condition of a gear is given by its set of relevant
79
indicators. Also for bearings and shafts, a relatively small set of indicators is su.cient to discriminate all conditions these components can inhibit.
Vibration based fault detection for mechanical components is typically based on estimating the normal state vibration signature i.e. the normal state values for a set of relevant indicators, and comparing subsequent obser-vations to this baseline. An observation displaying signi.cant deviation from the normal state baseline must be considered as an observation of a compo-nent in an abnormal condition. The challenge is estimating the baseline, i.e. the normal state envelope for the set of relevant indicators. This because the vibration signature of a mechanical component is speci.c not only to each design, but speci.c to each physical realization of a given design. The cause of this stems from microscopic di.erences in the way each component is forged and mounted. All component types su.er from this problem, al-though gears typically have larger variation in vibration signature between individual realizations than bearings and shafts. In any case, the normal state baseline must be estimated for each component, and re-estimated after major overhauls.
As the condition of a component degrades, its condition changes as a func-tion of time. Consequently, its vibrations signature and its set of relevant indicators changes as a function of time, where the function is determined by the failure mode. Observing a segment of a set of indicators, it is possible to estimate the function, or progression pattern, to which the segment cor-responds. The progression pattern estimate will in turn provide a pointer to which conditions the observed component is traversing, and to which failure mode this set of conditions corresponds. These assumptions form the base for indicator progression analysis as a feature extraction tool.
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