Measure of similarity between trajectories of condition indicators

`Y = trendability(X)`

`Y = trendability(X,lifetimeVar)`

`Y = trendability(X,lifetimeVar,dataVar)`

`Y = trendability(X,lifetimeVar,dataVar,memberVar)`

`Y = trendability(___,Name,Value)`

`trendability(___)`

returns the trendability of the lifetime data `Y`

= trendability(`X`

)`X`

. Use
`trendability`

as measure of similarity between the trajectories of a
feature measured in several run-to-failure experiments. A more trendable feature has
trajectories with the same underlying shape. The values of `Y`

range from
0 to 1, where `Y`

is 1 if `X`

is perfectly trendable
and 0 if `X`

is non-trendable.

returns the trendability of the lifetime data `Y`

= trendability(`X`

,`lifetimeVar`

)`X`

using the lifetime
variable `lifetimeVar`

.

returns the trendability of the lifetime data `Y`

= trendability(`X`

,`lifetimeVar`

,`dataVar`

)`X`

using the data
variables specified by `dataVar`

.

returns the trendability of the lifetime data `Y`

= trendability(`X`

,`lifetimeVar`

,`dataVar`

,`memberVar`

)`X`

using the lifetime
variable `lifetimeVar`

, the data variables specified by
`dataVar`

, and the member variable
`memberVar`

.

estimates the trendability with additional options specified by one or more
`Y`

= trendability(___,`Name,Value`

)`Name,Value`

pair arguments. You can use this syntax with any of the
previous input-argument combinations.

`trendability(___)`

with no output arguments plots a
bar chart of ranked trendability values.

When

`X`

is a tall table or tall timetable,`trendability`

nevertheless loads the complete array into memory using`gather`

. If the memory available is inadequate, then`trendability`

returns an error.

The computation of trendability uses this formula:

$$\text{trendability}=\text{}\underset{j,k}{\mathrm{min}}\left|\text{corr}\left({x}_{j},{x}_{k}\right)\right|,\text{}j,k\text{=}1,\mathrm{...},M$$

where *x _{j}* represents the vector of measurements of a feature on the

When *x _{j}* and

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*Proceedings of the Annual Conference of the Prognostics and Health Management
Society*. 2009.

[2] Coble, J. "Merging Data Sources to Predict Remaining Useful Life - An Automated Method to Identify Prognostics Parameters." Ph.D. Thesis. University of Tennessee, Knoxville, TN, 2010.

[3] Lei, Y. *Intelligent Fault
Diagnosis and Remaining Useful Life Prediction of Rotating Machinery*. Xi'an,
China: Xi'an Jiaotong University Press, 2017.

[4] Lofti, S., J. B. Ali, E. Bechhoefer,
and M. Benbouzid. "Wind turbine high-speed shaft bearings health prognosis through a
spectral Kurtosis-derived indices and SVR." *Applied Acoustics* Vol. 120,
2017, pp. 1-8.