# trendability

Measure of similarity between trajectories of condition indicators

## Syntax

## Description

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.

## Examples

## Input Arguments

## Output Arguments

## Limitations

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.

## Algorithms

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

*j*system and the variable

^{th}*M*is the number of systems monitored.

When *x _{j}* and

*x*have different lengths, the shorter vector is resampled to match the length of the longer vector. To facilitate this process, their time vectors are first normalized to percent lifetime, that is, [0%, 100%].

_{k}## References

[1] Coble, J., and J. W. Hines.
"Identifying Optimal Prognostic Parameters from Data: A Genetic Algorithms Approach." In
*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.

## Version History

**Introduced in R2018b**