Method for estimating the remaining service life of subject equipment
A method for estimating a Remaining Useful Life of a subject equipment, with a preliminary phase including the following steps: acquire test observations (step 10 ) and produce test time series (S x ) of at least one signature; partition the test time series to obtain severity classes corresponding to the ageing phases of the test equipment devices (step 14 ); carry out an initial learning of a diagnosis model on the test equipment devices (step 45 ); perform a second learning of a signature prediction model (step 51 ). There is also an operational phase including the following steps: acquire observations when in operation on the subject equipment and produce an extrapolated time series using the prediction model; classify the extrapolated time series using the diagnosis model and derive the remaining useful life of the subject equipment.
1. A method for estimating a Remaining Useful Life of a subject equipment, comprising a preliminary phase comprising the following steps:
acquire test observations on test equipment devices ( 1 a , 1 b , 1 c , 1 d ) similar to the subject equipment (step 10 );
produce, from the test observations, test time series (S x ) of at least one signature;
partition the test time series to obtain severity classes corresponding to ageing phases of the test equipment devices (step 14 );
carry out a first learning of a diagnosis model on the test equipment devices (step 45 );
perform a second learning of a prediction model of the signature (step 51 ); and an operational phase comprising the following steps:
acquire observations when in operation on the subject equipment;
produce an extrapolated time series representative of the evolution of the signature on the subject equipment using the prediction model;
classify the extrapolated time series using the diagnosis model;
calculate a membership function of the extrapolated time series to the severity classes;
deduce, from the membership function, the Remaining Useful Life of the subject equipment, the estimated Remaining Useful Life being such that:
= q−t
where q is an estimated end-of-life time and t is a current time, and where, at the estimated end-of-life time q, the last severity class membership function becomes greater than the penultimate severity class membership function.
2. The estimation method according to claim 1 , wherein a temporal consistency criterion is used to define a number of severity classes produced by the partitioning.
3. The estimation method according to claim 2 , wherein the temporal consistency criterion is evaluated using a first metric defined by:
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where x k (i) is an i th test observation acquired for the test equipment device k and where ct is a temporal consistency between two successive test observations and is defined using the following formula:
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where y k (i) is the severity class of the observation x k (i) .
4. The estimation method according to claim 1 , wherein a second metric, which is an energy metric, is evaluated to select a partitioning algorithm.
5. The estimation method according to claim 4 , wherein the energy metric is defined as:
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where Ω i is a set of test observations of an i th class, the x (j) ∈R p are the test observations, g i is a centre of gravity of the i th severity class, dis a distance measure and is defined by:
d ij 2 =d ( x (j) ,g i ) 2 =∥x (j) −g i ∥ d 2 =( x (j) −g i ) T A d ( x (j) −g i )
where A d is a positive semidefinite matrix defining a distance metric, and where the symbol “∥ ∥ d ” represents the norm corresponding to the distance d.
6. The estimation method according to claim 4 , wherein the partitioning algorithm is a C-Fuzzy Mean algorithm.
7. The estimation method according to claim 1 , wherein the prediction model is trained with a multi-step iterative method.
8. The estimation method according to claim 1 , wherein the prediction model is constructed from a non-linear SVR regression.
9. The estimation method according to claim 1 , wherein the first learning of the diagnosis model uses a Fuzzy SVM-FA classification algorithm.