Adaptive sensor model

1. A method of predicting output values ŷ of a physical system from stored on-line data comprising a set of measured inputs r j of the system, wherein at each time t when a prediction is made, the method comprises the following steps:

(a) updating the stored on-line data by storing the set of measured inputs r j (t i ) and the corresponding measured output y(t i ) at each of a predetermined number n of times t 1 . . . t n earlier than t;

(b) initializing a model of the system, which generates a predicted output ŷ(t) from the set of measurements r j (t), to a predetermined initial model using off-line data;

(c) using each of the predetermined number n of sets of measured inputs r j (t i ) and output y(t i ) to revise the model; and

(d) using the revised model to predict the output value ŷ(t) of the system at time t from the set of measured inputs r j (t) of the system at time t.

2. A method according to claim 1 , wherein step (c) uses the n sets of measurements r j (t i ) and y(t i ) in chronological order.

3. A method according to claim 1 , wherein the times t 1 . . . t n are the most recent n times preceding time t at which measurements were made.

4. A method according to claim 1 , wherein, for each of the n sets of measurements of the inputs and the output, step (c) comprises the following steps:

(c1) applying the model to the set of inputs r j (t i ) to generate a predicted output ŷ(t i ) at time t i ;

(c2) calculating an error ε(t i ) by finding the difference between the predicted output ŷ(t i ) and the measured output y(t i ) at time t i ; and

(c3) using the error ε(t i ) to revise a set of parameters b k of the model.

5. A method according to claim 4 , wherein step (c3) uses a recursive estimation algorithm to revise the parameters b k of the model.

6. A method according to claim 5 , wherein step (c3) uses a recursive least squares algorithm to revise the parameters b k of the model.

7. A method according to claim 5 , wherein the model further includes an error covariance matrix P, which is used in step (c3) to revise the parameters of the model; and wherein the method further comprises a step (c4) of using the measured input values r j (t i ) to revise the error covariance matrix P.

8. A method according to claim 7 , wherein in step (c4) the error covariance matrix P is revised using the measurements from time t i according to the following formula:

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where:

P(t i ) is the revised error covariance matrix based on the measured input values up to time t i ;

P(t i-1 ) is the previous error covariance matrix based on the measured input values up to time t i-1 ;

{tilde over (ω)}(t i ) is a vector representing the set of measured input values r j (t i ) at time t i and powers of those input values {r j (t i )} n that are used in the model; and

λis a scalar “forget factor” in the range 0<λ<1.

9. A method according to claim 8 , wherein:

in step (c2) the scalar error ε(t i ) is calculated in accordance with the following formula:

ε( t i )= y ( t i )−{circumflex over (θ)} T ( t i-1 ){tilde over (ω)}( t i )

where {circumflex over (θ)} is a vector representing the set of model parameters b k ;

and in step (c3) the parameters of the model are revised in accordance with the following formula:

{circumflex over (θ)}( t i )={circumflex over (θ)}( t i )ε( t i )

where μ is a vector calculated from the following formula:

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10. A method according to claim 1 , wherein the physical system is an item of plant.

11. A method according to claim 1 , wherein the physical system is a gas turbine engine.

12. A method for real-time prediction of the value of an output variable of a physical system from knowledge of the values of a plurality of input variables of the system, comprising the steps of:

storing off-line data comprising a generic set of n values of each of the input and output variables,

periodically sampling, with a periodicity of t, on-line data comprising the values of the input and output variables,

storing a set of m successive samples of the on-line data,

updating the stored on-line data at each sample period by adding recently sampled values of input and output variables and discarding the oldest sampled values of input and output variables,

initializing a model of the physical system at the beginning of each sample period t using the off-line data,

revising the model after each initialization using the updated stored on-line data, and

using the revised model to predict a value of the output variable.

13. A method according to claim 12 , in which the number n is much greater than the number m.

14. A method according to claim 12 , wherein the physical system is an item of plant.

15. A method according to claim 12 , wherein the physical system is a gas turbine engine.

16. Control apparatus for a physical system, the apparatus including a mathematical model of the physical system for predicting the value of an output variable of the system from measured values of input variables of the system in accordance with a method as defined in claim 1 or claim 12 .

17. A closed loop control system for an item of plant such as a gas turbine engine that has sensors installed therein for on-line measurement of plant behaviour by periodic sampling of on-line sensor signals by the control system, the on-line measurements being updated and stored at each sample period, the control system comprising:

a control function,

at least one adaptive sensor model derived from both off-line and on-line measurements of plant behaviour, the model comprising a first algorithm operative at each sample period to initialize the model using the off-line measurements, revise the initialized model using the updated stored on-line measurements, and derive for output from the model a synthetic sensor signal corresponding to one of the on-line sensor signals, and

selection logic, for selecting for input to the control function the synthetic sensor signal and the on-line sensor signals.

18. A closed loop control system according to claim 17 , wherein the selection logic implements a second algorithm that compares the on-line sensor signals and the synthetic sensor signal with a weighted average of their values, thereby to select a signal most likely to accurately represent engine behaviour.

19. A closed loop control system according to claim 17 , comprising a plurality of adaptive sensor models, each such model being operative to derive a synthetic sensor signal corresponding to a respective one of the on-line sensor signals.

20. A closed loop control system according to claim 17 , wherein the first algorithm implements a method of predicting output values ŷ of the plant from a set of measured inputs r j of the plant, wherein at each time t when a prediction is made, the method comprises the following steps:

(a) storing the set of measured inputs r j (t i ) and the corresponding measured output y(t i ) at each of a predetermined number n of times t 1 . . . t n earlier than t;

(b) initializing the model of the plant, which generates a predicted output ŷ(t) from the set of measurements r j (t), to a predetermined initial model;

(c) using each of the predetermined number n of sets of measured inputs r j (t i ) and output y(t i ) to revise the model; and

(d) using the revised model to output a predicted value ŷ(t) of the plant at time t from the set of measured inputs r j (t) of the plant at time t, the predicted value ŷ(t) being the synthetic sensor signal.

21. A closed loop control system according to claim 17 , wherein the first algorithm implements a method for real-time prediction of the value of an output variable of the plant from knowledge of the values of a plurality of input variables of the plant, comprising the steps of:

storing off-line data comprising a generic set of n values of each of the input and output variables,

periodically sampling, with a periodicity of t, on-line data comprising the values of the input and output variables,

storing a set of m successive samples of the on-line data,

updating the stored on-line data at each sample period t by adding recently sampled values of input and output variables and discarding the oldest sampled values of input and output variables,

initializing a model of the plant at the beginning of each sample period t using the off-line data,

revising the model after each initialization using the updated stored on-line data, and

using the revised model to predict a value of the output variable, the predicted value being the synthetic sensor signal.