Adaptive sensor model

• US 7,356,371 B2
• Filed: 02/11/2005
• Issued: 04/08/2008
• Est. Priority Date: 02/11/2005
• Status: Expired due to Fees

• Current Assignee: Ansaldo Energia IP UK Limited (Ansaldo Energia SPA)
• Original Assignee: Alstom Technology Ltd. (Alstom SA)
• Inventors: Pike, Andrew W, Dixon, Roger
• Primary Examiner(s): Pham; Thomas K
• Application Number:
  US11/056,619
• Publication Number:
  US 20060184255A1
• Time in Patent Office: 1,152 Days
• Field of Search: 700/28, 700/29, 700/30, 700/31, 700/32, 700/21, 700/79, 700/108, 700/110, 700/143
• US Class Current: 700/28
• CPC Class Codes: G05B 13/048 using a predictor
• CPC Class Codes: G05B 17/02 electric

Abstract

The invention provides a method of predicting output values of a physical system from a set of measured inputs of the system using an adaptive model. At each time when a prediction is made, the model is re-initialized to an initial, off-line model and is then refined to incorporate on-line data using a predetermined number of recent sets of measured inputs and outputs. The model thus always remains “tethered” to the initial, off-line model and if operating conditions remain steady, the model does not become too specific to those operating conditions.

Claims

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 t₁ . . . 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 t₁ . . . 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:

$P<br><br>\left(t_i\right)=\frac{1}{\mathrm{\lambda <br><br>}}<br><br>\left[P<br><br>\left(t_{i-1}\right)-\frac{P<br><br>\left(t_{i-1}\right)<br><br>\widetilde{\mathrm{\omega <br><br>}}<br><br>\left(t_i\right)<br><br>{\widetilde{\mathrm{\omega <br><br>}}}^T<br><br>\left(t_i\right)<br><br>P<br><br>\left(t_{i-1}\right)}{\mathrm{\lambda <br><br>}+{\widetilde{\mathrm{\omega <br><br>}}}^T<br><br>\left(t_i\right)<br><br>P<br><br>\left(t_{i-1}\right)<br><br>\widetilde{\mathrm{\omega <br><br>}}<br><br>\left(t_i\right)}\right]$

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

λ

is 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;

$\mathrm{\mu <br><br>}<br><br>\left(t_i\right)=\frac{P<br><br>\left(t_{i-1}\right)<br><br>\widetilde{\mathrm{\omega <br><br>}}<br><br>\left(t_i\right)}{\mathrm{\lambda <br><br>}+{\widetilde{\mathrm{\omega <br><br>}}}^T<br><br>\left(t_i\right)<br><br>P<br><br>\left(t_{i-1}\right)<br><br>\widetilde{\mathrm{\omega <br><br>}}<br><br>\left(t_i\right)}.$

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.

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.

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.

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 t₁ . . . 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.