초록 ▼

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 usin

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.

대표청구항 ▼

We claim: 1. A method of predicting output values ŷ of a physical system from stored on-line data comprising a set of measured inputs rj 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 th

We claim: 1. A method of predicting output values ŷ of a physical system from stored on-line data comprising a set of measured inputs rj 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 rj(ti) and the corresponding measured output y(ti) at each of a predetermined number n of times t1 . . . tn earlier than t; (b) initializing a model of the system, which generates a predicted output ŷ(t) from the set of measurements rj(t), to a predetermined initial model using off-line data; (c) using each of the predetermined number n of sets of measured inputs rj(ti) and output y(ti) 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 rj(t) of the system at time t. 2. A method according to claim 1, wherein step (c) uses the n sets of measurements rj(ti) and y(ti) in chronological order. 3. A method according to claim 1, wherein the times t1 . . . tn 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 rj(ti) to generate a predicted output ŷ(ti) at time ti; (c2) calculating an error ε(ti) by finding the difference between the predicted output ŷ(ti) and the measured output y(ti) at time ti; and (c3) using the error ε(ti) to revise a set of parameters bk of the model. 5. A method according to claim 4, wherein step (c3) uses a recursive estimation algorithm to revise the parameters bk of the model. 6. A method according to claim 5, wherein step (c3) uses a recursive least squares algorithm to revise the parameters bk 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 rj(ti) 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 ti according to the following formula: where: P(ti) is the revised error covariance matrix based on the measured input values up to time ti; P(ti-1) is the previous error covariance matrix based on the measured input values up to time ti-1; {tilde over (ω)}(ti) is a vector representing the set of measured input values rj(ti) at time ti and powers of those input values {rj(ti)}n that are used in the model; and λis a scalar "forget factor" in the range 0i) is calculated in accordance with the following formula: description="In-line Formulae" end="lead"ε(ti)=y(ti )-{circumflex over (θ)}T(ti-1){tilde over (ω)}(ti)description="In-line Formulae" end="tail" where {circumflex over (θ)} is a vector representing the set of model parameters bk; and in step (c3) the parameters of the model are revised in accordance with the following formula: description="In-line Formulae" end="lead"{circumflex over (θ)}(ti)={circumflex over (θ)}(ti)ε(ti) description="In-line Formulae" end="tail" where μ is a vector calculated from the following formula: 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 rj 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 rj(ti) and the corresponding measured output y(ti) at each of a predetermined number n of times t1 . . . tn earlier than t; (b) initializing the model of the plant, which generates a predicted output ŷ(t) from the set of measurements rj(t), to a predetermined initial model; (c) using each of the predetermined number n of sets of measured inputs rj(ti) and output y(ti) 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 rj(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.