Browse Prior Art Database

Model Parameter Identification Methodology to Match Model and Test Data

IP.com Disclosure Number: IPCOM000216000D
Publication Date: 2012-Mar-16
Document File: 5 page(s) / 96K

Publishing Venue

The IP.com Prior Art Database

This text was extracted from a PDF file.
This is the abbreviated version, containing approximately 30% of the total text.

Page 01 of 5

Model Parameter Calibration Method

Submitted as defensive publication

Problem

Model-based design has been growing significantly with the fast development of computer technology, and availability of commercial modeling tools, as well as increased need of reducing prototype build to reduce development cost. However this approach needs high fidelity model that is built with finite element method, but also calibrated to match real hardware characteristics.

Methodology

     The paper proposes a new approach to automate the process of parameter calibration based on the idea of real-time learning of a surrogate model to locally characterize the effects of model parameters to the model outputs, followed by an optimization step to change the parameters with respect to the identified surrogate model.

     The surrogate model is based on the Kalman filter implementation of the Recursive Least Square (RLS) method to on-line estimate the Jacobian approximation of the nonlinear model. The learned surrogate model is then used in an optimizer, which utilizes the Levenberg-Marquardt optimization method to calculate the input update that is the one-step calculation of the optimal direction. The method is implemented by using the readily available QP solvers to guarantee meeting all the constraints that the original method does not explicitly consider.

      The model parameter calibration problem is decomposed to a set of local mappings obtained at specific operating conditions p :

)

u

(

F

y p

= .

(1)

The objective is to find the input vector *


u that minimizes the error:


=
=

N

k

E

||

y

(

k

)

 t || y

2 2


(2)

1

in the presence of measurement noise. We are interested in an approach that guarantees fast convergence due to inherent expensive nature of the calibration experiments, i.e. the evaluation of the mapping between the (1).

We consider a simple surrogate model - linearized time varying (Jacobian) approximation of the nonlinear input- output mapping (1):

)

k

(

u

)

k

(

J

)

k

(

y D =

D


(3)

where

D

(

u

k

)

=

(

u

k

)

(

u

k

1

)

,

D

y

(

k

)

=

y

(

k

)

y

(

k

1

)

D , q


u Î

R

r


Dand


y Î

R


J


=

(

k

y


) s u

/

j

is a time dependent Jacobian matrix calculated by linearization at the operating point

( s

j

,

u

(

k

),

y

(

k

))

j 1 1 Î

Î

[

,

r

],

s

[

,

q

]


.The time varying Jacobian matrix plays the role of a surrogate model approximating the

unknown function )

(

Fp .

u

   It follows from (3) that for a known Jacobian the optimal input update minimizing the cost (2) can be calculated from the pseudoinversion of the Jacobian:

))

k

(

y

y

(

)

k

(

J

)

k

(

u

)

k

(

u

          t − +

+ +

1

=


(4)

where


Page 02 of 5

(

J + =

k

)

J T T

(

k

)(

J

(

k

)

J

(

k

)


+ )


r for q

I

1

r ³ (5i)

(

J + =

k

)

(

J

T

(

k

J

)

(

k

)

+ r for q

I

)

1

J

T

(

k

)

r £ (5ii)

          r in (5), where I is identical matrix of compatible size and r is a small positive constant, is analogous to the Tikhonov regularization matrix and improves the numerical conditioning of the inverse problem.

Diagonal...