Herman J. Woltring

12-07-1989, 04:47 AM

Dear Biomch-l readers,

Yesterday, I received a copy of Bengt Carlsson's PhD-thesis from Uppsala in

Sweden. This is the most recent result of a long-standing research programme

in optimal numerical differentiation of noisy data, originally started by Lars

Gustaffson & Haakan Lanshammar in the context of gait analysis and inverse

dynamic modelling (ENOCH - An integrated system for measurement and analysis of

human gait; PhD-thesis, Report UPTEC 7723R, Uppsala University, Uppsala, Sweden

1977). If you wonder why I should mention this: when I sent my own PhD-thesis

to Haakan in 1977, he replied with a letter explaining that he had valid rea-

sons for not being present at my public defense as apparent from his enclosure.

The enclosed thesis indicated that he was performing his public defense at the

same day as I was doing mine ...

Published versions of part of Haakan's work are available as

(1) On practical evaluation of differentiation techniques for human gait

analysis. Journal of Biomechanics 15(1982), 99-105.

(2) On precision limits for derivatives calculated from noisy data.

Journal of Biomechanics 15(1982), 459-470.

Hans Furn'ee's thesis recently announced on Biomch-L was largely influenced by

this work. One point of interest raised at Hans' public examination is the dif-

ference between accuracy and precision or resolution. Accuracy refers to bias-

es, i.e. the difference between a true value and an expected, observed value

(e.g., the mean of a large number of measurements); precision refers to the

(usually root-mean-square) difference between an observed and expected mean

value. It is precision which is addressed in Lanshammar's model for noise

influence assessment in differentiation, not accuracy. Thus, wide-band meas-

urement noise is accomodated by these models, but correlated skin-motion arte-

facts when measuring movement from externally affixed markers are not.

Bengt Carlsson informed me today that he has some copies of his thesis for

interested Biomch-L readers.

Herman J. Woltring, Eindhoven.

-----------------------------------

Thesis title: DIGITAL DIFFERENTIATING FILTERS AND MODEL BASED FAULT DETECTION

By: Bengt Carlsson, Automatic Control and Systems Analysis Group,

Department of Technology, Uppsala University, Box 534, S-751 21

Uppsala, Sweden. EMAIL: BC@SIGURD.SUNET.SE

Doctoral dissertation to be publicly examined in room 047 at the

Department of Technology, Uppsala University, on December 22, 1989

at 10.15 a.m., for the degree of Doctor of Technology.

Opponent: Professor Lennart Ljung, Linkoepings Univ., Sweden.

ABSTRACT

Carlsson, B., 1989. Digital differentiating filters and model based fault

detection. Acta Univ. Ups., Uppsala Dissertations from the Faculty of

Science 28}, 215pp., Uppsala. ISBN 91-554-2473-2.

This thesis treats two problems in digital signal processing:

Estimation of the derivative of a noise corrupted signal from discrete-time

measurements and the detection of faults in a dynamical system using an

estimated model.

The first part of the thesisis devoted to the design of digital differentiating

filters. General design strategies and characterizations of differentiating

filters are outlined. A design technique for constructing digital differentia-

ting filters based on stochastic signal and noise models is presented. IIR-

filters which minimize the mean square estimation error are calculated from a

spectral factorization and a linear polynomial equation. The filters can be

designed for prediction, filtering and smoothing problems. Furthermore, a

method for optimizing differentiating FIR-filters in the frequency domain is

presented. Illustrations and comparisons with other methods are provided.

The problem of tracking step changes in the true derivative is also studied.

Methods for detecting parameter changes are investigated and applied to the

differentiation problem. In a practical application, the temperature deriva-

tive of a reactor tank in a nuclear power plant is estimated by a simple

adaptive filter.

The second part of the thesis describes some approaches to off-line fault

detection based on estimated models. In practice, the estimated model is

subject to errors due to measurement noise and model misfit. Some statistical

tests based on standard asymptotic theory for system identification are com-

pared and illustrated. Two cases of model misfit are discussed: nonparametric

static nonlinearities and unmodelled linear dynamics. A proposal for a fault

detection procedure which accounts for undermodelling is given.

Key-words: Digital differentiators, Numerical differentiation,

Estimation, Filter design, Fault detection.

Yesterday, I received a copy of Bengt Carlsson's PhD-thesis from Uppsala in

Sweden. This is the most recent result of a long-standing research programme

in optimal numerical differentiation of noisy data, originally started by Lars

Gustaffson & Haakan Lanshammar in the context of gait analysis and inverse

dynamic modelling (ENOCH - An integrated system for measurement and analysis of

human gait; PhD-thesis, Report UPTEC 7723R, Uppsala University, Uppsala, Sweden

1977). If you wonder why I should mention this: when I sent my own PhD-thesis

to Haakan in 1977, he replied with a letter explaining that he had valid rea-

sons for not being present at my public defense as apparent from his enclosure.

The enclosed thesis indicated that he was performing his public defense at the

same day as I was doing mine ...

Published versions of part of Haakan's work are available as

(1) On practical evaluation of differentiation techniques for human gait

analysis. Journal of Biomechanics 15(1982), 99-105.

(2) On precision limits for derivatives calculated from noisy data.

Journal of Biomechanics 15(1982), 459-470.

Hans Furn'ee's thesis recently announced on Biomch-L was largely influenced by

this work. One point of interest raised at Hans' public examination is the dif-

ference between accuracy and precision or resolution. Accuracy refers to bias-

es, i.e. the difference between a true value and an expected, observed value

(e.g., the mean of a large number of measurements); precision refers to the

(usually root-mean-square) difference between an observed and expected mean

value. It is precision which is addressed in Lanshammar's model for noise

influence assessment in differentiation, not accuracy. Thus, wide-band meas-

urement noise is accomodated by these models, but correlated skin-motion arte-

facts when measuring movement from externally affixed markers are not.

Bengt Carlsson informed me today that he has some copies of his thesis for

interested Biomch-L readers.

Herman J. Woltring, Eindhoven.

-----------------------------------

Thesis title: DIGITAL DIFFERENTIATING FILTERS AND MODEL BASED FAULT DETECTION

By: Bengt Carlsson, Automatic Control and Systems Analysis Group,

Department of Technology, Uppsala University, Box 534, S-751 21

Uppsala, Sweden. EMAIL: BC@SIGURD.SUNET.SE

Doctoral dissertation to be publicly examined in room 047 at the

Department of Technology, Uppsala University, on December 22, 1989

at 10.15 a.m., for the degree of Doctor of Technology.

Opponent: Professor Lennart Ljung, Linkoepings Univ., Sweden.

ABSTRACT

Carlsson, B., 1989. Digital differentiating filters and model based fault

detection. Acta Univ. Ups., Uppsala Dissertations from the Faculty of

Science 28}, 215pp., Uppsala. ISBN 91-554-2473-2.

This thesis treats two problems in digital signal processing:

Estimation of the derivative of a noise corrupted signal from discrete-time

measurements and the detection of faults in a dynamical system using an

estimated model.

The first part of the thesisis devoted to the design of digital differentiating

filters. General design strategies and characterizations of differentiating

filters are outlined. A design technique for constructing digital differentia-

ting filters based on stochastic signal and noise models is presented. IIR-

filters which minimize the mean square estimation error are calculated from a

spectral factorization and a linear polynomial equation. The filters can be

designed for prediction, filtering and smoothing problems. Furthermore, a

method for optimizing differentiating FIR-filters in the frequency domain is

presented. Illustrations and comparisons with other methods are provided.

The problem of tracking step changes in the true derivative is also studied.

Methods for detecting parameter changes are investigated and applied to the

differentiation problem. In a practical application, the temperature deriva-

tive of a reactor tank in a nuclear power plant is estimated by a simple

adaptive filter.

The second part of the thesis describes some approaches to off-line fault

detection based on estimated models. In practice, the estimated model is

subject to errors due to measurement noise and model misfit. Some statistical

tests based on standard asymptotic theory for system identification are com-

pared and illustrated. Two cases of model misfit are discussed: nonparametric

static nonlinearities and unmodelled linear dynamics. A proposal for a fault

detection procedure which accounts for undermodelling is given.

Key-words: Digital differentiators, Numerical differentiation,

Estimation, Filter design, Fault detection.