CONFIDENCE BASED ESTIMATION AND DETERIORATION

INDICATION OF ON-LINE MEASUREMENT

Jari Näsi, Aki Sorsa

Control Engineering Laboratory,University of Oulu, P.O. Box 4300, FIN-90014 University of Oulu, Finland

Keywords: Reliability, validation, optimal estimation.

Abstract: In an industrial process, the accuracy and reliability of process creates basics for control system and

ultimately to product uniformity. Measurement results, whether from fast on-line sensors or from sample-

based laboratory analyses, is the key for selecting the method for process control and analysis. Intelligent

and advanced control methods, exploiting measurements, are of no benefit if the measurements cannot be

trusted. This paper presents an estimation method for combining real-time redundant signals, consisting of

sensor data, and analytical measurements. The validation of on-line measurement uses less frequently

updated but more accurate information to validate frequently updated but less accurate on-line

measurements. An estimate of the measured variable is obtained as a weighted average of the on-line

measurements and laboratory analyses. The weighting coefficients are recursively updated in real time when

new analysis and measurement results are available. The calculation of optimal estimate can be used in

several industrial applications for more precise process control. In addition, pre-processed data is used to

calculate a “need for maintenance indicator” to warn the operator for sensor breakdowns, wearing or

deterioration and detect calibration needs. The operator’s workload is reduced in problematic situations

where measurement and validation signals are not convergent, by offering calculated best estimation.

1 INTRODUCTION

The validation means the verification of the

measurement with other information or

measurements. The practical problem is to validate a

continuous measurement using its previous values or

a corresponding laboratory analysis as a reference.

Laboratory analyses are commonly used in process

industry, but the purpose of the use and criticality of

analyses vary. Normally, analyses are used either to

monitor the process, or to validate on-line

measurements. If based solely on laboratory

analysis, process control becomes inefficient

because of the infrequency of analyses. Several

factors make it difficult to validate sensor data and

to calculate confidence levels. The difference

between slight sensor failures and noisy sensor

readings is not easy to verify if the process and time

delay in reference analysis is not known. On the

other hand, laboratory analysis improves control

when it is used to validate and correct on-line

measurements. The calculation of the optimal

estimate has three parts: pre-processing, confidence

level estimation and the calculation of the estimate

(Figure 1).

Applied maximum and minimum limits are

defi

ned by process dynamics, not by analyzers

maximum measuring range. In this way, the

accepted area of the operation becomes more

realistic. Fuzzy limits are used for softening change

between reliable and non-reliable values. Example

data consists redundant sensor data from electrolytic

zinc production process, where analyzer measures

Fe

2+

content in the dissolution reactor. Deterioration

of the measurement device causes drifting and

occasional breakdowns. Measured value is used for

process monitoring, not for control and if working

properly, it gives useful information about process

condition.

340

Näsi J. and Sorsa A. (2005).

CONFIDENCE BASED ESTIMATION AND DETERIORATION INDICATION OF ON-LINE MEASUREMENT.

In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and

Control, pages 340-343

DOI: 10.5220/0001163703400343

Copyright

c

SciTePress

Classifier

Bias

correction

Confidence

level

Confidence

level

Confidence

level

based

reasoning

Laboratory

analysis

Continuous

signal

Signal validation

Optimal

estimate

Absolute and

Fuzzy limits

Det eriorat ion

indicator

Classifier

Bias

correction

Confidence

level

Confidence

level

Confidence

level

based

reasoning

Laboratory

analysis

Continuous

signal

Signal validation

Optimal

estimate

Absolute and

Fuzzy limits

Det eriorat ion

indicator

Figure 1: Different steps in the signal processing to the

optimal estimate

The confidence levels are estimated for both the

measurement and laboratory analysis. The

measurement’s confidence level is determined by

two criteria: change between measurements and the

deviation from the laboratory analysis. The

confidence level of the laboratory analysis depends

only on time since the analysis has been done. The

optimal estimate is calculated according to an

algorithm by using the pre-processed measurement,

laboratory analysis and the confidence levels.

Various control methods can be effective in

dealing with uncertain measurements, but

measurement noise and errors effect on their

performance. Outliers constitute a challenging

problem and detecting them is much easier for

human than for a computer. The self-validating

(SEVA) approach provides tools for the single

sensor signal validation (Henry, 1993). The

approach utilizes sensor fault detection and

uncertainty estimation to produce advanced

information about the measurement. Multi-sensor

data fusion can be used, when multiple sensors are

used to measure the same variable (Luo et al., 2002).

Thus a measurement is validated with other sensor

data.

In redundancy-based approaches, duplicate

measurements or a process model is used to generate

a residual vector by comparing the measurements

from multiple sensors or output of the process model

and actual measurements. The residuals can be

examined with many methods to make a decision

about the sensor malfunctioning. Such methods

include multi-sensor data fusion, voting systems,

expert systems, artificial intelligence, fuzzy logic

and neural network approaches (Amadi-Echendu,

1996). Model based fault detection and identification

(FDI) methods are thoroughly discussed in survey

papers by Isermann (1984) and Frank (1990). Voting

systems require three or more measurements of same

variable (Willsky, 1976). The deviating opinion

(measurement) is neglected as the decision is made

based on the majority of similar measurements. The

voting system may include advanced characteristics

as the differentiation between process upsets and

sensor failures may be included in the reasoning

(Stork & Cowalski, 1999).

2 OPTIMAL ESTIMATE

In this paper, the measurement validation problem is

converted into the calculation of an optimal estimate

of the measured variable based on the confidence

levels of the actual and reference measurements. The

calculation of the optimal estimate is divided into

signal validation, confidence level estimation and

calculation of the estimate.

2.1 Absolute and fuzzy limits

Absolute limits define the scale, where process

parameter can vary under normal process conditions.

The upper limit gives the maximum reliable value. If

measurement device gives larger values than this,

they should be ignored and replaced with other

process information. Similarly, smaller values than

minimum should be replaced. The limits can be

defined manually by experts, but they can be also

defined automatically from process data.

Fuzzy limits are used to narrow the area limited

by absolute limits and for softening change between

reliable and non-reliable measurement. Efficient use

of fuzzy limits, combined to the absolute limits and

reference measurement creates basics to the reliable

calculation of “optimal” signal (Figure 2).

2.2 Signal validation

After the definition of the absolute and fuzzy limits,

the classifier (Figure 1) detects the outliers and

deviating values and replaces them with an estimate.

If the measured value is inside the fuzzy limits, the

classifier considers it valid. In this case, the weight

of the measurement is 1. In the case of an outlier,

(measured value is beyond the absolute limits) the

weight of the measurement is 0 and the output of the

classifier is either the previous measured value or

the latest reference analysis. If the measurement is

inside the fuzzy zones, the output from the classifier

is a weighted average of the actual measured value

and the reference value. In this fuzzy zone, the

weight of the measurement decreases from 1 to 0.

CONFIDENCE BASED ESTIMATION AND DETERIORATION INDICATION OF ON-LINE MEASUREMENT

341

In the case of a gradual degradation (e.g., a sensor

drift), the faulty signal is not immediately

abandoned but its influence on measurement

estimation is diminished as a function of change and

deviation from the laboratory analysis. This is

achieved by decreasing the relative weight of the

degraded signal. When the degradation strengthens,

monotonic function diminishes its relative weigh.

2.3 Confidence levels and calculated

estimate

As earlier described, the pre-processing provides

practical signal for actual processing. The

confidence levels are calculated for analyzer and

laboratory analysis signals (Figure 2). The optimal

estimate is then calculated using the pre-processed

signals and confidence levels.

A bs o lu te lim it

Fuzzy limit

Measurem ent

Laboratory analysis

E s tim ate

A bs o lu te lim it

Fuzzy limit

Measurem ent

Laboratory analysis

E s tim ate

Figure 2: Limits, on-line measurement, laboratory analysis

and calculated estimate

The confidence level of the measurement is

determined by two criteria: the deviation of the

measurement from the laboratory analysis and

the

change between consecutive measurements. The

confidence level of laboratory analysis depends only

on time. When a new result is available, its

confidence level is 1. The aging of the analysis

decreases the confidence level closer to 0. However,

the laboratory analysis must be trusted (at least a

little) always and therefore its confidence level never

decreases to 0.

In the calculation of an estimate, the pre-processed

signal, laboratory analysis and calculated confidence

levels are used. Estimate is trusted always when its

confidence level is relatively high (the confidence

level of the laboratory analysis is decreased by a

coefficient (1 – C

m

)). The estimate (X

e

) is calculated:

lmm

llmcm

e

CCC

XCCXC

X

)1(

)1(

−+

−+

=

, where

C

m

is confidence level of the measurement

C

l

is confidence level of the laboratory analysis,

X

c

is validated measurement and

X

l

is laboratory analysis.

3 DETERIORATION INDICATOR

Information produced in the calculation of the

optimal estimate is used also for calculation of on-

line deterioration (need for maintenance) indicator.

Pre-processed data sets are combined in the

validation block, where difference between on-line

measurement and laboratory analysis is calculated

and changes in the bias error are turned to the on-

line deterioration indicator. In these cases, drift in

the indicator value shows on-going deterioration in

the measuring device (Figure 3).

A more sophisticated way to estimate changes in

the deterioration indicator is to calculate changes in

the measurements standard deviation (Figure 4). As

long as a measuring device works properly, standard

deviation should stay nearly constant.

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Figure 3: Bias error- based deterioration indicator,

calculated from on-line measurement and laboratory

analysis showing deterioration and breakdown. Data set

represents one week time period from real process

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Figure 4: Standard deviation- based deterioration indicator

to the same data as in Figure 3

Results from the indicator fall into two

categories: need for calibration and warning for

breakdown — depending on how the application is

adjusted. Beginning deterioration is compensated in

the pre-processing and in the calculation of the

estimate, but after a certain point confidence values

and confidence of the estimate descends. Warnings

may contain information about problems in the

measuring device (on-line analysis is not reliable

and estimate is based mainly to the laboratory

analysis).

4 CONCLUSIONS

Used data validation and estimation combines

information from laboratory analyses and

measurement device to calculate the optimal

estimate of the actual process variable. This

reconstructed data is then brought forward to

operators or used by the controller (the estimate can

be applied as a part of advisory or direct control

strategy depending on the target process).

Used limits in data validation are proven to be

critical, since too strict limits give laboratory

analyses unnecessarily big weight and lose fast and

short-time changes in the process. On the other

hand, limits too wide allow faulty measurement

device readings to be accepted and utilized in further

process control (malfunctions of the measurement

device are not differentiated from process upsets). If

a faulty measurement device is detected

(measurement device readings change more rapidly

than process dynamics will allow or signal is not

inside the area of operation) estimation algorithm

tends to follow laboratory analysis and only when

possible takes advantage from the measurement

device data.

Output of the classifier (weighted estimate of the

measured variable) is generated in the real time and

the admissible range is adjusted as a function of

process conditions. The effects of the failures and

measurements oscillation are taken into account by

diminishing their relative weight. Real data sets have

been collected from an operating plant.

A model of the physical process or expert

knowledge is not needed for successful calculation

of the estimate. Only prominent data period of

measurement device data and analytical

measurements are needed for basis of the process

parameters estimation. The pre-processing

manipulates measurements that are beyond the fuzzy

limits of the variable’s dynamic range and corrects

the static error between measurement device data

and laboratory readings.

The confidence level of the measurement is

determined by the deviation of the measurement

from the laboratory analysis and by change between

individual measurements. Respectively the

confidence level of laboratory analysis is only time-

dependent. The weight coefficients of the on-line

signal and laboratory measurements are adaptively

updated.

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Amadi-Echendu, J.E., 1996. Concepts for Validating

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Frank, P.M., 1990. Fault Diagnosis in Dynamic Systems

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Henry, M.P. & Clarke, D.W., 1993. The Self-validating

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Isermann, R., 1984. Process Fault Detection Based on

Modelling and Estimation Methods – A Survey.

Automatica, vol. 20, no. 4, 387-404.

Luo, R.C., Yih, C.-C. & Su, K.L., 2002. Multisensor

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Willsky, A.S., 1976. A Survey of Design Methods for

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