Remarks

At the beginning of this chapter, the reasons why testing the estimator with model- based measurements before using real plant data can reveal its potential applicability on a specific problem and the key pieces of information that can be obtained at this stage were presented.

Considering the results obtained with model-based measurements, it can be said that the following points should be at least taken into account when using the estimator with real plant data:

ˆ to improve the estimation of the state of coking of the system, the coking parame- ters should be re-calibrated in real-time increasing the flexibility of the estimator. In fact, given the high dimensionality of the state vector x if compared with the measurement vector y, it is not possible to obtain a good state estimate by just updating the state vector using the available measurements. It is then of funda- mental importance ensure that these measurements will be available in the on-line implementation of the estimator;

ˆ the plant measurements to be supplied to the estimator should be chosen according to their actual availability and their reliability. However, by testing the estimator using model-based measurements, it has turned out that the availability of pressure drop measurements is essential to obtain a good estimate of the state of coking of the furnace;

ˆ the effect of P0 on the results is important only when some ICs for the differential

variables involved in the model are modified. If not, since the simulation starts from clean tube conditions, there is no uncertainty on the initial state of the system; ˆ the choice of Q and R deeply affects the quality of the results that can be obtained

from the estimator. When using real-plant data, a fixed structure for Q and R should be identified in order to ease the on-line implementation of the estimator (i.e. its specification should be independent of the on-line measurements coming from the furnace).

(a) Pressure drop (b) Tube metal temperature

(c) Fuel flow rate (d) Mass fraction of ethane at the outlet

(e) Density of coke layer pass #2 (f ) Total coke deposited (all passes)

Figure 5.7: Results obtained using time-varying control inputs. Red lines: wrong model prediction. Black lines: orignal model prediction. Blue lines: estimator prediction. Specifications given to the estimator: P0 = diag(0.05; 0.05; 0; . . . ; 0), Q = diag(0.05; 0.05; 0.01; . . . ; 0.01), R = diag(1e − 4; 1e −

(a) Feed flowrate (b) Steam flow rate

(c) Coil inlet temperature _{(d) Coil outlet pressure}

Figure 5.8: Normalised time-varying supplied to the estimator. Set of data #1.

Additional problems, such as noise and structural inconsistencies, should be consid- ered when switching to real experimental data. However, knowing a priori the previous remarks has proved to be extremely beneficial for the final success of the project.

Results with real plant data

First, a brief introduction to the main aspects that need to be considered when using real plant data is given. Then, the weaknesses of the original model and how they have been adjusted using the estimator are discussed. The general structure of the model is then presented and the results obtained for all the four sets of data available are shown. The results that involve real plant data have been normalized and sanitized (i.e numbers are removed from axes) for confidentiality reasons.

Finally, a brief discussion on the results obtained is performed.

6.1

Introduction

Testing the estimator using model-generated measurements has proved to be ex- tremely beneficial to obtain a preliminary overview of the potential and the main limi- tations of the EKF on the Furnace model. Some important hints for the on-line imple- mentation of the estimator with real plant data have been obtained at this stage (§5.3). However, lots of complications can arise when real data are supplied to the estimator. First, the availability and reliability of data become a major point of concern (§4.2.3). It has already been pointed out that the availability and reliability of measurements in the real plant strongly depends on the state of repair of the installed measuring devices. The possibility that one or more measurements could not be available at some point of the furnace operation should be considered.

Second, structural inconsistencies in the data can deeply influence the estimator perfor- mance. It will be shown (§6.2) that, in some cases, available data are not consistent with conservation laws (e.g. they do not respect the conservation of mass). Luckily, the degree of confidence in the available data can be tuned modifying the measurement uncertainty covariance, thus reducing the ’weight’ of these inconsistencies on the estimator prediction. Third, when using plant measurements, being able to fix the weaknesses of the original model becomes a critical task to obtain a robust and reliable estimate of the state of the system. All the assumptions made in the original model contribute to the mismatch between its prediction and the plant observations: the task of the estimator is to offset these assumptions with the additional information brought in by the measurement vec- tor.

Finally, the computational performance of the estimator becomes important when its on-line implementation need to be considered. It has already been said (§4.2.6) that the computational time for every prediction step should never be higher than the frequency at which measurements are supplied to the estimator. This should be taken into account when testing the estimator.

As discussed in §4.2.3, the intrinsic use of the estimator is for on-line applications; however, its performance has been tested off-line using four different sets of plant data of the furnace. In the next few sections, the adjustments made to fix the model weaknesses

and the results obtained from the estimator are discussed.