(185z) Quantitative Risk Assessment of Soft Sensor Predictions Using Fast PDF Estimation

Soft sensors (also
referred to as virtual sensors) are algorithms that provide estimates of unmeasurable
quantities, based on mechanistic/empirical models and on experimental
measurements of other measurable quantities. More specifically, consider a
process including both measurable and unmeasurable variables, and assume we can
build a parametric model of such process. The rationale of conventional soft
sensors involves two steps in series: (I) calculation of the optimal values of the
most important parameters of the process model from prior and/or current data
and (II) use of the resulting model to compute estimates of some key unmeasurable
process variables.

Virtual sensors find
application in many different industrial sectors, including but not limited to
the chemical and pharmaceutical industry, and can be utilized for both
monitoring and closed-loop control purposes. In chemical plants, they are
responsible for most of the inferential composition measurements, e.g. top/bottom
tray composition in distillation columns^[1], and may as well be used
to detect fouling and catalyst deactivation issues. In the pharmaceutical
sector, soft sensors are equally important because they allow not only
estimation of key unmeasurable process variables, e.g. API (Active
Pharmaceutical Ingredient) temperature in freeze-drying processes^[2],
but also indirect evaluation of essential product quality indicators, e.g. dosage
API loading or tablet tensile strength.

Conventional virtual
sensors only provide point estimates of unmeasurable process variables, possibly
complemented with minimal statistical information. Typically, the latter
consists of the variance on the estimates of the unmeasurable variables of
interest, computed under restrictive assumptions: (I) use of a linear/linearized
version of the full-fledged process model and (II) presence of random uncorrelated
errors on the measurements of the (measurable) process states. Although these
conventional virtual sensors often perform satisfactorily in many process
applications, pharmaceutical systems may require more advanced soft sensors,
which provide extensive statistical information on the estimates of the
unmeasurable process variables of interest. This type of information may be
used for risk analysis purposes and, specifically, for quantitative risk
assessment.

Figure 1:
Simplified architecture of the new type of soft sensor proposed in this work.

This paper reports on
the development of a new type of soft sensor, which allows estimation of the marginal
PDFs (Probability Density Function) of unmeasurable process variables, at a
reasonable computational cost. This new type of sensor relies on a combination
of dynamic data reconciliation techniques^[3] and fast PDF estimation
strategies^[4] (see Figure 1). Specifically, first, all
the available measurements of the manipulated variables, of the disturbances
and of the (measurable) states of the process are used to compute the parameters
of the process model as well as the reconciled trajectories of manipulated
variables and disturbances. Then, these intermediate results are sent to a fast
PDF estimation algorithm, which computes the joint PDF of the model parameters.
Finally, this joint PDF is converted into the marginal distributions of the unmeasurable
process variables of interest, using numerical integration techniques () and/or a combination
of ad-hoc mapping strategies and dynamic simulation (). Note that, although
this new type of virtual sensor makes use of parallel computing techniques, it may
not be suitable for closed-loop control purposes. On the other hand, it is
valuable for monitoring purposes, allows rapid identification of off spec
product in continuous manufacturing lines, and provides very useful information
for risk analysis/assessment.

The new type of soft
sensor, proposed in this work, is demonstrated on a pilot scale plant for continuous
production of tablets, which includes multiple feeders and blenders, a roller
compactor and a tablet press. More specifically, we show how this new sensor
can be employed to estimate the marginal PDFs of several important unmeasurable
process variables, at an acceptable computational cost.

References

1. Ahmadreza G., Mehdi
S., Gholamabbas S., 2015, Soft Sensor Development for Distillation Columns
Using Fuzzy C-Means and the Recursive Finite Newton Algorithm with Support
Vector Regression (RFN-SVR), Industrial & Engineering Chemistry Research,
54, 12031-12039.

2. Bosca S., Barresi
A.A., Fissore D., 2014, Use of soft sensors to monitor a pharmaceuticals
freeze-drying process in vials, Pharmaceutical Development and Technology, 19,
148-159.

3. Martinez Prata D.,
Schwaab M., Lima E.L., Pinto J.C., 2009, Nonlinear dynamic data reconciliation
and parameter estimation through particle swarm optimization: Application for
an industrial polypropylene reactor, Chemical Engineering Science, 64,
3953-3967.

4. Rossi F., Mockus L.,
Manenti F., Reklaitis G., expected 2018. Assessment of accuracy and computational
efficiency of different strategies for estimation of probability distributions
applied to ODE/DAE systems. Computer Aided Chemical Engineering, accepted.