(201d) Stochastic Modeling Using Virtual Training Sets

ABSTRACT for AIChE
2016 Spring Meeting

Stochastic
Modeling using Virtual Training Sets

James C Cross III

The MathWorks, Inc.

james.cross@mathworks.com

617-605-5818

In a typical process plant, instrumentation data are archived,
providing a rich set of structured data that can be exploited for system
identification, efficiency optimization, and anomaly detection.  Combining
these data with process simulation results, plant operating heuristics, and
economic parameters, a detailed operating model affording the prediction of
output and associated expenses can be built to guide planning decisions.  This
is fairly common practice.

A more complicated situation arises when an organization
must decide how to operate a portfolio of assets producing the same products,
for example to maximize profit over a known time horizon for a specified total
output level.  Examples include resource extraction from oil and gas wells,
production of electricity from a pool of power generators, and water resources
management.  While most plants and other process equipment are designed to
operate consistently at or near design capacity, market fluctuations dictate
the need for part-load strategies and accordingly these types of analyses, as
has happened in recent times with the downturn in oil prices. 

To support planning, a single answer from a predictive model
is inadequate.  It can stand as a reference scenario, however diligent risk
management demands that the probability of alternative answers, such as would
arise from uncertainties associated with exogenous variables, be computed and
compared to the reference.  One could conceptually define a collection of
scenarios, and use the detailed models for all of the plants in the asset pool to
compute the global optimum for each scenario.  While this is appealing, it is
invariably impractical – the level of complexity of accurate plant models, the duration
of planning horizons, and the multitude of operating constraints combine to
make this an exceptionally burdensome computational challenge.   Is there a way
around this?

The application of machine learning methodologies to real
data sets has seen tremendous growth in the past decade.  In this work a machine
learning approach is used to extract important relationships from the optimized
operating scenarios calculated by the detailed optimization model.  The
simplified model that results from using these “virtual training sets” captures
the most influential factors embedded in the detailed model, and can be used to
run simulations across a statistically significant number of scenarios in a
reasonable time.

This talk elaborates the approach and offers a framework. 
The methodology is motivated through use of a simple illustrative example,
which reveals both the advantages and limitations of the approach.  Select open
questions and opportunities for further work are highlighted.