Projection Methods to Impose Equality Constraints on Algebraic Models

A computer implemented method for generating an improved predictive model of a process system, the method comprising:

• receiving data representing a process system in an industrial plant, the received data including independent variables and dependent variables, said receiving being by one or more digital processors;
• building an objective function configured to determine a linear model for the received data, said building being automatically performed by the one or more processors;
• receiving, by the one or more processors, at least one constraint equation, the at least one constraint equation representing at least one physical property of the process system;
• constructing, by the one or more processors, a numerical optimization problem whose input is based on a combination of the objective function and the received at least one constraint equation;
• generating an algebraic model having sets of model coefficients defining an algebraic relationship between the independent variables and each dependent variable, wherein the model coefficients are solutions of the numerical optimization problem, and wherein the generated model provides improved predictions of behavior of the process system that satisfy the at least one physical property, said generating being automatically performed by the one or more processors;
• and
• executing the generated model such that predictions of behavior of the process system are produced and applied in the industrial plant.

A computer implemented method for generating an improved predictive model of a process system, the method comprising:

• receiving data representing a process system in an industrial plant, the received data including independent variables and dependent variables, said receiving being by one or more processors;
• receiving, by the one or more processors, at least one constraint equation, the at least one constraint equation representing at least one physical property of the process system;
• determining at least one chosen dependent variable, said determining being responsively performed by the one or more processors;
• generating a linear model for the received data excluding the determined at least one chosen dependent variable, said generating being automatically performed by the one or more processors;
• solving the received at least one constraint equation for the determined at least one chosen dependent variable, said solving being automatically performed by the one or more processors;
• forming a model for the at least one chosen dependent variable using the solved at least one constraint equation and the generated linear model for the received data excluding the at least one chosen dependent variable, said forming being automatically performed by the one or more processors;
• generating an algebraic model comprised of the formed model for the at least one chosen dependent variable and the generated linear model for the received data excluding the at least one chosen dependent variable, the generated algebraic model providing improved predictions of behavior of the process system that satisfy the at least one physical property, said generating the algebraic model being automatically performed by the one or more processors;
• and
• executing the generated algebraic model such that predictions of behavior of the process system are produced and applied in the industrial plant.

A computer-based modeling system that generates an improved predictive model of an industrial process, the system comprising:

• a processor;
• and
• a process modeler executable by the processor and configured to:
• receive data representing a subject physics-based or chemistry-based process in an industrial plant, the received data including independent variables and dependent variables;
• receive at least one linear equality constraint equation having constraint coefficients, the at least one linear constraint equation representing at least one physical property of the subject process;
• automatically construct a constraint matrix including the constraint coefficients;
• automatically construct a coefficient matrix including potential coefficients, the potential coefficients defining linear relations between the independent variables and the dependent variables of the received data;
• responsively define, as constrained coefficients, the potential coefficients that make the product of the constraint matrix and the coefficient matrix zero;
• and
• automatically generate an algebraic model for the received data, the algebraic model having model coefficients defining an algebraic relationship between the independent variables and the dependent variables, wherein the model coefficients are constrained coefficients resulting from said defining, and wherein the generated model, upon execution, provides improved predictions of behavior of the subject process that satisfy the at least one physical property.

A non-transitory computer program product for generating an improved predictive model of an industrial process, the computer program product comprising:

• a computer-readable medium with computer code instructions stored thereon, the computer code instructions, when executed by a processor, causing an apparatus associated with the processor to:
• receive data representing a subject physics-based or chemistry-based process in an industrial plant, the received data having independent variables and dependent variables;
• receive at least one linear equality constraint equation having constraint coefficients, the at least one linear constraint equation representing at least one physical property of the subject process;
• construct a constraint matrix including the constraint coefficients;
• construct a coefficient matrix including potential coefficients, the potential coefficients defining linear relations between the independent variables and the dependent variables of the received data;
• define, as constrained coefficients, the potential coefficients that make the product of the constraint matrix and the coefficient matrix zero;
• and
• generate an algebraic model for the received data, the generated model having model coefficients defining an algebraic relationship between the independent variables and the dependent variables of the received data, wherein the model coefficients are the constrained coefficients resulting from the defining, and wherein the generated model provides improved predictions of behavior of the subject process that satisfy the at least one physical property.