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APMonitor Modeling Language

John Hedengren Brigham Young University

Advanced Process Solutions, LLC http://apmonitor.com Overview of APM

 Software as a service accessible through:

 MATLAB, Python, Web-browser interface

 Linux / Windows / Mac OS / Android platforms

 Solvers 1 1 2 3 3  APOPT , BPOPT , IPOPT , SNOPT , MINOS

 Problem characteristics: min J (x, y,u, z)  Large-scale  x  s.t. 0  f  , x, y,u, z  Nonlinear Programming (NLP)  t   Mixed Integer NLP (MINLP) 0  g(x, y,u, z)

 Multi-objective 0  h(x, y,u, z) n m m  Real-time systems x, y  u  z 

 Differential Algebraic Equations (DAEs)

1 – APS, LLC 2 – EPL 3 – SBS, Inc.

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Overview of APM

 Vector / matrix algebra with set notation

 Automatic Differentiation st nd  Exact 1 and 2 Derivatives

 Large-scale, sparse systems of equations

 Object-oriented access

 Thermo-physical properties

 Database of preprogrammed models

 Parallel processing

 Optimization with uncertain parameters

 Custom solver or model connections

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Unique Features of APM

 Initialization with nonlinear presolve

minJ(x, y,u) x  s.t. 0 f  ,x, y,u min J (x, y,u)  t  0 g(x, y,u) 0h(x, y,u)  x  minJ(x, y,u) x  s.t. 0 f  ,x, y,u s.t. 0  f  , x, y,u  t  0 g(x, y,u)  t  0 h(x, y,u) minJ(x, y,u) x  s.t. 0 f  ,x, y,u  t  0g(x, y,u) 0h(x, y,u) 0  g(x, y,u) minJ(x, y,u) x  s.t. 0  f  ,x, y,u  t  0  h(x, y,u) 0 g(x, y,u) 0 h(x, y,u)

 Explicit variable substitution every function call min J (x, y,u) min J (x, y,u) Intermediate s.t. y1  g1(x,u)  x  Variables s.t. 0  f  , x, y,u 0  g (x, y , y ,u)  t  2 1 2 0  g(x, y,u)  x  0  f  , x, y1, y2 ,u 0  h(x, y,u)  t 

0  h(x, y1, y2 ,u)

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Unique Features of APM

 Model development workflow Steady State Dynamic Sequential Simulate147 Estimate 2 5 - Optimize 3 6 -

 Solve higher index DAEs (Index 3+ with APM)

 Index-1 only (e.g. MATLAB ode15s)

 Index-1 + Index-2 Hessenberg (e.g. DASPK)

 Classes of problems

 LP, QP, NLP, DAE

 MILP, MIQP, MINLP, MIDAE

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Solver Benchmarking – Hock-Schittkowski (116)

100

60 APOPT+BPOPT APOPT 50 1.0 BPOPT 40 1.0 Percentage (%) IPOPT 3.10 30 IPOPT 2.3 SNOPT 20 6.1 MINOS 5.5 10

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Not worse than 2 times slower than the best solver ()

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Solver Benchmarking - Dynamic Optimization (37)

100

60 APOPT+BPOPT APOPT 1.0 50 BPOPT 1.0 IPOPT 40 3.10 Percentage (%) IPOPT 2.3 30 SNOPT 6.1 MINOS 20 5.5

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Not worse than 2 times slower than the best solver ()

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Solver Benchmarking – SBML (341)

100

70 APOPT+BPOPT APOPT 1.0 60 BPOPT 1.0 IPOPT 50 3.10

Percentage (%) IPOPT 2.3 40 SNOPT 6.1 MINOS 30 5.5

10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Not worse than 2 times slower than the best solver ()

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Computational Biology

 Drug treatment and discovery – large-scale models

HIV Virus Simulation 6.647

7 6.112

6 5.576

5 5.041 4 4.506

Log(Virus) 3 3.970 2 3.435 1 2 2.899

1.95 2.364 15 10 5 1.828 Log(kr ) 1.9 0 1 time (years)

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC BiologicalClick Kinetic to edit Models Master Modestly title style Sized

120 Mean = 20 100 Median = 10 80

Models 60

of 40 #

# of Physical Entities

Model sizes from 409 curated models in the Biomodels repository (http://www.ebi.ac.uk/biomodels-main/) ModelClick Size toLimited edit Master by Tools title style

We need better tools (parameter estimation, optimization) to deal with large models!

 Large ErbB signalling model (~504 physical entities)*  Parameter estimation (simulated annealing) took “24 hours on a 100-node cluster computer” *Chen et al. Mol Syst Biol. 2009;5:239 . Smart Grid Energy Systems

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Solid Oxide Fuel Cells

Fuel Power to Grid

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Flow Assurance for Oil and Gas Industry

 Fouling and Plugging largest loss category

 Billions $$$ per year in lost revenue

 Predictive Analytics

 Real-time or Off-line Monitoring Solution

 Empirical and First Principles Models

Safe Operations Reliability Targets Regulatory Reports Maximize Economics Training Simulators

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Engineering in Remote Locations

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Environmental Impact

 Safe, environmentally friendly, and economic operations

Safety: Velocity of Inlet Waste Gas

Safety: LEL of Waste Gas

Economic: Fuel Costs Environmental: Emission Levels

Economic: Size / Insulation

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Unmanned Aerial Systems

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC UAS System Dynamics

nd  Cable-drogue dynamics using Newton 2 law

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Dynamic System Example

Model Parameters ! time constant tau = 5 ! gain K = 2 ! manipulated variable u = 1 End Parameters Variables ! output or controlled variable x = 1 End Variables Equations ! first order differential equation tau * $x = -x + K * u End Equations End Model

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Optimization Under Uncertainty

4 u Conservative movement based on opt 3 worst case CV

2 Manipulated

1 0 2 4 6 8 10 12 14 16 18 20

15 x Upper Limit opt 10

Controlled 5

0 0 2 4 6 8 10 12 14 16 18 20

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Selecting a Model for Predictive Control

 Many model forms Continuous Form (SSc )  Linear vs. Non-linear x  Ax  Bu  Steady state vs. Dynamic y  Cx  Du

 Empirical vs. First Principles Discrete Form (SSd )  Select the simplest model x[k 1]  Ad x[k] Bd u[k]

 Accuracy requirements y[k]  Cd x[k] Dd u[k]  Steady State Gain Nonlinear Model  Dynamics – Time to Steady State 0  f x, x,u, p,d  Speed requirements

 PID < Linear MPC < Nonlinear MPC 0  g(x,u, p,d) 0  h(x,u, p,d)

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Friction Stir Welding

 A rotating tool creates heat and plasticizes the metal. This allows the metal to be “stirred” together

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Getting Started with APM

Download Software at APMonitor.com Bi-weekly Webinars

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Applications Deployed for Real-time Systems

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Future Development Plans

 APM Modeling Language

 MI-DAE systems

 Active Development Efforts

 Mixed Integer solvers that exploit DAE structure

 Interfaces to other scripting languages

 Industrial and Academic Collaborators

 APOPT and BPOPT MINLP solver development

 Additional information at INFORMS session WC04

Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC