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APMonitor Modeling Language

John HedengrenBrigham Young University

Advanced Process Solutions, LLChttp://apmonitor.com

APMonitor.com Advanced Process Solutions, LLCOct 14, 2012

Overview of APM

Software as a service accessible through: MATLAB, Python, Web-browser interface Linux / Windows / Mac OS / Android platforms

Solvers APOPT1, BPOPT1, IPOPT2, SNOPT3, MINOS3

Problem characteristics: Large-scale Nonlinear Programming (NLP) Mixed Integer NLP (MINLP) Multi-objective Real-time systems Differential Algebraic Equations (DAEs)

1 – APS, LLC2 – EPL3 – SBS, Inc.

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Overview of APM

Vector / matrix algebra with set notation Automatic Differentiation

Exact 1st and 2nd 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


Unique Features of APM

Initialization with nonlinear presolve

Explicit variable substitution every function call

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Intermediate

Variables

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Unique Features of APM

Model development workflow

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

Steady State Dynamic Sequential

Simulate 1 4 7

Estimate 2 5 -

Optimize 3 6 -


Solver Benchmarking – Hock-Schittkowski (116)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

90

100

Not worse than 2 times slower than the best solver ()

Per

cent

age

(%)

APOPT+BPOPTAPOPT1.0

BPOPT1.0

IPOPT3.10

IPOPT2.3

SNOPT6.1MINOS5.5


Solver Benchmarking - Dynamic Optimization (37)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

90

100


Per

cent

age

(%)

APOPT+BPOPTAPOPT1.0

BPOPT1.0

IPOPT3.10

IPOPT2.3

SNOPT6.1MINOS5.5


Solver Benchmarking – SBML (341)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510

20

30

40

50

60

70

80

90

100


Per

cent

age

(%)

APOPT+BPOPTAPOPT1.0

BPOPT1.0

IPOPT3.10

IPOPT2.3

SNOPT6.1MINOS5.5


Computational Biology

Drug treatment and discovery – large-scale models

05

1015

1.9

1.95

21

2

3

4

5

6

7

Log(

Viru

s)

HIV Virus Simulation

time (years)Log(kr1)

1.828

2.364

2.899

3.435

3.970

4.506

5.041

5.576

6.112

6.647

Click to edit Master title styleBiological Kinetic Models Modestly Sized

0

20

40

60

80

100

120

# of M

odels

# of Physical Entities

Mean = 20Median = 10

Model sizes from 409 curated models in the Biomodels repository (http://www.ebi.ac.uk/biomodels-main/)

Click to edit Master title styleModel Size Limited by Tools

Large ErbB signalling model (~504 physical entities)* Parameter estimation (simulated annealing) took “24 hours

on a 100-node cluster computer”

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

*Chen et al. Mol Syst Biol. 2009;5:239 .


Smart Grid Energy Systems


Solid Oxide Fuel Cells

Power to GridFuel


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 OperationsReliability TargetsRegulatory ReportsMaximize EconomicsTraining Simulators


Engineering in Remote Locations


Safe, environmentally friendly, and economic operations

Environmental Impact

Safety: Velocity of Inlet Waste Gas

Environmental: Emission Levels

Safety: LEL of Waste Gas

Economic: Fuel Costs

Economic: Size / Insulation


Unmanned Aerial Systems


UAS System Dynamics

Cable-drogue dynamics using Newton 2nd law


Dynamic System Example

ModelParameters

! time constanttau = 5! gainK = 2! manipulated variableu = 1

End ParametersVariables

! output or controlled variablex = 1

End VariablesEquations

! first order differential equationtau * $x = -x + K * u

End EquationsEnd Model


0 2 4 6 8 10 12 14 16 18 201

2

3

4

Man

ipul

ated

uopt

0 2 4 6 8 10 12 14 16 18 200

5

10

15

Con

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Optimization Under Uncertainty

Conservative movement based on worst case CV

Upper Limit


Selecting a Model for Predictive Control

Many model forms Linear vs. Non-linear Steady state vs. Dynamic Empirical vs. First Principles

Select the simplest model Accuracy requirements

Steady State Gain Dynamics – Time to Steady State

Speed requirements PID < Linear MPC < Nonlinear MPC

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Friction Stir Welding

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


Getting Started with APM

Download Software at APMonitor.com Bi-weekly Webinars


Applications Deployed for Real-time Systems


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

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