Requirements for the Simulation of Complex Requirements for the Simulation of Complex Heterogeneous...

Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 1

Requirements for the Simulation of Complex Heterogeneous Systems

8th Modelica Conference Dresden March 21, 2011

Peter Schwarz

Formerly withFraunhofer Institute for Integrated Circuits, Design Automation Division EAS Dresden, Germany


1. Properties of complex hetereogeneous systems2. Continuous systems3. Hybrid systems4. Spatially distributed systems5. Further requirements and wishes

6. Outlook

Outline


MagneticActuator

ElektrostaticSensor

MechanicalSensor

Electrical Circuit (analog)

Software:Signal Processing,

Control

Digital Hardware:Signal Processing,

Control

Properties

multi-domain,multi-physics

Time: discrete and continuous

Signal flow:directed and non-directed

Spatially concentrated (lumped) and distributed elements

Naturally partitioned

Complex Heterogeneous System (Example: Technical System)


MagneticActuator

MechanicalSensor

ElektrostaticSensor



Control

Digital Hardware: Signal Processing,

Control

Heterogeneous System

in general: non-directed signal-flow but also some uni-directional interconnections

Ideal: a heterogeneous model for one simulator – but this is not very realistic for large systems


Circuit simulator (analog)

DAE / ODE SimulatorFEM Simulator

MagneticActuator



Control

Digital Hardware: Signal Processing,

Control

Heterogeneous System

ElektrostaticSensor

MechanicalSensor

More realistic: a heterogeneous model and some coupled simulators

Digital simulator, signal processing simulator

in general: non-directed signal-flow but also some uni-directional interconnections



6. Outlook

Outline


x f (x,u, )t= F(x,x,u, ) 0t =

Control system,signal-flow diagram

Electrical circuit, multi-body system, fluidic system, …

Block diagram Multi-pole network (generalized network)

ODE Ordinary Differential Equation (explicit)

DAE Differential-Algebraic Equation (implicit)

Potential

Flow

+

-

Continuous Systems: Directed and Non-Directed Signal Flow


Simulation = sequential processing of statements noticed in correct order by the userMany mathematical algorithms (e.g. RUNGE-KUTTA) in textbooks for solving ODEsODE seems to be the „natural way“ to model the realityFirst DAE solvers

First general-pupose simulation software (e.g. CSMP, CSSL, ACSL) - but oriented on control systems or block diagrams with directed signal flow („block-oriented simulation“)

First simulators for specific technical disciplines (e.g. electrical circuits) with compilers for translating an user-friendly system description (e.g. netlist) into a mathematical model

Two simulation paradigms:

Directed signal flow Non-directed signal flowCausal equations Acausal equations (to be solved simultaneously)Automatic sorting of equations, Formulation of the mathematical description is not trivial:

algebraic loops are not allowed modeling languages and compiler were developed.ODE is the basic model DAE (implicit) is the „natural“ mathematical model Powerful simulation packages Powerful specialized simulators (Spice, ADAMS, …)

Transformation DAE ODE (matrix manipulation, graph sorting, index reduction):very complicated, very time-consuming for nonlinear DAEs, and not successful in some cases

1970

1980

1990

1960

Insight: DAE should be mainly used for „modeling the physical world“

History: Continuous System Simulation


History: Continuous System Simulation Hybrid Simulation

Insight: DAE should be mainly used for „modeling the physical world“- and should be coupled with discrete simulation

Consequences

New modeling languages for hybrid systems: Modelica, VHDL-AMS, …

New modeling paradigm: object-oriented modeling, component-based modeling, physical modeling

New powerful hybrid simulators (mixed-signal simulators in electronics)

New multi-physics libraries

This success is coupled with the Modelica community and its protagonists

Francois Cellier, Hilding Elmqvist, Martin Otter, Peter Fritzson, …and many others from universities, research institutions, and companies

But: ODEs are further used, if possible (control systems; partial transformation DAE ODE)

New application areas: code generation, real-time simulation (difficult on DAE basis: ODE)

1990

2000

2010



6. Outlook

Outline


MagneticActuator

ElektrostaticSensor

MechanicalSensor



Control


Control

continuousanalog

discretedigital

… with respect to time and / or values

Hybrid simulationMixed-signal simulation

Complex Heterogeneous System and Hybrid Simulation


Hybrid = continuous + discrete Structure of the model does nor change during simulation

For „simple systems“: state-of-the-art simulators

Hybrid = continuous + discrete Varying model structure during simulation + varying structure „Exotic applications“, but challenging research topic !

Complicated:- determination of the new system structure- re-formulation of system equations- re-initialization of variables in DAE

Not further considered in this paper

But: serious problems in some heterogeneous system !

Hybrid Systems / Hybrid Simulation


Continuous simulation (ODE, DAE)CSSL, Matlab, MatrixX (ODE); Spice (DAE)

Discrete event simulation (DEVS)GPSS; VHDL and Verilog simulators (electronics)

Extension: improved discrete control mechanisms: state charts, Petri nets

Typical: very large, stiff ODE / DAE,small number of events

Applications: chemical processes, robotics, mechanics, control systems

Extensions to continuous subsystems: Hybrid DEVS; DAE solvers (mixed-signal simulation)

Typical: hugh number of events ( billions ! )event queues, small number of ODEs / DAEs

Applications: manufacturing systems, analog + digital electronics (10 … 100 Mio. digital components)

Dymola, SimulationXMatlab/Simulink/Stateflow/Simscape

MatrixX, NI Labview, MapleSim

VHDL-AMS simulators Verilog-AMS simulators( AnyLogic )

Problem: very fast AND very slow AND very large number of eventssignal changes

Hybrid Systems / Hybrid Simulation - the Roots


UML state diagram

Discrete System: Graphical Description with State Charts (1)

Informal state diagram …extended to hybrid systems

A. Schneider, FhG IIS/EAS

SimulationX

U. Donath, FhG IIS/EAS


Discrete System: Graphical Description with State Charts (2)

State Graph Libraries (Modelica)

Many similar types of diagrams are in use!

No really accepted standard

UML could be considered as a de-facto standard

But: not ambiguous for simulation !!!

Additional definitions are necessary, e.g.:

- priority rules

- separate blocks for event scheduling

and should NOT be tool-dependent !


Example with the hybrid simulator AnyLogic:time-triggerd switching between differential equations

State 1

State 2

1 s 1 s

t in s

x2

x3

1 2 3 4

x1x1x2x3

x1´ = a1*x1 + a2*x2 + a3*x3

x2´ = b1*x1 + b2*x2 + b3*x3

x3´ = c1*x1 + c2*x2 + c3*x3

x1´ = d*x1 + 3

Hybrid Systems and State Charts

Root:x1(0) = 0, x2(0) = 0, x3(0) = 0,a1 = …, … ,d = …

Initial conditions


Complex Heterogeneous System: Timing Behavior

MagneticActuator

ElektrostaticSensor

MechanicalSensor



Control


Control

Time: discrete and continuous time scaleSignals: discrete and continuous valuesSignal activity: extreme large differences

Basis for partitioning !


Synchronization layer

very intensiveinteraction

time-consumingsimulation!

reduced,controlledinteraction

A slow A fast

D fast D slow

Partitioning w.r.t Timing Behavior

Not an academic idea!

It has been realized, e.g., in a SystemC-AMS simulation environment


SystemC-AMS Layer Approach for Synchronization

Introduction to SystemCIntroduction to SystemC--AMS Library PrototypeAMS Library Prototype Thomas Thomas UhleUhle, Karsten , Karsten EinwichEinwich, Fraunhofer IIS/EAS , Fraunhofer IIS/EAS DresdenDresden


Nonlinear DAESolver supporting

the synchronization interface

nonlinear module, node and variable

base classesLinear

behaviour

Linear electrical networks

Linear DAE solver

SystemC-AMS Layer Approach for Synchronization

Introduction to SystemCIntroduction to SystemC--AMS Library PrototypeAMS Library Prototype Thomas Thomas UhleUhle, Karsten , Karsten EinwichEinwich, Fraunhofer IIS/EAS , Fraunhofer IIS/EAS DresdenDresden


Modem IC: Analog + Digital + Software

Voice band 50 Hz … 12 kHz ( … XDSL: 2 MHz )Analog filter 100 kHzDigital filter 64 … 256 MHz clock, oversamplingMany prozessors programmable functionality

The Integrated Circuit has to be simulated together with its environment (simulation of adaptive behavior)

Clock pulses and analog signals:50 Hz up to 256 MHz (events: > 1 GHz)



6. Outlook

Outline


Two- or three-dimensional components (sometimes with very complicated geometryand coupled physical domains)- Solving partial differential equations (PDE) with boundary conditions- Application of FEM simulators (ANSYS, NASTRAN, …)

If the distributed components have to be considered together with other subsystems (sensors, signalprocessing, control, …):

Coupling with a system simulator (co-simulation)Powerful but very time consuming

Alternative:Approximate solution only with the system simulatorNecessary: models with reduced but sufficient

accuracy

-+

Spatially Distributed Components


Model generation: the PDE is numerically approximated by a system ofODEs or DAEs (e.g. with central differences)

-+

Model library

behavioral model(equations)




-+

Model library

structural model(e.g. equivalent network or circuit)

N elements(multi-poles)


electrical transmission line

damped mass-spring element

OR



-+

Model library

N elements(multi-poles)


structural model(e.g. equivalent network or circuit)

Pre-compiler (or manually)

Language construct

for – loop statement

behavioral model(equations)


Modelica.Electrical.Analog;package Lines

"Lossy and lossless segmented transmission lines and LC distributed line models"extends Modelica.Icons.Package;model OLine "Lossy Transmission Line"

Interfaces.Pin p1 ;Interfaces.Pin p2 ;Interfaces.Pin p3 ;SI.Voltage v13;SI.Voltage v23;SI.Current i1;SI.Current i2;parameter Real r "Resistance per meter";parameter Real l "Inductance per meter";parameter Real g "Conductance per meter";parameter Real c "Capacitance per meter";parameter SI.Length length "Length of line";parameter Integer N "Number of lumped segments";

one segment

Spatially Distributed Components: Electrical Transmission Line

C. Clauss, FhG IIS/EAS


protectedBasic.Resistor R[N + 1](R=fill(r*length/(N + 1), N + 1));Basic.Inductor L[N + 1](L=fill(l*length/(N + 1), N + 1));Basic.Capacitor C[N](C=fill(c*length/(N), N));Basic.Conductor G[N](G=fill(g*length/(N), N));

equationv13 = p1.v - p3.v;v23 = p2.v - p3.v;i1 = p1.i;i2 = p2.i;

connect(p1, R[1].p);for i in 1:N loop

connect(R[i].n, L[i].p);connect(L[i].n, C[i].p);connect(L[i].n, G[i].p);connect(C[i].n, p3);connect(G[i].n, p3);connect(L[i].n, R[i + 1].p);

end for;connect(R[N + 1].n, L[N + 1].p);connect(L[N + 1].n, p2);

end OLine;

Segment i

one segment

Spatially Distributed Components: Electrical Transmission Line

C. Clauss, FhG IIS/EAS


Fp

Fn

Fr

Fg

model Thread extends TwoFlange;parameter Integer N=10;parameter Real L = 1;parameter Real c = 1;parameter Real m = 1;parameter Real d = 0;parameter Real[2] s0 = {1, 0};parameter Real[2] v0 = {0, 0};SpringMass springMass[N-1]

(each L=L/N, each c=c,each m=m/(N-1), each d=d);Spring spring(L=L/N, c=c);

initial equationfor i in 1:N-1 loop

springMass[i].mass.s = s0/N*i;springMass[i].mass.v = v0/N*i;

end for;equation

connect(p, springMass[1].p);for i in 2:N-1 loop

connect(springMass[i-1].n, springMass[i].p);end for;connect(springMass[N-1].n, spring.p);connect(spring.n, n);

end Thread;A. Schneider, FhG IIS/EAS

Spatially Distributed Components: Pendulum



6. Outlook

Outline


Further Requirements and Wishes (1) Model interfaces A MUST

Very important for

- Model exchange between different simulation environments (based on the same modelinglanguage, e.g. Modelica)

- Embedding models with own simulation algorithm, independent of the modeling language(executable). This could be interpreted as a special form of co-simulation.

The advanced user needs some simulator-internal data (not only signal values)

Many papers on “Functional Model Interface – FMI” will be presented at this conference!

Co-Simulation A MUST

- Coupling with other commercial simulators (e.g. FEM simulators or Matlab/Simulink)

- Embedding special simulation algorithms:

Handling of very large continuous systems with reduced accuracy (e.g. iterated timing analysis: GAUSS-SEIDEL or GAUSS-JACOBI iteration of DAE)

DEVS algorithms optimized for a hugh number of events

Specialized simulators for hardware components (microcontroller, digital signal processors)


Further Requirements and Wishes (2) Code generation from model description A MUST(Hardware-in-the-loop simulation, controller design)

- Relatively simple from ODEs (see, e.g., Matlab/Simulink, since many years!)

- Complicated from DAEs: many restrictions, internal simplifications or approximations:is the user informed in necessary detail?

- How reliable are the guarantees for maximal sample rate?

Improvements of simulation algorithms Nice to have

- Exploiting the sparseness of large continuous system descriptions, sparse matrix techniques(SMT): symbolical and/or numericalThe effects strongly depend on simulator implementation!

- Handling of events in discrete systems: Very large number of eventsExplicit access to event queues (extensions of the modeling language are mostly necessary!)


Further Requirements and Wishes (3) Export of mathematical model descriptions Nice to have

- Complete set of equations?

Not really the goal of simulator vendors! But interesting for external model simplification, e.g., with the program “Analog Insydes” (symbolic approximation of nonlinear DAE systems)

- Partial model descriptions:

Linearized state equationsODEs or DAEs of linear subsystems

for external postprocessing:calculation of eigenvalues, model order reduction (MOR) for very large systems

Consideration of statistical effects Nice to have

Monte Carlo simulation, advanced statistical analysis (e.g. importance sampling), tolerances and parameter variations, reliability

See the SAE J 2748 VHDL-AMS Statistical Analysis Package“At the beginning of each simulation run the parameters are initialized using random values distributed in accordance with the associated probability density or cumulative density function. Every VHDL-AMS/VHDL simulator that allows for multiple runs can be used for setting up standard Monte Carlo experiments.”

( J. Haase, C Sohrmann, IEEE BMAS Conf. 2009 )


Further Requirements and Wishes (4) Co-existence of different modeling languages Acceptance is a MUST

Modelica VHDL-AMS Verilog-AMS SystemC-AMS ( OSCI standard ) Matlab/Simulink/Stateflow Simscape ???

Consequences for modeling guidelines: model structure, avoiding very special constructs, …

Automatic model transformation does not seem to be very successful

Improved graphical description of discrete systems A MUST

UML could become a de-facto standard, but is not ambiguous for simulation

Additional definitions are necessary for unambiguous simulation:

- As close as possible to the UML standard

- Tool-independent part of the modeling language!

- State-chart libraries are a first step to extended modeling languages


Further Requirements and Wishes (5) Improved user communication and simulator handling Very nice to have

- Error handling, debugging, and tracing: backtracking to the original model source code

- Tracing through the actual state (following the signal flow) and into the past

- Localization of the reasons of numerical problems and errors (overflow, extreme stiffness, infinite iteration loops, higher index DAE, …) - combined with backtracking to the original modelsource code

- Breakpoints and restart from different breakpoints

Coupling simulation with formal verification Nice to have

Goal: detect as many as possible errors without simulation – but use simulation if necessary

Principles (only some examples):

- Simple syntax check of model source code

- More sophisticated model analysis (model checking)

- Searching for deadlocks and infinite loops in Finite State Machines or PETRI nets

- Assertion-based simulation



6. Outlook

Outline


Outlook (1)A very interesting system simulation scenario:

- Large system of individuums (each one may be a multi-physics system or a very simple object)

- The individual systems have their own control algorithms and exchange information with their environment

- There are some global control algorithms

- The location of the individuums and the communication between them may be organized worldwide (delayed information)

- The individuums may switch off from / on to the community (“system with varying structure”)

- System monitoring, evaluation, control, and exchange of information need very large computational power (grids, clouds)

- Large influence of non-deterministic behavior (statistical parameter variation, random inputsignals, and non-deterministic control decisions)

Cyber-Physical SystemsA new buzzword or a serious trend in simulation of complex systems ?


Outlook (2)Cyber-Physical Systems CPS

A new buzzword or a serious trend in simulation of complex systems ?

Applications: worldwide traffic and transport systems, large communication systems, biologicaland social systems (including „swarm behavior“), …

Riscs:

- If our existing multi-physics simulators will not be enhanced in this direction, a lot of new modeling languages and simulators will arise during the next years

- But what if the CPS concept is only a nice dream …

The U.S. government (National Science Foundation NSF) started a large program to promote CPS (about 50 Mio $ annually)! Today is the deadline for applications

„The CPS program aims to reveal cross-cutting fundamental scientific and engineering principles that underpin the integration of cyber and physical elements across all application sectors. The CPS program will also support the development of methods and tools as well as hardware and software components, run-time substrates, and systems based upon these principles to expedite and accelerate the realization of cyber-physical systems in a wide range of applications.“


Thank you for your attention !

And my special thanks to my former colleagues at Fraunhofer IIS / EAS Dresden, especially to

Christoph Clauss Ulrich Donath Karsten Einwich Günther Elst

Joachim Haase Jürgen Haufe André Schneider Peter Schneider

Their experiences and support have strongly influenced this presentation.

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