Requirements for the Simulation of Complex Heterogeneous Systems

Requirements for the Simulation of Complex Heterogeneous Systems 8th Modelica Conference Dresden March 21, 2011 Peter Schwarz Formerly with Fraunhofer Institute for Integrated Circuits, Design Automation Division EAS Dresden, Germany Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 1

Outline 1. Properties of complex hetereogeneous systems 2. Continuous systems 3. Hybrid systems 4. Spatially distributed systems 5. Further requirements and wishes 6. Outlook Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 2

Complex Heterogeneous System (Example: Technical System) Properties Magnetic Actuator Mechanical Sensor Electrical Circuit (analog) Software: Signal Processing, Control Elektrostatic Sensor Digital Hardware: Signal Processing, Control multi-domain, multi-physics Time: discrete and continuous Signal flow: directed and non-directed Spatially concentrated (lumped) and distributed elements Naturally partitioned Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 3

Heterogeneous System Ideal: a heterogeneous model for one simulator but this is not very realistic for large systems Magnetic Actuator Mechanical Sensor Elektrostatic Sensor Electrical Circuit (analog) Software: Signal Processing, Control Digital Hardware: Signal Processing, Control in general: non-directed signal-flow but also some uni-directional interconnections Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 4

Heterogeneous System More realistic: a heterogeneous model and some coupled simulators FEM Simulator DAE / ODE Simulator Magnetic Actuator Mechanical Sensor Elektrostatic Sensor Electrical Circuit (analog) Software: Signal Processing, Control Digital Hardware: Signal Processing, Control Circuit simulator (analog) Digital simulator, signal processing simulator in general: non-directed signal-flow but also some uni-directional interconnections Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 5

Continuous Systems: Directed and Non-Directed Signal Flow Control system, signal-flow diagram Electrical circuit, multi-body system, fluidic system, Flow - + Potential Block diagram Multi-pole network (generalized network) x = f(x,u, t) F(x,x,u, t ) = 0 ODE Ordinary Differential Equation (explicit) DAE Differential-Algebraic Equation (implicit) Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 7

History: Continuous System Simulation 1960 1970 Simulation = sequential processing of statements noticed in correct order by the user Many mathematical algorithms (e.g. RUNGE-KUTTA) in textbooks for solving ODEs ODE seems to be the natural way to model the reality First 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: 1980 1990 Directed signal flow Non-directed signal flow Causal 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 Insight: DAE should be mainly used for modeling the physical world Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 8

History: Continuous System Simulation Hybrid Simulation 1990 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, 2000 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 2010 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) Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 9

Complex Heterogeneous System and Hybrid Simulation Magnetic Actuator Mechanical Sensor Elektrostatic Sensor continuous analog Electrical Circuit (analog) Hybrid simulation Mixed-signal simulation Software: Signal Processing, Control Digital Hardware: Signal Processing, Control discrete digital with respect to time and / or values Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 11

Hybrid Systems / Hybrid Simulation Hybrid = continuous + discrete Structure of the model does nor change during simulation For simple systems : state-of-the-art simulators But: serious problems in some heterogeneous system! 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 Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 12

Hybrid Systems / Hybrid Simulation - the Roots 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, SimulationX Matlab/Simulink/Stateflow/Simscape MatrixX, NI Labview, MapleSim VHDL-AMS simulators Verilog-AMS simulators ( AnyLogic ) Problem: very fast AND very slow AND signal changes very large number of events Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 13

Discrete System: Graphical Description with State Charts (1) UML state diagram SimulationX Informal state diagram extended to hybrid systems U. Donath, FhG IIS/EAS A. Schneider, FhG IIS/EAS Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 14

Discrete System: Graphical Description with State Charts (2) 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!!! State Graph Libraries (Modelica) Additional definitions are necessary, e.g.: - priority rules - separate blocks for event scheduling and should NOT be tool-dependent! Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 15

Hybrid Systems and State Charts Example with the hybrid simulator AnyLogic: time-triggerd switching between differential equations State 1 x1 = d*x1 + 3 x1 x2 x3 x1 1 s 1 s x2 State 2 x1 = a1*x1 + a2*x2 + a3*x3 x2 = b1*x1 + b2*x2 + b3*x3 x3 = c1*x1 + c2*x2 + c3*x3 Initial conditions Root: x1(0) = 0, x2(0) = 0, x3(0) = 0, a1 =,, d = 1 2 3 4 t in s x3 Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 16

Complex Heterogeneous System: Timing Behavior Magnetic Actuator Mechanical Sensor Elektrostatic Sensor Electrical Circuit (analog) Software: Signal Processing, Control Digital Hardware: Signal Processing, Control Time: discrete and continuous time scale Signals: discrete and continuous values Signal activity: extreme large differences Basis for partitioning! Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 17

Partitioning w.r.t Timing Behavior A slow D fast A fast D slow very intensive interaction time-consuming simulation! Not an academic idea! It has been realized, e.g., in a SystemC-AMS simulation environment Synchronization layer reduced, controlled interaction Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 18

SystemC-AMS Layer Approach for Synchronization Introduction to SystemC-AMS Library Prototype Thomas Uhle,, Karsten Einwich,, Fraunhofer IIS/EAS Dresden Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 19

SystemC-AMS Layer Approach for Synchronization Linear behaviour Linear electrical networks nonlinear module, node and variable base classes Linear DAE solver Nonlinear DAE Solver supporting the synchronization interface Introduction to SystemC-AMS Library Prototype Thomas Uhle,, Karsten Einwich,, Fraunhofer IIS/EAS Dresden Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 20

Modem IC: Analog + Digital + Software Voice band 50 Hz 12 khz ( XDSL: 2 MHz ) Analog filter 100 khz Digital filter 64 256 MHz clock, oversampling Many 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) Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 21

Spatially Distributed Components Two- or three-dimensional components (sometimes with very complicated geometry and 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 simulator Necessary: models with reduced but sufficient accuracy Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 23

Spatially Distributed Components Model generation: the PDE is numerically approximated by a system of ODEs or DAEs (e.g. with central differences) behavioral model (equations) Model library - + Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 24

Spatially Distributed Components Model generation: the PDE is numerically approximated by a system of ODEs or DAEs (e.g. with central differences) structural model (e.g. equivalent network or circuit) N elements (multi-poles) Model library electrical transmission line - + OR damped mass-spring element Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 25

Spatially Distributed Components Pre-compiler (or manually) Model generation: the PDE is numerically approximated by a system of ODEs or DAEs (e.g. with central differences) behavioral model (equations) structural model (e.g. equivalent network or circuit) N elements (multi-poles) Model library Language construct - + for loop statement Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 26

Spatially Distributed Components: Electrical Transmission Line 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"; one segment parameter Real c "Capacitance per meter"; parameter SI.Length length "Length of line"; parameter Integer N "Number of lumped segments"; C. Clauss, FhG IIS/EAS Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 27

Spatially Distributed Components: Electrical Transmission Line protected Basic.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)); equation v13 = 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 C. Clauss, FhG IIS/EAS Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 28

Spatially Distributed Components: Pendulum A. Schneider, FhG IIS/EAS Fr Fp F g F n 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 equation for 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; Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 29

Further Requirements and Wishes (1) Model interfaces Very important for A MUST - Model exchange between different simulation environments (based on the same modeling language, 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) Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 31

Further Requirements and Wishes (2) Code generation from model description (Hardware-in-the-loop simulation, controller design) A MUST - 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 numerical The effects strongly depend on simulator implementation! - Handling of events in discrete systems: Very large number of events Explicit access to event queues (extensions of the modeling language are mostly necessary!) Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 32

Further Requirements and Wishes (3) Export of mathematical model descriptions - Complete set of equations? Nice to have 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 equations ODEs 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 ) Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 33

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 Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 34

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 model source 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 Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 35

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 input signals, and non-deterministic control decisions) Cyber-Physical Systems A new buzzword or a serious trend in simulation of complex systems? Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 37

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, biological and 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. Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 38

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. Peter Schwarz 8th Modelica Conference Dresden March 21, 2011 39