2.3 FIELDS OF APPLICATION 9 model may serve to evaluate the power of a computer,which accesses its hard drive with a probability of x%and its tape deck with a probability of y%.Models containing at least one random variable are classified as stochastic.All others are called deterministic. A further option for the classification of models is the consideration of the 'outside world'of a model.If the model is isolated from the outside world and thus has no inputs and outputs.then it is called autonomous.All other models are called non-autonomous.An autonomous model produces a movement in the state space from itself,without taking in and producing data,whereas a non- autonomous model primarily converts values at the inputs into the outputs based upon the current state A final option for the classification of models is represented by the question of whether or not time crops up explicitly in the model equations.In the former case the model is time-variant,in the latter time-invariant 2.3 Fields of Application 2.3.1 Introduction If technical systems are to be developed,two main fields of application can be identified for the simulation:The validation of specifications and the verification of designs.In the ideal case the specification or design will be available immediately in model form,so that nothing stands in the way of direct simulation.Hitherto this has mainly been the case in the design of digital electronics using hardware description languages.Otherwise,modelling must take place first to bring about the transition from an arbitrary description to a simulatable model. The use of modelling and simulation is closely linked to the underlying design processes.These can be roughly divided in accordance with their design direction into top-down and bottom-up design flows.In what follows these will be briefly introduced and characterised by their influence upon modelling. 2.3.2 Bottom-up design Bottom-up design is the classic method of development of electronics and mechan- ics,see Figure 2.2.The initial starting point is a specification,which is typically drawn up in natural language.Then the basic components,e.g.transistors,resistors capacitors or springs,masses,shock absorbers,joints,etc.are added and combined successively to form ever more complex and abstract creations until a complete design emerges.This takes place on a structural level,so that the only thing that is determined each time is which submodules make up a module and how these are
2.3 FIELDS OF APPLICATION 9 model may serve to evaluate the power of a computer, which accesses its hard drive with a probability of x% and its tape deck with a probability of y%. Models containing at least one random variable are classified as stochastic. All others are called deterministic. A further option for the classification of models is the consideration of the ‘outside world’ of a model. If the model is isolated from the outside world and thus has no inputs and outputs, then it is called autonomous. All other models are called non-autonomous. An autonomous model produces a movement in the state space from itself, without taking in and producing data, whereas a nonautonomous model primarily converts values at the inputs into the outputs based upon the current state. A final option for the classification of models is represented by the question of whether or not time crops up explicitly in the model equations. In the former case the model is time-variant, in the latter time-invariant. 2.3 Fields of Application 2.3.1 Introduction If technical systems are to be developed, two main fields of application can be identified for the simulation: The validation of specifications and the verification of designs. In the ideal case the specification or design will be available immediately in model form, so that nothing stands in the way of direct simulation. Hitherto this has mainly been the case in the design of digital electronics using hardware description languages. Otherwise, modelling must take place first to bring about the transition from an arbitrary description to a simulatable model. The use of modelling and simulation is closely linked to the underlying design processes. These can be roughly divided in accordance with their design direction into top-down and bottom-up design flows. In what follows these will be briefly introduced and characterised by their influence upon modelling. 2.3.2 Bottom-up design Bottom-up design is the classic method of development of electronics and mechanics, see Figure 2.2. The initial starting point is a specification, which is typically drawn up in natural language. Then the basic components, e.g. transistors, resistors, capacitors or springs, masses, shock absorbers, joints, etc. are added and combined successively to form ever more complex and abstract creations until a complete design emerges. This takes place on a structural level, so that the only thing that is determined each time is which submodules make up a module and how these are
10 2 PRINCIPLES OF MODELLING AND SIMULATION Specification System Module 1 Submodule 1 Time Figure 2.2 Bottom-up design process to be connected together.Such a design can be performed using a circuit editor or a suitable tool for multibody systems. The primary advantage of bottom-up design is that the influences of a nonideal implementation can be taken into account at an early stage.For electronics these may be unavoidable parasitic resistances,capacitances and inductances.In the field of mechanics they may be friction effects,for example. However,one problematic aspect is coming upon the specification for the design. after having had to take a 'diversion'via the submodules and modules from the abstract functional description.This is because,as a result of the structure-oriented modelling,a system can only be simulated when it has been completely imple- mented.Thus errors and weaknesses in the system design are not noticed until a late stage,which can bring about considerable costs and delays. 2.3.3 Top-down design A significant characteristic of top-down design is the prevailing design direction from abstract to detailed descriptions,see Figure 2.3.The starting point is a pure behavioural model,the function of which already covers a good part of the speci- fication.The model is successively partitioned and refined until an implementation is obtained.It is necessary to describe a system or module of it in a functional manner.This was first made possible by the introduction of hardware description languages in the field of electronics.Using these the design is directly formulated as a model,so that most of the modelling can be dispensed with. The top-down design sequence has the following advantages: .Errors and weaknesses in the design are noticed early,in contrast to the bottom- up approach
10 2 PRINCIPLES OF MODELLING AND SIMULATION Time Specification Submodule 1 Module 1 ? System Abstraction Figure 2.2 Bottom-up design process to be connected together. Such a design can be performed using a circuit editor or a suitable tool for multibody systems. The primary advantage of bottom-up design is that the influences of a nonideal implementation can be taken into account at an early stage. For electronics these may be unavoidable parasitic resistances, capacitances and inductances. In the field of mechanics they may be friction effects, for example. However, one problematic aspect is coming upon the specification for the design, after having had to take a ‘diversion’ via the submodules and modules from the abstract functional description. This is because, as a result of the structure-oriented modelling, a system can only be simulated when it has been completely implemented. Thus errors and weaknesses in the system design are not noticed until a late stage, which can bring about considerable costs and delays. 2.3.3 Top-down design A significant characteristic of top-down design is the prevailing design direction from abstract to detailed descriptions, see Figure 2.3. The starting point is a pure behavioural model, the function of which already covers a good part of the speci- fication. The model is successively partitioned and refined until an implementation is obtained. It is necessary to describe a system or module of it in a functional manner. This was first made possible by the introduction of hardware description languages in the field of electronics. Using these the design is directly formulated as a model, so that most of the modelling can be dispensed with. The top-down design sequence has the following advantages: • Errors and weaknesses in the design are noticed early, in contrast to the bottomup approach
2.3 FIELDS OF APPLICATION 11 Specification System Module 1 Time Figure 2.3 Top-down design sequence The implementable part of the specification can be validated by simulations. The implementable part of the specification is available as a precisely defined reference for the verification of the design. The functional part of the specification is unambiguous and complete (in con- trast to a specification in natural language).In the event of doubt,a simulation is run. The implementable specification and the models of the individual design stages mean that full documentation is available,which however still remains to be supplemented by comprehensive commentary. In the case of mixed-signal design,the implementable specification can be made available to the test engineers at an early stage as part of a 'simultaneous engi- This removes the fixed sequence of design-production-test development and also saves a great deal of time on test development. However,the disadvantage of the use of implementable specifications is that some technical content can be expressed in a simpler,more compact and more easily understood form in natural language than in a formal modelling language. In addition,there is the question of adhering to the formally correct description of the desired semantics,which incurs an additional cost in relation to a paper specification.Finally,problems in the physical realisation,such as excessive delay times for certain blocks,are not recognised until a relatively late stage. For mechanics the top-down design sequence is still in the development stage A significant reason for this is that unified and standardised description methods for mechanical behaviour,with which a design can be taken incrementally from an abstract specification to a detailed implementation,are only now being developed
2.3 FIELDS OF APPLICATION 11 Time Specification System Submodule 1 Module 1 Abstraction Figure 2.3 Top-down design sequence • The implementable part of the specification can be validated by simulations. • The implementable part of the specification is available as a precisely defined reference for the verification of the design. • The functional part of the specification is unambiguous and complete (in contrast to a specification in natural language). In the event of doubt, a simulation is run. • The implementable specification and the models of the individual design stages mean that full documentation is available, which however still remains to be supplemented by comprehensive commentary. In the case of mixed-signal design, the implementable specification can be made available to the test engineers at an early stage as part of a ‘simultaneous engineering’ approach. Using a model for the testing machine a virtual test is created, in which test programmes can be developed on the workstation. This removes the fixed sequence of design → production → test development and also saves a great deal of time on test development. However, the disadvantage of the use of implementable specifications is that some technical content can be expressed in a simpler, more compact and more easily understood form in natural language than in a formal modelling language. In addition, there is the question of adhering to the formally correct description of the desired semantics, which incurs an additional cost in relation to a paper specification. Finally, problems in the physical realisation, such as excessive delay times for certain blocks, are not recognised until a relatively late stage. For mechanics the top-down design sequence is still in the development stage. A significant reason for this is that unified and standardised description methods for mechanical behaviour, with which a design can be taken incrementally from an abstract specification to a detailed implementation, are only now being developed
12 2 PRINCIPLES OF MODELLING AND SIMULATION Predictively valid Specification Structurally valid mplementation Figure 2.4 Level of validity and its significance for the design of a technical system 2.3.4 Relationship of design strategies to modelling In the case of the top-down design sequence,modelling is used for the specification of the desired behaviour or for the formulation of designs.In both cases the result can be directly checked through simulation;there is no such thing as modelling exclusively for the purpose of simulation.In this connection,an important classi- fication of such models by their level of validity can be made,see Figure 2.4.For ,predictive validity is sufficient -the manner in which the terminal behaviour of the specified systems and modules is individually generated is not relevant.A system design,on the other hand,ideally supplies a structurally valid model that describes both the terminal behaviour and the inner structure By contrast,if a technical system is to be developed using a bottom-up design sequence,then simulation can be used for checking the system design or parts of it after the conclusion of the design phase.Modelling is thus not an integral part of the design process;instead it is often performed exclusively for the purpose of the simulation,which raises questions regarding the verification and validation of the model. Where modelling is used outside a design process we can differentiate between the following two cases:structurally valid modelling in natural and social sciences in order to gain understanding of a system;and replicatively valid modelling in the field of training.The former plays only a lesser role in the consideration of technical systems.The latter is used primarily for the imitation of familiar behaviour.A well- known example is flight simulators that are used for the training of pilots in all feasible operational situations.Such simulators are now available on the market for almost all types of vehicle.But simulators can also be used for other types of training.Preparation for the repair of the Hubble telescope involved a great deal of expenditure on simulation due to the considerable costs and the narrow time frame for such measures in space,see Loftin [237]and [242]. 2.3.5 Modelling for the specification The main purpose of a specification is to describe the desired behaviour of a system to be developed and the associated boundary conditions.Classically,a specifica- tion is available on paper,which is associated with a whole range of problems
12 2 PRINCIPLES OF MODELLING AND SIMULATION Predictively valid Structurally valid Implementation Specification Figure 2.4 Level of validity and its significance for the design of a technical system 2.3.4 Relationship of design strategies to modelling In the case of the top-down design sequence, modelling is used for the specification of the desired behaviour or for the formulation of designs. In both cases the result can be directly checked through simulation; there is no such thing as modelling exclusively for the purpose of simulation. In this connection, an important classi- fication of such models by their level of validity can be made, see Figure 2.4. For a specification, predictive validity is sufficient — the manner in which the terminal behaviour of the specified systems and modules is individually generated is not relevant. A system design, on the other hand, ideally supplies a structurally valid model that describes both the terminal behaviour and the inner structure. By contrast, if a technical system is to be developed using a bottom-up design sequence, then simulation can be used for checking the system design or parts of it after the conclusion of the design phase. Modelling is thus not an integral part of the design process; instead it is often performed exclusively for the purpose of the simulation, which raises questions regarding the verification and validation of the model. Where modelling is used outside a design process we can differentiate between the following two cases: structurally valid modelling in natural and social sciences in order to gain understanding of a system; and replicatively valid modelling in the field of training. The former plays only a lesser role in the consideration of technical systems. The latter is used primarily for the imitation of familiar behaviour. A wellknown example is flight simulators that are used for the training of pilots in all feasible operational situations. Such simulators are now available on the market for almost all types of vehicle. But simulators can also be used for other types of training. Preparation for the repair of the Hubble telescope involved a great deal of expenditure on simulation due to the considerable costs and the narrow time frame for such measures in space, see Loftin [237] and [242]. 2.3.5 Modelling for the specification The main purpose of a specification is to describe the desired behaviour of a system to be developed and the associated boundary conditions. Classically, a specification is available on paper, which is associated with a whole range of problems
2.3 FIELDS OF APPLICATION 13 First of all it raises the question of its validity,i.e.whether the described system really corresponds with the desired system.Furthermore.it is doubtful whether a given(paper)specification is completely and unambiguously formulated.These questions can only be answered in a systematic manner when the transition is made to an implementable specification,which can then be validated by simulation,for example.A further advantage of this transition lies in the possibility of the veri fication of the individual design stages against the specification.Furthermore,this opens up the opportunity of performing a formal verification against the specifi- cation.In digital behavioural modelling asa specification is becoming increasingly prevalent,in all other domains it is still at a very early stage. Modelling for a specification is pure behavioural modelling.which-as is the case for a paper specification-may not anticipate the implementation.For a microprocessor.for example.a specification would describe only the instruction set and the associated actions.The way that the individual operations are realised cannot be the object of the specification.An executable specification for a memory module may consist of a large array for the memory content and some logic for the processing of read and write processes.The specification of an A/D converter could formulate the pure translation of analogue values into digital values and the resulting delay. 2.3.6 Modelling for the design Modelling for the checking of technical system designs for each simulation is the yu3q uonenups osn saut TNst uogeaddes This applies particularly in microelectronics.A manufacturing run typically lasts 6-12 weeks and is associated with significant costs.Repairs to manufactured chips are more or less impossible.Under such boundary conditions,one cannot afford to iterate the manufacturing process to rectify design errors.Instead,it is neces- sary to enter manufacture with a fundamentally error-free design,which-given the complexities that are currently possible,involving some tens of millions of transistors-cannot be achieved without simulation. If we consider discretely structured printed circuit boards,then it is slightly less critical that the circuit is fully checked in advance by simulation.The etching and fitting of circuit boards is significantly simpler and quicker than chip manufacture. Changes can be performed comparatively easily.The circuits are also less complex by orders of magnitude.So it can be worthwhile to solder a circuit together as a bread-board arrangement and check it by measurement.Nevertheless,the perfor- mance of virtual experiments on a computer is generally quicker and cheaper than the real experiment in the laboratory. For software,things are comparatively simple.The compilation of software can be regarded as rudimentary modelling,as software is executable after this stage,i.e. it is simulatable.The simulation sequence and the simulation result are normally
2.3 FIELDS OF APPLICATION 13 First of all it raises the question of its validity, i.e. whether the described system really corresponds with the desired system. Furthermore, it is doubtful whether a given (paper) specification is completely and unambiguously formulated. These questions can only be answered in a systematic manner when the transition is made to an implementable specification, which can then be validated by simulation, for example. A further advantage of this transition lies in the possibility of the veri- fication of the individual design stages against the specification. Furthermore, this opens up the opportunity of performing a formal verification against the specifi- cation. In digital electronics, behavioural modelling as a specification is becoming increasingly prevalent, in all other domains it is still at a very early stage. Modelling for a specification is pure behavioural modelling, which — as is the case for a paper specification — may not anticipate the implementation. For a microprocessor, for example, a specification would describe only the instruction set and the associated actions. The way that the individual operations are realised cannot be the object of the specification. An executable specification for a memory module may consist of a large array for the memory content and some logic for the processing of read and write processes. The specification of an A/D converter could formulate the pure translation of analogue values into digital values and the resulting delay. 2.3.6 Modelling for the design Modelling for the checking of technical system designs for each simulation is the classic application case. All engineering-science disciplines use simulation benefi- cially to this end. This applies particularly in microelectronics. A manufacturing run typically lasts 6–12 weeks and is associated with significant costs. Repairs to manufactured chips are more or less impossible. Under such boundary conditions, one cannot afford to iterate the manufacturing process to rectify design errors. Instead, it is necessary to enter manufacture with a fundamentally error-free design, which — given the complexities that are currently possible, involving some tens of millions of transistors — cannot be achieved without simulation. If we consider discretely structured printed circuit boards, then it is slightly less critical that the circuit is fully checked in advance by simulation. The etching and fitting of circuit boards is significantly simpler and quicker than chip manufacture. Changes can be performed comparatively easily. The circuits are also less complex by orders of magnitude. So it can be worthwhile to solder a circuit together as a bread-board arrangement and check it by measurement. Nevertheless, the performance of virtual experiments on a computer is generally quicker and cheaper than the real experiment in the laboratory. For software, things are comparatively simple. The compilation of software can be regarded as rudimentary modelling, as software is executable after this stage, i.e. it is simulatable. The simulation sequence and the simulation result are normally