chap1仿真与虚拟现实

1、Chapter 1: Introduction,System Modeling and Simulation -ch.1 Introduction,Overview,Simulation Systems Models Evaluation Conclusion,System Modeling and Simulation -ch.1 Introduction,Overview,Simulation Whats simulation When simulations are used Four reasons to use simulation Systems System State and

2、state changes Models Model categories Criteria Steps in a simulation study Conclusion,System simulation,Given a system, how do you evaluate its performance ? Three classic methods: Experiments: Use a concrete example of a system and try to measure its performance Analysis: Construct a mathematical a

3、bstraction of the system and derive equations describing the systems performance Simulation: Build a model (a representation) of the system, along with its operations, and use this model to numerically evaluate system performance usually with the help of computers Here: simulations!,System simulatio

4、n (cont.),Open questions What is a system? What is performance? On what does performance depend? What is a model? What are operations of a system? How to build a model? How to numerically evaluate it? How to interpret the results of such an evaluation?,Whats simulation,A simulation is The imitation

5、of the operation of a real-world process or system over time. A technique, whereby a model of a system, is run in compressed time, to perform experimentation for analyzing system performance. Whether done by hand or on a computer, simulation involves the generation of an artificial history of a syst

6、em, and the observation of that artificial history to draw inferences concerning the operating characteristics of the real system.,模拟与仿真,模拟：对某种现象或变化过程的模仿 仿真：用一套以计算机为主体的软硬件设备模仿实际系统的综合技术 技术层面-仿真,When simulation are used,Uses of simulation have evolved with hardware, software The early years (1950s-196

7、0s) Very expensive, specialized tool to use Required big computers, special training Mostly in FORTRAN (or even Assembler) Processing cost as high as $1000/hour for a sub-286 level machine,When simulations are used (cont.),The formative years (1970s-early 1980s) Computers got faster, cheaper Value o

8、f simulation more widely recognized Simulation software improved, but they were still languages to be learned, typed, batch processed Often used to clean up “disasters” in auto, aerospace industries Car plant; heavy demand for certain model Line under-performing Simulated, problem identified But dem

9、and had dried up simulation was too late,When simulation are used (cont.),The recent past (late 1980s) Microcomputer power Software expanded into GUIs, animation Wider acceptance across more areas Traditional manufacturing applications Services Health care “Business processes” Still mostly in large

10、firms Often a simulation is part of the “specs”,When simulation are used (cont.),The present Proliferating into smaller firms Becoming a standard tool Being used earlier in design phase Real-time control The future Exploiting interoperability of operating systems Specialized “templates” for industri

11、es, firms Automated statistical design, analysis,Four reasons to use simulation,To understand Model to understand the impact of solar radiation and greenhouse gases on the earths surface temperature To improve Model to reduce waiting time of patients in a hospital emergency room To predict performan

12、ce Simulation of a potential layout for a new factory To guide Simulation of student demand for computers in the A-1 building,Examples,Manufacturing Applications Military Applications Logistics, Transportation, and Distribution Applications Business Process Simulation Human Systems Ex1 ex2 ex3,仿真分类,

13、根据模型的种类分类 物理仿真：按照真实系统的物理性质构造系统的物理模型，并在物理模型上进行试验的过程。优点：直观、形象； 缺点：模型改变困难，试验限制多，投资大 数学仿真：对实际系统进行抽象，并将其特性用数学关系加以描述而得到系统的数学模型，对数学模型进行试验的过程称为数学仿真。也称为计算机仿真。 优点：方便、灵活、经济 缺点：数学模型不易建立，受限于系统建模技术。 半实物仿真：将数学模型与物理模型甚至实物联合起来进行试验。简单的建模，复杂的作实物模型，然后联合起来做试验。,仿真分类,根据仿真计算机类型分类： 模拟计算机仿真（50-60年代） 数字计算机仿真（计算机仿真指数字计算机仿真）数学模

14、型用计算机程序加以实现， 数字模拟混合仿真（60-70年代，数字计算机仿真技术不成熟）数字计算机和模拟计算机用数模和模数转换装置交换信息,仿真分类,根据仿真时钟与实际时钟的比例关系分类： 实时仿真、仿真时钟与实际时钟完全一致，仿真速度=运行速度， 条件：系统中存在物理模型或实物时。如训练仿真器 亚实时仿真、慢于实际时钟 条件：对仿真速度要求不苛刻时。如离线仿真。 超实时仿真：快于实际时钟 如：交通系统的仿真。,仿真分类,根据仿真的设备 逻辑仿真：只用计算机软硬件 含实物仿真 人在回路中的仿真 根据系统模型的特性分类：连续系统仿真、离散时间系统仿真,System,Almost all inves

15、tigation tasks have the notion of a “system” that is to be investigated, characterized System definition American Heritage Dictionary: 1. A group of interacting, interrelated, or interdependent elements forming a complex whole, 2. A group of interacting mechanical or electrical components Characteri

16、zed by its parts and their interactions System as a whole is also defined by its purpose or function Systems can be part of the real world or virtual entity,System (cont.),System notion depends on abstraction level On a higher level, system can be part of another system On a lower level, parts of a

17、system usually can be regarded as systems as well (subsystems) Systems are recursively structured In general, no atomic parts In practice, atomic parts are chosen depending on intentions of usage Choice of “system” abstraction depends on objective or purpose of usage,System state,In most systems, di

18、fferent modes or conditions of being can be distinguished: The system can be in different states Because of recursive nature of system, parts also (usually) have a state State can be expressed by the values of a set of variables System state is the aggregation of state of the parts State can be cont

19、inuous or discrete,System state changes,Interesting (dynamic) systems change their state over time Static systems do not change their state, passage of time plays no role In continuous systems, the state of the system is a continuous (in the mathematical sense) function of time E.g., typical systems

20、 of the natural sciences: airplane moving, planets turning, cars crashing In discrete systems, the state of the system changes instantaneously at separate points in time E.g., a cashier line in a supermarket, computer systems, communication networks,System Overview,Models,Sometimes, the actual syste

21、m is available for investigation (at reasonable cost and effort) Sometimes, only a model of a system can be used and usually has to be constructed explicitly A model of a system is also a system Build to capture some relevant properties of the original system Simplified with respect to original syst

22、em, reduced complexity Models appear in many different kinds, with many different characteristics,Kinds of models:Physical vs. mathematical,Physical models: scale representation of system E.g., build a little airplane and a wind tunnel to study aerodynamics with experiments Mathematical models: Repr

23、esent system with appropriate mathematical or logical formalism An airplane is described by the laws of aerodynamics Manipulate this representation, e.g., introduce external stimuli Move the rudders of the airplane = use different laws to represent it Try to deduce how the real system would react (p

24、rovided model is valid) Would such an airplane turn left or right? We will only consider mathematical models!,Kinds of models: Static vs. dynamic,Static model A model where only a certain, fixed state of a system is considered, state changes are not taken into account Evidently appropriate for stati

25、c systems (one without state changes) Sometimes appropriate even for dynamic systems, if only system properties in certain, fixed states are of interest Dynamic model Reflect the systems state changes as it evolves over time How to handle continuous or discrete systems?,Kinds of models: Continuous v

26、s. discrete,Continuous models A continuous model describes the system such that the state variables are a continuous function of time Typical description: differential equation(s), describing relationships between the rate of change of different state variables with each other and with time Discrete

27、 models Change of state only happens at discrete, well separated instances of time (the set of points in time where the state changes is a most countably infinite) In between such times, all state variables maintain their values, the state does not change At such points in times, events of the model

28、 occur, i.e., the state of the systems can only change when an event occurs (but need not necessarily change at every event),Kinds of models: Continuous vs. discrete (cont.),Note relationship between systems and models For continuous systems, continuous models are not necessarily used E.g., voice da

29、ta is a continuous system, but is for purposes of transmission modeled as a discrete system (quantization, sampling) For discrete systems, discrete models are not necessarily used E.g., traffic flow on a highway with discrete events of cars entering and leaving the highway could be modeled continuou

30、sly if only the behavior of large numbers if interesting Choice depends on intentions, objectives, feasibility,Kinds of Models: Deterministic vs. stochastic,A model where the evolution of state is completely described such that it only depends on the initial state is a deterministic model E.g., a se

31、t of differential equations describing concentration of different substances in a chemical reaction A model where the evolution of state depends on random events (random in both time of occurrence or nature) is a stochastic model E.g., model of a highway where the times when cars enter the highways

32、are described by a random variable Output/results for such model does not only depend on initial state, but also on the values of random variables - no fixed or single result for such models,Kinds of Models: Deterministic vs. stochastic (cont.),Again note relationship between system and its model So

33、metimes, stochastic systems are modeled deterministically E.g., chemical processes are actually random by their very nature (quantum mechanics), yet they are usually modeled deterministically (which is usually appropriate because of the large number of particles involved),Kinds of Models: Determinis

34、tic vs. stochastic (cont.),Sometimes, deterministic processes are modeled stochastically Commonly done when the deterministic laws underlying the actual system are too complicated to permit a simple model or are not even fully understood, yet the stochastic properties might be available for investig

35、ation E.g., cars entering a highway: from a God-like perspective, it would be possible to determine the times for all cars in advance (knowing the time when people get up, drive to work, etc.) impossible. Yet the average behavior might be easy to describe: “on average, a car enters the highway every

36、 k seconds” Such description looses detail, yet could be the only feasible one,Model Overview,Model criteria,Good models should be Appropriate representation of the system (depending on purpose of investigation) As small as possible without impeding appropriateness Reusable for similar systems, as a

37、 part in other systems Parameterizable Amenable to appropriate investigation method In acceptable time, with acceptable effort, with desired accuracy Method also depends on desired results,Simulation,Simulation of mathematical, dynamic,discrete models Discrete Event Simulation is the main focus of t

38、his course,Steps in a simulation study,Steps in a simulation study (cont.),1. Problem formulation. Every study should begin with a statement of the problem. 2. Setting of objectives and overall project plan. 3. Model conceptualization. 4. Data collection. 5. Model translation. Since most real-world

39、systems result in models that require a great deal of information storage and computation, the model must be entered into a computer-recognizable format. We use the term “program”,Steps in a simulation study (cont.),6. Verified? Verification pertains to the computer program prepared for the simulation model. Is the c