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...e to model systems composed of diverse components without losing accuracy due to model conversion [21,36] . Model composition can also be achieved without requiring elusive unified modeling standards =-=[37, 38]-=-. 5 Due to the long-term as well as renewed interest in compositional system modeling, many aspects of this approach have been well established. Some of these include: (1) system behavior can be segme...

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...ed unmanned aerial vehicle (UAV). 2.1 System Modeling Requirements System design research has long been interested in modeling system behavior by integrating different models from various disciplines =-=[48]-=-. Many specialties, including system engineering [1], control systems [49], multidisciplinary design optimization [35], software development [50], embedded systems [43], and modeling and simulation [2...

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...Dynamic systems include differential algebraic equations, infinite-dimensional dynamic systems [56], dynamic-stochastic systems, discrete time systems, discrete event systems [39], and hybrid systems =-=[57]-=-. All of these model types must compute outputs based on inputs [58]. In addition, dynamic systems have model state, state initialization, and state progression [59]. Dynamic systems might also requir...

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...2), we next formulate the system model structure. Model composition defines a relationship between component models: it is a one-way data transfer from the output of one model to the input of another =-=[34]-=-. Using graph theory terminology to represent compositional system models, composition (shown 24 as an arrow in Figure 2.1) is a doubly-connected directed edge between two component models or vertices...

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...clude empirical data, mathematical functions, stationary statistical processes, or dynamic systems [55]. Dynamic systems include differential algebraic equations, infinite-dimensional dynamic systems =-=[56]-=-, dynamic-stochastic systems, discrete time systems, discrete event systems [39], and hybrid systems [57]. All of these model types must compute outputs based on inputs [58]. In addition, dynamic syst...

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...ish these requirements, the system model components and their interactions must approximate the system components and interactions. A system, by definition, is built from distinct physical components =-=[54]-=-. Similarly, a compositional system model is built from distinct component models. In addition, component model interactions must approximate with sufficient accuracy the actual system’s component int...

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... model predicts a system’s response to stimulus [51]. This includes how a system responds not only to a distinct input, but more usefully, how a system responds to a sequence of inputs (a simulation) =-=[52]-=-. In addition, a system model’s prediction must be sufficiently accurate to be useful [53]. Therefore, a system model must approximate the actual system’s response to input sequences. To accomplish th...

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...2], (2) model composition allows models of various types and time domains to be coupled [16, 43, 44], (3) component models implemented in various design tools can be coupled into compositional models =-=[33,35,45]-=-, (4) various methods of classifying and sharing the diverse data transferred between component models have been developed [38, 46], and (5) dynamic analysis of compositional system models can predict...

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...Some of these include: (1) system behavior can be segmented and modeled using lower level component models [39–42], (2) model composition allows models of various types and time domains to be coupled =-=[16, 43, 44]-=-, (3) component models implemented in various design tools can be coupled into compositional models [33,35,45], (4) various methods of classifying and sharing the diverse data transferred between comp...

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... integrating different models from various disciplines [48]. Many specialties, including system engineering [1], control systems [49], multidisciplinary design optimization [35], software development =-=[50]-=-, embedded systems [43], and modeling and simulation [20] have contributed to the body of knowledge about compositional system modeling. From this broad array of research, this section identifies fund...

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...stem prototypes. New system behavior can also be predicted using system models. Compositional system modeling assumes that heterogeneous, discipline specific models can be combined into system models =-=[29]-=-. Rather than translating component models into a common modeling language, model composition enables heterogeneous component models to interact within a system model through model composition [15, 30...

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... has been demonstrated by digital logic’s rapid increase in capabilities and performance [17]. Digital logic (e.g., a computer’s microprocessor) is created from a few types of well-defined components =-=[18]-=-. Based on models of these components, digital logic design automation tools enable system design and modeling of 3 extremely complex digital logic circuits. This has resulted in the ability to reliab...

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...d in various design tools can be coupled into compositional models [33,35,45], (4) various methods of classifying and sharing the diverse data transferred between component models have been developed =-=[38, 46]-=-, and (5) dynamic analysis of compositional system models can predict system behavior [47] . Despite this ongoing interest in compositional system modeling, multidisciplinary system design frequently ...

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...r multidisciplinary systems. The many different types of components and their varied interactions complicate creating component models, describing component interactions, and developing system models =-=[19]-=-. As such, multidisciplinary systems require a more general method of creating and managing components and their interactions than is needed in digital logic design. From our study, the primary impedi...

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...ls [29]. Rather than translating component models into a common modeling language, model composition enables heterogeneous component models to interact within a system model through model composition =-=[15, 30]-=-. Compositional modeling has been implemented in commercial design tools such as iSight and Simulink [31, 32]. It is used frequently in multidisciplinary design optimization research [33–35]. Because ...

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...first, its output y1 is transferred to u2, and then C2 is evaluated [15]. In this dissertation, a system model is a model that combines component models by composition to describe a system’s behavior =-=[16]-=-. Additional levels such as sub-system and sub-component can be achieved by making a system model a component model within a higher level system model. Though simple in concept, the complexities of mo...

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...not only to a distinct input, but more usefully, how a system responds to a sequence of inputs (a simulation) [52]. In addition, a system model’s prediction must be sufficiently accurate to be useful =-=[53]-=-. Therefore, a system model must approximate the actual system’s response to input sequences. To accomplish these requirements, the system model components and their interactions must approximate the ...

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...nt types of components that have diverse interactions. System behavioral models, which provide an analytical method of predicting a system’s behavior, are often not developed as part of system design =-=[2]-=-. Even when developed, system behavioral models are rarely available early enough in system design to guide foundational design decisions [3]. This is because they are difficult to create and are chal...

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...ent model [14]. Model composition of y1 =C1(u1) and y2 =C2(u2) can be written y2 =C2(C1(u1)), where component model C1 is evaluated first, its output y1 is transferred to u2, and then C2 is evaluated =-=[15]-=-. In this dissertation, a system model is a model that combines component models by composition to describe a system’s behavior [16]. Additional levels such as sub-system and sub-component can be achi...

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...em design organizations have recently published initiatives aimed at improving the design of new systems in light of their growing complexity [21]. Initiatives have been announced by DARPA [22], NASA =-=[23]-=-, Lockheed Martin [24], and Boeing [25]. A unifying characteristic of these initiatives is that each seeks to design and model new systems based on reusable components (e.g., mechanics, propulsion, el...

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...or dynamic systems [55]. Dynamic systems include differential algebraic equations, infinite-dimensional dynamic systems [56], dynamic-stochastic systems, discrete time systems, discrete event systems =-=[39]-=-, and hybrid systems [57]. All of these model types must compute outputs based on inputs [58]. In addition, dynamic systems have model state, state initialization, and state progression [59]. Dynamic ...

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...model error vector vi CHAPTER 1. INTRODUCTION System design is the process of creating and integrating various components (which are frequently heterogeneous and dynamic) to satisfy system objectives =-=[1]-=-. To be effective and efficient at system design, a design team must predict with sufficient accuracy the effects of design decisions on system behavior at the time these decisions are being made. Thi...

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...emands for higher performance have increased system complexity. Simultaneously, the increased power of discipline specific modeling tools and fabrication techniques has increased component complexity =-=[20]-=-. Our ability to predict and design multidisciplinary systems has not increased correspondingly as has occurred in digital logic design [2]. This has resulted in increased design time, cost uncertaint...

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...ive chapters. 4 A number of leading multidisciplinary system design organizations have recently published initiatives aimed at improving the design of new systems in light of their growing complexity =-=[21]-=-. Initiatives have been announced by DARPA [22], NASA [23], Lockheed Martin [24], and Boeing [25]. A unifying characteristic of these initiatives is that each seeks to design and model new systems bas...

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...e to model systems composed of diverse components without losing accuracy due to model conversion [21,36] . Model composition can also be achieved without requiring elusive unified modeling standards =-=[37, 38]-=-. 5 Due to the long-term as well as renewed interest in compositional system modeling, many aspects of this approach have been well established. Some of these include: (1) system behavior can be segme...

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...design research has long been interested in modeling system behavior by integrating different models from various disciplines [48]. Many specialties, including system engineering [1], control systems =-=[49]-=-, multidisciplinary design optimization [35], software development [50], embedded systems [43], and modeling and simulation [20] have contributed to the body of knowledge about compositional system mo...

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...t model must encompass the different types of discipline specific models it could represent. These include empirical data, mathematical functions, stationary statistical processes, or dynamic systems =-=[55]-=-. Dynamic systems include differential algebraic equations, infinite-dimensional dynamic systems [56], dynamic-stochastic systems, discrete time systems, discrete event systems [39], and hybrid system...

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...behavior, are often not developed as part of system design [2]. Even when developed, system behavioral models are rarely available early enough in system design to guide foundational design decisions =-=[3]-=-. This is because they are difficult to create and are challenging to maintain as designs are refined. Rather, component-level models, designer expertise, and iterative physical prototyping are freque...

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... and are challenging to maintain as designs are refined. Rather, component-level models, designer expertise, and iterative physical prototyping are frequently used to validate system design decisions =-=[4]-=-. Consequently, the length of time between making system design decisions and verifying the results of these decisions can be long and result in an unpredictable system design process [5]. The separat...

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...gn decisions [4]. Consequently, the length of time between making system design decisions and verifying the results of these decisions can be long and result in an unpredictable system design process =-=[5]-=-. The separation between design decisions and design verification that is currently part of system design adds significant risk to the system design process [6]. Frequently, a system design that does ...

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...design that does not achieve its requirements continues to be developed, without discovering its limitations, until the full system integration and evaluation is performed an the end of system design =-=[7]-=-. At this point, a major system redesign could be necessary to meet system objectives. This was illustrated in the F-35 (Joint Strike Fighter) development, which is one of the leading system design pr...

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...h system models can be built. Therefore, we create and verify a mathematical formulation for creating system models using existing engineering models that are currently available within system design =-=[8]-=-. The second obstacle is ensuring that these system models can continue to compute feasible results in the continually changing system design environment [9]. We introduce a new theory and method of i...

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...e currently available within system design [8]. The second obstacle is ensuring that these system models can continue to compute feasible results in the continually changing system design environment =-=[9]-=-. We introduce a new theory and method of identifying the system model feasible domain. Using this, we develop several approaches to evaluate and improve the feasible domain, thus ensuring reliable sy...

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...s, we develop several approaches to evaluate and improve the feasible domain, thus ensuring reliable system model evaluation even as underlying component and system models change during system design =-=[10]-=-. Finally, to validate system design decisions, we must be able to quantify system model accuracy before the actual system behavior is known [11]. Current methods rely on system measurements, empirica...

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...omponent and system models change during system design [10]. Finally, to validate system design decisions, we must be able to quantify system model accuracy before the actual system behavior is known =-=[11]-=-. Current methods rely on system measurements, empirical evaluation, or differential error estimation and are insufficient to quantify the accuracy of system models early in system design [12]. To ove...

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...s known [11]. Current methods rely on system measurements, empirical evaluation, or differential error estimation and are insufficient to quantify the accuracy of system models early in system design =-=[12]-=-. To overcome this obstacle, we develop a theory to bound system model accuracy based on known component model errors and verify this theory analytically and numerically [13]. Together, this dissertat...

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...ls early in system design [12]. To overcome this obstacle, we develop a theory to bound system model accuracy based on known component model errors and verify this theory analytically and numerically =-=[13]-=-. Together, this dissertation introduces a mathematical framework enabling multidisciplinary system design decisions to be validated at the point they are made. This enables the system design process ...

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...bilities of discipline specific modeling tools. The benefit of using system models to validate design decisions has been demonstrated by digital logic’s rapid increase in capabilities and performance =-=[17]-=-. Digital logic (e.g., a computer’s microprocessor) is created from a few types of well-defined components [18]. Based on models of these components, digital logic design automation tools enable syste...

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...s have recently published initiatives aimed at improving the design of new systems in light of their growing complexity [21]. Initiatives have been announced by DARPA [22], NASA [23], Lockheed Martin =-=[24]-=-, and Boeing [25]. A unifying characteristic of these initiatives is that each seeks to design and model new systems based on reusable components (e.g., mechanics, propulsion, electronics). Some of th...

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...ublished initiatives aimed at improving the design of new systems in light of their growing complexity [21]. Initiatives have been announced by DARPA [22], NASA [23], Lockheed Martin [24], and Boeing =-=[25]-=-. A unifying characteristic of these initiatives is that each seeks to design and model new systems based on reusable components (e.g., mechanics, propulsion, electronics). Some of their motivations i...

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...n system design, and ongoing verification during a design’s implementation [6]. Currently, a very common method of determining a new system’s behavior is by developing and testing physical prototypes =-=[4,26]-=-. When verifying system design decisions using physical prototypes, a new system design is initially based on studies of previous systems, analysis of component models, and designer expertise. If this...

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...and designer expertise. If this new system is unable to accomplish its design objectives, the prototype system is studied to determine the causes of the shortfall and the system design cycle restarts =-=[27]-=-. This results in significant development risk because of the many design decisions that can only be verified much later when system prototypes are available [24]. Actual system behavior can diverge u...

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... prototypes are available [24]. Actual system behavior can diverge unchecked from the desired system behavior between system prototypes, causing numerous design iterations and long development cycles =-=[28]-=-. Iterative prototyping also limits system design exploration due to the effort needed to develop and evaluate physical system prototypes. New system behavior can also be predicted using system models...

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...heterogeneous component models to interact within a system model through model composition [15, 30]. Compositional modeling has been implemented in commercial design tools such as iSight and Simulink =-=[31, 32]-=-. It is used frequently in multidisciplinary design optimization research [33–35]. Because compositional system models are able to integrate component models implemented in different design tools, the...

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...heterogeneous component models to interact within a system model through model composition [15, 30]. Compositional modeling has been implemented in commercial design tools such as iSight and Simulink =-=[31, 32]-=-. It is used frequently in multidisciplinary design optimization research [33–35]. Because compositional system models are able to integrate component models implemented in different design tools, the...

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...2], (2) model composition allows models of various types and time domains to be coupled [16, 43, 44], (3) component models implemented in various design tools can be coupled into compositional models =-=[33,35,45]-=-, (4) various methods of classifying and sharing the diverse data transferred between component models have been developed [38, 46], and (5) dynamic analysis of compositional system models can predict...

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...2], (2) model composition allows models of various types and time domains to be coupled [16, 43, 44], (3) component models implemented in various design tools can be coupled into compositional models =-=[33,35,45]-=-, (4) various methods of classifying and sharing the diverse data transferred between component models have been developed [38, 46], and (5) dynamic analysis of compositional system models can predict...

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...stem models are able to integrate component models implemented in different design tools, they are able to model systems composed of diverse components without losing accuracy due to model conversion =-=[21,36]-=- . Model composition can also be achieved without requiring elusive unified modeling standards [37, 38]. 5 Due to the long-term as well as renewed interest in compositional system modeling, many aspec...

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...hods of classifying and sharing the diverse data transferred between component models have been developed [38, 46], and (5) dynamic analysis of compositional system models can predict system behavior =-=[47]-=- . Despite this ongoing interest in compositional system modeling, multidisciplinary system design frequently does not benefit from this method [3]. Several obstacles hinder its use to validate design...

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...imensional dynamic systems [56], dynamic-stochastic systems, discrete time systems, discrete event systems [39], and hybrid systems [57]. All of these model types must compute outputs based on inputs =-=[58]-=-. In addition, dynamic systems have model state, state initialization, and state progression [59]. Dynamic systems might also require simulation time as an input as well as the ability to request simu...