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A formal representation of process model equations
Pergamon
Computerschem.EngngVol.21, No. 10, pp. I105-1115,1997 Copyright© 1997ElsevierScienceLtd.All rightsreserved Printedin GreatBritain Plh S0098-1354(96)00321-3 0098-1354/97$17.00+0.00
A formal representation of process model equations R. Bogusch* and W. Marquardt Process Engineering, RWTH Aachen University of Technology, D-52056 Aachen, Germany Abstract
The lack of adequate support for the development of mathematical process models confines the application of model-based techniques in the design and operation of complex chemical processes. To overcome this problem considerable effort has to be put into the development of knowledge-based software tools. The development of such tools requires a proper structuring of process models followed by a formalization of their representation. In this contribution, elementary modeling objects for the representation of the behavioral aspects of chemical processes are defined. The introduced methodology is based on ontological principles and general systems theory. Its formalization in terms of the object-oriented data model VeDa allows the formal representation of the mixed types of equations and formalisms arising in mathematical process models. It provides generality and extensibility since new types of equations or formalisms can be incorporated easily. © 1997 Elsevier Science Ltd
Keywords: mathematical process models; computer-aided modeling, explicit conceptualization; formal ontology; object-oriented representation
1. Introduction
The development of adequate mathematical process models is a key requirement for the routine application of model-based techniques in the design and operation of complex chemical processes, especially if the solution of difficult design or control problems requires detailed and non-standard process models. Established commercially available tools for process modeling and simulation which may roughly be classified into block-oriented (or modular) and equation-oriented approaches (Marquardt, 1996b) give no adequate support for the development of mathematical models from scratch or for the customization and reuse of already existing models. In block-oriented approaches the model representations mainly focus on the flowsheet topology of the chemical process and provide only basic modeling entities like standardized unit models and streams to link these unit models. Modeling on the flowsheet level is either supported by a modeling language as in ASPEN PLUS (AspenTech, 1994a) or by a graphical model editor such as MODELMANAGER(AspenTech, 1994b). Although most process simulators allow to develop userdefined unit models, this is a time-consuming and error-
* To whom correspondence should be addressed. E-mail: [email protected];Fax: +49-241-8888-326.
prone task, because the user must derive model equations in a classical way with paper and pencil and then implement them into the chosen simulator. This is particularly true for equation-oriented approaches, since equation-based modeling languages such as SPEEDUP (AspenTech, 1993) rely purely on mathematical rather than phenomena-based descriptions and do not allow explicit representation of available physico-chemical knowledge about process quantities and their relations. Moreover, customization and reuse of existing models is difficult when modeling is performed in the equationoriented way, in particular if poorly documented code exceeds hundreds of lines. It is even impossible in blockoriented simulators when predefined models are buried within existing programs. Due to the shortcomings of current model representations, modeling tools using object-oriented representations with declarative and structured knowledge representation are being developed. These tools facilitate model development as well as the reuse and adaptation of available models. Models are recursively decomposed into a hierarchy of submodels and inheritance concepts are used to refine previously defined models into new models. Object-oriented modeling languages such as OMOLA (Nilsson, 1993), ASCEND (Piela et al., 1992), gPRoMS (Oh and Pantelides, 1996) and MODEL.LA (Stephanopoulos et al., 1990) allow the declarative representation of structured model families of varying granularity. Additionally, modeling assistants have been
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developed using expert system techniques with advanced user interfaces to assist the model developer during the modeling process. Examples of prototypical systems are DESIGN-KIT(Stephanopoulos et al., 1987), MODASS (Srdie, 1990) and PROFIT (Telnes, 1992). A review of the recent developments in computer-aided process modeling and a discussion of the technical aspects is for example presented by Marquardt (1996b). For the development of a knowledge-based modeling tool proper process model structuring is indispensable. A useful starting point is provided by the conceptual framework of general systems theory (e.g. Klir, 1985). One key concept is that the description of a general system can be organized along two complexity coordinates-the structural coordinate given by the structural entities and their interrelations, and the behavioral coordinate given by the behavior of each entity. The system structure together with the behavior of each structural part results then in the behavior of the whole system (Marquardt, 1992, Marquardt, 1996a). The development of mathematical process models follows these guidelines. First, the process model is recursively decomposed into submodels for devices such as process units, parts of process units or phases, and submodels for connections relating these devices such as pipe and signal lines or phase boundaries. After the model is structured the behavior of the submodels must be described. Elementary models which are not further decomposed are described by the occurring phenomena and by equations such as balance or constitutive equations expressing the physical laws. Composite models are characterized by the behavior associated with the submodels and their coupling. The main idea of our approach is to view the set of
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model equations associated with a structural entity themselves as a complex structured system which can be decomposed into a phenomena-based schema of interrelated process quantities and equations. This results in a directed acyclic bipartite graph consisting of two types of nodes--variables and e q u a t i o n s - - w h i c h are related with alternating and/or-edges. Figure 1 illustrates the behavioral decomposition of a model equation describing the material balance of the reacting gas phase in a reactor tube. The balance equation is composed of process quantities describing the basic phenomena and of mathematical operators. Both are referred to by andedges. Each process quantity might be refined alternatively by more than one constitutive equation which in turn contains other phenomenological quantities that can be determined by further constitutive equations, The alternative constitutive equations to refine a process quantity are referenced by or-edges. This is recursively repeated until all quantities are elementary variables such as computed states or design variables (e.g. parameters and forcing functions) which need not be further refined. The resulting graph can be interpreted in two ways. If some degree of completeness regarding the quantities and equations involved could be attained, the graph together with a suitable representation of the knowledge at each node is a comprehensive repository of chemical process modeling knowledge. On the other hand, the behavioral description of a structural entity is accomplished by defining a view on the repository by means of selecting one or more paths in the graph to depict alternative sets of equations representing the behavior of the entity in possibly alternative ways in the sense of multifacetted modeling (Zeigler, 1984). Object-oriented techniques allow the representation of
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detailed knowledge about process quantities and equations since the behavioral entities are treated as objects with attributes, methods and relations between each other rather than simple data structures as in equationoriented or even in most of the object-oriented modeling languages cited above. In particular, physico-chemical knowledge about process quantities and physical laws is not buried within mathematical equations, but it is explicitly represented within behavioral entities. Pruning rules and constraints for the selection and aggregation of behavioral entities as well as methods, e.g. for the mathematical analysis and symbolic manipulation of the model prior to its numerical solution, allow to guide the model development. Moreover, the object-oriented representation provides generality and extensibility since new types of variables and equations can be incorporated easily, e.g. for the representation of combined continuous and discrete simulation problems comprising mixed systems of integral, ordinary and partial differential as well as algebraic equations. Additional formalisms of qualitative process modeling such as influence graphs or qualitative physics (see e.g. Hangos, 1991 for a review) can be integrated with mathematical process models to generate richer descriptions which for instance allow to deduce the qualitative behavior of the system by means of inference methods. Consequently, all available knowledge, i.e. generic and specific as well as quantitative and qualitative process knowledge should be used and represented declaratively in a unifying framework to take into account the multifacetted nature of modeling and to extend the scope of current modeling tools.
2. Conceptualization and the role of ontologies Every knowledge-based system is committed to some conceptualization, i.e. in order to represent knowledge about an area of interest, it must know about the objects and concepts that are assumed to exist in the domain and the relationships that hold among them. A domain conceptualization therefore provides a coherent vocabulary for representing and communicating knowledge about the domain, but not the actual representational structure. In knowledge-based systems, explicit specifications of domain conceptualizations are called ontologies (Gruber, 1993). This term is borrowed from philosophy, in which ontology has a long history that can be traced back to the metaphysical categories of Aristotle and the medieval Scholastic philosophy. For the specification of domain conceptualizations it is interesting to study the philosophy of science, where ontology deals with modeling the existence of things in the world. Bunge's ontology, for example, describes a general framework that contains and interrelates ontological categories such as things, properties, states, laws, classes, kinds, changes, and events in order to systematically analyze the existence of entities and all forms of being in the world (Bunge, 1977; Bunge, 1979). Since
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computer science primarily aims at building intelligent systems that serve some purpose, rather than developing general theories of the world, an abstract, simplified view of the world suffices. Thus, for knowledge-based systems, what exists in the external world is exactly that what we like to represent in the system for some purpose (Gruber, 1993). The domain conceptualization should guide the development of applications and support flexible reasoning during problem solving. Moreover, if carefully designed, the conceptualization can be reused for different applications. To support reusability, it is important to identify useful concepts (such as variable, dimension, unit and equation in the domain of mathematical modeling) and distinguish between the generality of the concepts in the domain. These representational primitives together with taxonomic relationships (i.e. generalization and specialization) form a part of the ontology and should be task independent. They are the building blocks for modeling domain knowledge. Nevertheless, designing ontologies is rather difficult and time-consuming and therefore development cost is a major obstacle to the construction of large scale intelligent systems. Since many conceptualizations are intended to be useful for a wide variety of application tasks, an important means of reducing this effort is to encode ontologies in a reusable form so that large portions of an ontology for a given application can be assembled from ontology repositories. Therefore, some research groups aim at the construction of portable ontologies that can be mapped into multiple representation languages (e.g. Gruber, 1993). ONXOLINGUAfor example is a domain independent translation tool for describing ontologies in a form that can be mapped into representations of several systems (Gruber, 1992). An important property of an ontology is that it gives a precise and unambiguous definition of the concepts and relationships necessary for representing domain knowledge, without reference to representational aspects such as data structures or operations on these data structures. This puts ontologies at the knowledge level (Newell, 1982). As a consequence, considerations which have to do with the nature of the task a mathematical model serves, such as numerical simulation, rigorous optimization, model-based diagnosis or control, can be stated explicitly without confusing them with implementational details at the symbol level. During the eighties Newell's "knowledge-level hypothesis" became very popular and lead to a paradigm shift in the Artificial Intelligence research which had been focused too much on representational issues. Ideally, knowledge-based software components are designed with ontological commitments at the knowledge level in order to allow for sharing and communicating knowledge, rather than simple data structures. Since conceptualization is a crucial step in the design of every knowledge-based tool, we have developed an ontology for describing mathematical process models based on general systems theory (e.g. Klir, 1985) and the ontological principles de fined by Bunge in his "Treatise
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on Basic Philosophy" (Bunge, 1977; Bunge, 1979). It defines structural and behavioral modeling objects on different levels of abstraction which are organized in taxonomies with inheritance and aggregation relationships between them. The aim of this conceptualization is to define a minimum set of elementary modeling objects which are disjunct with respect to the knowledge they represent and allow an almost arbitrary aggregation to more complex objects. A particular process model can then be developed by selection, specification and aggregation of predefined modeling objects. Modeling objects especially for the representation of structural modeling entities such as devices, connections and couplings for the representation of complex objects have been defined recently in Marquardt et al. (1993b). In contrast, this contribution is concerned with modeling objects for the representation of behavioral modeling entities. A detailed description of the modeling methodology can be found in Marquardt (1996a).
3. Mapping ontological concepts to object-oriented representations Descriptions at the knowledge level can be divided into a conceptualization and formalization (Genesereth and Nilsson, 1987). While a conceptualization consists of "the entities that are assumed to exist in the world and their interrelationships", the formalization of knowledge entails the representation of knowledge about the domain as sentences in a formal language. Such a language must have syntax and semantics. The syntax describes the elements of the language and how these elements may be combined to form sentences. The exact relation between conceptualization and formalization is defined by the semantics, which formally relates sentences and elements of the language to entities and relations of the conceptualization (Alberts, 1993). Often some kind of predicate logic calculus is used as a representation means. Such representations provide formal declarative semantics but they cannot be easily understood by someone who is not trained in computer science. The application of such formalisms is therefore unnecessarily complicated. Instead, object-oriented approaches seem to be preferable because they overcome the disadvantages of predicate logic formalisms to a large extent. Particularly, they reflect a more natural view of the world that is to be modeled. Although the object-oriented paradigm is very popular in programming languages and conceptual modeling for database design, there is a lot of confusion about the objectoriented notion, mainly because it emerged as a programming construct, which is driven by implementation considerations. According to Newell (1982) we propose a knowledge-level approach where objects are a means to describe conceptual perceptions of the world. Using an appropriate representation formalism, those objects can be mapped into a formal representation language. Wand (1989), for example, presents a formal
approach to the object concept based on Bunge's scientific ontology (Bunge, 1977; Bunge, 1979) and maps the formal definitions of ontology to commonly used concepts of objects. Our work aims at the formal representation of knowledge about mathematical modeling independent of any implementation details. For that purpose, we are currently developing an application specific objectoriented data model called VEDA (Verfahrenstechnisches Datenmodell) that should capture all available knowledge about mathematical modeling in the chemical process engineering domain and support the construction of intelligent modeling applications (Marquardt et al., 1993a). VEDA is a representation language that builds on ontological principles outlined above.* It includes the core concepts of object-oriented data modeling as identified by Kim (1990) and several extensions which have been suggested in structured knowledge representation and data modeling research (e.g. King and Hull, 1987; Kim, 1990). VEDA defines frames for modeling concepts and modeling relations by tuples of attributes, laws (constraints) and methods. So called facets are used to characterize attributes (e.g. type and cardinality) or to add simple constraints (e.g. cross referential integrity constraint). The latter is used to explicitly state consistency requirements for attribute values referring to each other. Complex constraints relating one or more concepts are expressed by laws with the help of a predicate logic based declarative constraint language. Constraints are essential to automatically guarantee consistent specification and aggregation of modeling objects.
4. Definition of behavioral modeling objects Following many object-oriented and semantic data models we distinguish behavioral modeling concepts (BMCs) and behavioral modeling relations (BMRs). Generally, BMCs are used to represent entities of the behavioral description like variables, operators, dimensions or units whereas BMRs are needed to describe complex relations between those entities such as equations or systems of equations. The introduced types can be interpreted as classes which are organized in a taxonomy with inheritance between classes and their subclasses as depicted in Fig. 2 where classes are represented by an oval and inheritance relationships by arrows.
4.1. The SCALAR-VARIABLE Model equations consist of variables representing individual process quantities. Variables can be asso-
* VEDA means "comprehensive knowledge" in Sanskrit.
A formal representation of process model equations
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Fig. 2. Part of the taxonomy of behavioral modeling concepts, behavioral modeling relations and aggregates. ciated with a variety of attributes. For example, a variable representing the temperature inside a reactor tube may be characterized by a physical dimension "temperature", by a symbol "T", by a value "521.3" and a unit "Kelvin". To model such a process quantity the BMC SCALAR-VARIABLE is introduced as a refinement of TENSOR-VARIABLE. It contains an attribute for the name and a reference to the structural entity (a device or connection) which is described by the variable. In accordance with Batory and Kim (1985) we split up the different attributes of a variable into an interface and an implementation description to support multifacetted modeling, i.e. to have multiple models serving different purposes. This allows the use and implementation of a single variable (such as temperature) in different ways
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depending on the application context. For example, if different symbols are required, one can provide appropriate interfaces for that variable. Additionally, for a chosen interface several implementations are possible, e.g. an implementation to supply a fixed value and a further implementation, in which the value of the variable depends on an equation. Figure 3 shows individual frames defining a variable, its interface and its implementation. The attributes active-interface and isabstracting are used to relate a variable with its interface. Between both attributes a cross referential integrity constraint which is graphically depicted by a small square automatically guarantees consistency of the attribute values. Additionally, the attribute possibleinterfaces is defined in the frame for a variable to
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reference possible alternatives of interfaces. The relationship between a variable and its implementation is modeled analogously. The interface and the implementation of a variable can also be considered as two perspectives depicting different views on this variable. In this respect the multi-perspective knowledge representation scheme proposed by Marifio et el. (1990) is promising to reduce complexity in our representation.
4.2. The SCALAR-VARIABLE-INTERFACE and the SCALAR- VARIABLE-IMPLEMENTATION These two BMCs are introduced as sub classes of TENSOR-VARIABLE-INTERFACE and TENSOR-VARIABLE-IMPLEMENTATION, respectively, to represent the interface and the implementation of a variable. The interface description contains all information that is needed to reference and use a variable in a certain modeling context. It comprises for instance a symbol used as abbreviation of the variable name, a reference to the physical dimension, the support (continuous or discrete values, qualitative or fuzzy values), bounds (minimum and maximum value) and references to the coordinates the variable depends on (time, spatial coordinates etc.). The implementation description contains information about the value and its realization, e.g. references to the value in computational units, to the display-value used for communication with the user, and to a typical-value which can be used as default or for order-of-magnitude estimations. So called landmarkvalues are introduced to specify actions which must be taken if a certain landmark value is passed. Other attributes are added to the implementation for the system-theoretic classification of a variable as a state variable, a parameter or an input variable, for the classification as a design-or-computed variable, and to indicate that a variable is selected as a report variable for documentation purposes. The attributes possibleequations and active-equation refer to possible equations and the actually chosen equation to refine the behavior of the variable according to or-edges of the schema shown in Fig. 1.
since there is also a distinction between fundamental and deduced units. A unit, for instance the time unit, is characterized by a name "hour", a symbol "h", a standard-unit "s", and provides formulae to convert units to or from the standard unit. The BMC SCALARVALUE which is a subclass of TENSOR-VALUE represents an arbitrary value of a scalar variable. It contains internal-values used for calculations, communicationvalues for the interaction with the user, and references to the units of measurement. Moreover, process trends of variable values with respect to time can be recorded and analyzed.
4.4. The OPERATOR In addition to variables, differential operators such as the substantial derivative, gradient, divergence or Laplacian are further constituents of model equations, e.g. if modeling of distributed parameter systems is considered. In order to represent arbitrary kinds of differential operators the BMC OPERATOR is introduced. It is characterized by its name, operator-symbol, a reference to the operator-argument, to the operator-equation and to the actually used coordinate-system (Cartesian, cylindrical, spherical or general orthogonal coordinates). Since the intended coordinate system is not known in advance, the operator concept provides a method to derive an operator equation acting on the operator argument with respect to the chosen coordinates.
5. Aggregation of behavioral modeling objects This section introduces additional modeling concepts for the ,-ggregation of individual modeling objects into regular structures like vectors as well as BMRs for the aggregation of variables and operators into complex structures like equations and systems of equations.
5. I. The RECORD and the TENSOR 4.3. The DIMENSION, the UNIT and the SCALARVALUE Tile BMC DIMENSION is referenced by a variable interface and characterizes the physical dimension of a variabl~. We distinguish fundamental dimensions such as mass, length, temperature and deduced dimensions such as area or force. The latter contain a definition formula of the deduced dimension as a function of fundamental dimensions and are organized in a simple taxonomy with inheritance relationships. A dimension provides some possible-units and a computational-unit in which all calculations are carried out, e.g. the time dimension has seconds, minutes, hours as possible units. The BMC UNIT parallels the taxonomy of dimensions
These additional modeling concepts are defined as a refinement of the class AGGREGATE to provide arbitrary modeling objects with regular aggregation properties. The RECORD allows to aggregate elements of different type whereas the TENSOR with its refinements VECTOR and MATRIX restricts aggregation to elements of the same type. Using multiple inheritance aggregation properties can be inherited from records or tensors. As shown in Fig. 4 VECTOR-VARIABLE is a direct specialization of TENSOR-VARIABLE and VECTOR to allow VECTOR-VARIABLEs to be composed of SCALARVARIABLEs. The aggregation into tensors of higher degree (e.g. matrices) as well as the aggregation of other modeling objects such as equations is modeled analogously.
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5.4. The EQUATION-TYPE
5.2. The EQUATION Equations with refinements to TENSOR-EQUATION, SYSTEM-OF-EQUATIONS and VARIABLE-STRUCTURE-EQUATION describe the behavior of the structural modeling objects (devices or connections) introduced in Marquardt (1993b). A structural entity is linked with its behavioral description via the attributes active-behavior and possible-behaviors referencing equations (single equations or systems of equations) as illustrated in Fig. 4. Again this allows to have alternative behaviors for a structural entity and thus supports multifacetted modeling.
5.3. The TENSOR-EQUATION Tensor equations are refined to SCALAR-EQUATION, VECTOR- EQUATION and MATRIX-EQUATION by inheriting the corresponding aggregation properties in order to represent a single equation. As depicted in Fig. 4 equations can be viewed as complex objects which relate variables and operators. They are characterized by a name, the relation containing the equation in symbolic form, references to the variables and to the operators occurring in tile equation according to the and-edges of the graph of Fig. 1, by a norm to compute a residual value and by the actual residual of the equation. Moreover, methods are provided for example to check the dimensional consistency of an equation.
Many modeling tools are restricted to specific problem classes such as lumped parameter systems and allow the behavior to be described only in terms of mixed systems of ordinary differential and algebraic systems (DAEs). This is definitely an oversimplification since first principles based modeling of distributed parameter systems and particulate systems involves mixed sets of integral, partial or ordinary differential as well as algebraic equations (Marquardt, 1991). The BMR EQUATION-TYPE is introduced to capture all the information that must be provided to completely specify the properties of an equation. For example, boundary value problems of ordinary differential equations and partial differential equations must comprise boundary conditions. Different subclasses of EQUATION-TYPE are defined and organized in a taxonomy with inheritance relationships. The specializations of TENSOR-EQUATION inherit attributes from an EQUATION-TYPE according to their mathematical type. Some attributes are for example the equation-type (algebraic, differential, integral,...), the relation storing the equation and the initial-value or boundary-values if any.
5.5. The SYSTEM-OF-EQUATIONS Equations can be aggregated in the sense of a record to form a system of equations which is in general of mixed type. Therefore, SYSTEM-OF-EQUATIONS inherits aggregation properties from RECORD to allow aggregation of arbitrary equations. The attribute constituents contains a reference to an arbitrary equation which itself can be a SYSTEM-OF-EQUATIONS. This
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allows the representation of complex structured equation systems.
5.6. The VARIABLE-STRUCTURE-EQUATION Often, process models are not strictly continuous. They may discontinuously change their structure at certain points in state space. For instance, process inherent discontinuities like phase changes or flow reversals as well as process operations during start-up and shutdown operations may be reasons for discontinuities causing either a switch in the model equations or even in the structure and dimensionality of the model (Marquardt, 1991). The BMR VARIABLESTRUCTURE-EOUATION is capable of representing a system of equations with structural variance. According to Klir (1985) it consists of an initial-case (a system of equations), alternative eases to represent the structural variants and a set of transition-conditions to determine a switch from one case to another.
6. Related work
Our framework is similar to other work on engineering ontologies which has been quite popular within the knowledge representation community. A number of projects use ONTOLINGUA (Grnber, 1992), a tool for writing portable ontologies in a canonical format, such that they can be translated into a variety of representation and reasoning systems. This allows to maintain the ontology in a single, machine-readable form while using it in systems with different syntax and reasoning capabilities (Gruber, 1992). The syntax and semantics of Om'OmNCUAis based on the KIF knowledge interchange format (Genesereth and Fikes, 1992) which is an extended version of a first-order predicate calculus with a Lisp-like notation. Most closely related to our work is the ENGMATH ontology for mathematical modeling in engineering developed by Gruber and co-workers (Gruber and Olsen, 1994). The conceptualization builds on abstract algebra and measurement theory. It includes the conceptual foundations for scalar, vector, and tensor quantities, physical dimensions, units of measure, functions of quantities, and dimensionless quantities using the KIF specification language. The ontology is used as a communication language among cooperating engineering agents, and as a foundation for other engineering ontologies, but the main purpose is knowledge sharing. The authors offer also some evaluation criteria for designing such ontologies. Because the ENcMATU ontology is very generic and domain independent, it imposes little structure on the physical quantities and mathematical relations defined. Moreover, the ontology does not focus on the relations between physical quantities and physical laws which allows explicit representation of physico-chemical knowledge and guides the decomposition of model equations as in our work.
The Compositional Modeling Language (CML) is being designed collaboratively by leading qualitative physics research groups (Falkenhainer et al., 1994). CML is a general declarative modeling language for specifying the symbolic and mathematical properties of the structure and behavior of physical systems. The CML ontology is specified with ONTOLINCUA and includes concepts that are defined in the ENCMA'rH ontology. CML domain theories consist of so-called model fragment definitions, which describe a type of phenomena or entity in the domain's physics. Instances of definitions are said to be active whenever there exists a set of entities in a model that satisfies the conditions stated in the definition. A model fragment's consequences hold when an instance of a model fragment is active. Model fragment consequences are typically equations that describe the behavior of the entities. A specific system being modeled is called scenario. The model of a scenario in a domain theory consists of model fragment instances from the theory that are activated by the scenario definition. At present the expressiveness and usability of CML is evaluated in the domain of thermodynamics. The domain theory contains definitions for the primary conceptual objects including control volume, stream and steady-state flow process, which establishes the first law equations. Although CML allows to have multiple behavioral descriptions of physical systems, it is primarily based on qualitative physics and the expressiveness is restricted with respect to the different kinds of mathematical models that can be represented (e.g. partial differential equations cannot be represented). Alberts (1993) describes YMIR as a reusable ontology intended as the basis for the development of knowledgebased design systems in different engineering domains. It provides a vocabulary for modeling the structure and behavior of systems based on general systems theory (Klir, 1985) as well as a basic reasoning strategy for the synthesis of technical systems. The treatment of physical quantities in that ontology is quite restrictive as stated in (Gruber and Olsen, 1994). First, quantities are represented by variables that are annotated with a value, a symbolic quantity types, a unit, a value domain, and a time dependency. There is no means to define new complex quantity types, dimensions or units based on existing ones. Second, the values are unary scalar functions of time, i.e. models with vector or tensor quantities, as well as distributed parameters models with partial differential equations or phase space models cannot be represented, since time is the only dependent variable that is allowed. Third, the values of quantities are tuples of numbers and fixed units. In our work quantities are related to, but independent of values and units. This allows to have several implementations for one quantity, e.g. values with different units of measure or even an equation in order to calculate a value. The present work at the University of Twente is directed to the development of ontologies for physical systems staying as close as possible to the modern methods of general systems engineering. The PHvsSvs
A formal representation of process model equations ontology introduces several engineering ontologies that express different conceptual viewpoints upon physical systems, e.g. a component ontology that describes the structural decomposition of a system, a process ontology that describes the physical mechanisms underlying systems behavior, and a mathematical ontology defining the mathematics required to describe physical processes (Borst et al., 1994; Borst et al., 1995). They are based on the ENGMATH ontology and im plemented using ONTOLINGUA. The aim is to provide a basis for the development of structured model libraries for engineering design. The main difference to our work is that the behavioral view of the Pr~YsSvs ontology is formalized using the bond graph approach (see for e.g. Gawthrop and Smith, 1996). Each node represents a physical law (such as conservation of energy) and mathematically it is associated with a (algebraic or differential) constraint equation on the physical variables involved. The edges denote energy exchange links and mathematically they indicate the variables that are shared between equations. In practice, the approach is used as a graphical front end to computer algebra and numerical simulation systems. Again, guidance of the model development, e.g. by providing a comprehensive repository of chemical engineering knowledge in conjunction with pruning rules and constraints that support the selection of suitable model equations, is not considered.
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the phenomena-based decomposition of model equations. Moreover, a hypertext system is available to create comprehensive documentation that can be linked with modeling objects in order to record all assumptions and decisions taken, capture experience gained during the model development, or to provide background knowledge related to physico-chemical phenomena. An agenda manager is available on request that guides the user through the process of model development by suggesting modeling actions to be performed next depending on the modeling context and state of the model (Lohmann and Marquardt, 1996). Additionally, the process-centered environment PROART/CE (Drmges et al., 1996) which builds on concepts developed for requirements engineering and primarily aims at managing the evolution of models is being developed in close collaboration with the Information Systems group at RWTH Aachen. It supports capturing and recording all relevant information arising during the model development and maintenance in order to enable traceability, selective guidance and experience-based improvement of the process of model development (Jarke and Marquardt, 1995).
8. Conclusions
This paper presents a general framework for the representation of mathematical models which can be viewed as the foundation for creating an intelligent 7. Status of implementation computer-based modeling tool. It discusses the role of Implementations of VEDA are currently being carried ontologies for the conceptualization of the domain and out using different software platforms. The frame-based the use of object-oriented techniques for the representaknowledge representation language FRAMETALK tion of process model equations. The structuring of (Ratbke, 1991)--an object-oriented language based on model equations leads to a complex and/or-graph CLOS (Common Lisp Object System)--is used at relating variables and equations. Modeling objects for Stuttgart University. Gensym's G2 (Harmon, 1993)--a the declarative representation of this graph are defined complete application environment for creating intelli- using the object-oriented data model VEDA. The introgent systems, providing representational and reasoning duced formalism allows to explicitly represent physicoprimitives (objects and rules), a procedural language, a chemical knowledge about process quantities and equagraphical interface, links to external applications, data- tions and takes into account the multifacetted nature of bases and distributed control systems--is the basis for modeling. This is a prerequisite for the development of the modeling environment MoDKIT (Bogusch et al., sophisticated modeling tools that considerably reduce the modeling effort. In this respect the proposed 1996) at RWTH Aachen. MoDKIT consists of a graphical model editor that representation formalism offers a useful starting point to allows to create structural descriptions of chemical build a comprehensive repository of chemical engineerprocess models according to the methodology proposed ing knowledge, but at the same time it reveals the by Marquardt (1996a). The structural description can be considerable representational complexity and the tredecomposed into arbitrary hierarchical levels with mendous implementational effort. The implementational different model alternatives at each level of the hier- alternatives as discussed above are essential to prove archy. A taxomomy of structural modeling objects practicability of our approach and to provide feedback (SMCs) has been implemented. Each SMC is associated from expert and casual modelers. with a set of characterizing attributes and a corresponding behavioral description in an equation-oriented manner in order to support existing process simulators like SPEEDUP and gPRoMS. At present, the representation References framework proposed in this contribution is currently Alberts, L. K. (1993) YMIR: an ontology for engineerbeing implemented to allow the representation of the ing design. Doctoral dissertation. University of and/or-graph relating variables and equations as well as Twente, Enschede, The Netherlands.
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AspenTech (1993) SPEEDUP User Manual. Aspen Technology, Inc., Cambridge, MA. AspenTech (1994a) ASPEN PLUS User Guide. Aspen Technology, Inc., Cambridge, MA. AspenTech (1994b) ASPEN PLUS ModelManager Reference Manual. Aspen Technology, Inc., Cambridge, MA. Batory, G. and Kim, W. (1985) Modeling concepts for VLSI CAD objects. ACM Trans. Database Systems 10, 322-426. Bogusch, R., Lohmann, B. and Marquardt, W. (1996) Rechnergesttitzte Modellierung in der Verfahrenstechnik. GVC-Jahrestagung 1996, Dortmund, September 1996. To be published in Chem.-Ing.-Tech. Borst E, Pos, A., Top, J. L. and Akkermans, J. M. (1994) Physical systems ontology. Proc. European Conference on Artificial Intelligence ECAI '94. Workshop on comparison of implemented ontoiogies, Amsterdam, pp. 47-80. Borst, E, Akkermans, J. M., Pos, A. and Top, J. L. (1995) The PhysSys ontology for physical systems. Ninth International Workshop on Qualitative Reasoning, Amsterdam, pp. 11-21. Bunge, M. (1977) Treatise on Basic Philosophy. Vol. 3: Ontology I: The Furniture of the World. Reidel, Dordrecht, The Netherlands. Bunge, M. (1979) Treatise on Basic Philosophy. Vol. 4: Ontology II: A World of Systems. Reidel, Dordrecht, The Netherlands. D6mges, R., Pohl, K., Jarke, M., Lohmann, B. and Marquardt, W. (1996) PRO-ART/CE--An environment for managing the evolution of chemical process simulation models. Proc. lOth European Simulation Multiconference ESM '96, Budapest, Hungary, pp. 1012-1017. Falkenhainer, B., Farquhar. A., Brobow, D., Fikes, R., Forbus, K., Gruber, T. Iwasaki, Y. and Kuipers, B. (1994) CML: a compositional modeling language. Technical report KSL-94-16. Knowledge Systems Laboratory, Stanford University. Gawthrop, E and Smith, L. (1996)Metamodelling: Bond graphs and dynamic systems. Prentice Hall, Englewood Cliffs, NJ. Genesereth, M. R. and Nilsson, N. J. (1987) Logical foundations of artificial intelligence. Morgan Kauffmann, Los Altos. Genesereth, M. R. and Fikes, R. E. (1992) Knowledge Interchange Format, Version 3.0, Reference Manual. Report Logic-92-1. Computer Science Department, Stanford University. Gruber, T. R. (1992) Ontolingua: a mechanism to support portable ontologies. Internal report. Knowledge Systems Laboratory, Stanford University. Gruber, T. R. (1993) A translation approach to portable ontology specifications. Knowledge Acquisition 5, 3 199-220. Gruber T. R. and Olsen, G. R. (1994) An ontology for engineering mathematics. In Fourth International Conference on Principles of Knowledge Representation and Reasoning (J. Doyle, E Torasso, and E. Sandewall, Eds), Morgan Kaufmann, San Mateo, CA, pp. 258-269 Hangos, K. (1991) Qualitative process modeling. In Chemical Process Control CPC-IV (Y. Arkun and W. H. Ray, Eds), CACHE, Austin, AIChE, New York, pp. 209-236.
Harmon, P. (1993) G2: Gensym's real-time expert system. Intelligent Software Strategies 9, No. 3 Cutter Information Corp., Arlington, MA, pp. 1-16. Jarke, M. and Marquardt, W. (1995) Design and evaluation of computer-aided modeling tools. ISPE '95, Snowmass, Colorado. To be published in AIChE Syrup. Set. Kim, W. (1990) Introduction to object-oriented data bases. MIT Press, Cambridge. King, R. and Hull, R. (1987) Semantic database modeling: survey, applications, and research issues. ACM Comput. Surv. 19, 201-260. Klir, G. J. (1985) Architecture of Problem Solving. Plenum Press, New York. Lohmann, B. and Marquardt, W. (1996) On the systematization of the process of model development. Computers chem. Engng 20 Suppl., 213-218. Marifio, O., Rechenmann, E and Uvietta, E (1990) Multiple perspectives and classification mechanism in object-oriented representation. European Conf. on Artificial Intelligence, pp. 425-430. Marquardt, W. (1991) Dynamic process simulation-recent progress and future challenges. In Chemical Process Control CPC-IV (Y. Arkun and W. H. Ray, Eds), CACHE, Austin, AIChE, New York, pp. 131-180. Marquardt, W. (1994) Rechnergesttitzte Erstellung verfahrenstechnischer Proze6modelle. Chem.-Ing.Techn. 64, 25-40 (1992). English translation in Int. chem. Engng 34, 28-46. Marquardt, W. et al. (1993a) Objekt-orientierte Datenmo dellierung for die Repr~isentation yon verfah renstechnischen ProzeBmodellen. Internal draft report, University of Stuttgart and RWTH Aachen University of Technology. Marquardt, W., Gerstlauer, A. and Gilles, E. D. (1993b) Modeling and representation of complex objects: A chemical engineering perspective. Proc. of 6th Int. Conf. on IEA/AIE, Edinburgh, Scotland, pp. 219-228. Marquardt, W. (1996a) Towards a process modeling methodology. In Model-based Process Control (R. Berber, Ed.). NATO-ASI Series, Kluwer Press, The Netherlands, pp. 3-40. Marquardt, W. (1996b) Trends in computer-aided process modeling. Computers chem. Engng 20, 591-609. Newell, A. (1982) The knowledge level. Artifl Intell. 18, 87-127. Nilsson, B. (1993) Object-oriented modeling of chemical processes. Doctoral dissertation. Department of Automatic Control, Lund Institute of Technology, Sweden. Oh, M. and Pantelides, C. C. (1996) A modelling and simulation language for combined lumped and distributed parameter systems. Computers chem. Engng 20, 611-633. Piela, E C., McKelvey, R. D. and Westerberg, A. W. (1992) An introduction to Ascend: its language and interactive environment. J. Man. lnfo. Sci. 9, 91-121. Rathke, C. (1991) Implementing frames in an objectoriented programming language. Proc. of Ist European Conf. on Object-Oriented Programming, Bratislave, pp. 88-94.
A formal representation of process model equations S6rlie, C. F. (1990) A computer environment for process modeling. Doctoral dissertation. Laboratory of Chemical Engineering, Norwegian Institute of Technology, Trondheim. Stephanopoulos, G., Johnston, J., Kriticos, T., Lakshmanan, R., Mavrovouniotis, M. and Siletti, M. (1987) Design-Kit : An object-oriented environment for process engineering. Computers chem. Engng 11, 655-4574. Stephanopoulos, G., Henning, G. and Leone, H. (1990) ModeI.La. A language for process engineering. Part I and II. Computers chem. Engng 14, 813-869.
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Telnes, K. (1992) Computer-aided modeling of dynamic processes based on elementary physics. Doctoral dissertation. Division of Engineering Cybernetics, Norwegian Institute of Technology, Trondheim. Wand, Y. (1989) A proposal for a formal model of objects. In Object-Oriented Concepts, Databases, and Applications (W. Kim and E H. Lochovsky, Eds), pp. 537-559. Addison-Wesley, Reading, MA. Zeigler, B. P. (1984) Multifacetted Modelling and Discrete Event Simulation. Academic Press, London.
Computerschem.EngngVol.21, No. 10, pp. I105-1115,1997 Copyright© 1997ElsevierScienceLtd.All rightsreserved Printedin GreatBritain Plh S0098-1354(96)00321-3 0098-1354/97$17.00+0.00
A formal representation of process model equations R. Bogusch* and W. Marquardt Process Engineering, RWTH Aachen University of Technology, D-52056 Aachen, Germany Abstract
The lack of adequate support for the development of mathematical process models confines the application of model-based techniques in the design and operation of complex chemical processes. To overcome this problem considerable effort has to be put into the development of knowledge-based software tools. The development of such tools requires a proper structuring of process models followed by a formalization of their representation. In this contribution, elementary modeling objects for the representation of the behavioral aspects of chemical processes are defined. The introduced methodology is based on ontological principles and general systems theory. Its formalization in terms of the object-oriented data model VeDa allows the formal representation of the mixed types of equations and formalisms arising in mathematical process models. It provides generality and extensibility since new types of equations or formalisms can be incorporated easily. © 1997 Elsevier Science Ltd
Keywords: mathematical process models; computer-aided modeling, explicit conceptualization; formal ontology; object-oriented representation
1. Introduction
The development of adequate mathematical process models is a key requirement for the routine application of model-based techniques in the design and operation of complex chemical processes, especially if the solution of difficult design or control problems requires detailed and non-standard process models. Established commercially available tools for process modeling and simulation which may roughly be classified into block-oriented (or modular) and equation-oriented approaches (Marquardt, 1996b) give no adequate support for the development of mathematical models from scratch or for the customization and reuse of already existing models. In block-oriented approaches the model representations mainly focus on the flowsheet topology of the chemical process and provide only basic modeling entities like standardized unit models and streams to link these unit models. Modeling on the flowsheet level is either supported by a modeling language as in ASPEN PLUS (AspenTech, 1994a) or by a graphical model editor such as MODELMANAGER(AspenTech, 1994b). Although most process simulators allow to develop userdefined unit models, this is a time-consuming and error-
* To whom correspondence should be addressed. E-mail: [email protected];Fax: +49-241-8888-326.
prone task, because the user must derive model equations in a classical way with paper and pencil and then implement them into the chosen simulator. This is particularly true for equation-oriented approaches, since equation-based modeling languages such as SPEEDUP (AspenTech, 1993) rely purely on mathematical rather than phenomena-based descriptions and do not allow explicit representation of available physico-chemical knowledge about process quantities and their relations. Moreover, customization and reuse of existing models is difficult when modeling is performed in the equationoriented way, in particular if poorly documented code exceeds hundreds of lines. It is even impossible in blockoriented simulators when predefined models are buried within existing programs. Due to the shortcomings of current model representations, modeling tools using object-oriented representations with declarative and structured knowledge representation are being developed. These tools facilitate model development as well as the reuse and adaptation of available models. Models are recursively decomposed into a hierarchy of submodels and inheritance concepts are used to refine previously defined models into new models. Object-oriented modeling languages such as OMOLA (Nilsson, 1993), ASCEND (Piela et al., 1992), gPRoMS (Oh and Pantelides, 1996) and MODEL.LA (Stephanopoulos et al., 1990) allow the declarative representation of structured model families of varying granularity. Additionally, modeling assistants have been
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developed using expert system techniques with advanced user interfaces to assist the model developer during the modeling process. Examples of prototypical systems are DESIGN-KIT(Stephanopoulos et al., 1987), MODASS (Srdie, 1990) and PROFIT (Telnes, 1992). A review of the recent developments in computer-aided process modeling and a discussion of the technical aspects is for example presented by Marquardt (1996b). For the development of a knowledge-based modeling tool proper process model structuring is indispensable. A useful starting point is provided by the conceptual framework of general systems theory (e.g. Klir, 1985). One key concept is that the description of a general system can be organized along two complexity coordinates-the structural coordinate given by the structural entities and their interrelations, and the behavioral coordinate given by the behavior of each entity. The system structure together with the behavior of each structural part results then in the behavior of the whole system (Marquardt, 1992, Marquardt, 1996a). The development of mathematical process models follows these guidelines. First, the process model is recursively decomposed into submodels for devices such as process units, parts of process units or phases, and submodels for connections relating these devices such as pipe and signal lines or phase boundaries. After the model is structured the behavior of the submodels must be described. Elementary models which are not further decomposed are described by the occurring phenomena and by equations such as balance or constitutive equations expressing the physical laws. Composite models are characterized by the behavior associated with the submodels and their coupling. The main idea of our approach is to view the set of
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model equations associated with a structural entity themselves as a complex structured system which can be decomposed into a phenomena-based schema of interrelated process quantities and equations. This results in a directed acyclic bipartite graph consisting of two types of nodes--variables and e q u a t i o n s - - w h i c h are related with alternating and/or-edges. Figure 1 illustrates the behavioral decomposition of a model equation describing the material balance of the reacting gas phase in a reactor tube. The balance equation is composed of process quantities describing the basic phenomena and of mathematical operators. Both are referred to by andedges. Each process quantity might be refined alternatively by more than one constitutive equation which in turn contains other phenomenological quantities that can be determined by further constitutive equations, The alternative constitutive equations to refine a process quantity are referenced by or-edges. This is recursively repeated until all quantities are elementary variables such as computed states or design variables (e.g. parameters and forcing functions) which need not be further refined. The resulting graph can be interpreted in two ways. If some degree of completeness regarding the quantities and equations involved could be attained, the graph together with a suitable representation of the knowledge at each node is a comprehensive repository of chemical process modeling knowledge. On the other hand, the behavioral description of a structural entity is accomplished by defining a view on the repository by means of selecting one or more paths in the graph to depict alternative sets of equations representing the behavior of the entity in possibly alternative ways in the sense of multifacetted modeling (Zeigler, 1984). Object-oriented techniques allow the representation of
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detailed knowledge about process quantities and equations since the behavioral entities are treated as objects with attributes, methods and relations between each other rather than simple data structures as in equationoriented or even in most of the object-oriented modeling languages cited above. In particular, physico-chemical knowledge about process quantities and physical laws is not buried within mathematical equations, but it is explicitly represented within behavioral entities. Pruning rules and constraints for the selection and aggregation of behavioral entities as well as methods, e.g. for the mathematical analysis and symbolic manipulation of the model prior to its numerical solution, allow to guide the model development. Moreover, the object-oriented representation provides generality and extensibility since new types of variables and equations can be incorporated easily, e.g. for the representation of combined continuous and discrete simulation problems comprising mixed systems of integral, ordinary and partial differential as well as algebraic equations. Additional formalisms of qualitative process modeling such as influence graphs or qualitative physics (see e.g. Hangos, 1991 for a review) can be integrated with mathematical process models to generate richer descriptions which for instance allow to deduce the qualitative behavior of the system by means of inference methods. Consequently, all available knowledge, i.e. generic and specific as well as quantitative and qualitative process knowledge should be used and represented declaratively in a unifying framework to take into account the multifacetted nature of modeling and to extend the scope of current modeling tools.
2. Conceptualization and the role of ontologies Every knowledge-based system is committed to some conceptualization, i.e. in order to represent knowledge about an area of interest, it must know about the objects and concepts that are assumed to exist in the domain and the relationships that hold among them. A domain conceptualization therefore provides a coherent vocabulary for representing and communicating knowledge about the domain, but not the actual representational structure. In knowledge-based systems, explicit specifications of domain conceptualizations are called ontologies (Gruber, 1993). This term is borrowed from philosophy, in which ontology has a long history that can be traced back to the metaphysical categories of Aristotle and the medieval Scholastic philosophy. For the specification of domain conceptualizations it is interesting to study the philosophy of science, where ontology deals with modeling the existence of things in the world. Bunge's ontology, for example, describes a general framework that contains and interrelates ontological categories such as things, properties, states, laws, classes, kinds, changes, and events in order to systematically analyze the existence of entities and all forms of being in the world (Bunge, 1977; Bunge, 1979). Since
II 07
computer science primarily aims at building intelligent systems that serve some purpose, rather than developing general theories of the world, an abstract, simplified view of the world suffices. Thus, for knowledge-based systems, what exists in the external world is exactly that what we like to represent in the system for some purpose (Gruber, 1993). The domain conceptualization should guide the development of applications and support flexible reasoning during problem solving. Moreover, if carefully designed, the conceptualization can be reused for different applications. To support reusability, it is important to identify useful concepts (such as variable, dimension, unit and equation in the domain of mathematical modeling) and distinguish between the generality of the concepts in the domain. These representational primitives together with taxonomic relationships (i.e. generalization and specialization) form a part of the ontology and should be task independent. They are the building blocks for modeling domain knowledge. Nevertheless, designing ontologies is rather difficult and time-consuming and therefore development cost is a major obstacle to the construction of large scale intelligent systems. Since many conceptualizations are intended to be useful for a wide variety of application tasks, an important means of reducing this effort is to encode ontologies in a reusable form so that large portions of an ontology for a given application can be assembled from ontology repositories. Therefore, some research groups aim at the construction of portable ontologies that can be mapped into multiple representation languages (e.g. Gruber, 1993). ONXOLINGUAfor example is a domain independent translation tool for describing ontologies in a form that can be mapped into representations of several systems (Gruber, 1992). An important property of an ontology is that it gives a precise and unambiguous definition of the concepts and relationships necessary for representing domain knowledge, without reference to representational aspects such as data structures or operations on these data structures. This puts ontologies at the knowledge level (Newell, 1982). As a consequence, considerations which have to do with the nature of the task a mathematical model serves, such as numerical simulation, rigorous optimization, model-based diagnosis or control, can be stated explicitly without confusing them with implementational details at the symbol level. During the eighties Newell's "knowledge-level hypothesis" became very popular and lead to a paradigm shift in the Artificial Intelligence research which had been focused too much on representational issues. Ideally, knowledge-based software components are designed with ontological commitments at the knowledge level in order to allow for sharing and communicating knowledge, rather than simple data structures. Since conceptualization is a crucial step in the design of every knowledge-based tool, we have developed an ontology for describing mathematical process models based on general systems theory (e.g. Klir, 1985) and the ontological principles de fined by Bunge in his "Treatise
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on Basic Philosophy" (Bunge, 1977; Bunge, 1979). It defines structural and behavioral modeling objects on different levels of abstraction which are organized in taxonomies with inheritance and aggregation relationships between them. The aim of this conceptualization is to define a minimum set of elementary modeling objects which are disjunct with respect to the knowledge they represent and allow an almost arbitrary aggregation to more complex objects. A particular process model can then be developed by selection, specification and aggregation of predefined modeling objects. Modeling objects especially for the representation of structural modeling entities such as devices, connections and couplings for the representation of complex objects have been defined recently in Marquardt et al. (1993b). In contrast, this contribution is concerned with modeling objects for the representation of behavioral modeling entities. A detailed description of the modeling methodology can be found in Marquardt (1996a).
3. Mapping ontological concepts to object-oriented representations Descriptions at the knowledge level can be divided into a conceptualization and formalization (Genesereth and Nilsson, 1987). While a conceptualization consists of "the entities that are assumed to exist in the world and their interrelationships", the formalization of knowledge entails the representation of knowledge about the domain as sentences in a formal language. Such a language must have syntax and semantics. The syntax describes the elements of the language and how these elements may be combined to form sentences. The exact relation between conceptualization and formalization is defined by the semantics, which formally relates sentences and elements of the language to entities and relations of the conceptualization (Alberts, 1993). Often some kind of predicate logic calculus is used as a representation means. Such representations provide formal declarative semantics but they cannot be easily understood by someone who is not trained in computer science. The application of such formalisms is therefore unnecessarily complicated. Instead, object-oriented approaches seem to be preferable because they overcome the disadvantages of predicate logic formalisms to a large extent. Particularly, they reflect a more natural view of the world that is to be modeled. Although the object-oriented paradigm is very popular in programming languages and conceptual modeling for database design, there is a lot of confusion about the objectoriented notion, mainly because it emerged as a programming construct, which is driven by implementation considerations. According to Newell (1982) we propose a knowledge-level approach where objects are a means to describe conceptual perceptions of the world. Using an appropriate representation formalism, those objects can be mapped into a formal representation language. Wand (1989), for example, presents a formal
approach to the object concept based on Bunge's scientific ontology (Bunge, 1977; Bunge, 1979) and maps the formal definitions of ontology to commonly used concepts of objects. Our work aims at the formal representation of knowledge about mathematical modeling independent of any implementation details. For that purpose, we are currently developing an application specific objectoriented data model called VEDA (Verfahrenstechnisches Datenmodell) that should capture all available knowledge about mathematical modeling in the chemical process engineering domain and support the construction of intelligent modeling applications (Marquardt et al., 1993a). VEDA is a representation language that builds on ontological principles outlined above.* It includes the core concepts of object-oriented data modeling as identified by Kim (1990) and several extensions which have been suggested in structured knowledge representation and data modeling research (e.g. King and Hull, 1987; Kim, 1990). VEDA defines frames for modeling concepts and modeling relations by tuples of attributes, laws (constraints) and methods. So called facets are used to characterize attributes (e.g. type and cardinality) or to add simple constraints (e.g. cross referential integrity constraint). The latter is used to explicitly state consistency requirements for attribute values referring to each other. Complex constraints relating one or more concepts are expressed by laws with the help of a predicate logic based declarative constraint language. Constraints are essential to automatically guarantee consistent specification and aggregation of modeling objects.
4. Definition of behavioral modeling objects Following many object-oriented and semantic data models we distinguish behavioral modeling concepts (BMCs) and behavioral modeling relations (BMRs). Generally, BMCs are used to represent entities of the behavioral description like variables, operators, dimensions or units whereas BMRs are needed to describe complex relations between those entities such as equations or systems of equations. The introduced types can be interpreted as classes which are organized in a taxonomy with inheritance between classes and their subclasses as depicted in Fig. 2 where classes are represented by an oval and inheritance relationships by arrows.
4.1. The SCALAR-VARIABLE Model equations consist of variables representing individual process quantities. Variables can be asso-
* VEDA means "comprehensive knowledge" in Sanskrit.
A formal representation of process model equations
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Fig. 2. Part of the taxonomy of behavioral modeling concepts, behavioral modeling relations and aggregates. ciated with a variety of attributes. For example, a variable representing the temperature inside a reactor tube may be characterized by a physical dimension "temperature", by a symbol "T", by a value "521.3" and a unit "Kelvin". To model such a process quantity the BMC SCALAR-VARIABLE is introduced as a refinement of TENSOR-VARIABLE. It contains an attribute for the name and a reference to the structural entity (a device or connection) which is described by the variable. In accordance with Batory and Kim (1985) we split up the different attributes of a variable into an interface and an implementation description to support multifacetted modeling, i.e. to have multiple models serving different purposes. This allows the use and implementation of a single variable (such as temperature) in different ways
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depending on the application context. For example, if different symbols are required, one can provide appropriate interfaces for that variable. Additionally, for a chosen interface several implementations are possible, e.g. an implementation to supply a fixed value and a further implementation, in which the value of the variable depends on an equation. Figure 3 shows individual frames defining a variable, its interface and its implementation. The attributes active-interface and isabstracting are used to relate a variable with its interface. Between both attributes a cross referential integrity constraint which is graphically depicted by a small square automatically guarantees consistency of the attribute values. Additionally, the attribute possibleinterfaces is defined in the frame for a variable to
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reference possible alternatives of interfaces. The relationship between a variable and its implementation is modeled analogously. The interface and the implementation of a variable can also be considered as two perspectives depicting different views on this variable. In this respect the multi-perspective knowledge representation scheme proposed by Marifio et el. (1990) is promising to reduce complexity in our representation.
4.2. The SCALAR-VARIABLE-INTERFACE and the SCALAR- VARIABLE-IMPLEMENTATION These two BMCs are introduced as sub classes of TENSOR-VARIABLE-INTERFACE and TENSOR-VARIABLE-IMPLEMENTATION, respectively, to represent the interface and the implementation of a variable. The interface description contains all information that is needed to reference and use a variable in a certain modeling context. It comprises for instance a symbol used as abbreviation of the variable name, a reference to the physical dimension, the support (continuous or discrete values, qualitative or fuzzy values), bounds (minimum and maximum value) and references to the coordinates the variable depends on (time, spatial coordinates etc.). The implementation description contains information about the value and its realization, e.g. references to the value in computational units, to the display-value used for communication with the user, and to a typical-value which can be used as default or for order-of-magnitude estimations. So called landmarkvalues are introduced to specify actions which must be taken if a certain landmark value is passed. Other attributes are added to the implementation for the system-theoretic classification of a variable as a state variable, a parameter or an input variable, for the classification as a design-or-computed variable, and to indicate that a variable is selected as a report variable for documentation purposes. The attributes possibleequations and active-equation refer to possible equations and the actually chosen equation to refine the behavior of the variable according to or-edges of the schema shown in Fig. 1.
since there is also a distinction between fundamental and deduced units. A unit, for instance the time unit, is characterized by a name "hour", a symbol "h", a standard-unit "s", and provides formulae to convert units to or from the standard unit. The BMC SCALARVALUE which is a subclass of TENSOR-VALUE represents an arbitrary value of a scalar variable. It contains internal-values used for calculations, communicationvalues for the interaction with the user, and references to the units of measurement. Moreover, process trends of variable values with respect to time can be recorded and analyzed.
4.4. The OPERATOR In addition to variables, differential operators such as the substantial derivative, gradient, divergence or Laplacian are further constituents of model equations, e.g. if modeling of distributed parameter systems is considered. In order to represent arbitrary kinds of differential operators the BMC OPERATOR is introduced. It is characterized by its name, operator-symbol, a reference to the operator-argument, to the operator-equation and to the actually used coordinate-system (Cartesian, cylindrical, spherical or general orthogonal coordinates). Since the intended coordinate system is not known in advance, the operator concept provides a method to derive an operator equation acting on the operator argument with respect to the chosen coordinates.
5. Aggregation of behavioral modeling objects This section introduces additional modeling concepts for the ,-ggregation of individual modeling objects into regular structures like vectors as well as BMRs for the aggregation of variables and operators into complex structures like equations and systems of equations.
5. I. The RECORD and the TENSOR 4.3. The DIMENSION, the UNIT and the SCALARVALUE Tile BMC DIMENSION is referenced by a variable interface and characterizes the physical dimension of a variabl~. We distinguish fundamental dimensions such as mass, length, temperature and deduced dimensions such as area or force. The latter contain a definition formula of the deduced dimension as a function of fundamental dimensions and are organized in a simple taxonomy with inheritance relationships. A dimension provides some possible-units and a computational-unit in which all calculations are carried out, e.g. the time dimension has seconds, minutes, hours as possible units. The BMC UNIT parallels the taxonomy of dimensions
These additional modeling concepts are defined as a refinement of the class AGGREGATE to provide arbitrary modeling objects with regular aggregation properties. The RECORD allows to aggregate elements of different type whereas the TENSOR with its refinements VECTOR and MATRIX restricts aggregation to elements of the same type. Using multiple inheritance aggregation properties can be inherited from records or tensors. As shown in Fig. 4 VECTOR-VARIABLE is a direct specialization of TENSOR-VARIABLE and VECTOR to allow VECTOR-VARIABLEs to be composed of SCALARVARIABLEs. The aggregation into tensors of higher degree (e.g. matrices) as well as the aggregation of other modeling objects such as equations is modeled analogously.
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Fig. 4. Aggregation relationships within variables, equations and systems of equations• Relationships between behavioral and structural modeling objects.
5.4. The EQUATION-TYPE
5.2. The EQUATION Equations with refinements to TENSOR-EQUATION, SYSTEM-OF-EQUATIONS and VARIABLE-STRUCTURE-EQUATION describe the behavior of the structural modeling objects (devices or connections) introduced in Marquardt (1993b). A structural entity is linked with its behavioral description via the attributes active-behavior and possible-behaviors referencing equations (single equations or systems of equations) as illustrated in Fig. 4. Again this allows to have alternative behaviors for a structural entity and thus supports multifacetted modeling.
5.3. The TENSOR-EQUATION Tensor equations are refined to SCALAR-EQUATION, VECTOR- EQUATION and MATRIX-EQUATION by inheriting the corresponding aggregation properties in order to represent a single equation. As depicted in Fig. 4 equations can be viewed as complex objects which relate variables and operators. They are characterized by a name, the relation containing the equation in symbolic form, references to the variables and to the operators occurring in tile equation according to the and-edges of the graph of Fig. 1, by a norm to compute a residual value and by the actual residual of the equation. Moreover, methods are provided for example to check the dimensional consistency of an equation.
Many modeling tools are restricted to specific problem classes such as lumped parameter systems and allow the behavior to be described only in terms of mixed systems of ordinary differential and algebraic systems (DAEs). This is definitely an oversimplification since first principles based modeling of distributed parameter systems and particulate systems involves mixed sets of integral, partial or ordinary differential as well as algebraic equations (Marquardt, 1991). The BMR EQUATION-TYPE is introduced to capture all the information that must be provided to completely specify the properties of an equation. For example, boundary value problems of ordinary differential equations and partial differential equations must comprise boundary conditions. Different subclasses of EQUATION-TYPE are defined and organized in a taxonomy with inheritance relationships. The specializations of TENSOR-EQUATION inherit attributes from an EQUATION-TYPE according to their mathematical type. Some attributes are for example the equation-type (algebraic, differential, integral,...), the relation storing the equation and the initial-value or boundary-values if any.
5.5. The SYSTEM-OF-EQUATIONS Equations can be aggregated in the sense of a record to form a system of equations which is in general of mixed type. Therefore, SYSTEM-OF-EQUATIONS inherits aggregation properties from RECORD to allow aggregation of arbitrary equations. The attribute constituents contains a reference to an arbitrary equation which itself can be a SYSTEM-OF-EQUATIONS. This
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R. BoruscH and W. MARQUARDT
allows the representation of complex structured equation systems.
5.6. The VARIABLE-STRUCTURE-EQUATION Often, process models are not strictly continuous. They may discontinuously change their structure at certain points in state space. For instance, process inherent discontinuities like phase changes or flow reversals as well as process operations during start-up and shutdown operations may be reasons for discontinuities causing either a switch in the model equations or even in the structure and dimensionality of the model (Marquardt, 1991). The BMR VARIABLESTRUCTURE-EOUATION is capable of representing a system of equations with structural variance. According to Klir (1985) it consists of an initial-case (a system of equations), alternative eases to represent the structural variants and a set of transition-conditions to determine a switch from one case to another.
6. Related work
Our framework is similar to other work on engineering ontologies which has been quite popular within the knowledge representation community. A number of projects use ONTOLINGUA (Grnber, 1992), a tool for writing portable ontologies in a canonical format, such that they can be translated into a variety of representation and reasoning systems. This allows to maintain the ontology in a single, machine-readable form while using it in systems with different syntax and reasoning capabilities (Gruber, 1992). The syntax and semantics of Om'OmNCUAis based on the KIF knowledge interchange format (Genesereth and Fikes, 1992) which is an extended version of a first-order predicate calculus with a Lisp-like notation. Most closely related to our work is the ENGMATH ontology for mathematical modeling in engineering developed by Gruber and co-workers (Gruber and Olsen, 1994). The conceptualization builds on abstract algebra and measurement theory. It includes the conceptual foundations for scalar, vector, and tensor quantities, physical dimensions, units of measure, functions of quantities, and dimensionless quantities using the KIF specification language. The ontology is used as a communication language among cooperating engineering agents, and as a foundation for other engineering ontologies, but the main purpose is knowledge sharing. The authors offer also some evaluation criteria for designing such ontologies. Because the ENcMATU ontology is very generic and domain independent, it imposes little structure on the physical quantities and mathematical relations defined. Moreover, the ontology does not focus on the relations between physical quantities and physical laws which allows explicit representation of physico-chemical knowledge and guides the decomposition of model equations as in our work.
The Compositional Modeling Language (CML) is being designed collaboratively by leading qualitative physics research groups (Falkenhainer et al., 1994). CML is a general declarative modeling language for specifying the symbolic and mathematical properties of the structure and behavior of physical systems. The CML ontology is specified with ONTOLINCUA and includes concepts that are defined in the ENCMA'rH ontology. CML domain theories consist of so-called model fragment definitions, which describe a type of phenomena or entity in the domain's physics. Instances of definitions are said to be active whenever there exists a set of entities in a model that satisfies the conditions stated in the definition. A model fragment's consequences hold when an instance of a model fragment is active. Model fragment consequences are typically equations that describe the behavior of the entities. A specific system being modeled is called scenario. The model of a scenario in a domain theory consists of model fragment instances from the theory that are activated by the scenario definition. At present the expressiveness and usability of CML is evaluated in the domain of thermodynamics. The domain theory contains definitions for the primary conceptual objects including control volume, stream and steady-state flow process, which establishes the first law equations. Although CML allows to have multiple behavioral descriptions of physical systems, it is primarily based on qualitative physics and the expressiveness is restricted with respect to the different kinds of mathematical models that can be represented (e.g. partial differential equations cannot be represented). Alberts (1993) describes YMIR as a reusable ontology intended as the basis for the development of knowledgebased design systems in different engineering domains. It provides a vocabulary for modeling the structure and behavior of systems based on general systems theory (Klir, 1985) as well as a basic reasoning strategy for the synthesis of technical systems. The treatment of physical quantities in that ontology is quite restrictive as stated in (Gruber and Olsen, 1994). First, quantities are represented by variables that are annotated with a value, a symbolic quantity types, a unit, a value domain, and a time dependency. There is no means to define new complex quantity types, dimensions or units based on existing ones. Second, the values are unary scalar functions of time, i.e. models with vector or tensor quantities, as well as distributed parameters models with partial differential equations or phase space models cannot be represented, since time is the only dependent variable that is allowed. Third, the values of quantities are tuples of numbers and fixed units. In our work quantities are related to, but independent of values and units. This allows to have several implementations for one quantity, e.g. values with different units of measure or even an equation in order to calculate a value. The present work at the University of Twente is directed to the development of ontologies for physical systems staying as close as possible to the modern methods of general systems engineering. The PHvsSvs
A formal representation of process model equations ontology introduces several engineering ontologies that express different conceptual viewpoints upon physical systems, e.g. a component ontology that describes the structural decomposition of a system, a process ontology that describes the physical mechanisms underlying systems behavior, and a mathematical ontology defining the mathematics required to describe physical processes (Borst et al., 1994; Borst et al., 1995). They are based on the ENGMATH ontology and im plemented using ONTOLINGUA. The aim is to provide a basis for the development of structured model libraries for engineering design. The main difference to our work is that the behavioral view of the Pr~YsSvs ontology is formalized using the bond graph approach (see for e.g. Gawthrop and Smith, 1996). Each node represents a physical law (such as conservation of energy) and mathematically it is associated with a (algebraic or differential) constraint equation on the physical variables involved. The edges denote energy exchange links and mathematically they indicate the variables that are shared between equations. In practice, the approach is used as a graphical front end to computer algebra and numerical simulation systems. Again, guidance of the model development, e.g. by providing a comprehensive repository of chemical engineering knowledge in conjunction with pruning rules and constraints that support the selection of suitable model equations, is not considered.
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the phenomena-based decomposition of model equations. Moreover, a hypertext system is available to create comprehensive documentation that can be linked with modeling objects in order to record all assumptions and decisions taken, capture experience gained during the model development, or to provide background knowledge related to physico-chemical phenomena. An agenda manager is available on request that guides the user through the process of model development by suggesting modeling actions to be performed next depending on the modeling context and state of the model (Lohmann and Marquardt, 1996). Additionally, the process-centered environment PROART/CE (Drmges et al., 1996) which builds on concepts developed for requirements engineering and primarily aims at managing the evolution of models is being developed in close collaboration with the Information Systems group at RWTH Aachen. It supports capturing and recording all relevant information arising during the model development and maintenance in order to enable traceability, selective guidance and experience-based improvement of the process of model development (Jarke and Marquardt, 1995).
8. Conclusions
This paper presents a general framework for the representation of mathematical models which can be viewed as the foundation for creating an intelligent 7. Status of implementation computer-based modeling tool. It discusses the role of Implementations of VEDA are currently being carried ontologies for the conceptualization of the domain and out using different software platforms. The frame-based the use of object-oriented techniques for the representaknowledge representation language FRAMETALK tion of process model equations. The structuring of (Ratbke, 1991)--an object-oriented language based on model equations leads to a complex and/or-graph CLOS (Common Lisp Object System)--is used at relating variables and equations. Modeling objects for Stuttgart University. Gensym's G2 (Harmon, 1993)--a the declarative representation of this graph are defined complete application environment for creating intelli- using the object-oriented data model VEDA. The introgent systems, providing representational and reasoning duced formalism allows to explicitly represent physicoprimitives (objects and rules), a procedural language, a chemical knowledge about process quantities and equagraphical interface, links to external applications, data- tions and takes into account the multifacetted nature of bases and distributed control systems--is the basis for modeling. This is a prerequisite for the development of the modeling environment MoDKIT (Bogusch et al., sophisticated modeling tools that considerably reduce the modeling effort. In this respect the proposed 1996) at RWTH Aachen. MoDKIT consists of a graphical model editor that representation formalism offers a useful starting point to allows to create structural descriptions of chemical build a comprehensive repository of chemical engineerprocess models according to the methodology proposed ing knowledge, but at the same time it reveals the by Marquardt (1996a). The structural description can be considerable representational complexity and the tredecomposed into arbitrary hierarchical levels with mendous implementational effort. The implementational different model alternatives at each level of the hier- alternatives as discussed above are essential to prove archy. A taxomomy of structural modeling objects practicability of our approach and to provide feedback (SMCs) has been implemented. Each SMC is associated from expert and casual modelers. with a set of characterizing attributes and a corresponding behavioral description in an equation-oriented manner in order to support existing process simulators like SPEEDUP and gPRoMS. At present, the representation References framework proposed in this contribution is currently Alberts, L. K. (1993) YMIR: an ontology for engineerbeing implemented to allow the representation of the ing design. Doctoral dissertation. University of and/or-graph relating variables and equations as well as Twente, Enschede, The Netherlands.
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AspenTech (1993) SPEEDUP User Manual. Aspen Technology, Inc., Cambridge, MA. AspenTech (1994a) ASPEN PLUS User Guide. Aspen Technology, Inc., Cambridge, MA. AspenTech (1994b) ASPEN PLUS ModelManager Reference Manual. Aspen Technology, Inc., Cambridge, MA. Batory, G. and Kim, W. (1985) Modeling concepts for VLSI CAD objects. ACM Trans. Database Systems 10, 322-426. Bogusch, R., Lohmann, B. and Marquardt, W. (1996) Rechnergesttitzte Modellierung in der Verfahrenstechnik. GVC-Jahrestagung 1996, Dortmund, September 1996. To be published in Chem.-Ing.-Tech. Borst E, Pos, A., Top, J. L. and Akkermans, J. M. (1994) Physical systems ontology. Proc. European Conference on Artificial Intelligence ECAI '94. Workshop on comparison of implemented ontoiogies, Amsterdam, pp. 47-80. Borst, E, Akkermans, J. M., Pos, A. and Top, J. L. (1995) The PhysSys ontology for physical systems. Ninth International Workshop on Qualitative Reasoning, Amsterdam, pp. 11-21. Bunge, M. (1977) Treatise on Basic Philosophy. Vol. 3: Ontology I: The Furniture of the World. Reidel, Dordrecht, The Netherlands. Bunge, M. (1979) Treatise on Basic Philosophy. Vol. 4: Ontology II: A World of Systems. Reidel, Dordrecht, The Netherlands. D6mges, R., Pohl, K., Jarke, M., Lohmann, B. and Marquardt, W. (1996) PRO-ART/CE--An environment for managing the evolution of chemical process simulation models. Proc. lOth European Simulation Multiconference ESM '96, Budapest, Hungary, pp. 1012-1017. Falkenhainer, B., Farquhar. A., Brobow, D., Fikes, R., Forbus, K., Gruber, T. Iwasaki, Y. and Kuipers, B. (1994) CML: a compositional modeling language. Technical report KSL-94-16. Knowledge Systems Laboratory, Stanford University. Gawthrop, E and Smith, L. (1996)Metamodelling: Bond graphs and dynamic systems. Prentice Hall, Englewood Cliffs, NJ. Genesereth, M. R. and Nilsson, N. J. (1987) Logical foundations of artificial intelligence. Morgan Kauffmann, Los Altos. Genesereth, M. R. and Fikes, R. E. (1992) Knowledge Interchange Format, Version 3.0, Reference Manual. Report Logic-92-1. Computer Science Department, Stanford University. Gruber, T. R. (1992) Ontolingua: a mechanism to support portable ontologies. Internal report. Knowledge Systems Laboratory, Stanford University. Gruber, T. R. (1993) A translation approach to portable ontology specifications. Knowledge Acquisition 5, 3 199-220. Gruber T. R. and Olsen, G. R. (1994) An ontology for engineering mathematics. In Fourth International Conference on Principles of Knowledge Representation and Reasoning (J. Doyle, E Torasso, and E. Sandewall, Eds), Morgan Kaufmann, San Mateo, CA, pp. 258-269 Hangos, K. (1991) Qualitative process modeling. In Chemical Process Control CPC-IV (Y. Arkun and W. H. Ray, Eds), CACHE, Austin, AIChE, New York, pp. 209-236.
Harmon, P. (1993) G2: Gensym's real-time expert system. Intelligent Software Strategies 9, No. 3 Cutter Information Corp., Arlington, MA, pp. 1-16. Jarke, M. and Marquardt, W. (1995) Design and evaluation of computer-aided modeling tools. ISPE '95, Snowmass, Colorado. To be published in AIChE Syrup. Set. Kim, W. (1990) Introduction to object-oriented data bases. MIT Press, Cambridge. King, R. and Hull, R. (1987) Semantic database modeling: survey, applications, and research issues. ACM Comput. Surv. 19, 201-260. Klir, G. J. (1985) Architecture of Problem Solving. Plenum Press, New York. Lohmann, B. and Marquardt, W. (1996) On the systematization of the process of model development. Computers chem. Engng 20 Suppl., 213-218. Marifio, O., Rechenmann, E and Uvietta, E (1990) Multiple perspectives and classification mechanism in object-oriented representation. European Conf. on Artificial Intelligence, pp. 425-430. Marquardt, W. (1991) Dynamic process simulation-recent progress and future challenges. In Chemical Process Control CPC-IV (Y. Arkun and W. H. Ray, Eds), CACHE, Austin, AIChE, New York, pp. 131-180. Marquardt, W. (1994) Rechnergesttitzte Erstellung verfahrenstechnischer Proze6modelle. Chem.-Ing.Techn. 64, 25-40 (1992). English translation in Int. chem. Engng 34, 28-46. Marquardt, W. et al. (1993a) Objekt-orientierte Datenmo dellierung for die Repr~isentation yon verfah renstechnischen ProzeBmodellen. Internal draft report, University of Stuttgart and RWTH Aachen University of Technology. Marquardt, W., Gerstlauer, A. and Gilles, E. D. (1993b) Modeling and representation of complex objects: A chemical engineering perspective. Proc. of 6th Int. Conf. on IEA/AIE, Edinburgh, Scotland, pp. 219-228. Marquardt, W. (1996a) Towards a process modeling methodology. In Model-based Process Control (R. Berber, Ed.). NATO-ASI Series, Kluwer Press, The Netherlands, pp. 3-40. Marquardt, W. (1996b) Trends in computer-aided process modeling. Computers chem. Engng 20, 591-609. Newell, A. (1982) The knowledge level. Artifl Intell. 18, 87-127. Nilsson, B. (1993) Object-oriented modeling of chemical processes. Doctoral dissertation. Department of Automatic Control, Lund Institute of Technology, Sweden. Oh, M. and Pantelides, C. C. (1996) A modelling and simulation language for combined lumped and distributed parameter systems. Computers chem. Engng 20, 611-633. Piela, E C., McKelvey, R. D. and Westerberg, A. W. (1992) An introduction to Ascend: its language and interactive environment. J. Man. lnfo. Sci. 9, 91-121. Rathke, C. (1991) Implementing frames in an objectoriented programming language. Proc. of Ist European Conf. on Object-Oriented Programming, Bratislave, pp. 88-94.
A formal representation of process model equations S6rlie, C. F. (1990) A computer environment for process modeling. Doctoral dissertation. Laboratory of Chemical Engineering, Norwegian Institute of Technology, Trondheim. Stephanopoulos, G., Johnston, J., Kriticos, T., Lakshmanan, R., Mavrovouniotis, M. and Siletti, M. (1987) Design-Kit : An object-oriented environment for process engineering. Computers chem. Engng 11, 655-4574. Stephanopoulos, G., Henning, G. and Leone, H. (1990) ModeI.La. A language for process engineering. Part I and II. Computers chem. Engng 14, 813-869.
CAC[ 21-10-C
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Telnes, K. (1992) Computer-aided modeling of dynamic processes based on elementary physics. Doctoral dissertation. Division of Engineering Cybernetics, Norwegian Institute of Technology, Trondheim. Wand, Y. (1989) A proposal for a formal model of objects. In Object-Oriented Concepts, Databases, and Applications (W. Kim and E H. Lochovsky, Eds), pp. 537-559. Addison-Wesley, Reading, MA. Zeigler, B. P. (1984) Multifacetted Modelling and Discrete Event Simulation. Academic Press, London.