Scientific modelling is a scientific activity, the aim of, to make a particular part or feature of the world easier to understand, quantify, visualize, or simulate by referencing it to existing and commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and using different types of models for different aims, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, graphical models to visualize the subject. Modelling is an essential and inseparable part of many scientific disciplines, each of which have their own ideas about specific types of modelling; the following was said by John von Neumann.... The sciences do not try to explain, they hardly try to interpret, they make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena; the justification of such a mathematical construct is and that it is expected to work —, to describe phenomena from a reasonably wide area.
There is an increasing attention to scientific modelling in fields such as science education, philosophy of science, systems theory, knowledge visualization. There is growing collection of methods and meta-theory about all kinds of specialized scientific modelling. A scientific model seeks to represent empirical objects and physical processes in a logical and objective way. All models are in simulacra, that is, simplified reflections of reality that, despite being approximations, can be useful. Building and disputing models is fundamental to the scientific enterprise. Complete and true representation may be impossible, but scientific debate concerns, the better model for a given task, e.g., the more accurate climate model for seasonal forecasting. Attempts to formalize the principles of the empirical sciences use an interpretation to model reality, in the same way logicians axiomatize the principles of logic; the aim of these attempts is to construct a formal system that will not produce theoretical consequences that are contrary to what is found in reality.
Predictions or other statements drawn from such a formal system mirror or map the real world only insofar as these scientific models are true. For the scientist, a model is a way in which the human thought processes can be amplified. For instance, models that are rendered in software allow scientists to leverage computational power to simulate, visualize and gain intuition about the entity, phenomenon, or process being represented; such computer models are in silico. Other types of scientific models are in vitro. Models are used when it is either impossible or impractical to create experimental conditions in which scientists can directly measure outcomes. Direct measurement of outcomes under controlled conditions will always be more reliable than modelled estimates of outcomes. Within modelling and simulation, a model is a task-driven, purposeful simplification and abstraction of a perception of reality, shaped by physical and cognitive constraints, it is task-driven, because a model is captured with a certain task in mind.
Simplifications leave all the known and observed entities and their relation out that are not important for the task. Abstraction aggregates information, important, but not needed in the same detail as the object of interest. Both activities and abstraction, are done purposefully. However, they are done based on a perception of reality; this perception is a model in itself, as it comes with a physical constraint. There are constraints on what we are able to observe with our current tools and methods, cognitive constraints which limit what we are able to explain with our current theories; this model comprises the concepts, their behavior, their relations in formal form and is referred to as a conceptual model. In order to execute the model, it needs to be implemented as a computer simulation; this requires more choices, such as the use of heuristics. Despite all these epistemological and computational constraints, simulation has been recognized as the third pillar of scientific methods: theory building and experimentation.
A simulation is the implementation of a model. A steady state simulation provides information about the system at a specific instant in time. A dynamic simulation provides information over time. A simulation shows how a particular object or phenomenon will behave; such a simulation can be useful for testing, analysis, or training in those cases where real-world systems or concepts can be represented by models. Structure is a fundamental and sometimes intangible notion covering the recognition, observation and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science and art. A system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. In general, a system is a construct or collection of different elements that together can produce results not obtainable by the elements alone.
The concept of an'integrated whole' can be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and
Business reference model
Business reference model is a reference model, concentrating on the functional and organizational aspects of the core business of an enterprise, service organization or government agency. In enterprise engineering a business reference model is part of an Enterprise Architecture Framework or Architecture Framework. An Enterprise Architecture Framework defines in a series of reference models, how to organize the structure and views associated with an Enterprise Architecture. A reference model in general is a model of something that embodies the basic goal or idea of something and can be looked at as a reference for various purposes. A business reference model is a means to describe the business operations of an organization, independent of the organizational structure that perform them. Other types of business reference model can depict the relationship between the business processes, business functions, the business area’s business reference model; these reference model can be constructed in layers, offer a foundation for the analysis of service components, technology and performance.
The most familiar business reference model is the "Business Reference Model", one of five reference models of the Federal Enterprise Architecture of the US Federal Government. That model is a function-driven framework for describing the business operations of the Federal Government independent of the agencies that perform them; the Business Reference Model provides an organized, hierarchical construct for describing the day-to-day business operations of the Federal government. While many models exist for describing organizations - organizational charts, location maps, etc. - this model presents the business using a functionally driven approach. One of the first business reference models defined was the "IMPPACT Business Reference Model" around 1990, the result of a research project in the Computer Integrated Manufacturing field of the ESPRIT1 programme. Gielingh et al. described: The IMPPACT Business Reference Model is expressed in the generic language constructs provided by IDEF0... It describes the requirements for CIM seen from a business point of view.
Views modelled are manufacturing activities and information flow objects resource objects and organisational aspects. The complete manufacturing system is modelled by the IMPPACT Business Reference Model. Management covers both the planning of the production and the planning and control of this production; the term IMPPACT stood for Integrated Manufacturing of Products and Processes using Advanced Computer Technologies Furthermore, in its framework were incorporated CIMOSA as reference model, NIAM for information modelling, the data modeling language EXPRESS for information structure implementation. In the 1990s, business reference models were hardly an item. An exception was a 1991 book about IT management, which mentioned that the Kodak management had developed a business reference model 10 years earlier. A 1996 manual of the SAP R/3 enterprise resource planning software stipulated the existence on the business reference model of the R/3 System. However, in the 1990s there was a significant development of reference models in related fields, resulted in the developments of Integrated business planning, the Open System Environment Reference Model, the Workflow Reference Model, TOGAF and the Zachman Framework.
In the new millennium business reference models started emerging in several fields from network management systems, E-business, to the US Federal government. The US Federal government published it's "Business Reference Model", Version 1.0 in February 2002. Related developments in this decade were the development of the Treasury Enterprise Architecture Framework, the OASIS SOA Reference Model; the US Federal Government has defined a Federal Enterprise Architecture structures of the five FEA reference models: Performance Reference Model Business Reference Model Service Component Reference Model Technical Reference Model Data Reference Model The Federal Government Business Reference Model provides an organized, hierarchical construct for describing the day-to-day business operations of the Federal government. While many models exist for describing organizations - org charts, location maps, etc. - this model presents the business using a functionally driven approach. The Lines of Business and Sub-functions that comprise the BRM represent a departure from previous models of the Federal government that use antiquated, agency-oriented frameworks.
The BRM is the first layer of the Federal Enterprise Architecture and it is the main viewpoint for the analysis of data, service components and technology. Business model Business process modeling Enterprise Architecture framework Enterprise modelling Organizational architecture View model Peter Fettke, Peter Loos. Reference Modeling for Business Systems Analysis. Idea Group Inc. ISBN 1-59904-054-9
Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking principles to organize this body of knowledge; the individual outcome of such efforts, an engineered system, can be defined as a combination of components that work in synergy to collectively perform a useful function. Issues such as requirements engineering, logistics, coordination of different teams and evaluation, maintainability and many other disciplines necessary for successful system development, design and ultimate decommission become more difficult when dealing with large or complex projects. Systems engineering deals with work-processes, optimization methods, risk management tools in such projects, it overlaps technical and human-centered disciplines such as industrial engineering, mechanical engineering, manufacturing engineering, control engineering, software engineering, electrical engineering, organizational studies, civil engineering and project management.
Systems engineering ensures that all aspects of a project or system are considered, integrated into a whole. The systems engineering process is a discovery process, quite unlike a manufacturing process. A manufacturing process is focused on repetitive activities that achieve high quality outputs with minimum cost and time; the systems engineering process must begin by discovering the real problems that need to be resolved, identifying the most probable or highest impact failures that can occur – systems engineering involves finding solutions to these problems. The term systems engineering can be traced back to Bell Telephone Laboratories in the 1940s; the need to identify and manipulate the properties of a system as a whole, which in complex engineering projects may differ from the sum of the parts' properties, motivated various industries those developing systems for the U. S. Military; when it was no longer possible to rely on design evolution to improve upon a system and the existing tools were not sufficient to meet growing demands, new methods began to be developed that addressed the complexity directly.
The continuing evolution of systems engineering comprises the development and identification of new methods and modeling techniques. These methods aid in a better comprehension of the design and developmental control of engineering systems as they grow more complex. Popular tools that are used in the systems engineering context were developed during these times, including USL, UML, QFD, IDEF0. In 1990, a professional society for systems engineering, the National Council on Systems Engineering, was founded by representatives from a number of U. S. corporations and organizations. NCOSE was created to address the need for improvements in systems engineering practices and education; as a result of growing involvement from systems engineers outside of the U. S. the name of the organization was changed to the International Council on Systems Engineering in 1995. Schools in several countries offer graduate programs in systems engineering, continuing education options are available for practicing engineers.
Systems engineering signifies only an approach and, more a discipline in engineering. The aim of education in systems engineering is to formalize various approaches and in doing so, identify new methods and research opportunities similar to that which occurs in other fields of engineering; as an approach, systems engineering is interdisciplinary in flavour. The traditional scope of engineering embraces the conception, development and operation of physical systems. Systems engineering, as conceived, falls within this scope. "Systems engineering", in this sense of the term, refers to the building of engineering concepts. The use of the term "systems engineer" has evolved over time to embrace a wider, more holistic concept of "systems" and of engineering processes; this evolution of the definition has been a subject of ongoing controversy, the term continues to apply to both the narrower and broader scope. Traditional systems engineering was seen as a branch of engineering in the classical sense, that is, as applied only to physical systems, such as spacecraft and aircraft.
More systems engineering has evolved to a take on a broader meaning when humans were seen as an essential component of a system. Checkland, for example, captures the broader meaning of systems engineering by stating that'engineering' "can be read in its general sense. Enterprise Systems Engineering pertains to the view of enterprises, that is, organizations or combinations of organizations, as systems. Service Systems Engineering has to do with the engineering of service systems. Checkland defines a service system as a system, conceived as serving another system. Most civil infrastructure systems are service systems. Systems engineering focuses on analyzing and eliciting customer needs and required functionality early in the development cycle, documenting requirements proceeding with design synthesis and system validation while considering the complete problem, the system lifecycle; this includes understanding all of the stakeholders involved. Oliver et al. claim that the systems engineerin
Gradient-Enhanced Kriging is a surrogate modeling technique used in engineering. A surrogate model is a prediction of the output of an expensive computer code; this prediction is based on a small number of evaluations of the expensive computer code. Adjoint solvers are now becoming available in a range of Computational Fluid Dynamics solvers, such as Fluent, OpenFOAM, SU2 and US3D. Developed for optimization, adjoint solvers are now finding more and more use in uncertainty quantification. An adjoint solver allows one to compute the gradient of the quantity of interest with respect to all design parameters at the cost of one additional solve; this leads to a linear speedup: the computational cost of constructing an accurate surrogate decrease, the resulting computational speedup s scales linearly with the number d of design parameters. The reasoning behind this linear speedup is straightforward. Assume we run N primal solves and N adjoint solves, at a total cost of 2 N; this results in N + d N data.
Now assume that each partial derivative provides as much information for our surrogate as a single primal solve. The total cost of getting the same amount of information from primal solves only is N + d N; the speedup is the ratio of these costs: s = N + d N 2 N = 1 2 + 1 2 d. A linear speedup has been demonstrated for a fluid-structure interaction problem and for a transonic airfoil. One issue with adjoint-based gradients in CFD is that they can be noisy; when derived in a Bayesian framework, GEK allows one to incorporate not only the gradient information, but the uncertainty in that gradient information. When using GEK one takes the following steps: Create a Design of Experiment: The DoE or'sampling plan' is a list of different locations in the design space; the DoE indicates. With Kriging and GEK, a common choice is to use a Latin Hypercube Design design with a'maximin' criterion; the LHS-design is available in scripting codes like Python. Make observations: For each sample in our DoE one runs the computer simulation to obtain the Quantity of Interest.
Construct the surrogate: One uses the GEK predictor equations to construct the surrogate conditional on the obtained observations. Once the surrogate has been constructed it can be used in different ways, for example for surrogate-based Uncertainty Quantification or optimization. In a Bayesian framework, we use Bayes' Theorem to predict the Kriging mean and covariance conditional on the observations; when using GEK, the observations are the results of a number of computer simulations. GEK can be interpreted as a form of Gaussian process regression. Along the lines of, we are interested in the output X of our computer simulation, for which we assume the normal prior probability distribution: X ∼ N,with prior mean μ and prior covariance matrix P; the observations y have the normal likelihood: Y | x ∼ N,with H the observation matrix and R the observation error covariance matrix, which contains the observation uncertainties. After applying Bayes' Theorem we obtain a distributed posterior probability distribution, with Kriging mean: E = μ + K,and Kriging covariance: c o v = P,where we have the gain matrix: K = P H T − 1.
In Kriging, the prior covariance matrix P is generated from a covariance function. One example of a covariance function is the Gaussian covariance: P i j = σ 2 e x p ( − ∑ k | ξ j k − ξ i k | 2 2 θ k
Data modeling in software engineering is the process of creating a data model for an information system by applying certain formal techniques. Data modeling is a process used to define and analyze data requirements needed to support the business processes within the scope of corresponding information systems in organizations. Therefore, the process of data modeling involves professional data modelers working with business stakeholders, as well as potential users of the information system. There are three different types of data models produced while progressing from requirements to the actual database to be used for the information system; the data requirements are recorded as a conceptual data model, a set of technology independent specifications about the data and is used to discuss initial requirements with the business stakeholders. The conceptual model is translated into a logical data model, which documents structures of the data that can be implemented in databases. Implementation of one conceptual data model may require multiple logical data models.
The last step in data modeling is transforming the logical data model to a physical data model that organizes the data into tables, accounts for access and storage details. Data modeling defines not just data elements, but their structures and the relationships between them. Data modeling techniques and methodologies are used to model data in a standard, predictable manner in order to manage it as a resource; the use of data modeling standards is recommended for all projects requiring a standard means of defining and analyzing data within an organization, e.g. using data modeling: to assist business analysts, testers, manual writers, IT package selectors, managers, related organizations and clients to understand and use an agreed semi-formal model the concepts of the organization and how they relate to one another to manage data as a resource for the integration of information systems for designing databases/data warehouses Data modeling may be performed during various types of projects and in multiple phases of projects.
Data models are progressive. Instead a data model should be considered a living document that will change in response to a changing business; the data models should ideally be stored in a repository so that they can be retrieved and edited over time. Whitten et al. determined two types of data modeling: Strategic data modeling: This is part of the creation of an information systems strategy, which defines an overall vision and architecture for information systems. Information technology engineering is a methodology. Data modeling during systems analysis: In systems analysis logical data models are created as part of the development of new databases. Data modeling is used as a technique for detailing business requirements for specific databases, it is sometimes called database modeling because a data model is implemented in a database. Data models provide a framework for data to be used within information systems by providing specific definition and format. If a data model is used across systems compatibility of data can be achieved.
If the same data structures are used to store and access data different applications can share data seamlessly. The results of this are indicated in the diagram; however and interfaces are expensive to build and maintain. They may constrain the business rather than support it; this may occur when the quality of the data models implemented in interfaces is poor. Some common problems found in data models are: Business rules, specific to how things are done in a particular place, are fixed in the structure of a data model; this means that small changes in the way business is conducted lead to large changes in computer systems and interfaces. So, business rules need to be implemented in a flexible way that does not result in complicated dependencies, rather the data model should be flexible enough so that changes in the business can be implemented within the data model in a quick and efficient way. Entity types are not identified, or are identified incorrectly; this can lead to replication of data, data structure and functionality, together with the attendant costs of that duplication in development and maintenance.
Therefore, data definitions should be made as explicit and easy to understand as possible to minimize misinterpretation and duplication. Data models for different systems are arbitrarily different; the result of this is. These interfaces can account for between 25-70% of the cost of current systems. Required interfaces should be considered inherently while designing a data model, as a data model on its own would not be usable without interfaces within different systems. Data cannot be shared electronically with customers and suppliers, because the structure and meaning of data has not been standardised. To obtain optimal value from an implemented data model, it is important to define standards that will ensure that data models will both meet business needs and be consistent. In 1975 ANSI described three kinds of data-model instance: Conceptual schema: describes the semantics of a domain. For example, it may be a model of the interest area of an organization or of an industry; this consists of entity classes, representing kinds of things of significance in the domain, relationships assertions about associations between pairs of entity classes.
A conceptual schema specifies the kinds of facts or propositions that can be express
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
International Organization for Standardization
The International Organization for Standardization is an international standard-setting body composed of representatives from various national standards organizations. Founded on 23 February 1947, the organization promotes worldwide proprietary and commercial standards, it is headquartered in Geneva and works in 164 countries. It was one of the first organizations granted general consultative status with the United Nations Economic and Social Council; the International Organization for Standardization is an independent, non-governmental organization, the members of which are the standards organizations of the 164 member countries. It is the world's largest developer of voluntary international standards and facilitates world trade by providing common standards between nations. Over twenty thousand standards have been set covering everything from manufactured products and technology to food safety and healthcare. Use of the standards aids in the creation of products and services that are safe, reliable and of good quality.
The standards help businesses increase productivity while minimizing errors and waste. By enabling products from different markets to be directly compared, they facilitate companies in entering new markets and assist in the development of global trade on a fair basis; the standards serve to safeguard consumers and the end-users of products and services, ensuring that certified products conform to the minimum standards set internationally. The three official languages of the ISO are English and Russian; the name of the organization in French is Organisation internationale de normalisation, in Russian, Международная организация по стандартизации. ISO is not an acronym; the organization adopted ISO as its abbreviated name in reference to the Greek word isos, as its name in the three official languages would have different acronyms. During the founding meetings of the new organization, the Greek word explanation was not invoked, so this meaning may have been made public later. ISO gives this explanation of the name: "Because'International Organization for Standardization' would have different acronyms in different languages, our founders decided to give it the short form ISO.
ISO is derived from the Greek isos, meaning equal. Whatever the country, whatever the language, the short form of our name is always ISO."Both the name ISO and the ISO logo are registered trademarks, their use is restricted. The organization today known as ISO began in 1928 as the International Federation of the National Standardizing Associations, it was suspended in 1942 during World War II, but after the war ISA was approached by the formed United Nations Standards Coordinating Committee with a proposal to form a new global standards body. In October 1946, ISA and UNSCC delegates from 25 countries met in London and agreed to join forces to create the new International Organization for Standardization. ISO is a voluntary organization whose members are recognized authorities on standards, each one representing one country. Members meet annually at a General Assembly to discuss ISO's strategic objectives; the organization is coordinated by a Central Secretariat based in Geneva. A Council with a rotating membership of 20 member bodies provides guidance and governance, including setting the Central Secretariat's annual budget.
The Technical Management Board is responsible for over 250 technical committees, who develop the ISO standards. ISO has formed two joint committees with the International Electrotechnical Commission to develop standards and terminology in the areas of electrical and electronic related technologies. ISO/IEC Joint Technical Committee 1 was created in 1987 to "evelop, maintain and facilitate IT standards", where IT refers to information technology. ISO/IEC Joint Technical Committee 2 was created in 2009 for the purpose of "tandardization in the field of energy efficiency and renewable energy sources". ISO has 163 national members. ISO has three membership categories: Member bodies are national bodies considered the most representative standards body in each country; these are the only members of ISO. Correspondent members are countries; these members do not participate in standards promulgation. Subscriber members are countries with small economies, they can follow the development of standards. Participating members are called "P" members, as opposed to observing members, who are called "O" members.
ISO is funded by a combination of: Organizations that manage the specific projects or loan experts to participate in the technical work. Subscriptions from member bodies; these subscriptions are in proportion to each country's gross national trade figures. Sale of standards. ISO's main products are international standards. ISO publishes technical reports, technical specifications, publicly available specifications, technical corrigenda, guides. International standards These are designated using the format ISO nnnnn: Title, where nnnnn is the number of the standard, p is an optional part number, yyyy is the year published, Title describes the subject. IEC for International Electrotechnical Commission is included if the standard results from the work of ISO/IEC JTC1. ASTM is used for standards developed in cooperation with ASTM International. Yyyy and IS are not used for an incomplete or unpublished standard and may under some