62,363 research outputs found
How Classical Field Theory Can Help in Process Flowsheet and Equipment Modeling: General Principles and Practical Reductions
Chemical process and equipment modeling is central to chemical engineering, comprising much of textbook content and providing the basis for much of engineering practice. This body of knowledge is traditionally learned as an extensive family of equations. The unifying principles behind them are not always evident.
The models most widely employed actually derive from integrations of the diffusion-convection-reaction PDEs. While detailed 3-D integrations are seldom practical for modeling of equipment performance or flowsheets, the usual practical models are still in fact approximate integrations of the continuum model. Because of this, classical field theory may be applied to reveal useful properties present in the physics but not evident from the familiar equations.
The underlying continuum PDEs are shown to be derived from a unified variational principle with convexity properties provided by the underlying physics. Behavior is represented with a set of primal fields (generalized densities) and dual fields (potentials). Applying geometries, these fields are integrated (in principal) over submodel volumes to obtain compact algebraic descriptions. Important solution existence and uniqueness properties are obtained.
This canonical primal-dual approach to modeling offers several advantages. Larger systems may be assembled from sets of submodels by connections at interfaces, analogous to components in an electrical circuit. Numerical convergence via homotopy can be guaranteed. The goal is to enable software that can automatically generate models that solve robustly
Modeling and Analyzing Adaptive User-Centric Systems in Real-Time Maude
Pervasive user-centric applications are systems which are meant to sense the
presence, mood, and intentions of users in order to optimize user comfort and
performance. Building such applications requires not only state-of-the art
techniques from artificial intelligence but also sound software engineering
methods for facilitating modular design, runtime adaptation and verification of
critical system requirements.
In this paper we focus on high-level design and analysis, and use the
algebraic rewriting language Real-Time Maude for specifying applications in a
real-time setting. We propose a generic component-based approach for modeling
pervasive user-centric systems and we show how to analyze and prove crucial
properties of the system architecture through model checking and simulation.
For proving time-dependent properties we use Metric Temporal Logic (MTL) and
present analysis algorithms for model checking two subclasses of MTL formulas:
time-bounded response and time-bounded safety MTL formulas. The underlying idea
is to extend the Real-Time Maude model with suitable clocks, to transform the
MTL formulas into LTL formulas over the extended specification, and then to use
the LTL model checker of Maude. It is shown that these analyses are sound and
complete for maximal time sampling. The approach is illustrated by a simple
adaptive advertising scenario in which an adaptive advertisement display can
react to actions of the users in front of the display.Comment: In Proceedings RTRTS 2010, arXiv:1009.398
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
There is a hidden intrigue in the title. CT is one of the most abstract
mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a
recent trend in software development, industrially supported by standards,
tools, and the status of a new "silver bullet". Surprisingly, categorical
patterns turn out to be directly applicable to mathematical modeling of
structures appearing in everyday MDE practice. Model merging, transformation,
synchronization, and other important model management scenarios can be seen as
executions of categorical specifications.
Moreover, the paper aims to elucidate a claim that relationships between CT
and MDE are more complex and richer than is normally assumed for "applied
mathematics". CT provides a toolbox of design patterns and structural
principles of real practical value for MDE. We will present examples of how an
elementary categorical arrangement of a model management scenario reveals
deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Optimal control of fed-batch processes with particle swarm optimization
Optimal control problems appear in several engineering fields. These problems are often described by sets of nonlinear differential and algebraic equations, usually subject to constraints in the state and control variables. Some bioprocess optimal control problems are revisited and a numerical approach to its solution is introduced.
The numerical procedure used to solve the problems takes advantage of the well know modeling AMPL language, providing an external dynamic library that solve the nonlinear differential equations. The optimal control problem as generally presented belongs to the class of semi-infinite programming (SIP) problems. A transformation of the SIP problem results in a nonlinear optimization problem (NLP) that can be address by off-the-shelf optimization software. The NLP formulation results in nondifferentiable optimization problems were the global solution is mostly desirable. We apply a particle swarm optimization strategy implemented in the MLOCPSOA [13] solver. Particle swarm optimization (PSO) is a stochastic technique that mimics the social behavior of a swarm
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
Collaborative Verification-Driven Engineering of Hybrid Systems
Hybrid systems with both discrete and continuous dynamics are an important
model for real-world cyber-physical systems. The key challenge is to ensure
their correct functioning w.r.t. safety requirements. Promising techniques to
ensure safety seem to be model-driven engineering to develop hybrid systems in
a well-defined and traceable manner, and formal verification to prove their
correctness. Their combination forms the vision of verification-driven
engineering. Often, hybrid systems are rather complex in that they require
expertise from many domains (e.g., robotics, control systems, computer science,
software engineering, and mechanical engineering). Moreover, despite the
remarkable progress in automating formal verification of hybrid systems, the
construction of proofs of complex systems often requires nontrivial human
guidance, since hybrid systems verification tools solve undecidable problems.
It is, thus, not uncommon for development and verification teams to consist of
many players with diverse expertise. This paper introduces a
verification-driven engineering toolset that extends our previous work on
hybrid and arithmetic verification with tools for (i) graphical (UML) and
textual modeling of hybrid systems, (ii) exchanging and comparing models and
proofs, and (iii) managing verification tasks. This toolset makes it easier to
tackle large-scale verification tasks
A Vision of Collaborative Verification-Driven Engineering of Hybrid Systems
Abstract. Hybrid systems with both discrete and continuous dynamics are an important model for real-world physical systems. The key challenge is how to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires significant human guidance, since hybrid systems verification tools solve undecidable problems. It is thus not uncommon for verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) modeling hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks.
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