Construction and analysis of causally dynamic hybrid bond graphs

Engineering systems are frequently abstracted to models with discontinuous behaviour (such as a switch or contact), and a hybrid model is one which contains continuous and discontinuous behaviours. Bond graphs are an established physical modelling method, but there are several methods for constructing switched or ‘hybrid’ bond graphs, developed for either qualitative ‘structural’ analysis or efficient numerical simulation of engineering systems. This article proposes a general hybrid bond graph suitable for both. The controlled junction is adopted as an intuitive way of modelling a discontinuity in the model structure. This element gives rise to ‘dynamic causality’ that is facilitated by a new bond graph notation. From this model, the junction structure and state equations are derived and compared to those obtained by existing methods. The proposed model includes all possible modes of operation and can be represented by a single set of equations. The controlled junctions manifest as Boolean variables in the matrices of coefficients. The method is more compact and intuitive than existing methods and dispenses with the need to derive various modes of operation from a given reference representation. Hence, a method has been developed, which can reach common usage and form a platform for further study

Constitutive hybrid processes

Introduction When modeling a physical system, it is common practice to describe the components that constitute the system, using so-called constitutive relations on the physical variables that play a role in the system. The intersection of all these relations then forms a model of the system as a whole. The behavior of physical systems is usually assumed to be continuous and, therefore, the constitutive relations are often stated as differential algebraic equations. When part of the continuous behavior occurs very fast, however, as is for example the case when studying impact phenomena, it may be convenient to describe this behavior as being discontinuous. The constitutive relations that are used to describe the system, should in that case not only contain algebraic differential equations (for the large time-scale behavior), but using also equations that describe the discontinuous behavior (for the behavior during impact). In this report, we describe the constitutive relations of many more-or-less standard components in physical modeling, using the hybrid process algebra HyPA [4]. This algebra allows us to describe combinations of continuous and discontinuous behavior as one, hybrid, process (hence, the title of this report). As a vehicle for our thoughts, we use a graphical language named bond graphs [11] to formalize our physical models, before engaging in the construction of constitutive relations for them. Bond graphs generalize all domains of physics, such as electronics, hydraulics, and mechanics, in one framework. Recently, they have been extended with elements that are suitable for describing discontinuous behavior [10, 9, 1, 12]. This report, can therefore also be considered an attempt to give a formal semantics to hybrid bond graphs. Our expectation is, that after we have explained how to derive hybrid constitutive processes using hybrid bond graphs, it will also be easier to derive these processes directly, without using bond graphs as an intermediate step. Nevertheless, the construction of a bond graph sometimes gives additional insight in the workings of a system, and can facilitate analysis in many ways (see for example [8, 14, 3, 2]). In general, different model representations have strengths in different kinds of analysis. In the next section, we give a short discussion on the modeling of physical systems through constitutive relations, using an example from mechanical engineering. Then, we briefly explain the traditional bond graph modeling method and discuss the need for abstraction from small timescale behavior. In section 3 we briefly discuss the syntax and semantics of hybrid process algebra [4]. In section 4, we turn back to the bond graph modeling formalism, to see how the constitutive relations of the bond graph elements can be extended to include discontinuous behavior. In the last section, we give modeling examples that show how hybrid bond graph models can be made of several physical systems, and how these bond graph models can be turned into constitutive hybrid processes describing the systems algebraically

Constitutive hybrid processes

Introduction When modeling a physical system, it is common practice to describe the components that constitute the system, using so-called constitutive relations on the physical variables that play a role in the system. The intersection of all these relations then forms a model of the system as a whole. The behavior of physical systems is usually assumed to be continuous and, therefore, the constitutive relations are often stated as differential algebraic equations. When part of the continuous behavior occurs very fast, however, as is for example the case when studying impact phenomena, it may be convenient to describe this behavior as being discontinuous. The constitutive relations that are used to describe the system, should in that case not only contain algebraic differential equations (for the large time-scale behavior), but using also equations that describe the discontinuous behavior (for the behavior during impact). In this report, we describe the constitutive relations of many more-or-less standard components in physical modeling, using the hybrid process algebra HyPA [4]. This algebra allows us to describe combinations of continuous and discontinuous behavior as one, hybrid, process (hence, the title of this report). As a vehicle for our thoughts, we use a graphical language named bond graphs [11] to formalize our physical models, before engaging in the construction of constitutive relations for them. Bond graphs generalize all domains of physics, such as electronics, hydraulics, and mechanics, in one framework. Recently, they have been extended with elements that are suitable for describing discontinuous behavior [10, 9, 1, 12]. This report, can therefore also be considered an attempt to give a formal semantics to hybrid bond graphs. Our expectation is, that after we have explained how to derive hybrid constitutive processes using hybrid bond graphs, it will also be easier to derive these processes directly, without using bond graphs as an intermediate step. Nevertheless, the construction of a bond graph sometimes gives additional insight in the workings of a system, and can facilitate analysis in many ways (see for example [8, 14, 3, 2]). In general, different model representations have strengths in different kinds of analysis. In the next section, we give a short discussion on the modeling of physical systems through constitutive relations, using an example from mechanical engineering. Then, we briefly explain the traditional bond graph modeling method and discuss the need for abstraction from small timescale behavior. In section 3 we briefly discuss the syntax and semantics of hybrid process algebra [4]. In section 4, we turn back to the bond graph modeling formalism, to see how the constitutive relations of the bond graph elements can be extended to include discontinuous behavior. In the last section, we give modeling examples that show how hybrid bond graph models can be made of several physical systems, and how these bond graph models can be turned into constitutive hybrid processes describing the systems algebraically

Requirement-Guided Model Refinement

Medical device is a typical Cyber-Physical System and ensuring the safety and efficacy of the device requires closed-loop verification. Currently closed-loop verifications of medical devices are performed in the form of clinical trials in which the devices are tested on the patients

Automated Closed-Loop Model Checking of Implantable Pacemakers using Abstraction Trees

Autonomous medical devices such as implantable cardiac pacemakers are capable of diagnosing the patient condition and delivering therapy without human intervention. Their ability to autonomously affect the physiological state of the patient makes them safety-critical. Sufficient evidence for the safety and efficacy of the device software, which makes these autonomous decisions, should be provided before these devices can be released on the market. Formal methods like model checking can provide safety evidence that the devices can safely operate under a large variety of physiological conditions. The challenge is to develop physiological models that are general enough to cover the large variability of human physiology, and also expressive enough to provide physiological contexts to counter-examples returned by the model checker. In this paper, the authors develop a set of physiological abstraction rules that introduce physiological constraints to heart models. By applying these abstraction rules to a initial set of heart models, an abstraction tree is created. The root model covers all possible inputs to a pacemaker and derived models cover inputs from different heart conditions. If a counter-example is returned by the model checker, the abstraction tree is traversed so that the most concrete counter-example(s) with physiological contexts can be returned to the domain experts for validity check. The abstraction tree framework replaces the manual abstraction and refinement framework, which reduced the amount of domain knowledge required to perform closed-loop model checking. It encourages the use of model checking during the development of autonomous medical devices, and identifies safety risks earlier in the design process

Modelling and analysis of traffic networks based on graph transformation

This is an electronic version of the paper presented at the Symposium on Formal Methods for Automation and Safety in Railway and Automotive Systems, FORMS/FORMATS 2004 , held in Braunschweig on 2004We present the formal definition of a domain specific visual language (Traffic) for the area of traffic networks. The syntax has been specified by means of meta-modelling. For the semantics, two approaches have been followed. In the first one, graph transformation is used to specify an operational semantics. In the second one we include timing information and a denotational semantics is defined in terms of Timed Transition Petri Nets (TTPN). The transformation from the Traffic formalism into TTPN was also defined by graph transformation. Both approaches have been used for the analysis of Traffic models. The ideas have been implemented in the AToM3 tool and are illustrated with examples.Juan de Lara’s work has been partially sponsored by a grant from the E.U. SEGRAVIS research network (HPRN-CT-2002-00) and the Spanish Ministry of Science and Technology (TIC2002-01948). Hans Vangheluwe gratefully acknowledges partial support for this work by a National Sciences and Engineering Research Council of Canada (NSERC) Individual Research Grant