Hybrid System Models

Each model s core is the hybrid system model, imaging the failure-free system architecture with the use of Reliability Block Diagrams and the system behavior and interactions of the components with the use of Concurrent Finite State Machines. Based on this hybrid system model, the article on hand presents an optimization environment considering system reliability, residual reliabdities and additional static parameters for different system states. The optimization process is demonstrated using a generic electrical power supply system based on a single-aisle twin-jet commercial aircraft. 

Both methods combined form the hybrid system model approach for the reliability analysis. 

The coupling of the RBD and the CFSM environments forms the hybrid system modeling approach as shown in figure 1. This enables a user not only to consider different component states but also individual failure rates depending on their actual state as defined in section 2.2 (15). 

Using a depth-first search algorithm the hybrid system model can be used to generate the complete system state space, which corresponds to the state space using an according Markov chain. But instead of solving... 

As the optimization algorithm itself is not in the focus of this article, but the integration of the hybrid system model and the consideration of residual reliabilities as an objective, the used algorithm wiU only be discussed briefly. Considering the No Free Lunch theorem, further analyzes of the algorithm itself regarding the system structure of aircraft systems is necessary (20). 

Objective value evaluation Calculate nominal and degraded reliability values using the hybrid system model. If applicable, add further static parameters, like system weight or costs. 

As step two is of certain interest for the integration of the hybrid system model into the optimization environment, the following part concentrates on the objective evaluation using the generated set of state equations for nominal and degraded system states. 

This contribution has shown the recent advancements of the software tool S yRelAn and underlying methodology, which can be utilized in the pre-design of fault-tolerant systems within the context of rehability analysis and redundancy management. The hybrid system model forms the basis of this reliabihty analysis, consisting of an upper-level Reliability Block Diagram and a lower-level Concurrent Finite State Machine environment. 

Based on the hybrid system model and the non-dominated sorting genetic algorithm-II, an optimization approach has been presented regarding nominal reliability, residual reliability on different degradation levels and static parameters as objective parameters. The new method considers the individual state of each component and corresponding failure rates. 

Future work will include the optimization of complex aircraft systems based on a Performance Degradation Analysis using the hybrid system model (14). This would allow a multi-point reliability optimization in a single model, leaving the classical top event approach. Additionally, corresponding to the No Free Lunch theorem (20), detailed work considering an optimization algorithm for the structure of aircraft system models itself is essential. 

Section 1.2 gives a literature review of various approaches to a bond graph representation of hybrid system models. In particular, the section discusses the representation of fast switching devices by means of non-ideal switches with fixed mode-independent causality and addresses the equation formulation as a DAE system. 

Clearly, for FDI it is necessary that a system is structurally observable. As switches temporarily disconnect and reconnect model parts they change the structure of a hybrid system model. Consequently, control properties, i.e. structural observability and structural controllability as well as characteristics of the mathematical model derived fl om the bond graph, i.e. the number of state variables, or the index of a DAE system become system mode dependent. Chapters briefly addresses these issues by confining to switched LTI systems and provides some small illustrating examples. 

ARRs from a bond graph representing a hybrid system model and the condensation of structural information in a system mode dependent stmctural fault signature matrix are presented. The chapter concludes by addressing off-line numerical computation of ARR residuals. To that end, a model of a system subject to faults is coupled to a bond graph of the healthy system by means of so-called residual sinks. This way, faults may be deliberately introduced without any risk and their effect, detection and isolation may be studied. 

Borutzky, W. (2011). Analytical redundancy relations from bond graphs of hybrid system models. In A. Bruzzone, G. Dauphin-Tanguy, S. Junco M. A. Piera (Eds.), Proceedings of the 5th International Conference on Integrated Modeling and Analysis in Applied Control and Automation (IMAACA 2011) (pp. 43-49). Rome. 

Bond Graph Representations of Hybrid System Models... 

Adopting a hybrid system model entails a number of consequences. 

The numerical integration of the model equations often requires the determination of the time instant ofthe discrete events and a reinitialisation. Hence, the numerical computation of a hybrid system model may be viewed as the solution of a sequence of initial value problems (IVPs). Modern numerical solvers for DAE systems such as IDA [2] from the SUNDIALS suite or DASRT [3] provide a root finding feature such that the time instances of mode switches can be located. 

The computation of models with variable stmcture is still a subject of ongoing research as latest publications show [4, 5]. With regard to a modelling by means of bond graphs the question arises how to represent a hybrid system model in a bond graph framework. 

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