978-1-4799-7958-5/14/$31.00 ©2014 IEEE
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Dynamic system reliability modeling using extended
hybrid Petri nets
Xueliang Du, Shengkui Zeng
a,b
, Jianbin Guo
a,b
a: Science and Technology on Reliability and Environment Engineering Laboratory
b:School of Reliability and System Engineering Beihang University
Beijing, China
bh14dxl@126.com, zengshengkui@buaa.edu.cn, guojianbin@buaa.edu.cn
Abstract—Traditional system reliability model has almost
neglected the coupling between different states (normal, failures,
etc) and the continuous variation process of performance. This
paper presents a method of system reliability modeling based on
hybrid Petri nets (HPN), which combines the discrete state and
continuous performance together during the system to describe
the coupling relationship. Firstly, the system normal running
mode and fault mode were established using HPN to describe the
logical relationship between the discrete states; Secondly, on
account of each discrete state, the corresponding continuous
performance models were established and uncertain external
influencing factors were introduced. Besides, The degradation
process can be described by transitions among discrete states and
physical modeling by (physical) equations that govern the
degradation process. And the time-dependent transition rates
associated with model parameters were introduced to describe
the switch as a bridge between discrete states and continuous
performance characteristics; Finally, the running mechanism
were considered and a hydraulic case was modeled by this
method.
Keywords- dynamic system
;
reliability modeling
;
dynamic
characteristics
;
coupling
;
Petri nets
I. INTRODUCTION
Complex systems consist of large number of components
and each component might fail in a multiple ways[1]. Each
failure occurs under the effect of one or many fault modes.
When a fault condition arises in one of the components, not
only that component’s behavior but the interaction of that
component with the other components/subsystems also changes
through changing the continuous variation process of
performance[2][3]. Therefore, system has strong dynamic
characteristics. It also can be realized as that systems evolve
dynamically and failures can influence the dynamics and
reciprocally the dynamics (and its associated state variables)
can affect fault development and evolution. For example, the
faults of component can lead to mutations of system
performance, and the dynamic changes of some characteristics
(such as temperature, flow, power, etc) accelerate or decelerate
the occurrence of component or system failure, even led to the
component or system's failure directly. So the failure rate of the
system depends not only on the time, but also upon the status
of the system, such as vibration level, efficiency, number of
random shocks on the system, etc. any of which causes
degradation or failure.
Traditional system reliability model has almost neglected
the coupling between different states (normal, failures, etc) and
the continuous variation process of performance[4][5][6]. Chen
Yunxia described the state-of-the-art of IPaRA (Integrating
Performance and Reliability Analysis) that considered the
changes of performance under environment stochastic
influence when failures occurred, but it neglected the logical
relationship between component faults[7]. Li Jinghui and Ali
Mosleh presented the SimPRA simulation framework based on
DDET and Monte Carlo in which the interaction influence
between component fault and system performance were
partially considered, and it focused on automatic generation of
risk scenarios[8]. Wang Xin and Guo Jianbin presented hybrid
automata in which fault was regard as discrete event. With the
hydraulic test rig as an example, the interaction between
component fault and system performance is studied[9]. GA
Perez Castaneda carried out the reliability modeling and
evaluation of electric oven based on hybrid automata[10].
These researches provide a new idea for the research on system
reliability based on hybrid model. But they only considered the
logical relationship between component fault and system fault,
not considering that model parameters and environment
stochastic influence on the reliability.
Taking the advantage of the Petri net, we put forward a
system reliability simulation model based on extended HPN.
This reliability simulation model considers not only the
interaction between discrete state and continuous performance
model, but also the consideration of time-dependent transition
rates associated with model parameters and uncertain external
influencing factors. Based on this model, the reliability
characteristics can be simulated and analyzed.
This paper is organized as follows. The description of
dynamic system degradation process is given in Section Ⅱ.
The extended HPN is presented in Section Ⅲ . The run
mechanism is given in Section Ⅳ. Section Ⅴ shows the case
study.
II. D
YNAMIC SYSTEM DEGRADATION PROCESS
Dynamic system can be divided into two parts: one is
component which has discrete state and the other is continuous
variation process which is subject to certain physical laws[11].
The coupling between different states and continuous variation
process is shown in Figure 1.
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