=Paper=
{{Paper
|id=Vol-1507/dx15paper37
|storemode=property
|title=HyDiag: Extended Diagnosis and Prognosis for Hybrid Systems
|pdfUrl=https://ceur-ws.org/Vol-1507/dx15paper37.pdf
|volume=Vol-1507
|dblpUrl=https://dblp.org/rec/conf/safeprocess/ChantheryPRT15
}}
==HyDiag: Extended Diagnosis and Prognosis for Hybrid Systems==
https://ceur-ws.org/Vol-1507/dx15paper37.pdf
Proceedings of the 26th International Workshop on Principles of Diagnosis
H Y D IAG: extended diagnosis and prognosis for hybrid systems
Elodie Chanthery1,2 , Yannick Pencolé1 , Pauline Ribot1,3 , Louise Travé-Massuyès1
1
CNRS, LAAS, 7 avenue du colonel Roche, F-31400 Toulouse, France
e-mail: [firstname.name]@laas.fr
2
Univ de Toulouse, INSA, LAAS, F-31400 Toulouse, France
3
Univ de Toulouse, UPS, LAAS, F-31400 Toulouse, France
Abstract • (ζ0 , q0 ) ∈ ζ × Q, is the initial condition.
H Y D IAG is a software developed in Matlab by Each state q ∈ Q represents a behavioural mode that is
the DISCO team at LAAS-CNRS. It is currently characterized by a set of constraints Cq that model the lin-
a software designed to simulate, diagnose and ear continuous dynamics (defined by their representations
prognose hybrid systems using model-based tech- in the state space as a set of differential and algebraic equa-
niques. An extension to active diagnosis is also tions). A behavioural mode can be nominal or faulty (antic-
provided. This paper aims at presenting the na- ipated faults). The unknown mode can be added to model
tive H Y D IAG tool, and its different extensions to all the non anticipated faulty situations. The discrete part of
prognosis and active diagnosis. Some results on the hybrid automaton is given by M = (Q, Σ, T, q0 ), which
an academic example are given. is called the underlying discrete event system (DES). Σ is
the set of events that correspond to discrete control inputs,
autonomous mode changes and fault occurrences. The oc-
1 Introduction currence of an anticipated fault is modelled by a discrete
H Y D IAG is a software developed in Matlab, with Simulink. event fi ∈ Σf ⊆ Σuo , where Σuo ⊆ Σ is the set of unob-
The development of this software was initiated in the servable events. Σo ⊆ Σ is the set of observable events.
DISCO team with contributions about diagnosis on hybrid Transitions of T model the instantaneous changes of be-
systems [1]. It has undergone many changes and is cur- havioural modes. The continuous behaviour of the hybrid
rently a software designed to simulate, diagnose and prog- system is modelled by the so called underlying multimode
nose hybrid systems using model-based techniques [2; 3; 4]. system Ξ = (ζ, Q, C, ζ0 ). The set of directly measured vari-
An extension to active diagnosis has been also realized [5; ables is denoted by ζOBS ⊆ ζ.
6]. This article aims at presenting the native HyDiag tool An example of a hybrid system modeled by a hybrid au-
and its different extensions to prognosis and active diagno- tomaton is shown in Figure 1. Each mode qi is characterized
sis. by state matrices Ai , Bi , Ci and Di .
Section 2 recalls the hybrid formalism used by H Y D IAG.
Section 3 presents the native H Y D IAG tool that simulates Hybrid system
and diagnoses hybrid systems. Section 4 explains how H Y- q1 σ12 q2
D IAG has been extended in H Y D IAG P RO to prognose and u C1
x1(n+1)=A1x1(n)+B1u(n)
x2(n+1)=A2x2(n)+B2u(n)
Y1(n)=C1x1(n)+D1u(n) C2
diagnose hybrid systems. Section 5 presents the extension σ21
Y2(n)=C2x2(n)+D2u(n) y
to active diagnosis. Experimental results of H Y D IAG and its
σ1i
extension H Y D IAG P RO are finally presented in Section 6. σ
qi
xi(n+1)=Aixi(n)+Bu(n)
2 Hybrid Model for Diagnosis Ci Yi(n)=Cixi(n)+Diu(n)
…
H Y D IAG deals with hybrid systems defined in a monolithic
way. Such a system must be modeled by a hybrid automaton
[7]. Formally, a hybrid automaton is defined as a tuple S =
(ζ, Q, Σ, T, C, (q0 , ζ0 )) where:
Figure 1: Example of an hybrid system
• ζ is a finite set of continuous variables that comprises
input variables u(t) ∈ Rnu , state variables x(t) ∈
Rnx , and output variables y(t) ∈ Rny .
• Q is a finite set of discrete system states. 3 Overview of the native H Y D IAG diagnoser
• Σ is a finite set of events.
The method developed in [1] for diagnosing faults on-line
• T ⊆ Q × Σ → Q is the partial transition function
in hybrid systems can be seen as interlinking a standard di-
between states.
S agnosis method for continuous systems, namely the parity
• C = q∈Q Cq is the set of system constraints linking space method, and a standard diagnosis method for DES,
continuous variables. namely the diagnoser method [8].
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Proceedings of the 26th International Workshop on Principles of Diagnosis
3.1 How to use H Y D IAG ? of the system by triggering the current transition of the hy-
Step 1: hybrid model edition brid diagnoser that matches the current observation. It is
H Y D IAG allows the user to edit the modes of a hybrid au- possible to define in H Y D IAG a simulation scenario for the
tomaton S as illustrated in Figure 1. To model the system, modeled system with a duration and a time sample defined
the user must first provide in the Graphical User Interface of by the user.
the H Y D IAG software the following information: the num-
ber of modes, the number of discrete events that can be ob- 3.2 Software architecture with extensions
servable or unobservable, and the sampling period used for The general architecture of H Y D IAG and its two extensions
the underlying multimode system (defined by the set of state (see the next sections for their description) is presented on
matrices of the state space representation of each mode). Figure 3. Ellipses represent the objects handled by the soft-
There are optional parameters that are helpful to initialize ware, rectangles with rounded edges depict H Y D IAG func-
the mode matrices automatically before editing them: the tions and rectangles with straight edges correspond to exter-
number of entries for the continuous dynamics, the number nal D IA D ES packages. The behaviour automaton is at the
of outputs for continuous dynamics, the dimensions of each heart of the architecture as H Y D IAG and both its extensions
matrix A. The number of entries (resp. outputs) must be the rely on it to perform diagnosis, active diagnosis and prog-
same for all the modes. nosis.
The simulator of the edited model has no restrictions on
the number of modes or the order of the continuous dynam- ActHyDiag
ics, it is generically designed. Online computations are per- Specialized
AND/OR Conditional
ActDiades Active
formed using Matlab / Simulink. Results provided by Mat-
AO* Algorithm
Graph plan
diagnosers
lab can be reused if a special need arises. Figure 2 shows an Conditional plan
display
overview of the software interface.
HyDiag
Model display Additional Behaviour
Signature Automaton display Diagnoser display
event
Enriched
Behaviour Diagnoser
hybrid ARRs computation Diades
Automaton diagnosis
model
Diagnosis display
diagnosis
Prognoser Prognosis display
prognosis
prognosis
HyDiagPro
Figure 3: H Y D IAG architecture with its extensions H Y D I -
AG P RO and ACT H Y D IAG .
4 H Y D IAG P RO : an extension for Prognosis
H Y D IAG has been extended in order to provide a progno-
sis functionality to the software [4]. The prognosis function
computes (1) the fault probability of the system in each be-
Figure 2: H Y D IAG Graphical User Interface havioural mode, (2) the future fault sequence that will lead
to the system failure, (3) the Remaining Useful Life (RUL)
of the system.
Step 2: building the diagnoser In H Y D IAG P RO, the initial hybrid model is enriched
H Y D IAG automatically computes the analytical redundancy by adding for each behavioural mode a set of aging laws:
relations (ARRs) by using the parity space approach [9]. S + = (ζ, Q, Σ, T, C, F, (q0 , ζ0 )) where F = {F q , q ∈ Q}
Details of this computation can be found in [10]. and F q is a set of aging laws one for each anticipated fault
The idea of H Y D IAG is to capture both the continuous f ∈ Σf in mode q. The aging modeling framework that
dynamics and the discrete dynamics within the same math- is adopted in H Y D IAG P RO is based on the Weibull proba-
ematical object. To do so, the discrete part of the hybrid bilistic model [11] (see more details in [4]). The Weibull
system M = (Q, Σ, T, q0 ) is enriched with specific observ- fault probability density function W (t, βjq , ηjq , γjq ) gives at
able events that are generated from continuous information. any time the probability that the fault fj occurs in the sys-
The resulting automaton is called the Behaviour Automaton tem mode q. Weibull parameters βjq and ηjq are fixed by the
(BA) of the hybrid system. H Y D IAG then builds the diag- system mode q and characterise the degradation in mode q
noser of the Behaviour Automaton (see [8]) by using the that leads to the fault fj . Parameter γjq is set at runtime to
D IA D ES1 software also developed within the DISCO team memorize the overall degradation evolution of the system
at LAAS-CNRS (see an example of diagnoser in Figure 7). accumulated in the past modes [11].
Step 3: system simulation and diagnosis The prognoser uses the aging laws in S + to predict fault
Given the built hybrid diagnoser, H Y D IAG then loads a set occurrences (see Figure 3). The prognoser uses the cur-
of timed observations produced by the system and it pro- rent diagnosis result to update on-line these aging laws (the
vides at each observation time an update of the diagnosis parameters γjq ) according to the operation time in each be-
havioural mode. For each new result of diagnosis, the prog-
1
http://homepages.laas.fr/ypencole/DiaDes/ nosis function computes the most likely sequence of dated
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Proceedings of the 26th International Workshop on Principles of Diagnosis
faults that leads to the system failure. From this sequence is pump
Pump1 Pump 2
estimated the system RUL [4]. mode
1 ON ON
5 ACT H Y D IAG: Active Diagnosis 2 ON OFF
The second extension of H Y D IAG provides an active diag- 3 OFF OFF
nosis functionality to the software (see Figure 3). The inputs
are the same as for H Y D IAG but an additional file indicates 4 F il
Fail ON
the events of S that are actions, as well as their respective 5 ON Fail
cost. Based on the behaviour automaton, we compute a set
of specialised active diagnosers (one per fault): such a diag- 6 Fail OFF
noser is able to predict, based on the behaviour automaton, 7 OFF Fail
whether a fault can be diagnosed with certainty by applying
an action plan from a given ambiguous situation [6]. From 8 Fail Fail
these diagnosers, we also extract a planning domain as a
AND/OR graph.
At runtime, when H Y D IAG is diagnosing, the diagno- Figure 5: Water tank DES model
sis might be ambiguous. An active diagnosis session can
be launched as soon as a specialised active diagnoser can
analyse that the current faulty situation is discriminable by Table 1: Weibull parameters of aging models
applying some actions. If the active diagnosis session is Aging laws β η Aging laws β η
launched, an AO∗ algorithm starts and computes a condi- F q1 f1q1 1.5 3000 F q2 f1q2 2 3000
tional plan from the AND-OR graph that optimises an ac- f2q1 1.5 4000 f2q2 1 7000
tion cost criterion. It is important to note that in the case F q3
f1q3 1 8000 F q4
f1q4 NaN NaN
of a system with continuous dynamics, only discrete actions f2q3 1 7000 f2q4 2 4000
are contained in the active diagnosis plan issued by ACT H Y- F q5
f1q5 2 3000 F q6
f1q6 NaN NaN
D IAG. In particular, it is assumed that if it is necessary to f2q5 NaN NaN f2q6 1 7000
guide the system towards a value on continuous variables, F q7 f1q7 1 8000 F q8 f1q8 NaN NaN
f2q7 NaN NaN f2q8 NaN NaN
the synthesis of control laws must be performed elsewhere.
6 HyDiag/HyDiagPro Demonstration space:
Water tank system model X(k + 1) = AX(k) + BU (k)
(1)
Y (k) = CX(k) + DU (k)
Pump P1 Pump P2
where the state variable X is the water level in the tank,
continuous inputs U are the flows delivered by the pumps
P1 , P2 and the flow going through the valve, A = (1), B =
hmax !
eT e/S
h2
eT e/S with T e the sample time, S the tank base area
eT e/S
and ei = 1 (resp. 0) if the pump is turned on (resp. turned
h1 !
h
0
off), C = (1) and D = 0 .
0
Figure 4: Water tank system H Y D IAG results
Figure 6 presents the set of results obtained by H Y D IAG and
H Y D IAG P RO has been tested on a water tank system H Y D IAG P RO on the folllowing scenario. The time hori-
(Figure 4) composed of one tank with two hydraulic pumps zon is fixed at Tsim = 4000h, the sampling period is
(P1 , P2 ). Water flows through a valve at the bottom of the Ts = 36s and the filter sensitivity for the diagnosis is set
tank depending on the system control. Three sensors (h1 , as Tf ilter = 3min. The residual threshold is 10−12 . The
h2 , hmax ) detect the water level and allow to set the control scenario involves a variant use of water (max flow rate =
of the pumps (on/off). It is assumed that the pumps may 1200L/h) depending on user needs during 4000h. Pumps are
fail only if they are on. The discrete model of water tank automatically controlled to satisfy the specifications indi-
and the controls of pumps are given in Figure 5. Discrete cated above. Flow rate of P1 and P2 are respectively 750L/h
events in Σ = {h1 , h2s , h2i , hmax , f1 , f2 } allow the sys- and 500L/h.
tem to switch into different modes. Observable events are The diagnoser computed by H Y D IAG is given in Figure 7.
Σo = {h1 , h2s , h2i , hmax }. Two faults that correspond to Each state of the diagnoser indicates the belief state in the
the pump failures are anticipated Σf = {f1 , f2 } and are not model enriched by the abstraction of the continuous part of
observable.The Weibull parameter values of aging models the system, labelled with faults that have occurred on the
F = {F qi } are reported in Table 1. system. This label is empty in case of nominal mode. In the
The underlying continuous behaviour of every discrete scenario, fault f1 was injected after 3500h and fault f2 was
mode qi for i ∈ {1..8} is represented by the same state not injected.
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Proceedings of the 26th International Workshop on Principles of Diagnosis
f1
q_32,{}
q_75,{f2}
q_64,{f1}
q3,{}
Predicted dates of fault occurrence (h)
q7,{f2}
q6,{f1}
Remaining Useful Life (h)
q_23,{} df2
q_21,{}
q_57,{f2}
q8,{f1,f2}
q_46,{f1}
f1
q2,{} df1
q5,{f2}
q4,{f1}
q12,{} f1
q1,{}
Time (h) Time (h) Time (h)
Figure 6: Scenario: Diagnoser belief state (left), Prognosis results of degradations df1 and df2 (middle), System RUL (right).
results on an academic example are exposed in the paper.
An extension to active diagnosis is also presented. The ac-
tive diagnosis algorithm is currently tested on a concrete in-
dustrial case. H Y D IAG and its user manual will be soon
available on the LAAS website.
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7 Conclusion function for heterogeneous multi-component systems: appli-
H Y D IAG is a software developed in Matlab, with Simulink, cation to helicopters. In European Safety & Reliability Con-
by the DISCO team, at LAAS-CNRS. This tool has been ference, Troyes, France, September 18-22 2011.
extended into H Y D IAG P RO to simulate, diagnose and prog-
nose hybrid systems using model-based techniques. Some
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