This document provides an overview of process fault detection and diagnostics. It discusses key topics such as fault detection vs diagnosis, abnormal event management, components of a fault diagnosis framework, classes of failures, and desirable characteristics of a fault diagnostics system. Quantitative model-based methods are also introduced, including the use of redundancy, Kalman filters, and residual generation in dynamic systems.

1. Basics Of Process Fault Detection
And Diagnostics
By-Rahul Dey
EE14MTECH110331

2. Fault Detection
• Previously it was known as Fault Detection
Isolation and Recovery(FDIR).
• Fault is defined as an abnormal condition or defect
at the component equipment or sub-level which
may lead to failure [ISO/CD 10303-226]
• In simple words,it is a branch of control
engineering ,which deals with monitoring a
system,identifying when a fault has occurred and
to locate the fault is known as fault detection
2
Soure:wikipedia

3. Difference Between Detection &
Diagnosis
• Detection
It is the action or process of identifying the process
of something hidden
• Diagnosis
The identification of the nature of the problem by
examination of the symptoms
• Detection + Isolation = Diagnosis
3

4. Abnormal Event Management(AEM)
• AEM involves the timely detection of an
abnormal event ,diagnosing its causal origin &
then taking supervisory control decision and
action to bring back the process to a normal safe
operating state
• An abnormal event could arise from the
departure of an observed variable from the
acceptable range
4

5. Components of general fault diagnosis
framework
Figure 1 5

6. Classes of failure
• Gross parameter changes in a model
a) These are all the processes that cannot be
included in the model
b) All these processes are lumped to form a
single parameter,viz.gross parameter
c) In gross parameter interaction along the
system boundary is also included
d) Failure arises when there is disturbance in
the process through the environment
6

7. Classes of failure (contd..)
• Structural changes
a) These types of failure changes the process
itself
b) These types of failure changes various
information between variable
c) These types of failure occurs due to hard
failure in the component
d) For tackling such a failure,the diagnostic
system removes the model equation of the
faulty component & to change the other
equation accordingly
7

8. Classes of Failure(contd..)
• Malfunctioning Sensors & actuators
a) Serious error usually occurs with sensors &
actuators due to the following reasons:
1. Fixed failure
2. A constant bias
3. Out of range failure
b) Feedback signals,which are essential for control
of the plant.A failure in feedback component,
could result the plant go to unstablility,unless
failure is not detected quickly
8

9. Desirable characteristics of a fault
diagnostics system
• For comparing different diagnostic approach,there is a
set of desirable characteristics that a diagnostics
system should posses.
• With the help of the set of desirable characteristics
one can compare the different diagnostics classifier.
• When a fault occurs in a process,diagnostic classifier
would propose a set of fault that explains the fault
• The main aim of the diagnostic classifier would require
the actual faults to be subset of the proposed faults
• Resolution of diagnostics classifier would require the
proposed fault set to be minimum 9

10. Quick detection & diagnosis
• The diagnosis system should respond quickly in
detecting and diagnosing malfunction
• Quick response to 1
failure diagnosis Tolerable performance
during normal oprtn
• A system that has a quick response to any
failure,so it able to detect failure particularly the
impulsive changes quickly,so if the system is
prone to noise,it can lead to false alarming during
normal operation
10

11. Isolability
• It is the ability of the diagnostics system to
distinguish between different failures
• That is the diagnostics classifier should be able to
generate output that are orthogonal to the fault
that has not occurred
• But again here also there is a trade-off between
isolability and rejecting modelling uncertainities
Isolability 1
rejection of modelling
uncertainities
11

12. Robustness
• Robustness is the ability of the process to cope
with error & disturbances during operation
• Diagnostic system should be robust to various
noise and uncertainties
• It is better if the performance degrades gracefully
instead failing totally and abruptly
12

13. Novelty Identifiability
• Novelty identifiability,in simple words means
that,it is the threshold decided by the diagnostic
system whether the current process is functioning
normally or not,if not,whether the fault is a known
fault or an unknown fault
• Sufficient data may be available to model the
normal behaviour of the process,but we don’t have
large data available for modelling the abnormal
region
• Due to the unavailability of the data from
abnormal region,so it is possible that the abnormal
region has been not modelled properly.
13

14. Adaptability
• The diagnostic system should be adaptable to
changes such as :
a) Changes in external input
b) Structural changes due to retrofitting
c) Change in operating condition due to
disturbances
d) environmental condition,
• The diagnostic system should adaptable to
changes,and should gradually develop the system
as new cases and problem emerges
14

15. Explanation facility
• The job of the diagnostic system is not only
identifying faults but also providing on how the
fault started & propagated to the current situation
• It is actually the ability of the diagnostic system to
reason about cause and relationship in process
• The diagnostic system should justify its
recommendation so that operator can act
accordingly
• Also it is the job of the diagnostic system to justify
why certain fault were proposed and rest were
not 15

16. Multiple Fault Identifiability
• The ability to identify multiple fault is an
important but difficult task due to interacting
nature of the faults
• The interaction among the non linear is
synergistic that is it cant be determined by the
components
16

17. Quantitative Model-Based Methods
(Introduction)
• In this approach the most frequently used FDI
methods are observers,parity relations,Kalman
filters and parameter estimation
• Most of the work on quantitative model-based
approaches have been based on general input-
output and state-space models
• Both of the above types of model find an
important place in fault diagnosis studies
17

18. Quantitative Model-Based Methods
(Redundancy)
• Model-based FDI mainly relies on an explicit model
of the monitored plant
• There are two steps in any model based FDI
methods :-
1. Generating inconsistencies between the
actual and expected behavior, such
inconsistencies are also called residuals,these are
the ‘artificial signals’ reflecting potential faults
2. Choosing a decision rule for diagnosis
18

19. Redundancy(contd..)
• The check for inconsistency needs some form of
redundancy
• There are mainly two kind of redundancy :
a) Hardware redundancy b) Analytical redundancy
• Hardware redundancy
a) These kind of redundancy requires extra
sensors.
b) It is mainly used in the control of safety-critical
system such as aircraft,nuclear power plant
EX: Triple Modular Redundancy (TMR)
c) However hardware redundancy are costly to
implement,which is their main drawback
19

20. Redundancy(contd..)
• Analytical Redundancy
Also known as functional,inherent or artificial redundancy
is achieved from the functional dependencies among the
process variables & is usually provide by a set of algebraic
or time relating relationships among the states,input and
output of the systems
20
DIRECT TEMPORAL
This type of redundancy is accomplished by
algebraic relationship among different sensor
measurement
This type of redundancy is obtained from
differential or difference relationship among
different sensor output & actuator input
Such relation are useful in computing the
value of sensor measurement from
measurement of other sensors
This type of redundancy is useful for sensor
and actuator fault detection
The computed value is compared with sensor
data & a difference indicates a fault

21. 21
• The main characteristics of
analytical redundancy in FDI is
to compare the actual system
behavior against system model
for consistency
• Any inconsistency expressed as
residuals,can be used for
isolation and detection
• The residual should be close to
zero when no fault occurs but
show significant values when
there is fault
• For the generation of the
diagnostic residuals,we require
an explicit mathematical model
of the system
General scheme for using
analytical redundancy

22. Types Of Models
• Most of FDI methods use discrete black-box plant
models such as input-output or state space model &
assume linearity of the plant
• Considering a system with 𝑚 input & 𝑘 output
𝑢 𝑡 = [𝑢1 (𝑡) … … … . . 𝑢 𝑚(𝑡)] 𝑇
𝑦 𝑡 = [𝑦1 (𝑡) … … … . . 𝑦 𝑘 (𝑡)] 𝑇
• The basic model in state space form is
𝑥 𝑡 + 1 = 𝐴𝑥 𝑡 + 𝐵𝑢 𝑡
𝑦 𝑡 = 𝐶𝑥 𝑡 + 𝐷𝑢 𝑡
where 𝐴, 𝐵, 𝐶, 𝐷 are parameter matrices
• The same system can be expressed in the input-
output form
𝐻 𝑧 𝑦 𝑡 = 𝐺 𝑧 𝑢 𝑡
where 𝐻 𝑧 & 𝐺(𝑧) are polynomial matrices in 𝑧−122

23. Types Of Models(contd..)
𝐻 𝑧 is diagonal
𝐻 𝑧 = 𝐼 + 𝐻1 𝑧−1
+ 𝐻2 𝑧−2
+. . +𝐻 𝑛 𝑧−𝑛
𝐺 𝑧 = 𝐺0 + 𝐺1 𝑧−1
+ ⋯ + 𝐺 𝑛 𝑧−𝑛
• Both the above model are that of ideal situation,
where there is no fault, disturbance or noise
• State space model with fault
𝑥 𝑡 + 1 = 𝐴𝑥 𝑡 + 𝐵𝑢 𝑡 + 𝐸𝑝 𝑡
𝑦 𝑡 = 𝐶𝑥 𝑡 + 𝐷𝑢 𝑡 + 𝐸′
𝑝 𝑡 + 𝑞(𝑡)
• Input output model with fault
𝐻 𝑧 𝑦 𝑡 = 𝐺 𝑧 𝑢 𝑡 + 𝐻 𝑧 𝑞 𝑡 + 𝐹 𝑧 𝑝 𝑡
𝑞(𝑡) = output sensor fault
𝑝(𝑡) = actuator faults & certain plant faults,
disturbances as well as some input sensor faults23

24. Residual Generation In Dynamic System
• Both of above models, state space or input output
alike can be written as
𝑦 𝑡 = 𝑓 𝑢 𝑡 , 𝜔 𝑡 , 𝑥 𝑡 , 𝜃 𝑡
𝑦 𝑡 , 𝑢 𝑡 = measurable output & input
𝑥 𝑡 , 𝜔 𝑡 = unmeasurable state variable &
disturbances
𝜃 𝑡 = process parameter
• Process fault usually changes in the state variables
and/or changes in model parameters
• Based on the process model, one can estimate the
unmeasurable 𝑥 𝑡 𝑜𝑟 𝜃(𝑡) by observed
𝑢 𝑡 & 𝑦(𝑡) using state estimation or parameter
estimation 24

25. Kalman filters
• The plant disturbances are random fluctuations
and only the statistical parameters of the plants
are known
• FDI in such type of systems can be done by
monitoring the process or prediction error
• It can be done using the optimal state estimate
such as the Kalman filters
• KF is a recursive algorithm for state estimation
• The KF in s/s model is equivalent to an optimal
predictor for linear stochastic system in the input
output model
25

26. Kalman Filter Equations
• The system model is given as
𝑥 𝑡 + 1 = 𝐴𝑥 𝑘 + 𝐵𝑢 𝑘 + 𝑤(𝑘)
𝑦 𝑡 = 𝐶𝑥 𝑘 + 𝑣 𝑘
𝑤 𝑘 &𝑣 𝑘 are process and measurement noise
• Where 𝑤 𝑘 & 𝑣(𝑘) are standard gaussian with
zero mean
• 𝐶𝑜𝑣 𝑤 𝑘 = 𝐸 𝑤 𝑘 𝑤 𝑘 𝑇
= 𝑅1 𝑛×𝑛
𝐶𝑜𝑣 𝑣 𝑘 = 𝐸 𝑣 𝑘 𝑣 𝑘 𝑇
= 𝑅2 𝑚×𝑚
• Observer design
𝑥(𝑘 + 1) = 𝐴 𝑥(𝑘) + 𝐵𝑢 𝑘 + 𝐺(𝑘) 𝑛×𝑚[𝑦 𝑘 − 𝑦(𝑘)] 𝑚×1
26

27. Kalman Filter Equations(contd..)
• State Estimation Error
𝑒 𝑘 = 𝑥 𝑘 − 𝑥 𝑘
𝑒 𝑘 + 1 = 𝑥 𝑘 + 1 − 𝑥 𝑘 + 1
then substituting 𝑥 𝑘 + 1 from model equation
and 𝑥 𝑘 + 1 from observer equation,and
solving,we get
𝑒 𝑘 + 1 = 𝐴 − 𝐺𝐶 𝑒 𝑘 − 𝐺𝑣 𝑘 + 𝑤(𝑘)
to design an optimal-estimator such that
of estimation error, 𝑝 𝑘 is minimized
• minimized
o find 𝐺 𝑘 , minimize 𝑐𝑜𝑣 𝑒 𝑘 + 1
27

28. • But,
𝐸 𝑒 𝑘 + 1 = 𝐸 𝐴 − 𝐺𝐶 𝑒 𝑘 − 𝐸 𝐺𝑣 𝑘 + 𝐸 𝑤 𝑘
= 𝐸 𝐴 − 𝐺𝐶 𝑒 𝑘 − 𝐺𝐸 𝑣 𝑘
= 𝐴 − 𝐺𝐶 𝐸 𝑥 𝑘 − 𝑥 𝑘
nimize 𝑃 𝑘 + 1 with the help of decision variable
help of decision variable 𝐺 𝑘
28

29. • 𝑃 𝑘 + 1 = 𝐸 𝐴 − 𝐺𝐶 𝑒 𝑘 𝑒 𝑘 𝑇 𝐴 − 𝐺𝐶 𝑇 + 𝐺𝑣 𝑘 𝑣 𝑘 𝑇 𝐺 𝑇 + 𝑤 𝑘 𝑤 𝑘 𝑇
= 𝐴 − 𝐺(𝑘)𝐶 𝑃 𝑘 𝐴 − 𝐺(𝑘)𝐶 𝑇
+ 𝐺 𝑘 𝑅2 𝐺 𝑘 𝑇
+ 𝑅1
• Now let us assume that 𝐸[𝑒 𝑗 𝑒 𝑗 𝑇] is minimized for 𝑗 = 0,1. . , 𝑘
by selecting 𝐺 0 , 𝐺 1 , . . 𝐺(𝑘 − 1)
• Now we need to find 𝐺 𝑘 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑃(𝑘 + 1) is minimized
• 𝑃 𝑘 + 1 = 𝐴 − 𝐺(𝑘)𝐶 𝑃 𝑘 𝐴 − 𝐺(𝑘)𝐶 𝑇
+ 𝐺 𝑘 𝑅2 𝐺 𝑘 𝑇
+ 𝑅1
• Solving by adding and subtracting terms we will get,
• 𝑃 𝑘 + 1 = 𝐴𝑃 𝑘 𝐴 𝑇 + 𝑅1 − 𝐴𝑃(𝑘)𝐶 𝑇 𝑅2 + 𝐶𝑃 𝑘 𝐶 𝑇 −1
𝐶𝑃(𝑘)𝐴 𝑇
• 𝑃 𝑘 + 1 = 𝐴𝑃 𝑘 𝐴 𝑇 + 𝑅1 − 𝐺 𝑘 𝐶𝑃 𝑘 𝐴 𝑇
where,
• 𝐺 𝑘 = 𝐴𝑃(𝑘)𝐶 𝑇
[𝑅2 + 𝐶𝑃(𝑘)𝐶 𝑇
]−1
29

30. Kalman Filter Summary
• 𝑥 𝑘 + 1 𝑘 = 𝐴 𝑥( 𝑘 𝑘 − 1) + 𝐵𝑢 𝑘 + 𝐺(𝑘)[𝑦 𝑘 − 𝐶 𝑥( 𝑘 𝑘 − 1)]
• 𝐺 𝑘 = 𝐴𝑃( 𝑘 𝑘 − 1)𝐶 𝑇[𝑅2 + 𝐶𝑃( 𝑘 𝑘 − 1)𝐶 𝑇]
−1
• 𝑃( 𝑘 + 1 𝑘) = 𝐴𝑃 𝑘 𝑘 − 1 𝐴 𝑇 + 𝑅1 − 𝐺 𝑘 𝐶𝑃 𝑘 𝑘 − 1 𝐴 𝑇
30

31. 31