165 To calculate the conditional failure probability for the residual time model in
,
1 k
i k
i
t t
, given that it has survived at
1
k i
t has the following form
1 1
1 1
| 1
| ,
|
k i
k i
k i
t i
i i
t t
i i
i i
k i
k i
i k
i
dx x
p dx
x p
t X
t X
t P
8-21
Using the data from engine 83000128, we calculated the conditional failure probability from both approaches with
1
k
prediction step.
i
, 99
. |
99 .
1 i
k i
k i
W W
P
, |
1 1
i k
i k
i i
k i
t X
t X
t P
1 0.0015045
0.00165013 10
0.0015126 0.00162982
70 0.0015209
0.00188199 96
0.0015210 0.00179508
Table 8-5: Conditional failure probability from a beta wear model and the residual time model
By observing Table 8-5, it can be concluded that the conditional failure probability
using both approaches produces similar result. This implies that the system statecondition can be described by many measures, but they should provide similar
failure predictions provided they are formulated correctively.
8.7 Summary
In conclusion, the work covered in this chapter details an application of a wear prediction model based on oil monitoring information used in diesel engines. The model
is formulated within a stochastic filtering and hidden Markov framework, which is able to predict the current and future wear. In this study, the underlying state is assumed to
have a continuous value. This is done by using a beta distribution to represent the dynamics of the underlying state of the system. The relationship between the wear and
observed monitoring information is modelled by a probabilistic distribution where the scale parameter of the distribution of the observed monitoring information is a function
166 of the time and wear. Particular attentions have been devoted to numerical solutions as
the analytical solution cannot be found. Two approximation approaches, namely approximation grid based and particle filtering, are used. The model proposed has been
fitted to several sets of SOAP data for testing and validation. Also, an attempt to investigate the relationship between the beta wear model and the residual time model
develop in Chapter 6 has come to a conclusion that both models produced similar results.
167
9 CHAPTER 9: CONCLUSION, DISCUSSION AND
FUTURE RESEARCH
9.1 Conclusion of the Research
The primary objective of this thesis is to substantiate a maintenance decision-making by means of condition monitoring data. Thus, the thesis approached this idea by compiling the
literatures of condition monitoring modelling and its effect on maintenance decision- making. Several condition-monitoring techniques have been discussed and all of them have
concluded with the same question, that is, if the observed parameter is deviated from its normal value is it sure to know that something wrong has happened which could lead to a
failure? Since the deterioration process is hidden and the monitored observations can only tell us something indirectly with noise, should we carry out maintenance actions now or
wait for an opportunity window? Hence, it comes to a question on how we in a cost effective way, should capitalize the observed condition monitoring data to carry out
maintenance. Analysis of the literature discovers that there exist a few models that could be used to explain the relationship between the observed monitoring information and the
itemsystem condition. Then by using this information, a model for maintenance decision- making is developed.
In detail, the development of a model for maintenance decision-making consists of modelling the deterioration process and a decision strategy. In our study, a deterioration
process model describes the condition of the system based on the age and the observed condition monitoring data. Also, we the deterioration process is modelled by using a
concept called hidden Markov model approach, which assumes that an observed monitoring data could be used as a function of the underlying state or condition of the equipment. In
developing these models, we used discrete and continuous measure to define the underlying state before it can be used to predict the condition of the itemsystem. Two types of
condition monitoring information is used namely vibration and oil analysis data to show the examples of the modelling ideas. It shown that, the model solution is complex and time
168 consuming particularly when the underlying state is continuous, hence we explore
approximation approaches namely grid based method and particle filtering. In short, here we demonstrate several important conclusions from the study.
1. Defining the underlying state of the system and their relationship with the
condition monitoring towards a failure is important to quantify the condition of the system. If different variables are used to define the underlying state of the system,
they should produce similar outcome in predicting the failure.
2. This research proves that monitoring information plays an important role in
prediction the condition of the itemsystem concerned.
3. It is a crucial to explore the observed condition monitoring data before
fitting it into the model. Any presence of trends or other patterns in data can provide valuable information in the study.
4. A simulation approach is useful to help us in establishing and testing a
model before it can be applied with a real data.
5. Approximation by numerical techniques is used to overcome problems exist
in the analytical form. It provides us with a balance between result and computational effort to gain the result.
6. This research also proves that subjective information is helpful while facing
non-identifiable parameters estimation.
In the next section, the contributions of this study are presented.
9.2 Contributions of the Research