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Proceedings ArticleDOI

Performance Prediction using Neural Network and Confidence Intervals: a Gas Turbine application

01 Dec 2018-pp 2151-2159
TL;DR: A tool based on the implementation of Radial Basis Function Neural Networks was developed to support the maintenance function in the decision-making process and provides an additional level of information in terms of predicting the confidence interval around the prediction of the neural network.
Abstract: The combination of Condition Based monitoring techniques with the predictive capabilities of neural networks represents a topic of central importance when it comes to maximizing production profits and consequently reducing costs and downtime. The ability to plan the best strategy based on the prediction of potential damaging events can represent a significant contribution, especially for the maintenance function. In fact, optimization of the management of the equipment is a fundamental step to guarantee the competitiveness of companies in the current market. In this paper, a tool based on the implementation of Radial Basis Function Neural Networks was developed to support the maintenance function in the decision-making process. In addition to providing an indication of the status of the equipment, the current approach provides an additional level of information in terms of predicting the confidence interval around the prediction of the neural network. The confidence interval combined with the prediction of the future state of the equipment can be of fundamental importance in order to avoid strategic decisions based on a low level knowledge of the system status or prediction performance of the applied algorithm. The developed tool is tested on the prediction of a naval propulsion system gas turbine performance decay, where the statuses of both the turbine and the compressor of the system are predicted as well as predicting their confidence intervals.

Summary (3 min read)

INTRODUCTION

  • In the current market, the ability to react quickly to production problems and minimize downtime and costs has become a fundamental feature for the survival of companies.
  • The maintenance function has increasingly covered a key role in maximizing production performance and minimizing the costs incurred by the companies.
  • The authors analyses and selection of the attributes emphasize the importance of data understanding and pre-processing and show that they may simplify the analysis of the data through dimensionality reduction for example.
  • Motivated by the large number of attributes in the Naval propulsion system and the complexity and high correlation of the hidden patterns that represent fault and healthy conditions of the system, the authors then implement a Radial Basis Function Neural Network model (RBF) to predict the performance of the system.
  • In addition, RBF models can be trained much faster than other neural networks architectures, such as Multilayer Perceptron Neural Networks for example, and they are very stable, as discussed and demonstrated in [9] .

II. RADIAL BASIS FUNCTIONS

  • Radial Basis Function Neural Network (RBF) are a class of neural networks made of an input layer, a hidden layer, and an output layer.
  • The activation function of the hidden layer neurons is specified by the distance between the input vector and the prototype or target vector [8] .
  • The first layer of weights is dedicated to the parameters of the basis functions while the second layer represents the linear combinations of the basis function activation functions.
  • For further details please refer to [8] .

III. DATA

  • The analyzed dataset in this paper is an open access synthetic dataset generated from a Simulink® model of a Naval Gas Turbine [10] and it can be found at: (https://archive.ics.uci.edu/ml/machine-learningdatabases/00 316/).
  • The Gas Turbine model is made of 16 input features, listed in Table 1 and two outputs, the Compressor Decay coefficient and the Turbine Decay coefficient.
  • The first output variable is related to the decay of the performance of the gas turbine compressor and it varies in the range [0.95; 1], where 0.95 means that a 5% decay in the compressor performances is recorded.
  • The optimal number of hidden neurons in the RBF model is decided in the validation phase where the optimal number of hidden neurons is selected by calculating the error between the network prediction of the validation data set and their actual values.
  • In the final stage of the RBF model creation, the performance of the specified optimal structure is tested on the test dataset which is a sub-set of the original dataset that has normally never been seen before by the network.

IV. DATA PREPROCESSING

  • Before going on to the actual analysis, the dataset was preprocessed in order to remove the non-relevant features for the prediction of the system performance decay.
  • This is an important data analysis stage that is very often overlooked.
  • This will subsequently introduce unneeded noise, time delays in the results calculations, and more in general, reduction in the algorithm predictions performances.
  • The preprocessing of the dataset mainly includes the calculation of the correlation coefficients between the 16 input features and the 2 output variables.
  • Then, features 6 and 7, starboard propeller torque and port propeller torque, show identical correlation coefficients and indeed they have identical values, so one of them, feature 7, has been removed.

V. REGULARISATION WITH NOISE INTRODUCTION

  • As discussed before, the gas turbine data has been generated through simulation, therefore it is purely deterministic.
  • In order to mimic the real-world situation where sensors' noise and uncertainty are unavoidable, the authors added some noise to the outputs (turbine decay coefficient and compressor decay coefficient).
  • Some noise has also been introduced to the training data set and added to the 11-correlation based selected inputfeatures as a regularization mechanism for the neural network learning.
  • Given a random vector noise n and its probability p(n), the error used to determine the weights using the error equation 4 for the limit of an infinite number of data points can be rewritten as [8] : EQUATION.
  • Given that the noise amplitude is small enough to neglect the Taylor expansion high order terms, the minimization of the error with the noise added in the input is equivalent to the minimization of the error without the noise terms added to the input plus the regularization term in equation 12 .

VI. PREDICTION OF CONFIDENCE INTERVAL

  • An aspect that is often overlooked is the development of metrics that are suitable for measuring the accuracy of a specific prediction of neural networks.
  • When the accuracy of the forecast is not sufficiently precise, alternative decisions can be made in order to avoid worsening the situation if the machine learning algorithm is unable to provide reliable predictions within a certain range of precision.
  • The Confidence Interval (CI) of the network prediction has been used as a metric of the RBF prediction performance.
  • In order to be able to predict the confidence interval of the neural network estimates of the system decay, a second RBF network is used to estimate the calculated residual error values between the actual decays and estimated ones after the completion of the training of the RBF that estimates the decays.
  • This is the level that the authors aim to achieve in this work, therefore they expect to define a results accuracy level that allows for outliers only for 5% of the cases.

VII. NUMERICAL SIMULATION: EXPERIMENTS SETUP AND RESULTS

  • The RBF has been used to predict the system decay and the confidence interval of the prediction.
  • The complexity of the neural network then decreases with the increase in the noise level.
  • This residual error is then used as the target value for a second RBF network in order to determine the level of accuracy of the system decay prediction on the test dataset.
  • The incorrect interpretation of these false can lead to poor and potential harmful decisions as well as unneeded stoppages, thus increasing the costs of maintenance operations.
  • With the introduction of the CI, more careful attention can be given to the predictions that present a wider CI and therefore a lower reliability of the prediction.

VIII. CONCLUSIONS

  • In the context of Industrial Analytics, the performance prediction of a system represents a highly nonlinear and uncertain problem where the status of several attributes of the system and its components might or might not concur simultaneously to the overall performance decay.
  • This combined with the estimation of the result reliability through the CI implementation aims to provide a support for the maintenance strategic decision-making process with a reduction in the probability of false alarms.
  • The importance of understanding and preprocessing the data to select the relevant features only are emphasized.
  • It is shown that the noise in the input can in fact help in reducing the number of parameters of the trained RBF neural network.
  • This is mostly because the studied gas turbine problem is a standard regression problem for which the authors used and implemented dimensionality reduction techniques and universal function approximators.

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Performance Prediction using Neural Network and Confidence Intervals: a Gas
Turbine application.
Silvia Cisotto, Dr Randa Herzallah
Aston University
Systems Analytics Research Institute (SARI)
Birmingham, UK
cisottos@aston.ac.uk, r.herzallah@aston.ac.uk
Abstract The combination of Condition Based monitoring
techniques with the predictive capabilities of neural networks
represents a topic of central importance when it comes to
maximizing production profits and consequently reducing costs
and downtime. The ability to plan the best strategy based on the
prediction of potential damaging events can represent a
significant contribution, especially for the maintenance
function. In fact, optimization of the management of the
equipment is a fundamental step to guarantee the
competitiveness of companies in the current market. In this
paper, a tool based on the implementation of Radial Basis
Function Neural Networks was developed to support the
maintenance function in the decision-making process. In
addition to providing an indication of the status of the
equipment, the current approach provides an additional level of
information in terms of predicting the confidence interval
around the prediction of the neural network. The confidence
interval combined with the prediction of the future state of the
equipment can be of fundamental importance in order to avoid
strategic decisions based on a low level knowledge of the system
status or prediction performance of the applied algorithm. The
developed tool is tested on the prediction of a naval propulsion
system gas turbine performance decay, where the statuses of
both the turbine and the compressor of the system are predicted
as well as predicting their confidence intervals.
Radial Basis Function Neural Networks, Industry 4.0,
Confidence Interval, Predictive Maintenance.
I. INTRODUCTION
In the current market, the ability to react quickly to
production problems and minimize downtime and costs has
become a fundamental feature for the survival of companies.
Furthermore, the variability in terms of both product and
volume specifications exacerbates the potential consequences
of incorrect handling and maintenance of production
equipment [1].
In this context, the maintenance function has increasingly
covered a key role in maximizing production performance and
minimizing the costs incurred by the companies. Indeed, the
cost of the maintenance function has been quantified in the
automotive industry to be as high as $20,000 per minute of
downtime [2] whereas, as discussed in [3], maintenance costs
represent 15-40 % of total production costs.
A significant innovation in this field is represented by the
combination of Condition Based Monitoring (CBM) with the
Internet of Things (IoT) concepts and Machine Learning (ML)
principles. This combination has led to what is nowadays
called "Industry 4.0" where already known and developed
tools, such as CBM, are empowered by the analysis and
processing of data collected using IoT and cloud-based
solutions and processed using ML applications [4-7].
In this paper, a gas turbine synthetic dataset for marine
applications made of several attributes and numerous
instances is analyzed. Firstly the attributes are selected in
terms of correlation with the system performance decay in
order to minimize the complexity. Our analyses and selection
of the attributes emphasize the importance of data
understanding and pre-processing and show that they may
simplify the analysis of the data through dimensionality
reduction for example. Motivated by the large number of
attributes in the Naval propulsion system and the complexity
and high correlation of the hidden patterns that represent fault
and healthy conditions of the system, we then implement a
Radial Basis Function Neural Network model (RBF) to
predict the performance of the system. This is because RBF
networks are universal function approximators which can
approximate an arbitrary function in a given function class to
any degree of accuracy. In addition, RBF models can be
trained much faster than other neural networks architectures,
such as Multilayer Perceptron Neural Networks for example,
and they are very stable, as discussed and demonstrated in [9].
Moreover, they have a less complex architecture with input-
hidden-output layers and two layers of weights.
Finally, a metric that quantifies the performance of the
applied RBF model for predicting the future behavior of the
system given a certain status of the input features is developed
and tested. In particular, this metric is based on predicting the
accuracy of the neural network prediction by providing a
prediction for the residual error as a result of the estimation
process. Indeed, the system status information obtained are
enriched with the determination of the results confidence
interval, determined again using another RBF Neural Network
with the same structure as the one used to predict the system
performance decay, to support a more reliable and conscious
decision-making process in terms of system maintenance.
To reduce the obtained model complexity and simulate
real world situation where the sensor noise and uncertainty are
unavoidable, we introduced Gaussian noises to the input
attributes to add a regularization effect, and to the output to
represent measurement noise in the sensors measuring the
decays.

Although the separate techniques are already present in the
literature, the aim of this paper is to present an approach to the
system performance prediction that instead of focusing on the
optimization of a single aspect of the analysis, takes into
account different aspects, starting from the data pre-
processing to the use of neural networks as universal
approximators to the use of confidence interval prediction
with the scope of supporting the maintenance strategic
decision-making process.
This paper is organized in 8 Sections. In Section 2, the
theory behind the RBF model is introduced. Section 3 and 4
describe the dataset used in the experiment, as well as its pre-
processing and selection of the most relevant features with the
aim of dimensionality reduction. In Section 5, the introduction
of noise both in the input and the output features of the dataset
is discussed. The development of a metric to quantify the
accuracy of prediction is presented in Section 6. In Section 7,
the results obtained by a set of experiments run on the RBF
are shown. Conclusion remarks are given in Section 8.
II. R
ADIAL BASIS FUNCTIONS
Radial Basis Function Neural Network (RBF) are a class
of neural networks made of an input layer, a hidden layer, and
an output layer. The activation function of the hidden layer
neurons is specified by the distance between the input vector
and the prototype or target vector [8]. The RBF architecture
encompasses input-hidden-output layers and two layers of
weights. The first layer of weights is dedicated to the
parameters of the basis functions while the second layer
represents the linear combinations of the basis function
activation functions.
The output of the RBF network is calculated as [8]:
()=

∙
(
)
+


(1)
Where:
is the input vector;
=[1,..,]
is the j-th hidden neuron;
=[1,…,]
is the k-th output neuron;

are the weights from the hidden neurons to
output k;
(
)
is the activation function of the hidden
neuron j;

is the bias weight of output k.
There are different types of activation functions, such as
the Thin Plate Spline, Gaussian, and the Logarithmic. In this
paper the Gaussian activation function has been chosen:
(
)
=󰇧
−
2
󰇨
(2)
Where:
=|
|
is the distance between the input
vector and the vector of the centres of the basis
function
;
is the width of j-th hidden neuron basis function.
Being a supervised learning algorithm, the RBF network
encompasses three phases.
The first phase is the training phase, which is made of two
steps: firstly, the radial functions are determined by
unsupervised techniques on the input data and then the hidden
layer weights are found using fast linear supervised methods.
In the first step, the input vector is used to determine the basis
function parameters μj and σj for the Gaussian activation
function for each hidden neuron. Then, keeping these
parameters fixed, the second layer weights can be found by
linear matrix inversion techniques. So, if the bias in equation
1 is included in the weights assuming that for the bias, the
activation function value,
=1:
(
)
=

∙
(
)
→

(
)
=∙
(3)
At this point, the weights can be optimized by minimizing the
error between the prediction and the target calculated as:
=
1
2
(
−
)
(4)
Therefore, the error function is a quadratic function of the
weights and the weights can be determined as:
∙∙
=
∙
(5)
which can be written also as:
=
∙
(6)
where ϕ
is the pseudo-inverse of ϕ.
For further details please refer to [8].
III. D
ATA
The analyzed dataset in this paper is an open access
synthetic dataset generated from a Simulink® model of a
Naval Gas Turbine [10] and it can be found at:
(https://archive.ics.uci.edu/ml/machine-learningdatabases/00
316/).
The simulated naval gas turbine system model is not
discussed in this paper, but further information can be found
in [10].
The Gas Turbine model is made of 16 input features, listed
in Table 1 and two outputs, the Compressor Decay coefficient
and the Turbine Decay coefficient. The first output variable is
related to the decay of the performance of the gas turbine
compressor and it varies in the range [0.95; 1], where 0.95
means that a 5% decay in the compressor performances is

recorded. The second output variable is the system turbine
decay and, in this case, it varies in the range [0.975; 1].
TABLE I. I
NPUT
F
EATURES OF
G
AS
T
URBINE
S
YSTEM
.
Feature ID
Number
Description
1
Lever position
2
Ship speed
3
Gas Turbine shaft torque
4
Gas Turbine rate of revolutions
5
Gas Generator rate of revolutions
6
Starboard Propeller Torque
7
Port Propeller Torque
8
HP Turbine exit temperature
9
GT Compressor inlet air temperature
10
GT Compressor outlet air temperature
11
HP Turbine exit pressure
12
GT Compressor inlet air pressure
13
GT Compressor outlet air pressure
14
Gas Turbine exhaust gas pressure
15
Turbine Injection Control
16
Fuel Flow
In total, the dataset is composed of 11,934 samples where:
459 samples are purely related to the Compressor decay with
no decay in the turbine, 234 samples are pure turbine decay
related, and the remaining samples represent a combination of
decay status of both the compressor and the turbine. In this
paper, the entire dataset is considered in the experiments with
the aim of predicting the decay of system regardless if it is
generated by the compressor decay, the turbine decay or both.
As already mentioned in the introduction, RBF neural
network is a universal nonlinear function approximator that
can make data-driven predictions or decisions and they can be
trained much faster than other neural networks architectures
as well as being more stable, making them able to handle big
data in an efficient way. As such, we use an RBF neural
network to provide predictions for the gas turbine
performance decay.
Three data sets are commonly used in different stages of
the RBF model creation. The RBF model parameters are
initially optimized on a training data set. The optimal number
of hidden neurons in the RBF model is decided in the
validation phase where the optimal number of hidden neurons
is selected by calculating the error between the network
prediction of the validation data set and their actual values. In
this paper, the optimal structure in terms of number of centers
or hidden neurons has been determined by calculating the
minimum of the Normalized Error (NE) of the validation
phase, where the normalized error is calculated as:
=
(
−
)
(
−
)
(7)
Where:
is the target vector;
is the predicted output vector,

is the mean of the target vector.
In the final stage of the RBF model creation, the
performance of the specified optimal structure is tested on the
test dataset which is a sub-set of the original dataset that has
normally never been seen before by the network. In order to
give a measure of the reliability of the constructed RBF
model, the confidence interval has been implemented in this
paper, as discussed in more details in Section 5.
The dataset has been divided by randomly sampling the
original dataset without sample replacement into three
different sub-sets: 50% of data (5967 samples) are used for the
training phase of the RBF network, 30% (3580 samples) are
used for the validation phase, and the rest 20% (2387 samples)
are used for the test phase.
IV. D
ATA PREPROCESSING
Before going on to the actual analysis, the dataset was pre-
processed in order to remove the non-relevant features for the
prediction of the system performance decay. The main
objective of this step is the dimensionality reduction and the
avoidance of the “Garbage-in Garbage-out” effect [11].
This is an important data analysis stage that is very often
overlooked. Nevertheless, missing this step lead to an increase
in the computational capacity needed to perform the task as
well as an increase in the model complexity. This will
subsequently introduce unneeded noise, time delays in the
results calculations, and more in general, reduction in the
algorithm predictions performances.
The preprocessing of the dataset mainly includes the
calculation of the correlation coefficients between the 16 input
features and the 2 output variables. The calculated correlation
coefficients are shown in Table 2.
The Correlation coefficient has been calculated as:
,
=[,] (
∙
)
(8)
where:

[
,
]
=[(
)∙(−
)]
is the
covariance;
,
are the standard deviation of X and Y;
is the expectation;
,
are the means of X and Y.
This coefficient can vary in the range [-1; 1] where the
positive value indicates a direct correlation and the negative
indicates an inverse correlation.

Based on the value of the correlation coefficients, feature
1 and 2 (lever position and sheep speed) have been removed
due to their low correlation with the outputs and the fact that
they are both included in the constitutive model of the Gas
Turbine [10]. Features 9 and 12, compressor inlet air
temperature and compressor inlet air pressure, are constant
values and therefore have been removed. Then, features 6 and
7, starboard propeller torque and port propeller torque, show
identical correlation coefficients and indeed they have
identical values, so one of them, feature 7, has been removed.
TABLE II. CORRELATION COEFFICIENTS.
Feature ID
Number
Compressor
Correlation
Turbine
Correlation
1
1.54E-18 -2.88E-18
2
-6.20E-19 9.59E-18
3
0.002978258 0.000357638
4
0.001369908 -1.78E-05
5
-0.018837996 0.010000108
6
0.0007535 0.000104423
7
0.0007535 0.000104423
8
-0.03962512 -0.038463904
9
- -
10
-0.047176568 -0.01685505
11
0.008167586 -0.002718186
12
- -
13
0.008327871 -0.018303363
14
0.035285243 0.011794227
15
-0.032036625 -0.01887184
16
-0.013667655 -0.017326752
Based on the calculated correlation coefficients, the input
features have been reduced by 5 features. Thus, the
dimensionality of the input variables has been consequently
reduced, an aspect that has been overlooked by the authors in
[10].
We emphasize here the importance of data understanding
and pre-processing as the use of irrelevant information can
only introduce more complexity to the analyzed problem and
increase the computational complexity unnecessarily.
V. R
EGULARISATION WITH NOISE INTRODUCTION
As discussed before, the gas turbine data has been
generated through simulation, therefore it is purely
deterministic. In order to mimic the real-world situation where
sensors’ noise and uncertainty are unavoidable, we added
some noise to the outputs (turbine decay coefficient and
compressor decay coefficient). The noise introduced in the
output has been generated using Gaussian distributed values
of the order of 10
-4
as the output are defined in the range of
10
-3
. The main aim of this step is to represent the disturbances,
errors and uncertainties in the sensor’s readings in real
applications.
Some noise has also been introduced to the training data
set and added to the 11-correlation based selected input-
features as a regularization mechanism for the neural network
learning. Indeed, as extensively discussed in [8], introducing
noise during the training phase in the input vector can help in
controlling the network mapping complexity as well as
reducing the probability of data over-fitting.
Given a random vector noise n and its probability p(n), the
error used to determine the weights using the error equation 4
for the limit of an infinite number of data points can be re-
written as [8]:
=
1
2

[
(
)
−
]
∙
(
|
)
∙
(
)

(9)
Then, by introducing the noise:
=
1
2

[
(
+
)
−
]
∙
(
|
)
∙
(
)
()

(10)
The noise is usually chosen to be of zero mean and to be
uncorrelated between different inputs, therefore:

∙
(
)
=0

∙
∙
(
)
∙=∙

Using the Taylor series expansion for the error including the
noise and considering the zero mean and the noise variance
as defined above, then the error including the noise can be
expressed as function of the error without the introduction of
the noise in the input vector:
=+Ω
(11)
where:
Ω=
1
2
󰇩


+
1
2
(
(
)

)

󰇪
×
(
|
)
(
)

(12)
This is a regularization term added to the usual error (eq. 9).
Given that the noise amplitude is small enough to neglect the
Taylor expansion high order terms, the minimization of the
error with the noise added in the input is equivalent to the

minimization of the error without the noise terms added to the
input plus the regularization term in equation 12.
Further details on the definition of regularization functions
can be found in [8].
VI. P
REDICTION OF CONFIDENCE INTERVAL
An aspect that is often overlooked is the development of
metrics that are suitable for measuring the accuracy of a
specific prediction of neural networks. In fact, the
development of these metrics allows the introduction of a
better level of knowledge of the behavior of the system. When
the accuracy of the forecast is not sufficiently precise,
alternative decisions can be made in order to avoid worsening
the situation if the machine learning algorithm is unable to
provide reliable predictions within a certain range of
precision. In fact, Neural Networks are not able to
automatically provide an assessment of the accuracy of their
forecasts. In order to overcome this drawback, numerous
methods (Mean-Variance, Delta, Bayesian estimation, and
Bootstrap techniques), have been developed, as widely
discussed in [12].
In this paper, the Confidence Interval (CI) of the network
prediction has been used as a metric of the RBF prediction
performance.
The CI is calculated as:
=
(
−
)
(13)
where:
- t is the target output,
- y is the network predicted output.
In order to be able to predict the confidence interval of the
neural network estimates of the system decay, a second RBF
network is used to estimate the calculated residual error values
between the actual decays and estimated ones after the
completion of the training of the RBF that estimates the
decays.
Then, the vector of the calculated residual error values has
been passed as a target for this second RBF network with the
same optimal structure selected for the RBF that predicts the
system decays, and with the same 11 features input vector.
Once the second RBF network has been trained on the residual
error values, the input data for the test phase is passed to the
network in order to predict the confidence interval of a
prediction given a certain status of the 11 input features.
Therefore, the RBF is not only used to predict the equipment
status but also the accuracy of the algorithm in performing this
prediction.
The proposed RBF structure for estimating the system
decays and their confidence intervals is shown in figure 1.
The introduction of the CI allows the careful consideration
of the network prediction results focusing the attention on
wider CI interval, and therefore less reliable results. In the
context of maintenance, this needs to be considered during the
decision making related to the best strategy to apply to solve
a potential issue in the equipment.
Figure 1. Algorithm structure. Two RBFNN with 11 input features represented by (x1, x2,…,xn) and n hidden neurons. The
top RBF neural network target is represented by the System Decay Coefficients (T1) to be compared with the Compressor
Decay Prediction (Y1
c
) and the Turbine Decay Prediction (Y1
t
) to determine the error function. The bottom RBF neural
network target is represented by the Confidence Interval (T2) calculated during the training phase of the top RBFNN. This is
then compared with the Compressor Confidence Interval prediction (Y2c) and the Turbine Confidence Interval prediction
(Y2t) to calculate the error function.

Citations
More filters
Journal ArticleDOI
TL;DR: A Systematic Literature Review (SLR) on the usage of Business Analytics within the Industry 4.0 concept is performed, covering a selection of 169 papers obtained from six major scientific publication sources from 2010 to March 2020.
Abstract: The work of P. Cortez was supported by FCT - Fundacao para a Ciencia e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020. We would like to thank to the three anonymous reviewers for their helpful suggestions.

19 citations


Cites background or methods from "Performance Prediction using Neural..."

  • ...4 BSOA, GN, NII aHardware Connection (HC), Information Discovery (ID), Intelligent Production (IP), Predictive Maintenance (PdM). bAcoustic (Ac), Car Manufacturing (CM), Car Specification (CS), Chemical (Ch), Chemical Laboratory (ChL), Gas Turbine (GT), Gesture Images (GI), Image (I), Machine (Mc), Machine Centre (McC), Material (Ma), Network (N), Pellets Images (PI), Production (Pr), Reference Metadata (RM), Robotic (Rb), Sensor (S), Sheet Material (SM), Simulated Sensor (SimS), Solar Panel (SolP), Steel (St), Text (T), Time Series (TS), Welding Images (WI). cAerospacial (Ae), Automotive (A), Coil (C), Electronic (El), Energy (En), Food (Fo), Footwear (F), Furniture (Fu), Healthcare (Hc), Naval (Na), Not Disclosed (ND), Oil (O) Petrochemical (Pc), Polymer (Pl), Robotic (Rb), Semiconductor (SC), Spring (Sp), Steel Plate (SP), Transportation (Tr). dAdaptive Neuro-Fuzzy Inference Systems (ANFIS), Analysis of Variances (ANOVA), Artificial Neural Networks (ANN), Association Rules (AsR), Backtracking Search Optimization Algorithm (BSOA) Bagged Decision Trees (BDT), Bagged Trees (BagT), Bagging (Bag), Bayesian Filter (BF) Boosting Trees (BosT), Complex Fuzzy (CF), Conference Trees (CT), Convolutional Neural Networks (CNN), Decision Forest (DF), Decision Jungle (DJ), Decision Trees (DT), Deep Learning (DL), Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Discriminant Analysis (DA), Extreme Gradient Boosting (EGB), Extreme Learning Machine Boundary (ELMB), Extremely Randomized Trees (ERT), Fast Nearest Neighbours (FaNN), Feed Forward Neural Network (FeNN), Fog Computing (FC), Fuzzy-Logic (FL), Gaussian Model (GM), Gaussian Noise (GN), Genetic Algorithm (GA), Genetic Programming Based Symbolic Regression (GPBSR), Global Local Outliers in Sub Spaces (GLOSS), Gradient Boosted Regression Trees (GBRT), Gradient Boosted Tree Classifier (GBTC), Gradient Boosting (GB), Gradient Boosting Decision Trees (GBDT), Gradient Boosting Machine (GBM), H20 Deep Learning (h2oDL), Hidden Gama Process-Particle Filter (HGP-PF), Hidden Markov (HM), In Situ Classification System (ISCS), Isolation Forest (IF), Kalman Filter (KF), Kurtosis (K), K-Means (KM), K-Nearest Neighbor (KNN), Linear and Polynomial Fit (LPF), Linear Regression (LinR), Local Outlier Factor (LOF), Logistic Regression (LogR), Map Reduce (MR), Matlab Model Predictive Toolbox (MMPT), Mean and Standard Deviation (MSD), Mean Shift (MS), Microsoft Azure Machine Learning (MAML), Micro-Cluster Continuous Outlier Detection (MCCOD), Model Predictive Controller (MPC), Multiple Regression (MR), Multivariate Adaptive Regression Splines (MARS), Multi-Entity Bayesian Networks Regression (MEBNR), Multi-Layer Regression (MLR), Naive Bayes (NB), Neural Networks (NN), Neuro-Fuzzy Networks (NFN), Noise Impulse Integration (NII), Novelty Classifier (NOVCLASS), Out-of-Bag Error (OBE), Partial Least Squares (PLS), Particle Swarm Optimization (PSO), Principal Component Analysis (PCA), Pure Quadratic Regression (PQR), Quadratic Discriminant Analysis (QDA), Random Forest (RF), Random Support Vector Machine (RSVM) Recursive Partitioning (RP), Regression Trees (RT), Ridge Regression (RR), Rule-Based (RB), Skewness (Sk), Spectral and Agglomerative Clustering (SAC), SRT Model (SRTM), Stochastic Model Predictive Controller (SMPC), Support Vector Machines (SVM) Survival Analysis (SA), Time Series Forecasting (TSF), ZeroR (ZR)....

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  • ...Simple neural networks are used in several research works such as (Cisotto & Herzallah, 2018; Kabugo et al., 2020; Miškuf & Zolotov a, 2016; Soto et al., 2019; Spendla et al., 2017)....

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  • ...2 SRTM Cisotto and Herzallah (2018) PdM GT Na Used NNs in a system that support the maintenance function in the decision-making process....

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References
More filters
Book
01 Jan 1995
TL;DR: This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition, and is designed as a text, with over 100 exercises, to benefit anyone involved in the fields of neural computation and pattern recognition.
Abstract: From the Publisher: This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.

19,056 citations

Book ChapterDOI
TL;DR: The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue.
Abstract: Publisher Summary This chapter provides an account of different neural network architectures for pattern recognition. A neural network consists of several simple processing elements called neurons. Each neuron is connected to some other neurons and possibly to the input nodes. Neural networks provide a simple computing paradigm to perform complex recognition tasks in real time. The chapter categorizes neural networks into three types: single-layer networks, multilayer feedforward networks, and feedback networks. It discusses the gradient descent and the relaxation method as the two underlying mathematical themes for deriving learning algorithms. A lot of research activity is centered on learning algorithms because of their fundamental importance in neural networks. The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue. It closes with the discussion of performance and implementation issues.

13,033 citations


"Performance Prediction using Neural..." refers background or methods in this paper

  • ...The output of the RBF network is calculated as [8]:...

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  • ...For further details please refer to [8]....

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  • ...Further details on the definition of regularization functions can be found in [8]....

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  • ...Given a random vector noise n and its probability p(n), the error used to determine the weights using the error equation 4 for the limit of an infinite number of data points can be rewritten as [8]: = 12 [ ( ) − ] ∙ ( | ) ∙ ( ) (9)...

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  • ...Indeed, as extensively discussed in [8], introducing noise during the training phase in the input vector can help in controlling the network mapping complexity as well as reducing the probability of data over-fitting....

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Journal ArticleDOI
TL;DR: The quality of PIs produced by the combiners is dramatically better than the quality ofPIs obtained from each individual method and a new method for generating combined PIs using the traditional PIs is proposed.
Abstract: This paper evaluates the four leading techniques proposed in the literature for construction of prediction intervals (PIs) for neural network point forecasts. The delta, Bayesian, bootstrap, and mean-variance estimation (MVE) methods are reviewed and their performance for generating high-quality PIs is compared. PI-based measures are proposed and applied for the objective and quantitative assessment of each method's performance. A selection of 12 synthetic and real-world case studies is used to examine each method's performance for PI construction. The comparison is performed on the basis of the quality of generated PIs, the repeatability of the results, the computational requirements and the PIs variability with regard to the data uncertainty. The obtained results in this paper indicate that: 1) the delta and Bayesian methods are the best in terms of quality and repeatability, and 2) the MVE and bootstrap methods are the best in terms of low computational load and the width variability of PIs. This paper also introduces the concept of combinations of PIs, and proposes a new method for generating combined PIs using the traditional PIs. Genetic algorithm is applied for adjusting the combiner parameters through minimization of a PI-based cost function subject to two sets of restrictions. It is shown that the quality of PIs produced by the combiners is dramatically better than the quality of PIs obtained from each individual method.

481 citations

Journal ArticleDOI
TL;DR: A brief overview of condition based maintenance (CBM) with definitions of various terms, overview of some history, recent developments, applications, and research challenges in the CBM domain is provided in this paper.
Abstract: Purpose – The purpose of this paper is to provide a brief overview of condition based maintenance (CBM) with definitions of various terms, overview of some history, recent developments, applications, and research challenges in the CBM domain.Design/methodology/approach – The article presents the insight into various maintenance strategies and provides their respective merits and demerits in various aspects. It then provides the detailed discussion of CBM that includes applications of various methodologies and technologies that are being implemented in the field. Finally, it ends with open challenges in implementing condition based maintenance systems.Findings – This paper surveys research articles and describes how CBM can be used to optimize maintenance strategies and increase the feasibility and practicality of a CBM system.Practical implications – CBM systems are completely practical to implement and applicable to various domains including automotive, manufacturing, aviation, medical, etc. This paper p...

168 citations


"Performance Prediction using Neural..." refers methods in this paper

  • ...0" where already known and developed tools, such as CBM, are empowered by the analysis and processing of data collected using IoT and cloud-based solutions and processed using ML applications [4-7]....

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Journal ArticleDOI
01 Feb 2016
TL;DR: In this paper, a machine learning-based condition-based maintenance approach for ship propulsion systems is proposed to monitor the propulsion equipment by exploiting heterogeneous sensors, enabling diagnosis and prognosis of the propulsion system's components and their potential future failures.
Abstract: Availability, reliability and economic sustainability of naval propulsion plants are key elements to cope with because maintenance costs represent a large slice of total operational expenses. Depending on the adopted strategy, impact of maintenance on overall expenses can remarkably vary; for example, letting an asset running up until breakdown can lead to unaffordable costs. As a matter of fact, a desideratum is to progress maintenance technology of ship propulsion systems from breakdown or preventive maintenance up to more effective condition-based maintenance approaches. The central idea in condition-based maintenance is to monitor the propulsion equipment by exploiting heterogeneous sensors, enabling diagnosis and, most of all, prognosis of the propulsion system’s components and of their potential future failures. The success of condition-based maintenance clearly hinges on the capability of developing effective predictive models; for this purpose, effective use of machine learning methods is proposed...

135 citations


"Performance Prediction using Neural..." refers background or methods in this paper

  • ...DATA The analyzed dataset in this paper is an open access synthetic dataset generated from a Simulink® model of a Naval Gas Turbine [10] and it can be found at: (https://archive.ics.uci.edu/ml/machine-learningdatabases/00 316/)....

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  • ...An important point to make is that although the developed approach in this paper has been tested only on the Gas Turbine dataset application, the method we developed is definitely transferable to other applications....

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  • ...The Gas Turbine model is made of 16 input features, listed in Table 1 and two outputs, the Compressor Decay coefficient and the Turbine Decay coefficient....

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  • ...Thus, the dimensionality of the input variables has been consequently reduced, an aspect that has been overlooked by the authors in [10]....

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  • ...Based on the value of the correlation coefficients, feature 1 and 2 (lever position and sheep speed) have been removed due to their low correlation with the outputs and the fact that they are both included in the constitutive model of the Gas Turbine [10]....

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Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "Performance prediction using neural network and confidence intervals: a gas turbine application" ?

In this paper, a tool based on the implementation of Radial Basis Function Neural Networks was developed to support the maintenance function in the decision-making process. In addition to providing an indication of the status of the equipment, the current approach provides an additional level of information in terms of predicting the confidence interval around the prediction of the neural network.