E-Journal of Advanced Maintenance Vol. 6 (2014) 86-106
Japan Society of Maintenology

Process signal selection method to improve the impact mitigation of sensor
broken for diagnosis using machine learning
Hirotsugu Minowa1,*, Akio Gofuku1
1

Okayama University, 3-1-1 Tsushima naka, Kita-ku, Okayama 700-8530, Japan

ABSTRACT
Accidents of industrial plants cause large loss on human, economic, social credibility. In recent, studies ofdiagnostic methods using techniques of machine learning are expected to detect early and correctly abnormality
occurred in a plant. However, the general diagnostic machines are generated generally to require all process
signals (hereafter, signals) for plant diagnosis. Thus if trouble occurs such as process sensor is broken, thediagnostic machine cannot diagnose or may decrease diagnostic performance.
Therefore, we propose an important process signal selection method to improve impact mitigation without
reducing the diagnostic performance by reducing the adverse effect of noises on multi-agent diagnostic system.
The advantage of our method is the general-purpose property that allows to be applied to various supervisedmachine learning and to set the various parameters to decide termination of search.
The experiment evaluation revealed that diagnostic machines generated by our method using SVM improved theimpact mitigation and did not reduce performance about the diagnostic accuracy, the velocity of diagnosis,
predictions of plant state near accident occurrence, in comparison with the basic diagnostic machine which
diagnoses by using all signals.
This paper reports our proposed method and the results evaluated which our method was applied to thesimulated abnormal of the fast-breeder reactor Monju.
KEYWORDS

ARTICLE INFORMATION

Support Vector Machine(SVM), machine learning, process signals selection,
plant diagnosis, Monju plant, Multi-Agent System (MAS)

Article history:
Received 28 April 2014
Accepted 17 November 2014

1.

Introduction

Accidents on industrial plants cause large loss on human, economic, social credibility. In recent,studies of diagnostic methods using techniques of machine learning [1] such as support vector
machine [2] (hereafter, SVM) or artificial neural network [3] are expected to detect abnormality
occurred in a plant early and correctly. There were reported that these diagnostic machines have highaccuracy to diagnose the operating state of industrial plant on single abnormality occurred [4]-[9]However, the training time to generate machine learning increases according to the number n of
instances. Training time increases proportionately [10], [11] or exponentially, for example O (n 2 ) at
SVM [12], to the number n of instances. In addition, there is the possibility to fall the diagnosis
accuracy due to little bit of change of the signal when the more complex this diagnostic machine
becomes. To solve that problem, we use multi-agent diagnostic system [13]. Multi-agent diagnostic
system can prevent increasing the training time and the complexity of internal model of diagnostic
machine by each diagnostic machine specializes to diagnose each specific abnormality.
The problem is that the diagnostic machines include multi-agent diagnostic system also needs all
variables (signals) for diagnosis. Then if the input signal value was zero tentatively, the accuracy of
diagnosis will decrease because the displacement range of the signal value is different from the real
signal range.
Therefore, we propose the method to select important process signals to improve the diagnostic
tolerance not to decrease the diagnostic performance on multi-agent diagnostic system using machinelearning. The diagnostic machine on multi-agent diagnostic system specialized to diagnose a specificabnormality but other abnormalities and unknown abnormality. Therefore, the remove of less*Corresponding author, E-mail: minowa@sys.okayama-u.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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H. Minowa, et al./ Process signal selection method to improve the impact
mitigation of sensor broken for diagnosis using machine learning

important signals can improve diagnostic tolerance because the required signals are not change at thereason of the multi-agent diagnostic framework. The advantage of our method is the general-purpose
property that allows to be applied to various supervised machine learning. And it is easy to terminate
according to parameter of thresholds such as the maximum number selecting signals or the condition
whether or not containing the required signal.
This paper reports that our proposed method, and the result of that our method applied to target
abnormality of fast breeder Monju plant.

2.

Related works

This section explains the comparison with our method and conventional methods.
There are the method of Monroy [7], Chen [14] in the signal selection methods based on a
statistical method. The method of Monroy [7] extracts the training data from process signals todiagnose the accident occurrence in chemical plant correctly using SVM. The training data was dataof a signal period that has the large feature amount calculated by the principal component analysis andwas confirmed the significance by statistical function such as T2-statistic and Q-statistic. However
their method does not consider the feature amount of one signal but consider the signal
complementarity.
There are methods of Tomoyuki [15], Huang [16] to the methods using machine learning. The
Tomoyuki [15] method using genetic algorithm (hereafter, GA) converted the problem extracting
training data to an optimization problem to maximize the total performance of each the generalization
performance and classification performance under the trade-off restriction in machine learning. But,
the multi-agent framework which used in our method is not restricted by the trade-off restriction.
The Huang’s method [16] using GA optimized the signal combination and the parameters of costand gamma as training data. This method has a risk falling into a local solution because the search is
terminated when the evaluation value which calculated from the method based on GA which has risk
falling into a local solution is more than the defined threshold.
There are methods of Tanabe [17] to the selection method by prediction using machine learning.
The Tanabe [17] studied methods to predict components with high carcinogenic. This paper concluded
that the customized sensitivity analysis method improved the predicting accuracy to 77.5% comparedwith the correlation coefficient method, the F-score method [14]. In their sensitivity analysis method,
first step generates a predicting machine from the training data which composed from that the
explanatory variables are attribute of carcinogenic material and the objective variable is carcinogenic
rank value each material. Next step made the evaluating data where the values of explanatory variable
were averaged out in each row except a variable. Next step calculated the accuracy rate predicting the
carcinogenic rank value when the predicting machine evaluated the created evaluating data. The
accuracy rate indicates that the efficiency of each no averaged variable to determine the carcinogenic
rank. The higher accuracy is, the more important to determine the rank of carcinogenic rank. However
the sensitivity method also does not take account of multivariable.
There are methods of Chang [18], and Aoki [19] to the signal selection method by improving
kernel of SVM.
Their method cannot be applied to other machine learning except SVM. So these methods are notsuitable for our requirement mentioned in research background because they do not allow to be
applied to the other machine learning. This survey revealed that there are many variable selection
methods. And this survey also revealed that they don't have the mechanism to improve the impact
mitigation for multi-agent diagnostic system, and the general-purpose property which terminates
search depending on the parameters such as the number selected signal or the existence of specificsignal etc. Our method is difference from them at the point it can satisfy these requirements asmentioned above.

3.

Monju as target plant

3.1 Summary of Monju"Monju" is a fast-breeder reactor prototype which was built in Tsuruga City, Fukui Prefecture.

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mitigation of sensor broken for diagnosis using machine learning

The fast breeder reactor is a nuclear reactor that can enhance the utilization efficiency of uranium
resources by circulating the nuclear fuel cycle by producing the plutonium 239 as a fuel from uranium
238 during this plant running. The maximum electrical output is 280,000 kW.
3.2. Process signals for evaluation
This section explains process signals which were used in evaluation experiment. Our evaluation
uses the process signals of the A loop only in every the three loops of the secondary sodium andwater/steam in Monju. Signals used in our evaluation shows in Table 1, and location of the sensors tomeasure signal shows in Fig. 1[20].
Table 1 Name list of signals

No
Sig. 1
Sig. 2Sig. 3Sig. 4Sig. 5Sig. 6Sig. 7Sig. 8Sig. 9Sig. 10Sig. 11Sig. 12Sig. 13Sig. 14Sig. 15
Sig. 16

Name of signal
Outlet sodium temperature of reactor vessel
Inlet sodium temperature of superheater
Outlet sodium temperature of superheater
Outlet sodium temperature of evaporator
Secondary sodium flow rate
Rotation speed of secondary sodium circulation pump
Feedwater flow rate of evaporator
Inlet feedwater temperature of evaporator
Outlet steam temperature of evaporator
Inlet steam temperature of superheater
Outlet steam temperature of superheater
Main steam pressure
Inlet feedwater pressure of evaporator
Outlet steam pressure of evaporator
Outlet steam pressure of separator
Outlet steam pressure of superheater88

H. Minowa, et al./ Process signal selection method to improve the impact
mitigation of sensor broken for diagnosis using machine learning

Fig. 1 Location to measure signals

3.3. Simulated abnormality
Simulated abnormalities to evaluate our method are the minor abnormalities of four types in 45%
heat output of “Monju” [21] which was computed by the plant dynamics analysis code NETFLOW++[22]. The all simulated signal data of each unit time is called record. Each simulated process data wascomposed of 20,000 records which step size 1 [sec] time. Of the 20,000 records, each record of
1-10000 record is normal state and each record of 10001-20000 record is an abnormal.
Most of below events shows the similar signal transients between without or with the feedwater
control system because the control systems are inefficient. Only signal of the heat transfer degradationshows the different transient.

Abn. 1 Abnormality of feed water temperature degradation

There are 2 feed-water heaters, which one is low-pressure feed-water heater beside upstream of
feed-water pump and another is high-pressure feed-water heaters beside downstream of it, which
increase gradually the feed-water temperature by supplying the high-temperature steam extracted
from the turbine beside the copper side of the 2 feed-water heaters. This abnormality is defined as thefeed-water temperature decreases by loss of a part of feed-water heating which is caused from that the
supply of extracted steam was stopped due to the valve of extraction line was broken. The process
signal profiles of this abnormality are shown in Fig. 2, Fig. 3.
The feed-water temperature decreases if the steam is not supplied to the final stage of feed-water
heater by the failure of the steam-valve which something caused. The feed-water temperature goes
down by about 30 degree from initial 194 degree during several hundred seconds after the abnormal
occurrence at time t=10,000 as shown in Fig. 2. That result causes the decrease of outlet temperatureof evaporator. However the temperature of feed-water returns to a source temperature with flow
fluctuations because the feed-water flow narrows down by the feed-water control system.
System pressure tends to decrease slightly as in Fig. 3. The sodium temperature of the secondary
system shows the fluctuations as in Fig. 2, and its signal influence is spread in a wide range. The

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mitigation of sensor broken for diagnosis using machine learning

feed-water temperature seems to decrease if the fouling of water stain is attached to the feed-water
heater and its heat-transfer coefficient decreases. However, the decrease of feed-water is small and its
influence was revealed to be small even though the overall heat-transfer coefficient decreases up to
5kW/m2K. That is because the heat transfers area of a general water supply superheater designed witha margin.

Fig. 2 Signal transient of Abn.1-1

Fig. 3 Signal transient of Abn.1-2

Abn. 2 Abnormality of heat transfer rate decrease of an evaporator

Water heat-transfer coefficient degradation is caused by some reasons. The one of the reasons is
the water flowing inside the heat-transfer tube of evaporator includes the water stain. The water stain
generally takes long time to attach. However this event is defined as an abnormality that causes thedegradation of heat-transfer coefficient by the water stain attaches instantly. In addition, theevaporator outlet temperature control on the feed-water control system was removed to make it easy
for reader to understand this abnormality. The water stain assumed not to attach into the super-heater
turbine because the super-heated steam is supplied to the super-heater from the evaporator. That water
stain causes the degradation of the overall heat-transfer coefficient. The process signal profiles of thisabnormality are shown in Fig. 4, Fig. 5.
As in Fig. 4, Fig. 5, the outlet temperature of evaporator against the temperature of the third
system decreases to coincide with the system pressure not to be affected of fouling. The two-phaseflow in this event does not cause the dry out near the outlet of evaporator. As this result, the lower
energy steam and the large amount of droplet flow into the super heater. Therefore, the heat-transfer
rate of the super heater is increases, and the sodium temperature of the super heater output isdecreases.

Fig. 4 Signal transient of Abn.2-1

Fig. 5 Signal transient of Abn.2-2

Abn. 3 Abnormality of feed water supply control valve

The feed-water control valve is implemented to control the feed-water flow to supply to each thesteam generators of the 3 loops in Monju. This abnormality is defined as the decrease flow by about90

H. Minowa, et al./ Process signal selection method to improve the impact
mitigation of sensor broken for diagnosis using machine learning

10% continuously by one of these valves is broken. The outlet temperature of evaporator slightly
increases by the influence of the feed-water flow decreased at the same time of abnormality
occurrence, and restores to almost source temperature by system control. The amount of steam
generation decreases, and the pressure decreases slightly due to the decrease of enthalpy of feed-water
which supplied to the steam generator by the degradation of feed water temperature. The process
signal profiles of this abnormality are shown in Fig. 6, Fig. 7.
At this time, the outlet temperature of the evaporator increased as in Fig. 6 because thefeed-water system in the loop did not work correctly when the abnormality occurred. The other loop
system where the abnormality did not occur kept the initial state.

Fig. 6 Signal transient of Abn.3-1

Fig. 7 Signal transient of Abn.3-2

Abn. 4 Abnormality of main feed water pump degradation
Each system of the three heat transfer systems which are implemented inside the reactor
vessel in Monju is recycled by one main pump. This abnormality is defined as an event thatthe flow rate of main pump decreases slightly in the A-loop at 10,000 sec. The process signal
profiles of this abnormality are shown in Fig. 8, Fig. 9.
The flow rate of other two loops increases as if the control system supplements theoverall flow when the flow rate of the A-loop decreases. As a result, the outlet temperature of
main system changes slightly and the inlet temperature remains almost constant. There areslight changes of that the outlet temperature of the reactor vessel decreases by 0.2 degree andthe main steam pressure valve increases 0.5kg/cm2. The evaluation of plant parameters is
quasi-static. The evaluation of plant parameters is quasi-static. This event is desired to detectby machine because the operator is difficult to find this slight change.

Fig. 8 Signal transient of Abn.4-1

Fig. 9 Signal transient of Abn.4-2

3.4. Processing to the signal more similar

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mitigation of sensor broken for diagnosis using machine learning

The process signal data for evaluation in this paper [23] were generated by superimposing thenoise based on the AR model to the simulated signals data mentioned above. That reason is that the
raw simulated data does not have signal fluctuations. Therefore superimposing the AR model basenoise to the raw simulated signal data to characterize realistic specific to the raw signals. The method
to superimpose the noise based on the AR model is explained in below.
The fluctuation component from the measured data in usual operation in actual plant has a
distribution close to white noise in seemingly random but it has each distribution with the uniquecharacteristic to each channel. We estimated autoregressive model (AR model) by the Yule-Walker
method to reproduce this fluctuation component. AR Model was made as a signal with samecharacteristic of original signal by extracting from the signal specific of frequency region of theoriginal signal and giving a white noise signal as input. The AR model was coordinated to be closed to
the variance of the actual operating data by inputting the white noise of the average 0 and the variance
1, where are considered from the actual operating data 40% output of Monju plant.

4.

Prediction method to select signals

4.1. Methodology
Finding the important signals for diagnosis is difficult problem for improving the impact
mitigation of diagnostic machine without decreasing the diagnostic performance because of taking
account of the dynamics of target plant, the abnormalities to diagnose and the mechanism of
diagnostic machine. The reason is that the diagnosis of diagnostic machine which generated bygeneral machine learning is based on a border of diagnostic space which multi-dimensional mapping
space (MDMS) was mapped signals. MDMS is complex because it varies depending on the feature of
all signals. Therefore, it is not easy to reveal important signals for diagnosis. The statistical method
can find the important signals in short time, but it could not find important signals deeply enoughbecause it measures importance according to only the change of feature of single signal from previous
study [24]. Therefore, we took an approach to measure the diagnostic performance from MDMS in
the generated diagnostic machine for selecting more important signals. In the present study, theevaluation function to measure the importance of a signal is referred to as a model score. The section
4.2 explains the model score.
However, it takes a lot of time to measure the diagnostic performance based on the model score
calculated by generating the diagnostic machine from the signal combinations of every pattern.
Therefore, our approach uses the feature of the machine learning which can generate the function
which can predict correctly the relation of input and output. Our approach is that a prediction machine
which is generated by machine learning learned the relation of output the diagnostic performance forthe input signal combinations and predicts the diagnostic performance from the input signal
combination.
As mentioned above, the machine learning is generator of a function with high accuracy.
However generating a function with high accuracy requires 2 conditions below.
1.
2.

Training data which is data set with input and output data to predict input and output are exist
a lot
There is simple correlation between the signals generating the diagnostic machine and the
diagnostic performance of that diagnostic machine

About 1, it may be understand intuitively that accuracy of diagnosis is predicted to improve in
proportion with the number of training data.
About 2, the correlation of the output against the input is necessary for the function generated
machine learning. We concluded that the model score prediction can be realized by confirmed thecorrelativity which based on empirical hypothesis on the relation of the performance as output against
the input signals. The verification of this hypothesis was described in Section 4.3.

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An operating state of the normal or abnormal by a diagnostic machine is determined by thespatial proximity of target process signal against the border line of multi-dimensional space which
created from signal data of the normal and abnormal operating state. The determination of theoperating state of normal or abnormal by the diagnostic machine varies at each record data of signals
due to the fluctuation of the process signals. Therefore, determination of the normal or abnormal
operating state per a record is hereafter called the prediction of operating state. On the other hand, thediagnosis which is the final determination of operating state is defined as an most numerous operatingstate in operating states which were predicted based on some records.
4.2. Model Score
This section explains the model score, which is the diagnostic performance score of a diagnostic
machine. The model score is an average of the percentage of correct answers in the diagnosis ofnormal and abnormal operating conditions. The model score is calculated by Formula (1).
M=


n
n 
1
 w n An + w a Aa 
wn + wa 
n Sn
n Sa 

(1)

In Formula(1), n Sn and n Sa are the total numbers of recorded normal and abnormal conditions,
respectively; n An and n Aa are the recorded numbers of answers for the diagnosis of normal andabnormal conditions which were correct, respectively; and wn and wa are the weight coefficients.
In this study, wn = wa . If a diagnostic machine which detects abnormalities more correctly is desired,wa should be large.
4.3. Empirical hypothesis of prediction diagnostic performance
The law of the diagnostic performance against the signal combination need exist to predict
correctly the diagnostic performance against the signal combination by the diagnostic machine. We
found the empirical law which described below holds at the relation between the diagnostic
performance and the signal combination.
a. The diagnostic performance is not improved highly when combined the signals with highperformanceb. The diagnostic performance as a whole is hardly improved when combined the signals with low
performancec. The diagnostic performance as a whole is hardly improved when combined the signals withhigh performance and low performanced. The performance might be improved highly by information complementarity for diagnosis in
signal if different type (e.g. normal state / abnormal state) of signals are combinede. The performance of sensors which are same measuring location and same instrumentation typeand measurement mechanism are almost same
Below explains about the consideration of these empirical laws and the evaluation result which
verified these empirical laws which applied to the signals of Abn.3. The result which measured themodel score of the diagnostic machine generated from single signal in Abn3 shows in Table2.
Table 2 Model score measured from each signal
No
Sig. 1
Sig. 2Signal nameOutlet Sodium temperature of reactor vessel
Inlet Sodium temperature of superheater

93

Model Score
0.916
0.910

H. Minowa, et al./ Process signal selection method to improve the impact
mitigation of sensor broken for diagnosis using machine learning
Sig. 3Sig. 4Sig. 5Sig. 6Sig. 7Sig. 8Sig. 9Sig. 10Sig. 11Sig. 12Sig. 13Sig. 14Sig. 15
Sig. 16

Outlet Sodium temperature of superheater
Outlet Sodium temperature of evaporator
Secondary Sodium flow rate
Rotation speed of secondary Sodium circulation pump
Feedwater flow rate of evaporator
Inlet feedwater temperature of evaporator
Outlet steam temperature of evaporator
Inlet steam temperature of superheater
Outlet steam temperature of superheater
Main steam pressure
Inlet feedwater pressure of evaporator
Outlet steam pressure of evaporator
Outlet steam pressure of separator
Outlet steam pressure of superheater

0.938
0.974
0.544
0.506
0.795
0.717
0.940
0.947
0.930
0.950
0.769
0.701
0.673
0.616

Table3 shows the model scores when evaluated signals combined a signal of Sig.12 Main steampressure with the high 0.95 model score and another signal. From the left-most column of Table3, thecolumns shows the signal identification number, the signal name which combined with Sig.12, themodel score which combined with Sig.12, the combining single signal, the difference between 2
signals. The model score was improved to maximum 0.981 when combined with signals of Sig.12 andSig.4. However the model scores of signals when combined with Sig.12 and another signal with thehigh model score were not improved. Originally, there is no room for improving the diagnostic
performance on combination with the signal with the high model score. However, the model scores ofsignals when combined with each signal of high model score were remained high. The results in Table
3 showed that the growth rate of the performance of the signal combination with signals which rank
greater than Sig.2 was low but was improved than before the combination.
Table 3 Model score of 2 signals include main steam pressure
No

Signal nameSig. 4 Outlet Sodium temperature of evaporator
Sig. 1 Outlet Sodium temperature of reactor vessel
Sig. 3 Outlet Sodium temperature of superheater
Sig. 9 Outlet steam temperature of evaporator
Sig. 10 Inlet steam temperature of superheater
Sig. 11 Outlet steam temperature of superheater
Sig. 2 Inlet Sodium temperature of superheater
Sig. 7 Feedwater flow rate of evaporator
Sig. 8 Inlet feedwater temperature of evaporator
Sig. 13 Inlet feedwater pressure of evaporator
Sig. 15 Outlet steam pressure of separator
Sig. 5 Secondary Sodium flow rate
Sig. 14 Outlet steam pressure of evaporator
Sig. 16 Outlet steam pressure of superheater
Sig. 6 Rotation speed of secondary Sodium circulation pump

Score of 2
signal
0.981
0.957
0.957
0.957
0.957
0.957
0.952
0.928
0.916
0.914
0.912
0.909
0.909
0.909
0.908

Score of 1
signal
0.974
0.916
0.938
0.940
0.947
0.929
0.910
0.795
0.717
0.769
0.673
0.544
0.701
0.616
0.506

Difference
0.007
0.041
0.019
0.017
0.010
0.028
0.042
0.133
0.199
0.145
0.239
0.365
0.208
0.293
0.402

About the empirical laws b and c, signals were low performance due to that the deviation of thesesignals are small or these signals involved the time lag between abnormality occurrence and deviation
occurrence. The empirical law b will be established depending on case the combining effect waslimited unless the performance is improved by the effect to the multiple signals complementarity withlow performance. The signals which satisfy the empirical law c are no effect to improve theperformance. Rather, there is possibility to decrease diagnostic performance by the diagnostic
machine generated from signals with the low diagnostic performance. In fact, the model score ofsignal combination of the Sig.12 signal and a single signal which the rank is lower than the signal
Sig.7 in Table 3 was decrease to 0.950 or lower. The empirical law c was guessed to be established94

H. Minowa, et al./ Process signal selection method to improve the impact
mitigation of sensor broken for diagnosis using machine learningfrom this fact.
Table 4 shows the measured model scores when the Sig.6 signal with the 0.506 low model scoreand another signal were combined for verifying the empirical law b and c. The model score was
improved only maximum 0.002 when signals with low performance of the Sig.5 and Sig.16 andSig.15 were combined. Further, there was no improvement on model score when combined with aSig.6 signal and another signal having the high diagnostic performance.
Thus the diagnostic performance is not expected to improve by combination of signals with the
low model scores. The signals with low performance are not useful for diagnosis.
Table 4 Model score of 2signals include Rotation speed of secondary Sodium circulation pumpNo
Signal nameSig. 4 Outlet Sodium temperature of evaporator
Sig. 10 Inlet steam temperature of superheater
Sig. 9 Outlet steam temperature of evaporator
Sig. 3 Outlet Sodium temperature of superheater
Sig. 11 Outlet steam temperature of superheater
Sig. 1 Outlet Sodium temperature of reactor vessel
Sig. 2 Inlet Sodium temperature of superheater
Sig. 12 Main steam pressure
Sig. 7 Feedwater flow rate of evaporator
Sig. 13 Inlet feedwater pressure of evaporator
Sig. 8 Inlet feedwater temperature of evaporator
Sig. 14 Outlet steam pressure of evaporator
Sig. 15 Outlet steam pressure of separator
Sig. 16 Outlet steam pressure of superheater
Sig. 5 Secondary Sodium flow rate

Score of 2 signal
0.973
0.944
0.939
0.938
0.927
0.914
0.909
0.908
0.795
0.769
0.713
0.701
0.672
0.617
0.546

Score of 1 signal
0.974
0.947
0.940
0.938
0.929
0.916
0.910
0.948
0.795
0.769
0.717
0.701
0.673
0.616
0.544

Difference-0.001-0.003-0.0010-0.002-0.002-0.001-0.04
00-0.0040-0.001
0.001
0.002

The empirical law d could not be verified because there were no signals suitable for thisverification in this study. However the empirical law d appears to be a reasonable.
About the empirical law e, the performance of the diagnostic machines generated from thesimilar signals such as same location and same physical quantity on time and same process type arealmost same because the parameters which decide the feature of plant process were whole same. For
example, the result of Table2, the model scores of diagnostic machine generated from Sig.9 andSig.10 signals are the 0.940 and 0.947 almost same value. That result revealed that the performancesof the diagnostic machine which generated from these signals under same parameter conditions weresame performance. The model score of a Sig.15 signal which was measured at location between Sig.9
and Sig.10 signals was 0.673 low. The reason is that these signals were different on process typebecause that Sig.9 and Sig.10 signals were the data in measurement of water/steam and a Sig.15 signal
was the data in the pressure measurement. That caused that the pressure process of Sig.15 signal did
not correspond with the change of abnormality than the water/stream process of Sig.9 and Sig.10
signals.
Summarized to mention above, the diagnostic machine having high performance can be expected
to be generated from signals having high model scores.

5.

Algorithm of proposed method

5.1. Preliminary description
This section describes preliminary explanation to explain our method. The each n signal istdefined as Pi (1 ≤ i ≤ n ) . The value of signal Pi at time t defined as xi . The operating state atttime t is defined as y . The function Score( x, y ) is defined to compute the vectors of modelscores from predicted accuracy rate of records at each time t by the diagnostic machine whichttttgenerated from the training data ( x1 , x 2 ,..., xi ) of the operating state y against each signal of i95

H. Minowa, et al./ Process signal selection method to improve the impact
mitigation of sensor broken for diagnosis using machine learning

species. The total number of signal combinations selected all signal up to 1 − l from m signals is
described as in Formula (2). Thus the all signal combinations is defined as nC m ,m .

nC m ,l = ∑b =1 ( m C b )(2)

1, if signal i is exist
ei = 
0, if signal i is not exist(3)l

The unit element e has a value of 0/1. The value of ei is 1 if signal i is exists in a signal
combination. The value is 0 if signal i is not. The function is defined as in Formula (3).

The function Comb is the function returns a vector which is the signal combinations uwhich composed of the unit element e in the k Ci signal combinations which composed of the isignals selected from the k signals of P . The function is defined as in Formula (4).
Comb( P, i ) = ( eu ,1 , eu , 2 ,..., eu ,k ); (1 ≤ u≤ k Ci )(4)
The function Re store , is defined as in Formula (5), is the function returns the vector of thesignal data which restored according to the values of element e in the vector u in the signal
combination E composed of the n unit element e .
Re store( E u ) = x1eu ,1 ,..., x n eu ,n ; ( E u = {eu ,1 ,..., eu ,n })(5)
The Add ( p, q ) function adds vector q to the tail of vector p .
5.2. Algorithm
Step 1 Screening of signals
Step 1-1 Calculation of base model score
The base model score S B as a threshold to select signals is calculated as in Formula (6).

S B = Score( x, y )(6)

Step 1-2 Calculation of model scores of each signal
The model scores of each signal are calculated as in Formula (7).

S i = Score( xi , y )(7)

Step 1-3 Selection of signal
The important signal candidates Pj2 (1 ≤ j ≤ m ) are selected as in Formula (8).
The Formula (8) indicates to select the signals Pj2 , which has the model score more than thebase model score S B , or the rank is greater than equal to b , from the signals S i .

{Pj2 | S B ≤ S i ∨ b ≥ Order ( S i )}(8)

Step 2 Selection of the signals considering the signal combinations
Step 2-1 Measurement of the actual model score from the combination of m all signals
The model scores which evaluated the signal combination which composed of the selected csignals are calculated as in Formula (9)-(13).
A signal selection number k is initialized at m . The signal combinations E and modelscores RS of each record are initialized as in formula (9). The vector TE is composed of theg unit element e representing the signal combination which selected the m signals from2

signals P . The vector TE is calculated as in formula (10), (11). The vector TE is stored tothe tail of E .
The model scores TRS g were calculated from E as in Formula (12), and stored to RS as in
(13).

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E = φ , RS = φ(9)TE g = Comb( P , k ); (1 ≤ g≤ m C k )(10)

E = Add ( E , TE g )(11)

TRS g = Score({Re store( E ), y})(12)

RS = Add ( RS , TRS g )

(13)

2

The value of k is updated to 1 and this search processing shifts to Step 2-2.
Step 2-2 Measurement of the actual model scores at from the combination of k signals
E and RS are updated according to the value k as in Formula(10)-(13).
Step 2-3 Calculation of prediction score
This step calculates the predicting model scores TPS which predicted model score from therelationships between the signal combinations E and the measured model scores RS as in
Formula (14), and stores the calculated prediction score to total list PS as in Formula (15).
(14)
TPS = Score( E , RS )(15)
PS = Add ( PS , TPS )Example of a vector which composed of {R, RS , PS } is showed in Table 5.
Table 5 Example of a vector composed with the measured and predicted model scoresNo.

Signal 1 … Signal m RS (Measured model score) PS (Predicated model score)
1

…

0

0.990

0.989

2

0

…

0

0.888

0.890

…

…

…

…

…

1

…

1

0.994

0.995

…

1

nC m ,mStep 2-4 Termination of search according to thresholds
The search terminates when satisfied the thresholds for example the time period or the number of
selected signals. The current method terminates the search by the difference between the prediction
model and actual score as in formula (16). However, if the minimal search c is set, search is not
terminated at k ≥ c . And the search terminates if k = m − 1 as in Formula (17).
If search terminates, this process of search shifts to Step2-5. Otherwise this process updates k
as in Formula (18) and shifts to Step2-2.
This algorithm can terminate according to the other thresholds such as the number of signals,
inclusion of necessary signal depending on the sensor failure.

average(| RS − PS |) < Avg .T∨ | SD ( RS − PS ) |≤ SD.T

(16)

∨ k = m −1

 Eq(16) ∧ k ≥ c; if c is existed; if c is not existed Eq(16)

(17)
(18)

k = k +1

Step 2-5 Selection of important signal
If the search terminated in k < m − 1 , the optimized signals are the signals with highest
predicted model score in all signal combinations. If search terminates in k = m − 1 , the optimized
signals are with highest measured model score in all signal combinations.
The function Best which returns a vector with the highest value from the vectors vec of the97

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measured model scores or the predicted model scores is defined as in the formula (19).
vec = PS ; if k < m − 1(19)Best signals = Best ( vec )  vec = RS ; if k = m − 1

6.

Evaluation Experiment6.1. Evaluation of prediction performance
In this experiment, we measured the performance predicting the model score every the number ofsignal combination which generated from 13 signals except for 3 signals of Sig.4, Sig.5, Sig.14 in all
16 signals for reducing the amount of calculation. The removed 3 signals were the Outlet Sodium
temperature of evaporator (Sig.3) which is similar to the Outlet Sodium temperature of superheater,
the outlet steam temperature of evaporator (Sig.9) which is similar to the inlet steam temperature ofsuperheater (Sig. 10), the outlet steam pressure of evaporator (Sig.14) which is similar to the outlet
steam pressure of separator (Sig.15). The result which measured the performance predicting the modelscore are shown in Fig. 10-Fig. 13.

Fig. 10 Average and standard deviation of prediction on Abn.1

Fig. 11 Average and standard deviation of prediction on Abn.2

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Fig. 12 Average and standard deviation of prediction on Abn.3

Fig. 13 Average and standard deviation of prediction on Abn.4

The horizontal axis of graph of Fig. 10-Fig. 13 shows the signal combinations. Our description
method of axis item value expresses the 13 C{1− q ,13} which indicates signal combination involved thevalue of the combinations selected each 1, ..., q(1 ≤ q ≤ 12),13 signals from all 13 signals. For
example, the 13 C{1,13} (=14 patterns) indicates the combination with the combinations 13 C13 （=1）
selected all 13 signals and the combinations selected 1 signal from 13 signals.
The vertical axis of graphs shows the value of average “Average diff.(All)” or standard deviation“SD diff.(All)” of absolute difference between the measured model score and the predicted modelscore on all signal combinations 13 C{1,...,q ,13} . And the vertical axis shows average “Average diff.
(Only Predicated)” and standard deviation “SD diff. (Only Predicated)” of the absolute difference
between the measured model score and the predicted model score on the 13 C{q −12} signal
combinations selected signals which are not used for generating diagnostic machine.
The prediction performance on both “Average diff.(All)” and “Average diff.(Only Predicated)”
were low when the number of the signal combinations were only a few(e.g. = 13 C{1,13} ). However, thenumber of signals more increased, the prediction performances were more improved. The evaluation
result revealed that the prediction method realized 0.01 or less accuracy on the average and standard
deviation of model score except the standard deviation of Abn.3 when the signal combinations forprediction include 3 or more signals.
The standard deviation of “SD diff.(All)” was no longer decrease halfway in Fig. 13. That reason isthat the change amount of signal of the about 0.5 model score became low when combined with two
or more other signals but the change amount of that signals became high when combined with a single
signal with high model score. Therefore, the error about 0.01 was raised because the prediction
machine predicted a 0.7 model score instead of the correct 0.5 model score by mistake.
6.2. Applied method99

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Our method was applied to the signal data “Monju” for evaluating the diagnostic accuracy andthe early detection. Step1 screens out the effective less signals from all 16 signals. The threshold b
to select signals was set 8 in this evaluation. So this search process selected the 8 signals with higher
the model score because there was no signal Pi which the model score was more than S B . And it
proceeds to Step2. Step2 analyzed the remained signals with the parameter Avg .T = 0.001 ,Sd .T = 0.001 , the number of minimum search c = 3 .

Table 6 shows the comparison of the diagnostic machine (hereafter, Opt-SVM) which was
generated from the signals which our method selected, and the diagnostic machine (hereafter,
Basic-SVM) which was generated from 16 all signals. Column No. which is Leftmost in tableindicates the number of simulated abnormality of “Monju”. The column ① indicates the model scoreof "Basic-SVM", the column ② indicates the model score of "Opt-SVM". The column ③ shows
the number of the signal that has taken over the analysis to Step 2 from Step1 of search process. The
column ④ shows the finally selected signal number at the end of Step 2. The smaller selected
number indicates the early end of search. The performance of the opt-SVM generated from the signals
reduced to 3 to 8 was almost same performance with Basic-SVM without performance degradation.
Table 6 Evaluation of diagnostic performanceNo①Basic-SVM ②Opt-SVM ③ ④

Abn. 1

0.999

0.999

8 3

Abn. 2

0.999

0.999

8 4

Abn. 3

0.980

0.978

8 3

Abn. 4

0.994

0.993

8 4

Selected signal
Sig. 4. Outlet Sodium temperature of evaporator
Sig. 7. Feedwater flow rate of evaporator
Sig. 15. Outlet steam pressure of separator
Sig. 7. Feedwater flow rate of evaporator
Sig. 8. Inlet feedwater temperature of evaporator
Sig. 12. Main steam pressure
Sig. 16. Outlet steam pressure of superheater
Sig. 1. Outlet Sodium temperature of reactor vessel
Sig. 2. Inlet Sodium temperature of superheater
Sig. 3. Outlet Sodium temperature of superheater
Sig. 4. Outlet Sodium temperature of evaporator
Sig. 9. Outlet steam temperature of evaporator
Sig. 10. Inlet steam temperature of superheater
Sig. 11. Outlet steam temperature of superheater
Sig. 12. Main steam pressure
Sig. 1. Outlet Sodium temperature of reactor vessel
Sig. 2. Inlet Sodium temperature of superheater
Sig. 12. Main steam pressure

Next step evaluates the diagnostic time. The diagnosis was determined when the number
diagnosed as abnormal were more than half 30 among the 60 records for avoiding misdiagnosis by thenoise in the signal. The time to diagnose the simulated abnormality of "Monju" shows Table 7. The
shorter time to complete diagnosis was underlined. Large loss of accuracy was not observed from theevery compared result.
Table 7 Abnormality detection timeNo
Abnormality
Opt-SVM [sec] Basic-SVM [sec]Abn. 1 A feed water temperature decrease
10057
10036
Abn. 2 A heat transfer decrease in evaporator
10031
10031
Abn. 3 A decrease of feed water flow rate
10240
10257
Abn. 4 A decrease of main sodium circulation flow rate
10167
10151

6.3. Profile of near when abnormality occurredFig. 10-Fig. 13 shows the profile which plotted the operating state which our diagnostic machine100

H. Minowa, et al./ Process signal selection method to improve the impact
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detected near time each abnormality occurred.

Fig. 14 Profile of the operating state of Abn.1 (Left: by Basic-SVM, Right: by Opt-SVM)

Fig. 15 Profile of the operating state of Abn.2 (Left: by Basic-SVM, Right: by Opt-SVM)

Fig. 16 Profile of the operating state of Abn.3 (Left: by Basic-SVM, Right: by Opt-SVM)

Fig. 17 Profile of the operating state of Abn.4 (Left: by Basic-SVM, Right: by Opt-SVM)

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In Fig. 14-Fig. 17, The horizontal axes show the diagnostic time, and the vertical axes show each
operating states from top is that “Correct (Abnormal State)” was plotted when diagnosis were correct
in abnormal state, “Wrong (Abnormal State)” was plotted when diagnosis were wrong in abnormal
state, “Wrong (Abnormal State)” was plotted when diagnosis were wrong in abnormal state, “Correct(Normal State)” was plotted when diagnosis were wrong in normal state. The diagnostic results ofboth the Opt-SVM and the Basic-SVM were visually confirmed the same from these profiles.
6.4. Comparing with the other method
This section shows the result compared with other method as sensitivity analysis method [17]and F-Score Method [14]. The number selecting signals in these comparing methods was set the same
number of our method because there is no description of the algorithm to terminate the search.
The sensitivity analysis method could not calculate the score in many signals. The model scorethat could be carried out the procedure to select signals of Abn.3 was 0.974. The model score of the
Opt-SVM of same Abn.3 was 0.978 is higher by 0.4%. The reason was guessed that the just createddiagnostic machine diagnosed with the either normal or abnormal operating states from the every
records of training data which averaged of each variable except one variable. As a result, thesensitivity analysis method could not compute the selecting score because the standard deviation
became zero at a single regression analysis.
The compared result of the each model score calculated from our selection method and the
F-Score method shows in Table 8. The Table 8 revealed that the model score of the proposed method
was slightly better or equal to the F-Score method.
Table 8 Comparison with F-Score method
Abn

Score
Opt-SVM

1

0.999

0.998

2

0.999

0.999

3

0.978

0.975

4

0.993

0.993

Selected signals
F-Score method (Score order)
Sig. 4 Outlet Sodium temperature of evaporator
Sig. 7 Feedwater flow rate of evaporator
Sig. 8 Inlet feedwater temperature of evaporator
Sig. 3 Outlet Sodium temperature of superheater,Sig. 7 Feedwater flow rate of evaporator
Sig. 9 Outlet steam temperature of evaporator
Sig.10 Inlet steam temperature of superheater
Sig. 1 Outlet Sodium temperature of reactor vessel
Sig. 2 Inlet Sodium temperature of superheater
Sig. 3 Outlet Sodium temperature of superheater
Sig. 4 Outlet Sodium temperature of evaporator
Sig. 7 Feedwater flow rate of evaporator
Sig. 9 Outlet steam temperature of evaporator
Sig.10 Inlet steam temperature of superheater
Sig.11 Outlet steam temperature of superheater
Sig. 1 Outlet Sodium temperature of reactor vessel
Sig. 2 Inlet Sodium temperature of superheater
Sig. 12 Main steam pressure

6.5. Discussion
The result in chapter 6.1 which evaluated the prediction performance of our method revealed that
our method could predict model scores of each signal combination correctly. For example thepredicting accuracy of average and standard deviation were 0.01 or less, when training data wascomposed of signals from 3 to 4.
The evaluation result in chapter 6.2 revealed that the performance and the diagnostic time were102

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almost same when our method reduced to 3-8 a number of signals of training data. The reason is thatthe difference of performance was 0-0.02 or less and the delay of the diagnosed time was within
seconds from -17 to 16.
The diagnosed profiles which applied our method in chapter 6.3 were confirmed visually thesame with the diagnosed profile which generated by general machine learning of time near theabnormality occurs. The mentioned results which applied our method were same accuracy despite of
reducing the number of signals to generate the diagnostic machine. That indicates that the diagnostic
machine which applied our method can continue to diagnose with same accuracy even if data of a partof signals are not obtained.
The result compared with the sensitivity analysis method and F-Score method in chapter 6.4
revealed that our method improved of 0-0.3% than both methods.
In Abn.1, our proposal method and the F-Score method selected Sig.4 and Sig.7. However, ourproposal method selected the Sig.15, which was shown in Fig. 18, and the F-score method selected
the Sig.8, which was shown in Fig. 19 in selecting a remained signal. The variation width of Sig.8 waslarge, but that signal could not detect the abnormal immediately since there is a time lag in the change
from the abnormal occurrence.

Fig. 18 Sig.15, which our method selected in Abn.1 Fig. 19 Sig.8, which F-Score selected in Abn.1

In Abn.2, the fluctuation of the signals Sig.8, 12, 16 which our proposed method selected wereover the magnitude of the regular level after abnormality occurred except Fig. 7 which only is acommon signal, shown as in Fig. 20. On the other hand, the F-Score method selected the signals
Sig.3, 9, 10 which were displaced clearly, shows as in Fig. 21.

Fig. 20 Sig. 8, 12, 16 selected by our method in
Abn.2

Fig. 21 Sig. 3, 9, 10 selected by F-Score in Abn.2

In Abn.3, both of our proposal method and F-Score method selected the same signals Sig. 1, 2,
3, 4, 9, 10, 11. The difference of selection was that our proposal method selected Sig.12 and, on theother hand, the F-Score method selected Sig.7. The feature of signals which our proposed method

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selected reacted immediately according to an abnormality occurrence and converged from signal
amplitude state, as same as Abn.2.

Fig. 22 Sig.12, which our method selected in Abn.3 Fig. 23 Sig.7, which F-Score selected in Abn.3

In Abn.4, our proposed method selected the Sig. 1, 2, 12 signals of Abn.4 as same as the F-Score
method. That might indicate that the signals have not displacement useful for diagnosis, except the
selected signals.
We indicate the study about the difference of signals selected by our proposal method andF-Score method in each Abn.1-4 as below. The signals selected by the F-Score method as shown in
Fig. 19, Fig. 21, Fig. 23 have feature that the waveforms of these signals displace largely whenabnormality occurred. The score of F-Score method becomes large due to the F-Score method's
mechanism when the difference of average values of signal in an abnormal and normal state is large
or the standard deviation of each signal in an abnormal and normal state is small. That is, it is usefulto lead to good score if the signal’s displacements are stable and their regions are clearly separated bya certain value when abnormality occurred.
On the other hand, the fact was revealed from Fig. 18 and Fig. 20, Fig. 22 that the SVM of our
method selected signals with complex displacement that the value range of signals of an abnormal andnormal state couldn’t be linearly separated, unlike F-Score method. The reason for this, we guessed
the diagnostic accuracy was improved when our method selects signals which reaction speed was
faster contributed to make the hyper plane of our proposal method maximum-margin by dividing
clearly the regions of an abnormal and normal state.
Summary to say that, our method could improve the diagnostic performance a little than F-Score
method. Unfortunately, the improvement of our method was low in comparison with other method.
That reason is due to the deviation of evaluation signals was separated clearly about the same as thesignal to be separable linearly enough, judging from Fig. 19, Fig. 21, Fig. 23. However our method
can be expected to improve the more diagnostic performance when the target is more complex signal
because our method is non-linear analytical method can analyze deeply more than a liner analyticalmethod such as F-Score.
6.6. Experiment environment
The codes for this evaluation experiment implemented libSVM[25] ver.2.88 to generate SVM
diagnostic machine, and was perfomed on Windows7. The SVM diagnostic machines were generated
with the parameter that a kernel was RBF kernel, a cost was 1, a gamma was 0.2.

7.

Conclusion
We proposed the optimizing method to select important signals to generate supervised machinelearning which diagnoses industrial plant for improving the impact mitigation.The evaluated results
which applied our method to process data of fast-breeder "Monju" revealed that the diagnostic
accuracy and the diagnostic time were almost same despite of reduced the number of signals. Our
method was 0.4% higher than maximum of the sensitivity analysis method, and was 0.1% higher than104

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maximum of the F-Score method. The improvement were low because the evaluated process data
might be simple.
In future works, we propose a diagnostic method using this proposed method to diagnose
correctly similar abnormality in virtual plant in which various abnormalities occurs.

Acknowledgement
This present study includes some of the results of “Anomaly detection agents by advanced hybrid
processing of Monju process data” entrusted to Okayama University by the Ministry of Education,
Culture, Sports, Science and Technology of Japan (MEXT). The authors are grateful to Japan Atomic
Energy Agency for providing the observed data of Monju. The authors would like to thank Prof.
Hiroyasu Mochizuki of Fukui University and Prof. Makoto Takahashi of Tohoku University forproviding the simulated data of Monju with artificial noises.

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