On-line Adaptive Data-Driven Fault Prognostics of Complex Systems

Datong Liu, Shaojun Wang, Yu Peng, Xiyuan Peng Department of Automatic Test and Control

Harbin Institute of Technology Harbin, China, 150080

Email: liudatong@hit.edu.cn

Abstract—Data-driven prognostics based on sensor or historical test data have become appropriate prediction means in prognostics and health management (PHM) application. However, most traditional data-driven forecasting methods are off-line which would be seriously limited in many PHM systems that need on-line predicting and real-time processing. Furthermore, even in some on-line prediction methods such as Online SVR, there are conflicts and trade-offs between prognostics efficiency and accuracy. Therefore, in different PHM applications, prognostics algorithms should be on-line, flexible and adaptive to balance the prediction efficiency and accuracy. An on-line adaptive data-driven prognostics strategy is proposed with five different improved on-line prediction algorithms based on Online SVR. These five algorithms are improved with kernel combination and sample reduction to realize higher precision and efficiency. These algorithms can achieve more accurate results by data pre-processing, moreover, faster operation speed and different computational complexity can be achieved by improving training process with on-line data reduction. With these different improved Online SVR approaches, varies of demands with different precision and efficiency could be fulfilled by an adaptive prediction strategy. To evaluate the proposed prognostics strategy, we have executed simulation experiments with Tennessee Eastman (TE) process. In addition, the prediction strategies are also tested and evaluated by traffic mobile communication data from China Mobile Communications Corporation Heilongjiang Co., Ltd. Experiments and test results prove its effectiveness and confirm that the algorithms can be effectively applied to the on-line status prediction with excellent performance in both precision and efficiency.

Keywords-Data-Driven Prognostics; Online Prediction; Adaptive Prediction Strategy; Online SVR

I. INTRODUCTION The desire and need for accurate diagnostic and real-time

prediction have been around since human beings began operating complex and expensive machinery. Recently, intensive research has presented on fault detection, diagnosis, prognosis and prediction of the various systems or applications [1, 2]. Accurate prognostics and remaining useful life (RUL) estimation is the key technique in prognostics and health management (PHM). With the advances of computer, communication and sensor technologies, it is feasible and practical to monitor the performance and health state of a complex system at several different levels included system

level, board level and even chips level etc. Generally speaking, fault diagnosis and prognosis methods can be broadly classified into three categories, namely data-driven method, model-based method and statistical-based method. In model-based methods, models should be derived from the fundamental understanding of the mechanism of a system [3], thus it can only be applied to systems with clear mechanics description. However, it is difficult to find the accurate models in most applications of the complex systems especially for electronic complicated systems. Furthermore, statistical-based methods are based on large number of samples, while they are not suitable for the individual system or subsystem.

Because of increased automation, faster sampling rate and advances in computing, large amount of data is available on-line. Many researchers have attached great importance to the data-driven methods in diagnosis and prognosis [4, 5]. Therefore, data-driven prognostics based on the sensor or historical test data, such as artificial neural networks (ANN), Support Vector Regression (SVR) and other computational intelligence method, have become the primary prediction approaches for complex systems. In data-driven methods, status monitoring and prediction become the main factors in real application to complex systems. Besides various data-driven approaches, more and more research focused on the fault prediction application in time series forecasting theory and its development [4].

SVR algorithm is a machine learning method based on statistical learning theory and widely applied in time series prediction. It can also be used for status monitoring and forecasting. However, SVR cannot meet the demands of on-line and real-time application because of the time-consuming computation. In the same way, most of traditional off-line forecasting data-driven methods are facing the same challenge. Hence many training algorithms, such as incremental algorithm and decremental algorithm [6, 7], have been proposed to update these methods to on-line style and further decrease the computing complexity. However, in some on-line prediction methods such as Online SVR, conflicts and trade-offs between prediction efficiency and accuracy still exist.

In PHM systems, regarding the demand for fast monitoring and predicting, it is essential to develop an adaptive model for on-line prediction. Since for different application, the needs with operation speed and prediction precision are different. In

978-1-4244-9363-0/11/$26.00 ©2011 IEEE

some demands, the high efficiency is needed while more accurate prediction capacity is required for other applications. Therefore, adaptive prediction strategy becomes essential for PHM systems, especially for those on-line applications due to complicated conditions in real industrial systems.

For the realization of the complex systems running on-line prediction, this paper first introduces on-line time series prediction model for prognostics in application. With plenty of operating sampled data, the future trend of system state as well as the possible breakdown can be predicted. A new approach included five improved Online SVR algorithms previously proposed in our research are applied to realize adaptive on-line statues monitoring and fault prognostics. Experimental results with the Tennessee Eastman process fault data as well as mobile traffic data show that the algorithms can be effectively applied to the on-line status prediction with excellent performance in both efficiency and precision.

The rest of this paper is organized as follows. Firstly, in section II, the Online SVR algorithm is introduced. Then the on-line adaptive data-driven prognostics strategy based on five improved Online SVR approaches is described in detail in section III. Section IV gives the experimental result based on TE process and mobile traffic forecasting to evaluate the efficiency of the proposed method. Finally, conclusion and future work are discussed in section V and VI respectively.

II. ONLINE SVR FOR STATUS PREDICTION Given a status monitoring data as time series training set,

1 1{( , ), , ( , )} ( )l

l lT x y x y X Y= ∈ × , where n

ix X R∈ = ,

iy Y R∈ = ,

1,i l= , the main task of SVR is to construct a linear regression function,

( ) ( )Tf x W x bφ= + (1)

in feature space F. W is a vector in F, and ( )xφ maps the input x to a vector in F. The W and b in equation (1) are obtained by solving an optimization problem:

2 *

, 1

*

1n ( ).2

. . (( ) ) , 1,2, , ,(( ) ) , 1,2, , ,

0, 1,2, , ,

l

i iw b i

i i i

i i i

i

mi P w C

s t w x b y i ly w x b i l

i l

ξ ξ

ε ξε ξ

ξ

=

= + +

+ − ≤ + =− + ≤ + =

≥ =

∑i …

i ……

(2)

Here the slack variables iξ and *iξ , penalty parameter C, ε-

insensitive loss. Convert the responding Lagrange as:

* * * *

,

*

1

*

1min ( )( ) ( ) ( )2

. . ( ) 0,

0 , , 1,2,...,

i

l l l l

ij i i j j i i i i ii j i i

l

i ii

i i

Q y

s t

C i ll

α αα α α α ε α α α α

α α

α α

=

− − + + − −

− =

≤ ≤ =

∑∑ ∑ ∑

∑ (3)

Define kernel function: ( ) ( ) ( , )Tij i j i jQ x x K x xφ φ= = , then the

regression function can be described as:

*

1( ) ( ) ( , )

l

i i ii

f x K x x bα α=

= − +∑ (4)

Due to KKT (Karush-Kuhn-Tucker) conditions, we can get:

i i

i i

i i

i i

i i

h(x ) , Ch(x ) , C 0- h(x ) , 0h(x ) , 0 Ch(x ) , =C

ε θε θ

ε ε θε θ

ε θ

≥ = −⎧⎪ = − < <⎪⎪ ≤ ≤ =⎨⎪ = < <⎪⎪ ≤ −⎩

(5)

here *i i iθ α α= − ,

1( ) ( )

l

i i ij j ij

h x f x y Q y bθ=

≡ − = − +∑ .

Depending on the sign of ( )i if x y− , we can get:

(a) The E Set: { }iE i Cθ= =

(b) The S Set: { 0 }iS i Cθ= < <

(c) The R Set: { 0}iR i θ= =

Batch SVR retrains the model when the data updates. With the retraining of SVR each time, it brings the problems of low speed and inefficiency while the new sample adds. The Online SVR trains with incremental algorithm and decremental algorithm when data set updates. The structure of Online SVR adjusts dynamically to meet the KKT conditions [7, 8].

Let cx be a new training sample, corresponding define cθ , then compute ( 1,2,..., )i i nθ = , iθΔ and cθΔ to meet the KKT conditions.

1( ) ( , ) ( , )

n

i i c c i j ji

h x K x x K x x bθ θ=

Δ = Δ + Δ + Δ∑ (6)

10

n

c ii

θ θ=

+ =∑ (7)

For S set,

( , ) ( , )i j j i c cj S

j cj S

K x x b K x x

i S

θ θ

θ θ∈

∈

Δ + Δ = − Δ

Δ = −Δ

∈

∑

∑ (8)

The detail of computation is discussed in paper [8]. Through the training process described above, the Online SVR implements the update of the S Set, the E Set and the R Set without retraining all the data set.

III. ON-LINE ADAPTIVE DATA-DRIVEN PROGNOSTICS STRATEGIES

In our previous research, we have proposed five improved and optimized Online SVR algorithm according to a variety of prediction needs and data sets with various features. Accordingly, considering the influence of kernel function

types and sample scales on the Online SVR algorithm, we focus on improving the precision and efficiency of on-line time series prediction with kernel combination and sample reduction. Therefore, in order to achieve complex equipment or system on-line monitoring and status prediction, we can select one of those algorithms or combined different models under the different applications conditions of fault prognostics.

A. Five improved Online SVR algorithms The five improved Online SVR algorithms which are

previously proposed to achieve trade-off between prediction precision and efficiency are described as following.

a) Kernel Combined Online SVR - KCO-SVR[9].

The most important work for Online SVR is the choice of kernel function. For complicated and non-stationary nonlinear status prediction, suitable kernel function should be adopted according to the features of the complicated data. There are two types of kernel functions: global kernel and local kernel whose characteristics are different.

The learning ability of the local kernel is strong but the generalization performance is weak, at the same time, the learning ability of the global kernel is weak but the generalization performance is strong. Keerthi [11, 12] proved that the RBF kernel function can replace the polynomial kernel function with the choice of appropriate parameters. For most off-line applications, sufficient prior knowledge, plenty of analysis for data samples and the selection of the appropriate type of kernel function and its parameters can be obtained in advance. Therefore, the RBF kernel is used for modeling and the result would not be too bad under this off-line condition.

However, because of unpredictable on-line updated data series and on-line modeling data length restrictions, it can be of difficulty to select some kind of kernel function for on-line modeling and forecasting. The data with long distance influenced the value of the global kernel functions, while only the data in neighborhood decide the value of the local kernel almost. Linear kernel and polynomial kernel are global while Radial Basis Function (RBF) kernel and Gaussian kernel are local for SVR.

The KCO-SVR combines different characteristics of global and local kernel functions to fit the diversity of the complicated fault data sets. Therefore, this algorithm is more suitable and convenient for prognostics than the single kernel Online SVR.

b) Variance Prediction Compensation Local Online Support Vector Regression - VPCLO-SVR[12].

The KCO-SVR algorithm combined the two types of kernels to increase the prediction accuracy compared with the single kernel Online SVR in on-line data forecasting. However, the use of different kernel functions together would get low operation efficiency.

Therefore, in order to improve the efficiency of combined forecasting method, we consider to replacing the global kernel Online SVR algorithm as the off-line algorithm. With the local off-line SVR algorithm, the on-line combined models became simple and fast.

Consequently the VPCLO-SVR used the global kernel to fit and approximate trend properties of time series. Then the predicting residual with the real data stream is calculated. Finally, the residual for the predicted value is predicted on Online SVR to compensate predicted value with the local SVR. Compared to KCO-SVR algorithm, the VPCLO-SVR algorithm can efficiently improve the efficiency while keeping the prediction precision.

c) Accelerated Decremental Fast Online SVR - ADF-SVR[13].

With the increase size of on-line modeling data, the efficiency would decline. If the initial training data set is large, it is difficult to obtain higher prediction efficiency, and there is an interaction between the precision and efficiency. In order to obtain fast prediction, the on-line modeling data length should be cut shorter. Therefore, to improve the efficiency of the Online SVR algorithm is to reduce the online sample set size.

The ADF-SVR approach first selects non-support vectors as the decremental samples, and then an accelerated decremental training is used to reduce the online training data set. As a result, the efficiency of the method increases with less online data set.

d) Serial Segmental Online SVR – SOSVR[14].

To improve the poor precision of Online Support Vector Regression (Online SVR) on condition that a more efficient result is obtained in complicated and nonlinear time series prediction, a novel segmental online SVR (SOSVR) algorithm for time series forecasting. Fast training speed is achieved by cutting the training data set short. A segmental strategy is applied and the Online SVR model is stored by segments. The most suitable segmental model is selected to output the prediction value according to the matching degree between prediction neighborhood data and all the segmental models. As a result, the forecasting precision is improved.

e) Multi-scale Parallel Online SVR - MSPO-SVR[15].

For complex non-linear and non-stationary time series, they contain long sequences trend as well as strong neighborhood correlation. If a single fast on-line prediction model is used, the limit of sample size makes it difficult to obtain satisfactory results of prediction accuracy and efficiency because the algorithm could not take into account all relevant factors.

Therefore, the multi-scale reconstruction of time series with data sampling could reflect the characteristics of series long trends and short neighborhood non-linear features. Data reconstruction can effectively reduce the size of the on-line data sets and preserve rich historical knowledge of samples. Independent parallel sub-models could be obtained by modeling to the sub-time-sequences with Online SVR algorithm respectively. Through the multi-scale reconstruction of the time series, the length of on-line modeling data is reduced. Meanwhile, the prediction efficiency could be improved and faster prediction can be achieved. Based on above analysis, we proposed a multi-scale parallel Online SVR algorithm (abbreviated as MSPO-SVR).

B. On-line prognostics strategies To solve the problem with different application, an on-line

adaptive data-driven fault prognosis and prediction strategy is presented as shown in figure 1.

Figure 1. Model of on-line fault prognostics strategies

The key problem for the algorithm application is how to choose the best models to do the prediction. In this paper, on-line prognostics methods and models first need to consider actual conditions, such as application goal and system resource, prediction accuracy and efficiency, and then corresponding algorithm is chosen according to the characteristics of data. As a result, various forecasting demands can be implemented.

Fault prognostics models selection criterion is recommended as follows.

(a) When the prediction accuracy is preferred, we recommend the kernel functions combined Online SVR. The approach combines the excellent trend fitting characteristic of global kernel function and powerful neighborhood nonlinear approximation ability of local kernel functions. This approach can achieve higher prediction accuracy compared with the single kernel function methods.

(b) When the operation efficiency is focused, we introduce the accelerated Online SVR algorithm, but the prediction accuracy is relatively the worst. The serial segmental Online SVR and the parallel multi-scale Online SVR use the serial and parallel strategies to cut the data set short, the former efficiency is higher than the latter. If the data reflect the time-domain multi-scale features, we suggest choosing the latter.

(c) If the equipment or system resources including computing, memory, etc, are enough to support more complicated on-line algorithms, we can also use the strategies of model fusion with different Online SVR algorithms. As a result, we can achieve complementary between the predicted results.

The on-line prognostics system based on adaptive Online SVR algorithms is shown in figure 2.

On-line data acquisition can be done with the data acquisition unit, monitoring unit, or embedded BIT unit of the system itself. These acquired data constructed the original on-line time series data samples for prediction. On-line pre-processing is necessary to the raw data, such as data reduction, uncertainty management, components analysis, etc.

Figure 2. Structure of on-line adaptive monitoring prediction system

On-line status monitoring and prediction system can select the corresponding algorithm and model for different application demands. As well the on-line model could be selected according to some prior system knowledge. And if the system computing resource is enough, the prediction algorithm and model could be operated on-line and real-time in the system embedded CPU controller. In the end, the forecasting output can display locally or output to dedicated data interface with other sub-system. Meanwhile, according to forecast results, the operator can take appropriate maintenance strategy or health management.

IV. EXPERIMENTS AND EVALUATION

A. Simulation Experiments with TE process To evaluate the proposed methods, we have done

experiments with Tennessee Eastman (TE) process data. TE process, published by the Tennessee Eastman Company, is a challenge problem for process control and it is often used as a process simulation for academic research. Tennessee Eastman process, involves five major units including a two-phase reactor, a partial condenser, a separator, a stripper, and a compressor. The schematic flow diagram and instrumentation of the TE process is shown in figure3. There are 33 faults, 16 bidirectional faults and 1 unidirectional fault in this case study. Figure 5 shows the TE process [16, 17].

Figure 3. Tennessee Eastman Process Schematic

The Reactor Level data are simulated by TE process tool in MATLAB. In TE process, the normal operation of the state of Reactor Level should be around 75. When the Reactor Level is under lower limit between 72 and 73, the TE process failed and

the system operation terminated. If the Reactor Level of the process can be effectively predicted, the failure could be avoided. The raw data is sampled by every 24 seconds in MATLAB.

To verify the generality of our methods and strategies, we sampled the data containing both normal running status and failure mode. One-step prediction results are shown in figure 4.

Figure 4. On-line Reactor Level prediction with Online SVR algorithm

From the on-line one-step prediction result (the first 200 steps), we can conclude that when the system is running effectively, the prediction model output can reflect the change trends of system status without any wrong alarm information. Before the event of non-normal operation appears, the prediction model forecasts the failure status in advance, and a warning is sent ahead of the failure at the same time.

To evaluate the method quantitatively and test the proposed algorithms performance, we compared the proposed approaches with the fundamental Online SVR algorithm. Two evaluation criterions are adopted that are Mean Absolute Error (MAE) and Normalized Root Mean Square Error (NRMSE). They are defined as follows.

~

1

1 ( ) ( )n

i

MAE x i x in =

= −∑ (9)

~2

1

~2

1

1 [ ( ) ( )]

1 [ ( ) ]

n

i

n

i

x i x in

NRMSEx i x

n

=

=

−=

−

∑

∑ (10)

where n is the number of sample, ( )x i is the real value of

series, ~( )x i is the prediction value, and

~x the mean value of

the series. The prediction results are shown as in table 1.

TABLE I. EXPERIMENTAL RESULTS OF ON-LINE STATUS PREDICTION

From table I, we compare the prediction accuracy and efficiency of several on-line prediction algorithms, the results

can verify the fitness for fault prognostics with the proposed strategies.

In the experiment, we also computed the average time of one-step prediction of all these algorithms. If the one-step operating time is smaller, it means that the corresponding algorithm is of higher efficiency. The KCO-SVR algorithms can improve precision with 10%, while the ADF-SVR algorithm improves operating efficiency with up to 50%. With multiple improved Online SVR algorithms, it is adaptive to realize different demands for online applications. According to the evaluation result, the trade-offs between prediction efficiency and accuracy can be adjusted easily with adaptive multi-models. As a result, the strategies could be used to meet different application demands. As for multi-step prediction, more data pre-processing analysis and transformation should be considered.

B. Application for Mobile Traffic Forecasting In the mobile communication network, it accumulated large-

scale communication traffic data during the actual operation. Moreover, these monitoring data can reflect the real-time condition of the mobile networks. With the development of network size and user groups, the mobile communication network expands rapidly. In particular, the scale of traffic flow data also grew rapidly. Take the Heilongjiang Mobile as example, there are about 500,000 traffic records every day, and every record is about 120 bytes length. So that, the data volume is about 58MB every day and the amount of data storage will be at least 21GB in each year for the whole province.

Mobile communication traffic flows reflect the occupied condition of the mobile networks. As a result, the traffic monitoring and prediction is undoubtedly important for both mobile network management and maintenance. With the traffic monitoring and prediction, it can help to reduce the call dropping rate and improve the quality of voice services. On the other hand, with the analysis and forecast, it can play a role on supporting the network optimization and building for network management.

Index Algorithm MAE NRMSE Average Time of one-step prediction(Seconds)

1 KCO-SVR 0.432 0.690 3.92 2 VPCLO-SVR 0.439 0.731 2.13 3 ADF-SVR 0.455 0.743 1.54 4 SOSVR 0.442 0.735 1.89 5 MRPO-SVR 0.433 0.727 2.56 6 Online SVR 0.474 0.792 2.90

Alarm level

We have applied three types of fast prediction algorithms for mobile traffic on-line monitoring and prediction with data provided by China Mobile Communications Corporation Heilongjiang Co., Ltd. The prediction strategies are shown as figure 5 and the traffic analysis and prediction software is shown as figure 6.

Figure 5. On-line mobile traffic algorithm strategies

At present, it is incompatible for the network status information processing technology with its rapid growth. While the networks optimization and construction is lack of data analysis or further processing. Therefore, efficient and accurate

monitoring and forecast the operation status of the mobile network has become a necessary mobile communications work, and its application for mobile operators is beyond doubt.

Figure 6. On-line mobile traffic prediction system

Fig.7 to fig.9 show three typical mobile traffic prediction results (168 hours, continuous one-step prediction) with different algorithms on different mobile base stations (such as commercial districts, traffic junks, etc.).

Figure 7. Traffic prediction of the HOA026B with ADF-SVR algorithm

Figure 8. Traffic prediction of the HPA001A with SOSVR algorithm

Figure 9. Traffic prediction of the HPA026A with MRPOSVR algorithm

From these three prediction results, we can see that with the ADF-SVR and SOSVR and MRPOSVR algorithms, mobile communication traffic can be accurately forecasted. Detail experimental results are shown in Table II.

TABLE II. EXPERIMENTAL RESULTS OF ON-LINE TRAFFIC PREDICTION

index Base station algorithms MAE NRMSE Time/sec

1 Commercial

areas (HUAM28A)

ADF-SVR 0.048 0.134 84.56

SOSVR 0.050 0.145 173.26

MSPO-SVR 0.041 0.125 384.59

Online SVR 0.053 0.151 175.46

2 College

areas (HPA026A)

ADF-SVR 0.069 0.985 160.22

SOSVR 0.043 0.945 473.28

MSPO-SVR 0.028 0.722 1074.36

Online SVR 0.066 0.963 469.25

3 Residential

areas (HOA026B)

ADF-SVR 0.066 0.310 146.61

SOSVR 0.061 0.290 259.38

MSPO-SVR 0.063 0.268 504.62

Online SVR 0.067 0.300 258.56

4 Traffic trunk

(HPA001A)

ADF-SVR 0.065 0.235 185.23

SOSVR 0.043 0.171 320.25

MSPO-SVR 0.047 0.182. 728.43

Online SVR 0.044 0.177 320.08

From the application for mobile traffic monitoring and on-line prediction, we can conclude that， for the randomly selected mobile base, the ADF-SVR algorithm can achieve higher efficiency while the MSPO-SVR algorithm can obtain prediction accuracy increased by 10% compared with the basic Online SVR algorithm.

Experiments results show that the whole strategy is of high efficiency, and as well, the prediction precision keeps unchanged compared to Online SVR. According to the status of network traffic monitoring and forecasting, the mobile network overload warning can be given in advance so as to provide predictive CBM maintenance for mobile networks.

V. CONCLUSION This paper explores an on-line prognostics strategy as well

as applies five improved Online SVR algorithms which previously proposed in our research for on-line system status prediction. The proposed approach can implement adaptive prediction that can meet different application demands with precision and efficiency. The experimental results demonstrate that the adaptive on-line data-driven prognostics with time series of proposed Online SVR algorithms show better prospect in complex system on-line status monitoring and prediction. It can be applied in industrial fields for system maintenance and health management. This adaptive status monitoring and forecasting strategies show better prospective with both simulation and application.

VI. FURTHER WORK In future, we will apply these improved algorithms to

develop application software for complex system. Multi-step on-line prediction and RUL on-line prediction for complex system will be focused later. For some more complicated application, models fusion with combined prediction methods or parallel forecasting with multi-models should be considered in the future research work.

ACKNOWLEDGMENT This research project is supported by China Mobile

Communications Corporation Heilongjiang Co., Ltd. Thanks to Mr. Jiang Yu and Qiang Chen for their support and help

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