Ann Elman Fcm.19

8/12/2019 Ann Elman Fcm.19

1/11

A hybrid FDD strategy for local system of AHU based on articial neural network

and wavelet analysis

Bo Fan, Zhimin Du, Xinqiao Jin*, Xuebin Yang, Yibo Guo

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China

a r t i c l e i n f o

Article history:

Received 2 February 2010

Received in revised form

30 May 2010

Accepted 31 May 2010

Keywords:

Fault detection and diagnosis

Elman neural network

Fuzzyc-means

Wavelet analysis

a b s t r a c t

This paper presents a self-adaptive sensor fault detection and diagnosis (FDD) strategy for local system ofair handing unit (AHU). This hybrid strategy consists of two stages. In the rst stage, a fault detection

model for the AHU control loop including two back-propagation neural network (BPNN) models is

developed. BPNN models are trained by the normal operating data of system. Based on sensitive analysis

for the rst BPNN model, the second BPNN model is constructed in the same control loop. In the second

stage, a fault diagnosis model is developed which combines wavelet analysis method with Elman neural

network. The wavelet analysis is employed to process the measurement data by extracting the

approximation coefcients of sensor measurement data. The Elman neural network is used to identify

sensor faults. A new approach for increasing adaptability of sensor fault diagnosis is presented. This

approach gains clustering information of the approximations coefcients by fuzzy c-means (FCM)

algorithm. Based on cluster information of the approximation coefcients, the unknown sensor fault can

be identied in the control loop. Simulation results in this paper show that this strategy can successfully

detect and diagnose xed biases and drifting fault of sensors for the local system of AHU.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

Variable air volume (VAV) air-conditioning system is widely

applied in the building cooling and heating systems. Sensor faults

in VAV air-condition system may result in abnormal systems

operation and inefcient usage of energy. The automated fault

detection and diagnosis (FDD) methods can ensure reliable oper-

ation of VAV air-condition system and improve its efciency.

Air handing unit (AHU) is an important component in the VAV

air-conditioning system. Faults of AHU air-conditioning system

include actuator fault, sensor fault and component fault. Reliability

and accuracy of the sensor measurements is essential to perfor-

mance monitoring and implementation of optimal control strate-

gies. Sensors of AHU often fail during operating periods due toabnormal physical changes in the components, inadequate main-

tenance and even poor quality. Sensor faults may result in inaccu-

rate measurement and increasing energy consumption of HVAC

system, as well as slight sensor fault may lead to complex system

fault after accumulation. Subsequently, performance degradation

or damage to the component may occur. Sensor faults include four

categories such as complete failure, xed bias, drifting bias and

precision degradation. The xed and drifting biases may result in

the invalidation of normal strategy. Because the fault feature of the

complete failure is more obvious than other faults, it is more easily

detected and identied.

Summarily, two main methods of FDD have been developed in

the HVACeld. One is the model-based method [1], and the other is

the data-driven method. In the model-based method, whether the

fault occurs or not can be judged by comparing the real process

output values with the predicted values from models. It has been

mostly widely developed. Shaw et al. [2,3] compared the actual

energy consumption of fan with the predicted one in the VAV

system to diagnose the fan fault of AHU. Howell and Maddison[4]

presented a FDD method based on physical model that was used to

diagnose some common faults of AHU. Wang and Wang [5] pre-sented a calculation method for residual and developed a model-

based strategy to diagnose the faults of temperature sensor and the

faults of ow rate sensors. Reddy [6] developed and evaluated

a FDD method based on a simple model that is used to diagnose

process faults of large chillers. Obviously, diagnosis efciency of the

model-based FDD method considerably depends on accuracy of the

models.

The data-driven methods such as condition-based adaptive

statistical method, articial intelligence techniques, principal

component analysis (PCA) and so on, have been widely applied in

the AHU system. The data-driven methods seldom construct* Corresponding author. Tel./fax:86 21 34206774.

E-mail address:[email protected](X. Jin).

Contents lists available at ScienceDirect

Building and Environment

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ l o c a t e / b u i l d e n v

0360-1323/$ e see front matter 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.buildenv.2010.05.031

Building and Environment 45 (2010) 2698e2708
mailto:[email protected]://www.sciencedirect.com/science/journal/03601323http://www.elsevier.com/locate/buildenvhttp://dx.doi.org/10.1016/j.buildenv.2010.05.031http://dx.doi.org/10.1016/j.buildenv.2010.05.031http://dx.doi.org/10.1016/j.buildenv.2010.05.031http://dx.doi.org/10.1016/j.buildenv.2010.05.031http://dx.doi.org/10.1016/j.buildenv.2010.05.031http://dx.doi.org/10.1016/j.buildenv.2010.05.031http://www.elsevier.com/locate/buildenvhttp://www.sciencedirect.com/science/journal/03601323mailto:[email protected]


2/11

physical models buttake advantage of the intrinsic mathematicand

statistic relations variables. The relation can be deduced from the

process data under both normal and faulty operation conditions. So

the diagnosis efciency of data-driven method mainly depends on

accuracy and reliability of the process data. Wang and Cui [7]

employed PCA method to detect and diagnose sensor faults of

centrifugal chiller. Jin and Du [8e11] developed PCA model for

single fault and multiple faults, as well as used sher discriminant

analysis (FDA) and joint angle analysis (JAA) to diagnose the sensorfaults in AHU.

Among data-driven methods, articial neural network (ANN) is

an active research area and has given promising results for sensor

fault diagnosis in AHU. Lee et al. [12,13] presented a scheme for

detecting faults in an AHU using residual and parameter identi-

cation methods in 1996. Based on this scheme, a two-stage ANN is

trained to identify the subsystem where a fault occurs and diag-

nose the specic cause of a fault at the subsystem level. A scheme

for on-line FDD based on general regression neural network

(GRNN) at subsystem level in an AHU is developed and imple-

mented by Lee in 2004 [14]. Wang and Chen [15] presented

a strategy on the basis of neural network models. The neural

network models are trained using the data collected under various

normal conditions and employed to diagnose the measurementfaults of the outdoor and supply ow rate sensors. Based on the

wavelet analysis and PCA analysis methods, Xu et al.[16]presented

a robust sensor fault detection and diagnosis and estimation

(FDD&E) strategy for the chiller system. The research of this FDD&E

strategy show that the waveletePCA-based strategy is better than

the conventional PCA-based strategy fails for the wavelet trans-

form can separate noises and obvious dynamics. It can improve the

detection and diagnosis efciency signicantly. Du et al. [17]

employed the wavelet neural network to diagnose the xed and

drifting biases of sensor in VAV air-condition system. The wavelet

neural network-based method is more efcient than the single

neural network-based method.

Clustering analysis is the assignment of a set of observation

into subsets so that observations in the same cluster are similar in

some sense. Clustering methods include subtractive clustering,

c-means clustering, fuzzy c-means (FCM) clustering and so on.

Based on FCM and articial immune systems, Jaradat and Langari

[18] proposed a hybrid approach for multiple sensor fusion and

fault detection. This approach does not require prior knowledge or

information about the sensors and learning processes of system

behavior. It can adaptively detect and diagnose fault of the

multiple sensors. Doan et al. [19] proposed a scheme, which

combined subtractive clustering with microgenetic algorithm

(MGA), that can extract the most representative data from the raw

data set.

This paper presents an adaptive sensor FDD strategy for the

AHU. It includes a fault detection model and a fault diagnosis

model. The fault detection model is employed to distinguish

between the normal and the faulty conditions. It includes two

back-propagation neural network (BPNN) models, which are

trained by historical data under the normal operation conditions.

The BPNN fault detection model I is developed based on variables

correlation in the control loop. Then the sensitivity of the BPNN

fault detection model I to the input variables was analyzed. The

input variable, which has most inuence on prediction of the

BPNN fault detection model I, is gained and employed to construct

the BPNN fault detection model II on the basis of sensitivityanalysis.

The fault diagnosis model, which combines wavelet analysis

with Elman neural network, is developed to diagnose the specic

cause of the fault at the control loop. The wavelet analysis is

employed to obtain approximation coefcients of the input data.

These approximation coefcients are used to train Elman neural

network fordiagnosing sensorfaults. FCMalgorithm is employed to

cluster the approximation coefcients of the fault data for obtain-

ing respective cluster centers of different kinds of fault data.

Euclidean distances between approximation coefcients of new

data and cluster center of known fault data are used as criterions

whether new data represent unknown fault data. Adaptability and

exibility of model for fault diagnosis can be improved by this

approach.

2. Fault detection and diagnosis methodology

2.1. Articial neural network

2.1.1. BPNN

BPNN is the most popular neural network technique in engi-

neering application [20,21]. In the BPNN, there are many weights,

each of which contributes to more than one output. Therefore,

the BPNN might be appropriate for the application to the

complicated process. The BPNN Learning algorithms mainly

include gradient descent algorithm, conjugationegradient algo-

rithm, Gausse

Newton algorithm and LM (Levenberge

Marquardt)etc. LM algorithm has quick convergence rate, so it is often used

to train BPNN [22].

2.1.2. Elman neural network

Elman neural network mainly consists of three layers involved

in input layer, hidden layer and output layer. Elman neural

network can adjust the weights connecting each two neighboring

layers. It is considered as a special kind of feed-forward neural

network with additional memory neurons and local feedback

[23]. The self-connections of the context nodes in the Elman

network make it also sensitive to the history of input data which

is very useful in dynamic system modeling [24]. So the Elman

architecture has the memorizing capability and the dynamic

character.

Nomenclature

C control signal

h Euclidean distance

M ow rate (kg/s)

MAPE the mean absolute percentage error

R correlation coefcient

RMSE Root mean square error

RMSPE Root mean square percentage error

T temperature (C)

Greek symbols

q threshold of fault detection

3 relative error

Subscripts and superscripts

sa supply air

w water

wr return water

ws supply water

set set point

oa outdoor airre return air

B. Fan et al. / Building and Environment 45 (2010) 2698e2708 2699


3/11

In this paper, the Elman neural network is trained by the

approximation coefcients of sensor measurement data, which are

extracted from original measurement data by wavelet analysis. It is

used to diagnose the sensor faults in HVAC system.

2.2. Wavelet analysis

Wavelet analysis, also called wavelet transform, is a kind of

variable window technology, which can use a shorter time interval

to analyze the high frequency components of a signal and a longer

one to analyze the low frequency components of the signal

[25e27]. So wavelet transform does much better in the local

timeefrequency domain and is used to analyze the transient signals

and the time-varying signals. The wavelet transform includes the

continue wavelet transform (CWT) and the discrete wavelet

transform (DWT). The wavelet transform can be expressed by Eqs.

(1) and (2).

CWTa; s 1ffiffiffiffiffiffijajpZ N

Nxtj*

ts

a

dt (1)

Where a represents the scale parameter, s represents the

translation parameter,jrepresents the motherwavelet andj*is

the complex conjugate ofj.

DWTa; s 1

ffiffiffiffiffi2jp

Z N

N

xtj*

t 2jk2j

!dt (2)

Where a and srepresents 2j and 2jk, respectively. The DWT can

be represented withlters concept as a complementary lters. The

complementarylters contain of a high-pass lter and a low-pass

lter, which is obtained from high frequency [detail coefcients

(Dj)] and low frequency [approximation coefcients (Aj)] wavelet

coefcients, respectively. Because the observed signals are discrete

in practical situation, DWT is used to analyze signals in actual

analysis. The raw data can be decomposed into detail coefcients

and approximation coefcients by DWT. When xed biases and

drifting fault of sensors occur in AHU system, the event will appear

strongly in the coarser scales represented with approximation

coefcients [16]. So the approximation coefcients, which are

extracted by wavelet analysis, are used to train Elman neural

network to diagnose the sensor faults in the AHU system.

2.3. FCM clustering

The fuzzy c-means (FCM) algorithm is a typical clustering

algorithm[28]. It has been utilized in a wide variety of engineering

and scientic disciplines[29,30]. FCM partitions a given data set,

X fx1;.;xn 3Rpg , into c fuzzy subsets by minimizing thefollowing objective function.

JmU; V Xci 1

Xnk 1

umikkxkvik2 (3)

Fig. 1. Schematic diagram of VAV systems.

Fig. 2. Developing BPNN fault detection model.

B. Fan et al. / Building and Environment 45 (2010) 2698e27082700


4/11

Wherecis the number of clusters and selected as the specied

value in this paper, n is the number of data points, uik is the

membership ofxk in class i, m the quantity controlling clustering

fuzziness andVthe set of cluster centers (viRp). The matrixUwith

the ik-th entry uik is constrained to contain elements in the range [0

1] such asPc

i1uik 1, (k 1, 2,.,n).The function Jm is minimized by a famous alternate iterative

algorithm.

In this paper, FCM algorithm is employed to gain the

clustering centers of the fault data. Euclidean distances

between approximation coefcients of new data and cluster

centers of the known fault data are calculated. These Euclidean

distances are used to nd out unknown fault data from the

new data.

3. AHU system and fault diagnosis strategy

3.1. Dynamic simulation of AHU system

The typical HVAC systems can be partitioned into water side and

air side. As to the air side, it is shown inFig. 1,main control loops

include the Tsacontroller to ensure the proper supply air temper-

ature through adjusting the chilled water valve and the Msacontroller to maintain the outdoor air requirement through

adjusting the outdoor, recycle and exhaust air dampers. In the two

control loops, measurement parameters of all sensors are interde-

pendent. The control failure of control loop can be caused by

whichever sensor failure in control loop, which will inuence

normal operation of the system.

Fig. 3. Adaptive sensor fault detection and diagnosis strategy ow.

Table 1

BPNN model sensitivity analysis and corresponding error measurement parameters (the rst step).

BPNN model Input BPNN model training BPNN model testing

RMSE RMSPE R MAPE RMSE RMSPE R MAPE

1 Cw,Mw,T,Tws 0.0337 0.0026 0.9786 0.0019 0.0344 0.0026 0.9776 0.0019

2 Cw,Twr,Tws 0.0583 0.0045 0.9348 0.0032 0.0581 0.0045 0.9349 0.0032

3 Mw,Twr,Tws 0.0671 0.0051 0.9124 0.0037 0.0667 0.0051 0.9130 0.0037

4 Cw,Mw,Tws 0.0719 0.0055 0.8989 0.0038 0.0751 0.0055 0.8997 0.0038

5 Cw,Mw,Twr 0.0385 0.0030 0.9721 0.0023 0.0376 0.0029 0.9732 0.0021



5/11

3.2. Sensor fault detection model

Based on sensitivity analysis and correlation of control variables

in the control loop, fault detection model including two BPNN

models are developed as shown inFig. 2.

The fault detection strategy is as follows.

(1) As shown in Fig. 2, control parameter y and correlation

parameter [x1,x2,.,xn] in the control loop are used to develop

the BPNN fault detection model I. LM algorithm is selected as

the training way for BPNN.

After training convergent,BPNN is used to predict the controlparameter y of the control loop. Predictor yp of the BPNN is

calculated. e is set to the relative error betweeny andyp.q is set

to the threshold for fault detection. Ife>q, it implies the faulty

condition; ife q, it represents the normal operation condition.Structure of the BPNN and q will inuence the detection

accuracy of the fault detection model.

(2) In order to determine which of the input variables has

more inuence on the BPNN model I, two steps are fol-

lowed [31]:

(1) Quantity of the input variables of BPNN model is decreased

from n to n 1. In each time, a different variable is removedfrom the input set.

(2) Based on the rst step, the input variables are orderly by

their inuence in BPNN model. Different BPNN models aredeveloped each time one variable is removed from input

variables, until number of the input variables is 1.

The following error measurement parameters are used

in evaluating the performance of the developed BPNN

model:

RPn

i 1yiy

ypiyp

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni 1yiy

q 2Pni 1ypiyp2

(4)

RMSEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

n

Xni 1

ypiyi

2vuut (5)

RMSPE

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

ni1

ypiyi2.

n

r

yp

(6)

MAPE 1n

Xni 1

jypiyiyi

j (7)

WhereR is the correlation coefcient, RMSE is the root mean

square error, RMSPE is the root mean square percentage error,

MAPE is the mean absolute percentage error,y i is the measure

data,ypi is the BPNN model predictions, y is the mean value of

the measure data, yp is the mean value of the BPNN model

predictions, andn is the number of data points.

According to sensitivity analysis for BPNN fault detection

model I, input variable xk has signicant inuence on

prediction accuracy and network performance of BPNN faultdetection model I. So xk and [x1,., xk1, xk1., xn, y] inthe control loop are selected as the prediction and input

variables of BPNN fault detection model II respectively.

(3) The fault detection model including BPNN fault detection

models I and II are established.

Table 2

BPNN model sensitivity analysis and corresponding error measurement parameters (the second step).

BPNN model Input BPNN model training BPNN model test


1 Cw,Mw,Twr, Tws 0.0337 0.0026 0.9786 0.0019 0.0344 0.0026 0.9776 0.0019

2 Cw,Mw,Twr 0.0489 0.0037 0.9546 0.0029 0.0491 0.0038 0.9539 0.0029

3 Cw,Twr 0.0556 0.0043 0.9409 0.0030 0.0491 0.0038 0.9539 0.0029

4 Twr 0.0678 0.0052 0.9107 0.0037 0.0555 0.0043 0.9407 0.0030

Fig. 4. Fault detection based on BPNN fault detection model I. Fig. 5. Fault detection based on BPNN fault detection model II.



6/11

3.3. Sensor fault detection and identication

Adaptive sensor FDD strategy includes ve steps. It combines

ANN, wavelet analysis and FCM clustering algorithm. It is shown in

Fig. 3. Diagnosis ow of adaptive sensor FDD strategy will be

detailed in the following sections:

Step 1: The BPNN fault detection model is established. It

includes the BPNN fault detection model I and the BPNN fault

detection model II.

Step 2: The new input data are analyzed for distinguishing the

normal and the faulty conditions by the BPNN fault detection

model. The BPNN fault detection model is used to detect

whether the fault occurred in the control loop. If there is no faultin the control loop, FDD strategy will be ended, else return to

step 3.

Step 3: The wavelet transform is used to extract approximation

coefcients from the historical data (including the fault data and

normal data). Extracting approximation coefcients are used to

develop an Elman neural network to diagnose the sensor fault in

the AHU system. FCM clustering algorithm is employed to

cluster the approximation coefcients of the fault data to obtain

respective cluster centers of different kinds of the fault data.

Step 4: Input the new data to diagnose. If the BPNN fault

detection model detects the fault occurring in control loop,

approximation coefcients of the new datawill be extracted and

clustered for identifying whether they represent a kind of new

fault data. Calculating Euclidean distance heObetween approx-imation coefcients and clustering center of each known fault

data. The maximum heOmax of Euclidean distances heO are

obtained. Euclidean distances he between approximation coef-

cients of new data and clustering centers of known faults are

calculated. The relative error eh between he and heOmax is

calculated.qh is set to a threshold for identifying whether new

data represent a kind of new fault data. If eh qh, the fault isidentied as the known fault type, it can be diagnosed by Elman

neural network. Ifeh>qh, the fault is identied as the unknown

fault.

Step5: If the new data are distinguished as the known fault data,

the well-trained Elman neural network is used to more accu-

rately diagnose and identify the fault type from the new data; if

these data are distinguished as unknown fault data, return to

step 3. These data will be added to the historical data to train

new Elman neural network.

4. Strategy validation and discussion

4.1. Control loop based on Tsacontroller

4.1.1. Fault detection model based on BPNN

Main variables of control loop based on Tsacontroller includeTsa(supply air temperature), Cw (water valve control signal), Mw (water

ow rate), Twr (return water temperature) and Tws (supply water

temperature). According to interrelation of variables in this control

loop,Cw,Mw,Twrand Twsare selected as the input variables of theBPNN fault detection model I. The variable Tsa is selected as

prediction of the BPNN fault detection model I. The training data

and testing data for BPNN are generated by simulating the VAV air-

conditioning system [8]. A total of 842 normal samples and 280

normal samples are used in training and testing the BPNN fault

detection model I. The estimation number of the hidden layer

neuron can be given by:

Fig. 6. Fault detection efciency BPNN fault detection model I (left) and model II (right).

Fig. 7. Euclidean distances between four kinds of data and clustering center of fault 1.



7/11

Y

ffiffiffiffiffiffiffiffiffiffiffiffiffim

n

p

a (8)

Where Yis the hidden nodes, m is the input neurons, and n is the

output neurons;a ranges from 1 to 10; its value can be selected by

design program. According to Eq. (8), 8 hidden neurons are

selected.

Results of sensitivity analysis for the BPNN fault detection

model I are listed inTables 1 and 2. Results show that the variable

Twr has the most inuence on the prediction of BPNN of fault

detection model I. So it is selected as prediction of BPNN of fault

detection model II. Input variables of the BPNN fault detection

model II includeTsa, Cw, Mw and Tws. According to the correlation

coefcients of sensitivity analysis that are presented in Tables 1

and 2, thresholds q for fault detection can be set to 0.5%, 1%, 2%

and 3%.

Through the simulation model of the fault generator, ve

sensor faults are simulated to test the fault detection model. Five

sensor faults include xed bias of 1.5C for supply air temperaturesensor, xed bias of1.5C for supply air temperature sensor,drifting fault for supply temperature sensor, supply temperature

sensor failure fault and xed bias of 1C for return watertemperature sensor. Five sensor faults occurred at 12:00, 10:00,

10:00, 11:00 and 12:00. The well-trained BPNN fault detection

model I and model II are used to detect fault in the control loop.

The detection results of ve faults are shown in Figs. 4 and 5.

When thresholds q for fault detection are set to 0.5%, 1%, 2% and

3%, detection efciencies of the BPNN fault detection model I and

model II are shown in Fig. 6. Figs. 4 and 5 show the difference

between the prediction of BPNN and the real value of system

operation is very signicant when fault occurs. The sensor fault

occurring time can be easily detected.The fault detection rate can be dened by Equation(9):

Detection rate% FnumDnum

100% (9)

Where Dnum means the sample number under different fault

conditions,Fnumis the fault detection number under different faultconditions.

When thresholdsq for fault detection are selected to 0.5%, 1%,

2% and 3%, average efciencies of the BPNN fault detection

model I for fault detection are 85.5%, 73.0%, 59.4% and 46.1%,

while average efciencies of the BPNN fault detection model II

for fault detection are 98.7%, 93.7%, 89.7% and 86.4%. Detection

results show that fault detection efciency of fault detection

model based on two BPNN models is more accurate than that

based on single BPNN model. Meanwhile the fault detection

model based on two BPNN models can more easily detect supply

temperature sensor fault than other sensor fault types. BPNN

fault detection model II can more efciently detect xed bias of

1.5C and drifting fault for supply air temperature sensor thanmodel I.

4.1.2. Fault diagnosis and cluster analysis

The number of the original samples for developing adaptive

sensor FDD strategy under normal and faulty conditions is 2350.

After these original samples are decomposed and processed by

three-level wavelet, 150 samples remain to develop the adaptive

sensor FDD strategy. These samples include 50 samples of normal

data, 50 samples ofxed bias of 1.5C for sensor Tsa(fault 1) and50 samples ofxed bias of 1C for sensor Twr(fault 2). The faultdiagnosis model for control loop based on Tsa involves ve vari-

ables. Vector [Tsa, Cw, Mw, Twr, Tws] represents the original vector

with single sample of these variables, it can be decomposed to

approximation coefcients vector [LTsa, LCw, LMw, LTwr, LTws] by

three-level wavelet, which is selected as input variables of Elmanneural network for control loop based on Tsacontroller. According

to Eq.(8), hidden neurons number of Elman neural network is 8. If

the output is close to (1, 0, 0, 0), it represents the normal oper-

ation condition. The output close to (0, 1, 0, 0) represents the xed

bias of 1.5C for sensor Tsa (fault1) occurring. The output close to(0, 0, 1, 0) represents the xed bias of 1C for sensor Twr (fault2)occurring. If the out variable of Elman neural network is close to

(0, 0, 0, 1), it represents a kind of unknown fault. Then its clus-

tering center is calculated by FCM algorithm for fault diagnosis in

the next section.

When new input data sets that include another kind of

unknown fault are detected and diagnosed using this strategy,

the second kind of unknown fault data are identied and added

to historical data to construct new Elman neural network for

Fig. 8. Euclidean distances between four kinds of data and clustering center of fault 2.

Table 3

Clustering centers of fault 1, fault 2, fault 3 and fault 4.

Clustering center LTsa LCw LMw LTwr LTws

Fault 1 37.56 1.80 12.60 36.65 21.22

Fault 2 36.85 1.36 9.48 38.79 21.20

Fault 3 37.97 2.83 19.80 31.51 21.23

Fault 4 36.77 1.01 7.09 45.57 21.21

Fig. 9. Spatial distribution I of approximation coefcients.



8/11

fault diagnosis in the next section. Out variable (0, 0, 0, 2) of new

Elman neural network represents the second kind of unknown

fault. So unknown fault type can be distinguished, this approach

can improve adaptive performance of sensor FDD strategy.

Here thresholdqfor fault detection is set to 1% and threshold qhfor fault diagnosis is set to 5%.

When 40 samples of fault 1 (data 1) and 40 samples of fault 2

(data 2) are added to new data sets for detecting and diagnosing,

they are identied and distinguished as the known faults. Figs. 7

and 8 show that samples of fault 1 and fault 2 cannot be

completely distinguished only by threshold qh of fault detection.

Elman neural network is used to diagnose fault types of these

samples, it can more accurately distinguish between fault 1 data

and fault 2 data, fault diagnose rate is close to 95%.

When 40 samples of drifting fault for sensor Tsa (data 3) are

detected and diagnosed by this strategy, they are identied as

samples of unknown fault. These samples of unknown fault are

added to historical data sets to train new Elman neural network.

The output of new Elman neural network close to (0, 0, 0, 1)

represents drifting fault for sensor Tsa (fault 3) occurring. Clustering

center of fault 3 samples is gained by FCM algorithm.

When 40 samples ofxed bias of1.5C for sensor Tsa(data 4)are detected and diagnosed by this strategy, it is identied as

samples of the second kind of unknown fault. New Elman neural

network is developed. The output of new Elman neural networkclose to (0, 0, 0, 2) represents xed bias of1.5C for sensor Tsa(fault 4).

Fig. 7 shows Euclidean distances between four kinds of data

(data 1, data 2, data 3 and data 4) and clustering center of fault 1

data.Fig. 8shows Euclidean distances between four kinds of data

(data 1, data 2, data 3 and data 4) and clustering center of fault 2

data. When thresholdqhfor fault diagnosis is set to 5%, most fault

types can be distinguished.

Table 3shows the clustering centers of the fault 1 data, fault 2

data, fault 3 data and fault 4 data.

The dimensional-reduction method is used to visually display

clustering results. According to the correlations among the vari-

ables in the control loop based on the Tsa controller, LTsaand LTwr

among approximation coefcients vector [LTsa,LCw,LMw,LTwr,LTws]are selected to establish a two-dimensional graphic. It is shown in

Fig. 9.

4.2. Control loop based on Moa controller

4.2.1. BPNN fault detection model

The main variables include Moa (outdoor air ow rate), Moa,set(set point of outdoor air ow rate),Msa(supply air ow rate), Mre(return air ow rate) and Coa (control signal of supply fan) in the

control loop based on Msa.

According to interrelation of variables in this control loop, Moa,

set, Msa, Mre and Coa are selected as input variables of the BPNN fault

detection model I. The variableMoais selected as prediction of the

BPNN fault detection model I. Similarly, 8 hidden neurons are

selected by Eq.(8). The training data for neural network model are

gained by simulating the VAV air-conditioning system [32]. A total

of 810 normal samples and 270normal samples are used in training

and testing BPNN fault detection model I in this control loop.

Results of sensitivity analysis for the BPNN fault detection model

I are listedin Tables 4 and 5. Results of sensitivity analysis show that

Msa is the most relevant to the prediction of the BPNN fault

detection model I. It is selected as prediction of the BPNN fault

detection model II. Input variables of BPNN fault detection model II

include Moa,set, Moa, Mre and Coa. According to the correlation

coefcients that are listed inTables 4 and 5,thresholdsq for fault

detection can be set to 0.5%, 1%, 2% and 3%.

Through the simulation model of the fault generator, three kinds

of sensor faults are gained to test the fault detection model basedon BPNN. Sensor faults include xed bias of 20% for supply air ow

rate sensor, xed bias of 20% for outdoor air ow rate sensor and

xed bias of 20% for return air ow rate sensor. Three kinds of

sensor faults occurred at 12:00, 12:00 and 10:00. The trained BPNN

fault detection model I and model II are used to detect whether

fault occur in this control loop. The detection results of three kinds

of faults are shown inFigs. 10 and 11.

When thresholdsq for faultdetection are set to0.5%,1%,2% and3%,

average efciencies of the BPNN fault detection model I for fault

detection are 100%, 100%,100% and 66.7%, while average efciencies

of theBPNN fault detectionmodelII forfault detectionare 100%,100%,

100% and 100%.Results showxedbias of outdoor airowrate sensor

is more difcultly detected than other two kinds of sensor faults.

4.2.2. Fault diagnosis and fault clustering

The number of the original samples for developing adaptive

sensor FDD strategy is 1110. After these original samples are

Table 4

BPNN model sensitivity analysis and corresponding error measurement parameters (the rst step).



1 Ms, Mre, Coa,Moa,set 0.0087 0.0094 0.9992 0.0076 0.0084 0.0091 0.9993 0.0075

2 Mre,Coa,Moa,set 0.0149 0.0161 0.9971 0.0122 0.0153 0.0166 0.9970 0.0123

3 Ms, Coa,Moa,set 0.0131 0.0142 0.9978 0.0107 0.0133 0.0144 0.9977 0.0107

4 Ms, Mre, Moa,set 0.0093 0.0101 0.9989 0.0082 0.0094 0.0102 0.9989 0.0083

5 Ms, Mre, Coa 0.0082 0.0089 0.9993 0.0072 0.0126 0.0137 0.9981 0.0098

Table 5

BPNN model sensitivity analysis and corresponding error measurement parameters (the second step).



1 Msa, Mre,Coa,Moa,set 0.0087 0.0094 0.9992 0.0076 0.0084 0.0091 0.9993 0.0075

2 Msa, Coa,Moa,set 0.0131 0.0142 0.9978 0.0107 0.0133 0.0144 0.9977 0.0107

3 Msa, Moa,set 0.0318 0.0342 0.9870 0.0219 0.0317 0.0343 0.9870 0.0222

4 Msa 0.1620 0.1756 0.5659 0.1217 0.1622 0.1756 0.5666 0.1218



9/11

decomposed and processed by three-level wavelet,120 samples are

selected to develop adaptive sensor FDD strategy. These samplesinclude 40 samples of normal operation, 40 samples ofxed bias of

20% for supply air ow rate sensor (fault 5) and 40 samples ofxed

bias of 20% for outdoor air ow rate sensor (fault 6). The fault

diagnosis model for the control loop based on Moa involves ve

variables. Vector [Moa,Moa,set,Msa,Mre,Coa] represents the original

vector with single sample of these variables, it can be decomposed

to approximation coefcients vector [LMoa, LMoa,set, LMsa, LMre, LCoa]

by three-level wavelet. Approximation coefcients vector data are

selected as input variables of Elman neural network for control loop

based onMoacontroller. Hidden neurons number of Elman neural

network is set to 8. If the output is close to (1, 0, 0, 0), it represents

the normal operation. The output close to (0, 1, 0, 0), represents the

xed bias of 20% for sensorMsaoccurring. The output close to (0, 0,

1, 0), represents the xed bias of 20% for sensorMoa. Similarly, theoutput close to (0, 0, 0, 1), represents the unknown fault. Here

thresholdqfor fault detection is set to 1% and threshold qhfor fault

diagnose is set to 5%.

Samples of fault 5 and fault 6 are clustered and gained clustering

centers by FCM algorithm. When 40 samples of fault 5 and 40

samples of fault 6 are added to new data sets, they are all detected

and diagnosed as the known faults. According to Figs. 12 and 13,samples of fault 5 and fault 6 cannot be completely distinguished

only by thresholdqhfor fault detection. They can also be diagnosed

by the trained Elman neural network. Fault diagnosis efciency of

Elman neural network can reach to 98%. When 40 samples ofxed

bias of 20% for sensor Mre(fault 7) are detected and diagnosed by

this strategy, they are identied as samples of a kind of unknown

fault, so these samples are added to historical data to train new

Elman neural network. The output of new Elman neural network

close to (0, 0, 0, 1) representsxed bias of 20% for sensorMre(fault

7) occurring. Clustering centers of fault 5, fault 6 and fault 7 are

listed inTable 6.

Fig. 12shows Euclidean distances between three kinds of data

(data 5, data 6 and data 7) and clustering center of fault 5. Fig. 13

shows Euclidean distances between three kinds of data (data 5,

data 6 and data 7) and clustering center of fault 6. Figs. 12 and 13

show that most fault types can be distinguished when threshold

qhfor fault diagnose is set to 5%.

LMoaand LMsaamong approximation coefcients vector [LMoa,

LMoa,set, LMsa, LMre, LCoa] are selected to establish a two-dimen-

sional graphic as shown inFig. 14.

Fig. 10. Fault detection based on BPNN fault detection model I.

Fig. 11. Fault detection based on BPNN fault detection model II.

Fig.12. Euclidean distances between two kinds of data and clustering center of fault 5.

Fig.13. Euclidean distances between two kinds of data and clustering center of fault 6.



10/11

5. Conclusion

In this paper, the hybrid FDD strategy for local system of AHU is

presented. This strategy consists of two stages which are the fault

detection stage and the fault diagnosis stage, respectively. In the

rst stage, the BPNN fault detection model is used for generating

estimates of sensor values that are compared to actual values toproduce residuals. Faults can be detected when residuals exceed

thresholds established for normal operation. The BPNN fault

detection model is trained using an abundance of characteristic

information from the historical data in the HVAC system. The

trained BPNN model can identify the local control system and

detect the abnormal condition. Because it does not need to apply

mathematical model to deduce physical relevance of the variables

in the control loop, the fault detection model in the fault detection

stage has the adaptability and exibility for fault detection. Sensi-

tive analysis for the rst BPNN model can nd out which input

variable has signicant inuence for prediction precision of therst

BPNN model. So the most main variable from the variables of the

control loop based on different controllers by sensitive analysis can

be found. It is employed to construct the second BPNN model. Andthe fault detection accuracy of BPNN fault detection model I and

BPNN fault detection mode II are different when different faults

occur. As a whole, fault detection results show that fault detection

efciency based on the combination of two BPNN fault detection

model is more accurate than that based on the single BPNN fault

detection model. And it is necessary to select proper threshold q for

increasing fault detection accuracy. If too large threshold q is

selected, the fault detection accuracy will be decreased. Similarly if

too small thresholdqis selected, incorrect diagnosis will occur. The

thresholdq is set to 1% that is recommended.

In the second stage, the fault diagnosis model is developed

which combines wavelet analysis with Elman neural network, to

diagnose the specic cause of fault in the control loop. Because

wavelet analysis method is used to process and analyze the raw

data, we can reduce the input data of Elman neural network and

improve the capability and reliability of the sensor fault diagnosis.

Clustering data of different kind of fault data are gained by FCM

algorithm. Here the thresholdqhis set to a threshold for identifying

whether the new data represent a kind of new fault data. When the

thresholdqhis set to 5%, most of the known faults and new faults

can be distinguished. The simulation results show that this strategy

can be successfully used in the control loop based on Tsacontroller

and the control loop based onMoa controller. If some kind of sensor

fault data is not used to train Elman neural network, this fault

represents unknown sensor fault for this FDD model. It can be

distinguished by fault diagnosis ow of hybrid FDD strategy. So this

strategy can adaptively detect and diagnose the sensor fault for

local system of AHU, when the new unknown fault occurs in HVAC

system. For the real HVAC systems, because of the development of

the energy management and control system, the historical data and

operation data can be easily obtained. So this hybrid FDD strategy

for local system of AHU is promising for fault detection and diag-

nosis in the HVAC system.

Acknowledgements

This project is nancially supported by National Natural Science

Foundation of China (No. 50976066).

References

[1] Isermann R. Supervision, fault detection and fault diagnosis methods an faultdiagnosis methods an introduction. Control Engineering Practice 1997;5(5):639e52.

[2] Shaw SR, Norford LK, Luo D, et al. Detection and diagnosis of HVAC faults viaelectrical load monitoring. HVAC & R Research 2002;8(1):13e40.

[3] Norford LK, Wright JA, Buswell RA, et al. Demonstration of fault detection anddiagnosis methodsfor air-handing units. HVAC & R Research2002;8(1):41e71.

[4] Howell J, Maddison EJ. Fault detection in HVAC plants based on constraintsuspension. Building Services Engineering Research and Technology 1995;16(4):207e13.

[5] WangSW, WangJB. Robust sensor faultdiagnosis andvalidation in HVAC systems.

Transactions of the Institute of Measurement and Control 2002;24(3):231e

62.[6] Reddy TA. Development and evaluation of a simple model-based automated

fault detection and diagnosis (FDD) method suitable for process faults of largechillers. ASHRAE Transactions 2007;113(2):27e39.

[7] Wang SW, Cui JT. Sensor-fault detection, diagnosis and estimation forcentrifugal chiller systems using principal-component analysis method.Applied Energy 2005;82(3):197e213.

[8] Du Z, Jin X. Detection and diagnosis for sensor fault in HVAC systems. EnergyConversion and Management 2007;48:693e702.

[9] Du Z, Jin X, Wu L. Fault detection and diagnosis based on improved PCA withJAA method in VAV systems. Building and Environment 2007;42:3221e32.

[10] Du Z, Jin X. Detection and diagnosis for multiple faults in VAV systems. Energyand Buildings 2007;39:923e34.

[11] DuZ, JinX. Multiplefaults diagnosis forsensors inair handlingunitusing Fisherdiscriminantanalysis. Energy Conversionand Management 2008;49:3654e65.

[12] Lee WY, Park C, Kelly GE. Fault detection in an air-handing unit using residualand recursive parameter identication methods. ASHRAE Transactions1996;102(1):528e39.

[13] Lee WY, House JM, Shin DR. Fault diagnosis and temperature sensor recovery

for air-handling unit. ASHRAE Transactions 1997;103(1):621e

33.[14] Lee W-Y, House JM, Kyong N-H. Subsystem level fault diagnosis of a buildings

air-handling unit using general regression neural networks. Applied Energy2004;77:153e70.

[15] Wang SW, Chen YM. Fault-tolerant control for outdoor ventilation airow ratein building based on neural network. Building and Environment 2002;37(7):691e704.

[16] Xu X, Xiao F, Wang S. Enhanced chiller sensor fault detection, diagnosis andestimation using wavelet analysis and principal component analysis methods.Applied Thermal Engineering 2008;28:226e37.

[17] Du Z, Jin X, Yang Y. Wavelet neural network-based fault diagnosis in air-handling units. HVAC & R Research 2008;14(6):959e73.

[18] Jaradat MAK, Langari R. A hybrid intelligent system for fault detection andsensor fusion. Applied Soft Computing 2009;9:415e22.

[19] Doan CD, Liong SY, Karunasinghe DSK. Derivation of effective and efcientdata set with subtractive clustering method and genetic algorithm. Journal ofHydroinformatics 2005;4(07):219e33.

[20] Rumelhart DE, Hinton GE, Williams RJ. Learning representations by back-

propagating errors. Nature 1986;323:533e

6.

Table 6

Clustering centers of fault 5, fault 6 and fault 7.

Clustering center LMoa LMoa,set LMsa LMre LCoa

Fault 5 2.76 2.69 21.88 19.13 0.60

Fault 6 2.95 2.89 19.92 19.52 0.50

Fault 7 2.75 2.70 16.23 19.15 0.60

Fig. 14. Spatial distribution II of approximation coefcients.



11/11

[21] Dai H, Macbeth C. Effects of learning parameters on learning procedure andperformance of a BPNN. Neural Networks 1997;10(8):1505e21.

[22] Kollias S, Anastassiou D. An adaptive least squares algorithm for the efcienttraining of articial neural networks. IEEE Transactions on Circuits andSystems 1989;36(8):1092e101.

[23] Sastry PS, Santharam G, Unnikrishnan KP. Memory neuron networks foridentication and control of dynamic systems. IEEE Transactions on NeuralNetworks 1994;5:306e19.

[24] Elman JL. Finding structure in time. Cognitive Science 1990;14:179e211.[25] Kumar P, Foufoula-Georgiou E. Wavelet analysis for geophysical applications.

Reviews of Geophysics 1997;35(4):385e

412.[26] Baydar N, Ball A. Case study detection of gear failures via vibration and

acoustic signals using wavelet transform. Mechanical Systems and SignalProcessing 2003;17(4):787e804.

[27] Wang WJ, Mcfadden PD. Application of orthogonal wavelets to early geardamage detection. Mechanical Systems and Signal Processing 1995;9(5):497e507.

[28] Bezdek JC. Pattern recognition with fuzzy objective function algorithms. NewYork: Plenum Press; 1981.

[29] Xie X, Beni GA. Validity measure for fuzzy clustering. IEEE Transactions onPattern Analysis and Machine Intelligence 1991;13(8):841e7.

[30] Zhang DQ, Chen SC. Clustering incomplete data using kernel-based fuzzyc-means algorithm. Neural Processing Letters 2003;18:155e62.

[31] Yalcintas M. Energy-saving predictions for building-equipment retrots.

Energy and Buildings 2008;40:2111e

20.[32] Du Z, Jin X, Yang X. A robot fault diagnostic tool for ow rate

sensors in air dampers and VAV terminals. Energy and Buildings2009;41:279e86.


Documents

Ann Elman Fcm.19