Fault-tolerant control and data recovery in HVAC monitoring system

Size: px

Start display at page:

Download "Fault-tolerant control and data recovery in HVAC monitoring system"

Janis Maxwell
5 years ago
Views:

http://wwwpapereducn Energy and Buildings 37 (2005) 175 180 wwwelseviercom/locate/enbuild Fault-tolerant control and recovery in HVAC monitoring system Xiaoli Hao a,b, Guoqiang Zhang a, Youming Chen

China Received 12 April 2004; received in revised form 25 May 2004; accepted 15 June 2004 Abstract It is necessary that a reliable and optimal control system has the ability of fault tolerance, which

measurement space into two subspaces, one principal component subspace (PCS) and the other residual subspace (RS) When the faulty or missed is observed, it will be projected into PCS and RS It is

1 Energy and Buildings 37 (2005) wwwelseviercom/locate/enbuild Fault-tolerant control and recovery in HVAC monitoring system Xiaoli Hao a,b, Guoqiang Zhang a, Youming Chen a, * a College of Civil Engineering, Hunan University, Changsha, Hunan, , China b College of Energy and Safety Engineering, Hunan University of Science and Technology, Xiangtan, Hunan, , China Received 12 April 2004; received in revised form 25 May 2004; accepted 15 June 2004 Abstract It is necessary that a reliable and optimal control system has the ability of fault tolerance, which recovers the faulty and/or missed in time Principal component analysis (PCA) is presented to model HVAC monitored systems by using the measured under normal operation condition (NOC) PCA splits the measurement space into two subspaces, one principal component subspace (PCS) and the other residual subspace (RS) When the faulty or missed is observed, it will be projected into PCS and RS It is then recovered by sliding the faulty or missed to PCS via iteration Examples of HVAC monitoring system have demonstrated that the approach has good performance to recover faulty or missed and thus can be embedded into the system to achieve fault-tolerant control # 2004 Elsevier BV All rights reserved Keywords: Faulty ; Missed ; PCA; Data recovery; Fault-tolerant control; HVAC monitoring system 1 Introduction In principle, reliable control and optimal operation of a system are determined by reliability and accuracy of its measured However, the measured sometimes has large, and even the is bad or missed, due to the unreliable measured instrument and the interference from environment This abnormal can always result in bad control of an automation control system, which not only causes huge waste of energy but also affects the safety of equipment operation For an air-conditioning system, it can influence the thermal comfort of occupant and indoor air quality Therefore, it is necessary that the control system have the ability of fault-tolerant control, so that system can be controlled properly even if the fault measured occurs In order to fulfill this need, a fault detection and diagnosis system should be embedded in control system When fault exists in the measured, it can be detected, identified, and recovered by FDD system Then it is the recovered and not the measured to be sent to the control system Therefore, at that time, the accuracy of * Corresponding author Tel: ; fax: address: ymchen@hnucn (Y Chen) controlling depends on the accuracy of recovered and the control will be reliable only if the can be recovered accurately So, it is vital and useful to research how to recover accurately and to develop recovery approach As for a certain system, it is not absolutely independent among various measured but it has correlation among them, which is exterior reflection of inner basic laws of physics or chemistry, such as the law of energy conservation and the law of mass conservation It is just the utilization of measurement correlation that the fault or missed can be recovered by the others measured which are accurate Few researches have been carried out on recovery Maquin proposed the approach of finding optimal solution of uncertain models to recover [1] But the approach is mathematically complicated and difficult in finding solution A regression equation was presented to recover an estimate of supply air temperature sensor, which was used in the feedback loop to regain control of the actual supply air temperature [2] However, the accuracy of recovery is relied on the precision of the regression model If a large existed in model, the result of recovery will not be accurate A neural network model was presented to detect, /$ see front matter # 2004 Elsevier BV All rights reserved doi:101016/jenbuild

http://wwwpapereducn 176 X Hao et al / Energy and Buildings 37 (2005) 175 180 Fig 1 Flowchart of general control diagnose and recover faults of outdoor air flow rate sensor and supply air flow rate

network Therefore, in this study, it is aimed to present an approach to recover accurately and quickly and use it to achieve fault-tolerant control Principal component analysis (PCA) is a kind of

2 176 X Hao et al / Energy and Buildings 37 (2005) Fig 1 Flowchart of general control diagnose and recover faults of outdoor air flow rate sensor and supply air flow rate sensor, which accomplished the fault-tolerant control of outdoor air flow [3] Neural network approach is subjective in choosing network structure and it also needs much measured to train neural network Therefore, in this study, it is aimed to present an approach to recover accurately and quickly and use it to achieve fault-tolerant control Principal component analysis (PCA) is a kind of approach of multi-dimension statistic, which models the system by using measured of system in normal operation condition and captures major part of measurement correlation by few principal components It partitions the measured space into principal component subspace (PCS) and residual subspace (RS) Data recovery is essentially a process of seeking a best estimate of normal corresponding to faulty by sliding the faulty to PCS The approach of principal component analysis was used to detect, identify and reconstruct fault in a boiler process [4] In this paper, it will be used to recover in HVAC monitoring system 2 Strategy of fault-tolerant control Fig 1 shows a flowchart of typical control system with computer After measured by the sensor and converted by A/ D converter, a controlled variable y is directly sent to the control system, in which it is compared with set-value, and the deviation is used as an input of the controller According to the controlling rule, a controlling signal is output by controller, which is used to control the controlled object via actuator after it is converted back by D/A converter Under this control strategy, sensor should measure the controlled variable accurately Otherwise, the output of controller is a wrong output and the control to controlled object is a bad control if the measurement is not accurate or it includes fault To ensure that controller can make a correct control at any case, it is required that the control system has ability of fault-tolerance Fig 2 is a flowchart of fault-tolerant control system Under this control strategy, the measurement signal is not sent to controller directly but to fault detection and diagnosis (FDD) system first, which is used to detect and diagnose fault in system If the result of FDD shows that there is no fault in measured, it will be sent to controller, otherwise it will be sent to recovery system, where the fault will be recovered, and then sent to the controller Therefore, it can be sure that every datum sent to controller reflects the real value of controlled variable and that every control made by controller is correct When FDD system finds a fault in measured it will send information to central managing computer and make alarm to inform the manager that a fault occurred in system so that the maintainer can repair or recover the fault in time Fig 2 Flowchart of fault-tolerant control

3 It is obvious that the key of fault-tolerant control is that the FDD system can detect and diagnose fault in time and the recovery system can recover the accurately A reliable approach of FDD was proposed by Chen and Hao in 2002[5] Therefore, an approach of recovery is presented in this paper X Hao et al / Energy and Buildings 37 (2005) Modeling process and geometric meaning of PCA Let x (x2r m ) represents a measured sample including m measured variables and X (X2R nm ) represents a measured matrix including n measured samples x Each column of X is zeroized, which means that every element of each column of X is subtracted by the mean value of this column According to principle of PCA, matrix X can be decomposed as follows, X ¼ ˆX þ X (1) where ˆX represents the modeled of measured variables and X represents the residual of measured variables, which is random noise under normal condition ˆX and X can be expressed as, ˆX ¼ TP T (2) X ¼ T P T (3) In equation, matrix T (T2R nk ) is score matrix, which is actually coordinate value of measured in various principal component directions, and matrix P (P2R m k )is loading matrix, whose column vectors are the eigenvectors corresponding to the k largest eigenvalues, l i (i =1tok), of matrix R, which is the covariance matrix of X Each column sector of P denotes one direction of principal component Matrix Tð T 2 R nðm kþ Þ is coordinate value of measured in various non-principal component directions Column sectors of matrix Pð P 2 R mðm kþ Þ are, respectively, the left m-k eigenvectors of matrix R k is the most optimal number of principal components of model, which is determined via minimizing the unreconstructed variance [6] It is obvious that matrix ½ P P Š is orthogonal because each column of P and P is eigenvector of matrix R Itcan be known that PCA method is actually a orthogonal transformation,in which the magnitude of variance of measured does not change but, the distribution of it changes The direction, in which the variance mostly distributesiscalledthefirstprincipal component In the order of variance decreasing, it is sequentially called the second principal component, the third principal component, and so on According to the statistic principle, the covariance matrix of X can be estimated by the followed equation, R ¼ COVðXÞ XT X n 1 (4) So,thesystemcanbemodeledbymeasuredunder normal operation condition with PCA From the process of modeling system, it can be found that PCA partitions measured space into two subspaces, PCS and RS After model of system was built, a new measured sample can be decomposed into two parts, that is, x ¼ ˆx þ x (5) where, Fig 3 Geometrical meaning of PCA approach x ¼ PP T x ¼ Cx (6) x ¼ P P T x ¼ðI CÞx ¼ Cx (7) ˆx is the projection of x on PCS and x is the projection of x on RS Under normal condition, the projection of x is mostly on PCS, and the projection of x on RS, x, is very small But, when fault occurs, the projection of x on RS will increase notably Therefore, the recovery can be achieved by decreasing the projection of x on RS Fig 3 shows the geometrical meaning of PCA approach Measured space is divided into two subspaces, principal component subspace and residual subspace ˆx and x are projection of x on PCS and RS, respectively 4 Approach of recovery The process of recovery is essentially a process of seeking the best estimate of normal corresponding to fault It may assume that only one fault occurs in system at one time because the probability of occurring multi-fault is very small It is assumed that the ith entry of sample x included fault So ˆx i can be computed with Eq (6), ˆx i is also an estimate of normal, x i *, but not the best estimate, which also included fault However, fault included in ˆx i is smaller than that included in x i Therefore, ˆx i is nearer to x i * than x i Ifestimateofx i * is computed again with Eq (6) using ˆx i,insteadforx i,thenewestimate will approach more to x i * than to the old one So the best estimate can be gained via iteration like that

http://wwwpapereducn 178 X Hao et al / Energy and Buildings 37 (2005) 175 180 From Eq (6), ˆx ¼ Cx, it can infer ðxþ T ¼ x T C(C is symmetric matrix), that is, 2 3 ˆx 1 ˆx 2 ˆx 6 i 4 7 5 ˆx m T

so, process of iteration can be expressed as follows, ˆx new i ¼bc T i 0 c T þi c x þ c iiˆx old i (8) where b c T i 0 c T þi c denotes the ith column sector of C with 0 instead for c ii It can be

4 178 X Hao et al / Energy and Buildings 37 (2005) From Eq (6), ˆx ¼ Cx, it can infer ðxþ T ¼ x T C(C is symmetric matrix), that is, 2 3 ˆx 1 ˆx 2 ˆx 6 i ˆx m T therefore, ¼ ½x 1 x 2 x i x m Š 2 c 11 c 12 c 1i c 21 c 22 c 2i c i1 c i2 c ii 6 4 c m1 c m2 c mi ˆx i ¼ ½x 1 x 2 x i x m Š ½c 1i c 2i c ii c mi Š T ¼bc T i 0 c T þi c x þ c iix i c 1m c 2m c im c mm so, process of iteration can be expressed as follows, ˆx new i ¼bc T i 0 c T þi c x þ c iiˆx old i (8) where b c T i 0 c T þi c denotes the ith column sector of C with 0 instead for c ii It can be proved that the iteration is always converged if c ii is not equal to one [4] That is, x i ¼ b ct i 0 c T þi c x 1 c ii (9) In Eq (9), c ii can not equal to one If c ii equals to one, it means that the variable can not be recovered by others because it is not correlation with others variables Therefore, Fig 4 Geometric interpretation of recovery process to achieve recovery, it is really unnecessary to calculate via iteration, it can be gained with Eq (9) directly Iteration is a process of projecting on PCS time after time Fig 4 shows the geometric meaning of iteration Under ideal condition, should be in PCS But, in fact the measured (empty dot) is often near PCS instead of in PCS due to measured noise When fault occurs, the faulty (solid dot) will depart from PCS due to existence of fault It assumed that fault exist in variable x 2, therefore, process of recovery along direction of j is a process of seeking dot R First dot A is projected to PCA and ˆx is gained and dot B can be found Then dot B is projected on PCS again and dot C can be found Just do like that, time after time, estimate value will gradually approach to real value, dot R Of course, dot R is not just always in PCS but it must be very near to the PCS For the case of missed, can be recovered with the same approach just giving an initial value (zero is often given) randomly to the entry that is missed 5 Description of monitoring system in HVAC system In order to validate the ability to recover fault of approach proposed in this paper, it is used to recover measured from monitoring system in HVAC system Fig 5 Scheme of chilled plant in air-conditioning system

5 X Hao et al / Energy and Buildings 37 (2005) Fig 5 shows scheme of chilled plant in a air-conditioning system In this system, two same chillers are included and each of them equipped with one primate pump, which has constant flow volume, in order to keep the constant flow rate of chilled water in evaporator of each chiller Two second pumps, which has various flow volume are used to supply chilled water for buildings Second pump varies flow rate via frequency conversion according to the variable building load Surplus chilled water from primate circuit flows back through bypass A chiller and its corresponding primate pump will be turned off, when the flow rate of chilled water in bypass is larger than that of one primate pump, and a chiller and its corresponding primate pump will be turned on, when the flow rate of chilled water in bypass is negative and this state is kept for some time The chiller and its corresponding pump is controlled by the strategy of first on, first off, and first off, first on in order to keep approximately equivalency of operational time The installed site and types of sensor in system are also shown in Fig 3 There are four flow rate meters, including the supply water flow of chiller 1 and chiller 2, the building supply water flow, and the bypass flow, and five temperature sensors, including the supply water temperature of chiller 1 and chiller 2, the building supply water temperature, the building return water temperature, and the return water temperature of chiller According to the given building load, system was simulated on the platform of TRNSYS for four workdays with a sampling interval of one minute Five thousand groups of simulated in stable state were chosen and zeroized and used to model monitoring system with the approach presented First, the most optimal number of principal component was determined via minimizing the unreconstructed variance In this example, the most optimal principal component number is three The three largest principal components were used to model system Fig 6 Comparison of recovery, fault and normal Table 1 Precision of fault recovery Fault Normal Recovered Absolute Relative s, which are ratio between absolute s and corresponding normal, are all below 5% It shows that fault can be accurately recovered by PCA approach 6 Examples of recovery 61 Recovery of fault To show the ability to recover fault of PCA, a drift fault was added into the measured of building return water temperature sensor, and it was recovered with the model built by PCA Comparison of recovery, faultandnormalisshowninfig 6 Itcanbe found from Fig 6 that recovery approaches to normal very much It illustrates that PCA has good ability to recover fault and ability to denoise in some degree Recovered result of ten groups of fault, which was randomly chosen from computational result, is shown in Table 1 From Table 1, it can be learnt that absolute s, which are difference between recovered and corresponding normal, are very small and relative Fig 7 Recovery of missed

6 180 X Hao et al / Energy and Buildings 37 (2005) Table 2 Precision of missed recovery Given initial value 62 Recovery of missed It assumed that the measured of building return water temperature was missed and zero was given as the initial value of missed and then it was also recovered with the model built by PCA Recovered was shown in Fig 7 Result shows that recovered is almost same as normal and it illustrates that the PCA approach also has good ability to recover missed Recovered result of ten groups of missed, which was also chosen randomly from computational result, is shown in Table 2 In Table 2, absolute and relative are both very small and it verified that missed can be recovered very well by PCA approach 7 Conclusions Normal Recovered Absolute Relative It is very important for reliable and optimal operation of system that control system has the ability of fault-tolerance which, can recover faulty or missed in time PCA approach, which partitions measured space into PCS and RS, is proposed to model system with measured of system in normal operation condition and to capture correlation of variables with few principal components Fault is projected into PCS and RS and it is recovered by sliding the fault to PCS to decrease projection of it in RS via iteration Fault and missed are recovered with PCA, and recovered result approaches to normal highly It shows that PCA has excellent ability of recovery and can be embedded into monitoring system to reinforce the fault-tolerant ability of system Acknowledgement The research work of this paper is financially supported by the Teaching and Research Award Program for Outstanding Young Teacher in Higher Education Institution of MOE, PR China References [1] D Maguin, O Adrot, J Ragot, Data reconciliation with uncertain models, ISA Transactions 39 (2000) [2] WY Lee, JM House, DR Shin, Fault diagnosis and temperature sensor recovery for an air-handling unit, ASHARE Transactions I (103) (1997) [3] Y Chen, S Wang, Proceeding The 4th international conference on indoor air quality, Ventilation and energy conservation in buildings, 2001, pp [4] R Dunia, SJ Qin, TF Edger, TJ McAvoy, Identification of faulty sensors using principal component analysis, AICHE Journal 42 (10) (1996) [5] YM Chen, XL Hao, JG Peng, Sensor fault detection and diagnosis in HVAC system, Measurement & Control Technology 21 (11) (2002) 1 4 [6] SJ Qin, R Dunia, Proceeding IFAC dynamic and control of process systems, Determining the number of principal components for best reconstruction, 1998, pp

Energy Conversion and Management

Energy Conversion and Management 51 (2010) 1015 1024 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman Fault detection, diagnosis