STUDY ON FAULT DETECTION AND DIAGNOSIS OF WATER THERMAL STORAGE HVAC SYSTEMS

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1 STUDY O FAULT DETECTIO AD DIAGOSIS OF WATER THERAL STORAGE HVAC SYSTES Song Pan and ingjie Zheng Research Laboratory, SAKO Air Conditioning Co, Ltd. agoya JAPA obuo akahara Deartment of Architecture, Faculty of Engineering,Kanagawa University Yokohama JAPA ABSTRACT When some faults take lace in a thermal storage HVAC system, changing attern of the temerature rofiles of the thermal storage tank is useful to infer where some faults exist. Authors designed some arameters calculated from the temerature rofiles of the thermal storage tank in HVAC system and their Fourier Transform to detect the difference between the normal and faulty state. Further, resent aer shows racticality of two methods of arameter otimization, a differentiation rate increment method and a variable selection method, with an actual alication to a hosital. ITRODUCTIO The thermal storage system has been widely used in Jaan for the sake of ower security, ower demand shift, energy conservation, economy in construction and oeration, and obtaining other advantages. In site of its oularity, there are many cases where the design and/or oeration are imroer. alfunction often takes lace in control strategy in both heat um side and in HVAC side. Therefore, the thermal stotrage system needs aroriate commissioning rocess over lifecycle. Authors have discussed how to detect and diagnose the control malfunctions using characteristic temerature rofiles of the tank obtained from fault simulations [][]. ost imortant thing in this method is to find out otimal arameters corresonding to each object system. The resent aer reorts usability of this method in alication to actual system and two methods of selecting otimal arameters for fault detection and diagnosis are introduced. FAULT DETECTIO AD DIAGOSIS ETHOD () Creating data base ) Data base in normal state After modulating the thermal storage HVAC system well and making sure it is being oerated normally, the water temerature distribution of each tank which comose so-called multi-connected comlete mixing tanks shall be measured every hour to form the data base of temerature rofiles in normal state. ) Data base in various faulty states ethod :Generate various faults in the same system as above and collect data to form data base of temerature rofiles in faulty oeration. ethod :Run the dynamic tye of thermal storage simulation rogram to calculate the temerature of each tank in normal state. After making sure the simulated results almost coincides with the normal data base gathered as above, run the rogram again in various kinds of faulty staes to form the faulty data base. () Selecting otimal arameters ) Analyzing both normal and faulty data in data base with Fourier Transform, the dynamic roerties such as the hase and frequency can be recognized. Two-dimensional Fourier Transform is exressed as equation (). [ F] πk r πl s cos cos C C CC k l CS k l aa xrs S S SC k l SS k l r s πk r πl s sin sin k,, / l,, / < k < / < l < / a a k, / l, / () While, F : Fourier Transform of with k and l for the number of Fourier transform along time and sace. rs : temerature of tanks in two-dimensional real cyclical function of s, the number of tank, and r, time C, S : each cosine and sine arts of., : the number of samles along time axis and tanks connected in a series. ) Using statistical analysis, reliminary arameters are derived from the real temeratures of the tank and their Fourier Transform values. The cluster analysis will be then used ot classify arameters into grous with high correlation coefficient each other, thus

2 reducing to small number of indeendent arameters, which are the candidates of otimal arameters. 3) Generally, the more the number of arameters are, the higher rate of fault detection and diagnosis is exected. However, it is not smart way to use all the arameters. Although each arameter is effective to exlain eculiar hemomena of fault oeration, some other arameters which are in high corelation often lay most art of roles. Therefore, it is necessary to find useful methods for selecting combination of otimal arameters. In the resent aer authors develoed two rograms to otimize arameters and number of dimension, i.e., differentiation rate increment method [3], and variable selection method [4]. The Fig. and Fig. shown later are the calculation flowcharts of the rogram of differentiation rate increment method and variable selection method, resectively. Differentiation rate increment method It is generally understood that the more the number of arameters grows, the smaller the differentiation rate increment would be when a arameter is newly added. Therefore, the differentiation rate increment could be used to distinguish whether newly added arameter is effective or not. If eqution () is tenable,it is useful to add arameter from q to q+r. Judgement standard a is determined by the number of learning data. P (q+r) max -P (q) max <a () While, (q+r) P max (q) and P max are the otimum rate of differentiation for q+r and q dimensions, resectively. variable selection method Generally, the longer D q, ahananobis generalized distance, equation(4), between the average values of arameter vector(y,y,,y q ) of both normal and faulty states, the lower the error differential rate becomes. The F-distribution for freedom(r,-q-r+) could be used to distinguish whether the increment of ahananobis generalized distance caused by adding arameters from q to q+r is just the calculation error or the arameters substantial differentiating effect. When the number of measured data is large, it is said aroriate to make judgement with F standard [5]. q r + Dq+ r Dq F r ( + ) + D ( + ) q (3) Where,,, are the number of normal and faulty data, resectively. Start decide convergence condition,a initialize:k, -calculate detection rates of arameters, P(), I -arrange them in order of magnitude in detection rate -select to arameters in order of magnitude Z,jZ,j()(j) k P i () kk k -calculate detection rates of (-k) arameters in k dimension, -calculate P (k) m,i (m,;,-k) -arrange them in order of magnitude -select to vectors Z k,j {Z (k),,z (k) k }(j) Y P max (k) -P max (-) >a? rint out Z k- { Z (k-),,z (k-) k- } End :condition for judging convergence : number of dimensions : number of vectors to be calculated in k-th dimension- : total number of arameters : detection rate in one dimension using i-th arameter Pm,i(k) : detection rate in k dimensions obtained by combining i-th arameter with the selected m-th vector at stage of k- dimensions Pmaxj(k) (j,): to detection rate in k dimensions vector, arranged in order of magnitude Pmax(k) : detection rate of otimal vector in k dimension Zk,j : a vector consisted of the number of otimal arameters in k dimension Zk(k) : number of k-th arameter in k dimension Fig. Flowchart of otimization rogram for decting arameter with differentiation increment method

3 Start -calculate arameters with learning data -initialize:, Fa -calculate (i) with variance for each arameter when one arameter is used -arrange them in order of magnitude - Fmax()max(Fj()), Z(){P() } j F max () Fa Y + - calculate (i) with ahananobis' generalized distance - arrange them in order of magnitude F max () max( () ), j Z () {P (),,P i () } - F max () Fa Y -calculate FF k (i) with ahananobis' generalized distance -arrange them in order of magnitude FF min () min(ff k () ), k Eliminate P () Z () {} Y FF min () Fa Z (-) {P (-),,P i- (-) } To rint Z (-) End Fa : condition for judging convergence : number of arameter(i~) () FF k : index to evaluate contribution of Pk() in i otimal arameters {P(),,Pk-(),Pk(),,Pi()} on the generalized distance calculated for other i- otimum arameters arameters () FF min : minimum value of FF () k (k,i) i>: the index to evaluate contribution of newly added j-th arameter on the generalized distance calcualted for i- otimal arameters. i: variance of j-th arameters. F () () max : maximum value of (j) () P k : the number of i-th otimum arameter (k) Z () : vector consisting of number of i otimum arameters (), Fig. Flowchart of otimization rogram for decting arameter with variable selection method 3

4 (3) Fault detection/diagnosis with ahananobis generalized distance ) With ahananobis generalized distance based on otimum arameters vector selected, differentiation function for normal and faulty state shall be inut into BES/BOFD comuter as the knowledge data. When arameter vector Y follows normal distribution, ahananobis generalized distance is calculated by equation (4). D ( y y µ σ σ σ T µ ) ( y T [ y y y3 y ] T [ µ µ µ 3 µ ] σ σ σ σ σ σ σ σ σ σ σ σ (4) Generally, if the number of measured data exceeds 5 and largest value of samle variance and covariance of all states is lower than twice of the smallest one, the mean value, variance and covariance may be calculated with measured data. ) The otimal arameter vector calculated with data of instantaneous temerature distribution of the thermal storage tank to be maesured online is then evaluated using ahananobis generalized distance as follows whether the vector is distinguished as normal or fault. The mean values of otimal arameters selected should be calculated first, which are to be the centers of distribution in various states. If all ossible kinds fault data base have been reared beforehand, the state distribution of which center is nearest from the any data is the one that data belongs. Thus all data differentiated, the state of storage oeration is judged whether it is normal or any kind of fault. APPLICATIO TO A REAL SYSTE () Outline of the system and data measured Table and figure 3 show outline of the objective building and simlified diagram of the thermal storage HVAC system of it. The chilled water tank consistes of comlete mixing subtanks. The temerature of each tank and its changing rofiles with time were measured from ay 995 to arch 996. In the early stage of measurements, from ay to July, 995, a fault henomenon was found, which was caused by imroer oeration of the threeway valve V shown in Figure 3, where the suly µ ) V Figure 3 Simlified thermal storage HVAC system diagram Table Outline of the building and HVAC system Site Tokyo Structure R.C. Total area 7, m Stories Six-stories,two-stories underground Use Hosital Heat lant Turbo-refrigerator(3USRT) Boiler(48kg/h) HVAC Thermal Storage tank - - Thermal storage tank AHU+FCU(ward system) AHU(for fresh air)+ Terminal AHU(consulting room) AHU+reheater(oerating room) ulti-connected comlete mixing style subtanks,78m 3 water to the chiller was drawn only from the highest temerature tank. The figure 4 shows temerature rofile of the tank and Fourier transform of it during normal satate, while Figure 5 shows those in faulty state. As seen in these figures, temerature in the subtank of the lowtemerature side is ket low during normal oeration, while it becomes higher in faulty oeration. The temerature variation is seen more frequent in normal oeration along the time axis, as comared to that in faulty oeration. It means that higher frequency comonent of Fourier transform C k C l is larger in normal state than that in fault state. Therefore, the maximum value C C becomes smaller in normal state than that in fault state. From the measured data it was recognized that almost no chilled water was used between October 8, 995 and Aril 4, 996, so that the data during this eriod are useless. As the result, data for 65 days between ay to July, 995 were assumed as faulty and data for 57 days between July and Set. 3, 995 lus those between Aril 5 and Set. 3, 996 were V V3 4

5 5 4 3 / Tim e / Sace P in ( j, i / ) (5) ) Average value of daily maximum temerature difference in each tank (P) P j ( max i max i i, ax ( min i ) / (6) ), min i in ( i, ) Figure 4 Temerature rofile of tank and its Fourier transformation values in normal state(july 6,995) / Tim e / Sace Figure 5 Temerature rofile of tank and its Fourier transformation values in faulty state(july 5,995) assumed as normal in this study on fault detection and diagnosis, FDD, for actual system. () Design arameters for FDD! " ) inimum value of daily average temerature in each tank (P) 3) Variance of average temerature of all tanks over all time (P3) P3 / / / (7) i j i j 4) aximum value of average temerature of all tanks over all time (P4) P 4 ax, i j / (8) 5) inimum value of average temerature of all tanks over all time (P5) P 5 in, i j / (9) 6) Difference between maximum and minimum value of average temerature of all tanks over all time (P6) P6 ax /, in, i i j j / () 7) Variance of maximum temerature differences of all tanks at each time (P7) P 7 ( ) / / mnj mnj () i i mnj ax ( ) in ( ) j, j, 8) aximum value of maximum temerature differences of all tanks at each time (P8) P8 ax ax i, j, ( ) in( ) () j, 9) inimum value of maximum temerature differences of all tanks at each time (P9) P9 in ax i, j, ( ) in( ) (3) j, ) Difference between maximum and minimum values of maximum temerature differences of all tanks at each time (P) 5

6 P ax ax i, j, in i, ax j, ( ) ( ) in j, ( ) in ( ) (4 ) j, ) Sum of Fourier transformation (P) P k l F ) orme F of Fourier transformation (P) P k l F (5 ) (6) 3) aximum value in C k C l comonents of Fourier transformation (P3) ( F ) k, l, (7) P3 ax 4) aximum value in C k S l comonents of Fourier transformation (P4) ( F ) k, l, (8) P4 ax 5) aximum value in S k C l comonents of Fourier transformation (P5) ( F ) k, l, (9) P5 ax 6) aximum value in S k S l comonents of Fourier transformation (P6) ( F ) k, l, ( ) P6 ax 7) Average value of maximums in each comonent of Fourier transformation (P7) ( P3 + P4 + P5 P6) / 4 ( ) P 7 + 8) Sum of average value of cycles which exceed threshold value b (P8) P8 k k k l k k Fl ( k + l) Fl / > F b Fl F b k l l k < l l ( ) ( ) l l < ( ) 9) orme Fl of average value of cycles which exceed threshold value b (P9) P9 k k k l k k Fl ( k + l) Fl / > F b Fl F b k l l l k < l l l < ( ) ( ) ( 3) ) Frequency for the magnitude of cycles to exceed threshold value b (P) Fl F > b P Fl (4) k l Fl F b ) aximum value of cycles varied along time axis which exceed threshold value b (P) P ax ( Fa ) ( 5 ) k k > F > b Fa k k < F b ) aximum value of cycles varied along sace axis which exceed threshold value b (P) P ax ( Fb ) ( 6 ) l l > F > b Fb l l < F b 3) Thermal quantity of storage tank (P3) P3 ( i +, j j, i ) ( i +, j j, i ) < ( 7) j i i 4) Thermal quantity of heat dissiated (P4) P4 ( ) ( ) ( ) +,, +,, 8 i j j i i j j i j i i (3) Selecting otimal detecting arameters Table and Table 3 show the rocedure of selecting otimal arameters for FDD with both variable selection method and differentiation rate increment method,resectively. The FF in Table is an index for releasing useless arameters, with which the degree of contribution of each arameter on the other arameters is evaluated. In order to test if the result is otimal, another method, exhaustion method[3], which needs much more time for calculation but more correct, was also alied. The table 4 shows detecting rate about the data for 995 and diagnosing rate about the data for 996 using three otimal detecting arameters selected by the above-mentioned rocedure. It also comares the calculation time with a mainframe high erformance comuter. It should be noted that the fault detection and diagnosis model is formed with normal and faulty data for 995, that detecting rate means a roortion of faulty data successfully cllasified at the data eriod when the model was established, i.e. 995 in this case, and that diagnosing rate is a roortion of normal data successfully classified at the following data time eriod, i.e. 996 in this case. The table 4 illustrates the following. ) Detecting rate and diagnosing rate calculated with arameter vector (P,P3) selected by differentiation rate increment method is a bit higher than that 6

7 Table Calculation rocedure of variable selection method One dimension : arameter () Two dimension : P, arameter 7,,7 () () FF k 55.. Three dimension : P+7, arameter 7+, +,7 +7, (3) Four dimension : (3) FF k P+7+, arameter 7++9, ++9,7 +7+9, +7+,9 (4) (4) FF k Five dimension (end): P+7++9, (5) Table 3 Calculation rocedure of differentiation rate increment method One dimension arameter P P5 P8 P3 P9 P4 P P P differentiation rate Two dimension arameter P+P3 P+P7 P+P4 P+P4 P+P P+P8 differentiation rate differentiation rate increment Three dimension (end) arameter P+P3+P P+P3+P9 P+P3+P4 P+P3+P6 differentiation rate differentiation rate increment.... Table 4 Comarison of three otimum methods Detection/ Diagnosis 5//7,995 4/59/3,996 Calculation* ethod Parameter umber Differentiation rate umber Diagnosis rate time [minutes] Variable selection method P,P,P9,P Differentiation rate P,P increment method Exhaustion method P,P,P3,P * with a high erformance mainframe comuter calculated with arameter vector (P,P,P9,P7) selected by variable selection method. It is because, in case of variable selection method, the degree of contribution for newly added arameter to the otimal vector, merely ays attention to the one which was selected at the receding ste. It means that some other combinations of arameters, which had been released at the receding ste as non-otimal due to lower detecting rate, may become more otimal by adding new arameter. 7

8 ) Detecting rate and diagnosing rate of arameter vector determined by differentiation rate increment method is a little lower than the otimal arameter vector selected by exhaustion method, however, the calculation time of the former is far shorter than the latter, i.e. two minutes vs. sixty minutes, so that the differentiation rate increment method is considered more ractical. 3) The diagnosing rate for the data for 996 with the two arameter vectors, selected by differentiation rate increment method and exhaustion method, is only a little smaller than the detecting rate for learning data of 995. It means that the differnce of diagnosing rate is little between the two models in site of the difference of cooling load attern between two years, once the FDD model is roerly identified.. (4) Discussion on FDD maing for a case Fig.6 shows the detecting result for 996 data with arameter (P,P3). The ovals shown are boundaries of.5 times in ahananobis generized distances from the centers of both normal and fault data grous for 995. Figure 6 Fault detection/diagnosis maing with arameter (P,P3) ) While most of arameter values calculated with normal data for 996 are in the overlaing range between normal and faulty state sace ovals which were constructed with data for 995, most of them are correctly classified as the normal, for they are in the closest distance from the center of the normal sace. That means, the arameter vector (P,P3) could exress the difference of temerature variation roerty in low-temerature between normal state and faulty one. ) A few vector lots calculated with normal data for 996 disribute aart from normal and faulty state sace. It may be because some other abnormal henmena other than a fault in the resent attention, the fault in three way valve in suction line of heat um have taken lace. COCLUSIO The summary of the resent fault detection/diagnosis methods for alication to actual HVAC thermal storage system is as follows. ) In order to aly resent methods effectively, it is necessary to reare database for each tye of normal and faulty states and to design arameters roerly for each state. ) The differentiation rate increment method may not be the best method of choosing otimal arameters, but it seems to be an otimal method considering that the detecting and diagnosing rate is sufficiently high and that calculation time is much shorter, comared with more correct but time-consuming exhaustion method. 3) The most effective arameters can be selected automatically by the resent fault detection and diagnosis methods, however, it should be noted that each state sace is classified statistically and that errors are naturally robable for fault detection and diagnosis. ACKOWLEDGEET The authors acknowledge r. iyasaka, Yamatake Buiding Systems Co. Ltd. for his efforts in rearing temerature data, and Prof. Sagara, ie University and FDD Working Grou members of the Thermal Storage Otimizaion Committee in SHASE. REFERECES []ingjie Zheng and obuo akaharastudy on Fault Detection and Diagnosis of Thermal Storage Control Systems with Pattern Recognition, Transactions of the Society of Heating, Air-Conditioning and Sanitary Engineers of Jaano.63, Oct., 996 []obuo akahara, ingjie Zheng and Yoshihiko ishitani: Simulation and Fault Detection of the Thermal Storage Systems, Proceedings of BUIDIG SIULATIO '87,Set.,997, Prague [3] ingjie Zheng, Song Pan and obuo akahara: Study on Fault Detection of Thermal Storage System with Pattern Recognition (art 5 Online Detecting ethod and Otimization of Detecting Vector). Proceedings of AIJ Academic eeting, 998, Fukuoka, in Jaanese [4] Song Pan,ingjie Zheng and obuo akahara: Study on Fault Detection of Thermal Storage System with Pattern Recognition (art 4 Develoment of Otimum Program for Detecting Parameter), Proceedings of AIJ Tokai Chater Academic eeting, 998, agoya, in Jaanese [5]Takaiti Sugiyama: Elementary Course of altile Variable Analysis, 983, Asakusa Bookstore, in Jaanese. 8