2000-2001 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Chen, YM

Wang, SW

2000-2001 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishedVoR allowe

PolyU Institutional Repository

　? 27?　? 5? 湖　南　大　学　学　报　 (自然科学版 ) Vo1. 27, No. 5　　 2000? 10? 　 Journal o f Hunan Univ ersity( Na tural Sciences Edition) Oct. 2000????: 1000-2472( 2000) 05-0071-07????????????????? 陈友明 1 , 王盛卫 2( 1.?????????? ,?? ??　 410082; 2.????????????? ,?? ?? )　　?　?: 基于墙体热传导的理论频率响应提出了计算多层墙体响应系数的频域回归方法 . 首先在所要关心的频率范围内计算出总的传导矩阵的频率响应 ;然后求解线性方程组得到墙体内外表面吸热及传热的简单的多项式 s-传递函数 ,该多项式传递函数与双曲型 s-传递函数在频率特性上是等价的 ;最后由多项式传递函数计算出墙体的响应系数 . 实例验证表明 ,该方法非常简单高效 ,计算精度高、速度快 .???:频域回归方法 ;多层墙体 ;响应系数?????: TU111　　　　　　　　?????:　 AFrequency Domain Reg ression Method to CalculateResponse Factors of M ul tilayer WallsCHEN You-ming1 , W ANG Sheng-wei2( 1. Co llege o f Civil Engineering , Hunan Univ , Chang sha　 410082, China;2. Dept o f Building Se rv ices Engineering , The Hong Kong Poly technic Univ ersity,Kow loon, Hong Kong , SAR, China )　　 Abstract: Frequency domain reg ression( FDR) method is developed to calcula te theresponse factors of multilay er w alls in this paper. This method is based on thetheo retical f requency cha racteristics of transient heat conduction through a buildingconstruction to estima te a simple po lyminial s-transfer function. The simple polynomials-transfer function is completely equivalent to the hyperbolic s-transfer function o f thew all in terms o f f requency characteristics. Fi rst , the f requency characteristics of the totalt ransmission matrix are calculated w ithin the f requency range concerned. Then, a set oflinea r equations is solv ed to yield a simple polynomial s-transfer function fo r internal ,cross and ex ternal hea t conduction, respectiv ely. Final ly, the w all response facto rs areobtained simply by applying inverse Laplace t ransfo rms on the polynomia l s-transferfunction. The compa risons and validations show that this method is v ery simple and ????: 2000-01-20????:???????????? ( 59578004) ;?????????? ( G. S869)????:??? ( 1966- ) ,? ,????? ,??????? ,?? .ef ficient , andhas high accuracy and fast computa tiv e speed.Key words: FDR method; mul tilayer wall; response factors??????????????、?????? ,?????????????????????????????????? ( EMCS)??????????????? [1, 2 ] . ?????? (?????? )?????????? HV AC????????????? . ??????????????????????? . ?????????????????? HVAC?????????? ,?????????? . ????????????????????????? ,????????????? .?????? z-????? [ 3, 4]?????????????????????????????? . ???????? z-????????? . ??????????????????????? . ??????????????????? . ?????????????????????、????、?????? . ?? , Hi t tle??????????????????????? [ 5] . ?? ,???? [6 ]? Davies [7 ]????????????????????????? . ???????????????????? ,?????? . ?????????????????? ,???????????? .????????????????????????????????? ?????? .1　?????????????????????????????????? ,????????????? .????????????? . ??????????????????????????????????????????????? ,????:　　　　　　 Ti (s )qi (s )=A (s ) B (s )C (s ) D (s )To (s )qo (s ). ( 1)?? , T??? ; q??????? ; A ,B ,C? D?????????????? ; s????? ;?? i? o????????? . ?????????? n??? ,?????????????????:A (s ) B (s )C (s ) D (s )=A i (s ) B i (s )Ci (s ) Di (s )A1 (s ) B 1 (s )C1 (s ) D1 (s )… An (s ) Bn (s )Cn (s ) Dn (s )Ao (s ) Bo (s )Co (s ) Do (s )( 2)?????????????????????????:　　　　　　 Ak= Dk= cosh (Lk s /amk ) , ( 3)　　　　　　 Bk= Rk sinh(Lk s /amk ) /( Lk s /amk ) , ( 4)　　　　　　Ck= Lk s /amk /sinh (Lk s /amk ) /Rk . ( 5)?? amk= (λk /dkCp k ) ,λk ,dk ,Cp k ,Rk ? Lk ?????? k??????、???? ( W /m72　　　　　　　　　　　　　　?????? (????? )　　　　　　　　　　　　　 2000?· K)、?? ( kg /m3 )、??? ( J/ ( kg· K) )、?? ( m2 K /W )??? ( m ) .? ( 1)????????　　　　　　 qi (s )qo (s )=GX (s ) - GY (s )GY (s ) - GZ (s )Ti (s )To (s ). ( 6)?? GX (s ) , GZ (s )? GY (s )???????、??? s-??????? s-?????? .???????????? s-???? .?? A (s )D(s ) - C (s )B (s )= 1,?????????　　　　　　 GX (s )= A (s ) /B (s ) , ( 7)　　　　　　 GY (s )= 1 /B (s ) , ( 8)　　　　　　 GZ (s )= D(s ) /B (s ) . ( 9)? s= jk( j= - 1)??? ( 7)～ ( 9) ,???????? GX ( jk)、 GZ ( jk)? GY ( jk) ,??????、??????????????? [8 ] ,???? G( jk) .2　?????? s-??????????? ,???????????????????? ,??????????????? . ?????? ,????? (??????????? )????? (????????? )???????????????? .?????????? s-????????????????????????? ,??????? s-??????????????? s-???? . ????? s-????????????????????????????? . ???????????????? s-??????? .???????????? s?????? s-????　　　　　　 G(s )= U0+ U1s+ U2s2+ …+ Ursr1+ T1s+ T2s2+ …+ Tm sm = B (s )1+ A (s ) , ( 10)?? A (s )= T1s+ T2s2+ …+ Tm sm; B (s )= U0+ U1s+ U2s2+ …+ Ursr;Ti?Ui?????? ;G(s )????? s-???? . ? s= jk,??? s-??????????　　　　　　 G( jk)= U0+ U1 jk+ U2 ( jk) 2+ …+ Ur ( jk) r1+ T1 jk+ T2 ( jk) 2+ …+ Tm ( jk)m = B ( jk)1+ A ( jk) . ( 11)????????????? N???? (k1 ,k2 ,… ,kN ) ,?? k???? kk ,??? G( jk)???????????? ,?　　　　　　 G( jkk )= Gk= Pk+ jQk . ( 12)???? ( 13)??????? ,????? ( 14)?? .　　　 J (θ)= ∑Nk= 1|B ( jkk ) - G( jkk ) [1+ A ( jkk ) ]|2= ∑Nk= 1|B ( jkk ) - Gk ( jkk ) - Gk|2 , ( 13)　　　　　　θT= [U0　U1　U2　U3　U4　…　T1　T2　T3　T4　… ]. ( 14)?????? θ^ ??????? ,? J (θ)|θ^ = min,??????? ( 15)?????73　? 5?　　　　　　　????:????????????????? 　　　　　　　　　?? ,?? ( 16)? ( 17)?????? . ? θ^??? ( 18)?? .　　　　　　 Vi=∑Nk= 1kik ,　　　Si= ∑Nk= 1kik PkW i= ∑Nk= 1kik Qk ,　　Ui= ∑Nk= 1kik ( P2k+ Q2k ), ( 15)　　　Γ=V0 0 - V2 0 V4 … W 1 S2 - W 3 - S4 W 5 …0 V2 0 - V4 0 … - S2 W3 S4 - W5 - S6 …- V2 0 V4 0 - V6 … - W 3 - S4 W 5 S6 - W 7 …0 - V4 0 V6 0 … S4 - W5 - S6 W7 S8 …V4 0 - V6 0 V8 … W 5 S6 - W 7 - S8 W 9 …  W1 - S2 - W3 S4 W5 … U2 0 - U4 0 U6 …S2 W 3 - S4 - W 5 S6 … 0 U4 0 U6 0 …- W3 S4 W5 - S6 - W7 … - U4 0 U6 0 - U8 …- S4 - W 5 S6 W 7 - S8 … 0 - U6 0 U8 0 …W5 - S6 - W7 S8 W9 … U6 0 - U8 0 U10 … ,( 16)　　　ΘT= [S0　W1　 - S2　 - W 3　S4　…　 0　U2　 0　U4　 0　… ] , ( 17)　　　θ^ = Γ- 1Θ. ( 18)??? θ^?????? s-???????U^ 0～ U^ r? T^ 1～ T^ m . ???????????? ( FDR)?? . FDR???????????? s-????????????? s-???? . ? GX ( jk) ,GZ ( jk)? GY ( jk)?? G( jk) ,???????????????????????? s-???? .3　??????????????????? G(s )??? 1+ A (s )???? m???? ( - si , i= 1, 2,… ,m ) (???? s-??????? ) ,?? si???? . t= 0??????????:???????? t < 0????????????????? ,?????????? t= 0???ZKh- 1????? . ???????????? (Z= 1)??? ,????? qn 0 ( t )(? ,??? s-???? GY (s )??? )????　　　　　　qn0 ( t )= L- 1 (GY (s )s2)= L- 1 (B (s )s2 ( 1+ A (s ) ))= Kt+ ∑mi= 1Wi ( 1 - e- si t ) . ( 19)?? K????????? ;Wi ( i= 1, 2,… ,m )? GY (s ) /s2?? i?????? ,??????　　　　　　Wi= - B ( - si ) / [s2i A′( - si ) ]. ( 20)74　　　　　　　　　　　　　　?????? (????? )　　　　　　　　　　　　　 2000?t= 0??????????????? t= - Δf?????????、?? t= 0??????Z= - 2???????? t= Δf??????????? . ??????????????????????:　　　　　　　Qn0 ( t )= qn 0 ( t -Δf)- 2qn 0 ( t )+ qn 0 ( t+ Δf) ( 21)???? Y ( 0) , Y ( 1) , Y ( 2) ,…?? Qn 0 ( t )? t= 0Δf, 1Δf, 2Δf,…???? (?? Δf?? 1?? ) . ??? ,????? Y ( 0)???????????????? t= 0???? ,????????????????? .????????? (??????? )????????????????? 0℃? ,?? i??????????????????????　　　　　　qn0, i= Y ( 0) T0, i+ Y ( 1) T0, i- 1+ …+ Y (k ) T0, i- k+ … . ( 22)???? n?????????? n?????????????? ,?? 0??????? 1???????????? .???????? ,??????????????????????????????? ,???????????????????????????? . ?? ,??????????????? ,???????、?? .?? ,?????????????? z -???? ,????? .4　????????????????????????????? .Step1: ??????????λ,d,Cp ,?? L ,???????????? R0? Ri .?????????? [10- n1 , 10- n 2 ]????? N . n1 , n2? N?????? 10, 3?9(n1 - n2 ) .Step2: ?????????????????? N ???? (?: kk =10- n 1+ (k- 1) (n1- n2) /( N - 1) (k= 1, 2,… , N ) ) . ????kk (k= 1, 2,… , N ) ,? s= jkk??? ( 3)～ ( 5)??????????? ,???? ( 2)???????????????????? A ( jkk ) , B ( jkk )? D ( jkk ) ,???? ( 7)～ ( 9)??????????? GX ( jkk ) ,GY ( jkk )? GZ ( jkk ) .Step3: ????? 1+ A (s )? B (s )??? m? r ,???? 5.? GY ( jkk )?? Gk ,?? ( 19)?? GY (s )???Ti ( i= 1, 2,… ,m )?Ui ( i= 0, 1, 2,… , r ) .Step4:? m????? 1+ A (s )= 0???? ,?? ( 20)????????Wi ( i= 1,2,… ,m ) ,???? ( 21)?????? Y (k ) .??? ,? GX ( jk)? GZ ( jk)???????????? z -?????? . ???????????? ,????????????????????????????????? ,?? ,?????????、??????? .75　? 5?　　　　　　　????:????????????????? 　　　　　　　　　5　?????? FDR?????????????????????????? ,??????????????????????????? . ????????????????? FDR?? ,???????????? .????? Haghighat[ 6]????????????????????????????? Y (k ) (k= 0, 1, 2, 3,… ) .??????????????????????? ,????? SI?????? 1? . ? FDR?????????????? s-??????:GX (s)=- 4. 90351E - 5s5+ 2. 35096E- 7s4- 6. 99650E- 10s3+ 1. 38768E- 12s2 - 1. 77507E - 15s+ 1. 13961E - 18s5+ 3. 19462E - 3s4+ 3. 59719E - 6s3+ 1. 49979E - 9s2+ 1. 21286E- 13s+ 2. 30188E- 18???????????? Y (k ) . ?????????????? 2????? , FDR???????????? .? 1　?????????　　? L /m λ/ (Wm- 1K- 1 ) d/( kg m- 3) C p / ( Jkg- 1K- 1 ) R / (m2KW- 1)????? 0. 050 0??? 0. 089 1. 730 0 2 235 1 106 0. 051 4??? 0. 127 0. 074 4 24 992 1. 707 0??? 0. 089 1. 730 0 2 235 1 106 0. 051 4????? 0. 160 0　　　　? 2　?????????? Y ( k )???　　　　Wm- 2K- 1k FDR?? ????? ?????0 0. 000 015 21 0. 000 017 71 0. 000 015 491 0. 001 634 41 0. 001 640 78 0. 001 645 412 0. 008 492 18 0. 008 526 82 0. 008 528 843 0. 016 008 25 0. 016 063 51 0. 016 058 044 0. 021 272 37 0. 021 328 61 0. 021 324 825 0. 024 533 70 0. 024 581 89 0. 024 583 766 0. 026 300 43 0. 026 341 17 0. 026 345 357 0. 026 978 39 0. 027 014 26 0. 027 016 818 0. 026 876 82 0. 026 909 51 0. 026 908 279 0. 026 229 75 0. 026 257 74 0. 026 254 2910 0. 025 213 28 0. 025 233 50 0. 025 231 3111 0. 023 959 04 0. 023 970 17 0. 023 971 1812 0. 022 564 62 0. 022 568 61 0. 022 571 5513 0. 021 101 58 0. 021 102 07 0. 021 104 0214 0. 019 621 66 0. 019 621 03 0. 019 620 3015 0. 018 161 59 0. 018 159 49 0. 018 157 0816 0. 016 746 74 0. 016 741 30 0. 016 739 6717 0. 015 393 96 0. 015 384 25 0. 015 384 8618 0. 014 113 77 0. 014 101 04 0. 014 103 1019 0. 012 912 01 0. 012 898 71 0. 012 900 1776　　　　　　　　　　　　　　?????? (????? )　　　　　　　　　　　　　 2000?6　?　??????????????????????? . ?????????????????????????? ,?????????????????????????????? . ????????????????????? . ????????????????? . ????????: FDR??????????????????s-???????????? s-???? ;? FDR??????????????????????????? .??????????? ,?????????????????? ,???????????? .?? ,???? FDR????????????????? ;??????? ,??????????? HV AC?????????????? .????:[ 1 ]　 KUSUDA T. Ear ly histor y and future prospects o f building s sy stem sim ulation [ C]. Proceedings ofBuilding simulation '99, Volume I, Kyo to , Japan, Sept, 1999.[ 2 ]　W ANG S W. Dynamic Simula tion of a building V AV Air-conditioning sy stem and evalua tion ofEMCS online contrlol stra tegies [ J]. Building and Environment, 1999, 34: 681- 705.[ 3]　 STEPHEN SON D G, MITALAS G P. Coo ling load calculations by th ermal r esponse fac to r s [ J].ASHRAE Transactions, 1967, 73(Ⅲ ): 1. 1- 1. 7.[ 4 ]　 S TEPHEN SON D G, M IT ALAS G P. Ca lcula tion of heat conduction transfer functions fo rmultilay er slabs [ J]. ASHRAE Transactions, 1971, 77(Ⅱ ): 117- 126.[ 5 ]　 HITTLE D C, BISHOP R. An improved ro o t-finding procedure for use in ca lcula ting tr ansient heatflow th rough multila yer slabs [ J]. Int J Hea t Mass T ransfer , 1983, 26( 1): 1685- 1693.[ 6]　 OUYANG K, HAGHIGHAT F. A procedure fo r calcula ting therma l r esponse factor s o f multilay erwa lls-state-space method [ J]. Building and Env ironment, 1991, 26( 2): 370- 395.[ 7]　 DAV IES M G. Wall tr ansient heat flow using tim e-domain ana ly sis [ J]. Building and Environment,1997, 32( 5): 427- 446.[ 8 ]　 CHEN Y M , CHEN Z K. A neural-netw o rk-based expe rimental technique fo r dete rmining z-transfer function coefficients o f a building envelope [ J]. Building and Engvironment, 2000, 35( 3):181- 189.77　? 5?　　　　　　　????:????????????????? 　　　　　　　　　

Frequency domain regression method to calculate response factors of multilayer walls

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