Characterization of Impact Test Response of PCCP with System Identification Approaches

Transcription

1 7th World Conference on Nondestructive Testing, Oct 2008, Shnghi, Chin Chrcteriztion of Impct Test Response of PCCP with System Identifiction Approches Astrct Zheng LIU, Alex WANG, nd Dennis KRYS NRC Institute for Reserch in Construction 200 Montrel Rod, Building M-20, Ottw, Ontrio KA 0R6 Cnd Tel: , Fx: E-mil: We: In this study, impct test ws crried out to ssess the condition of prestressed concrete cylinder pipe (PCCP). The impulse response of the test is modeled with system identifiction pproches. The model of the impulse response cn e further used to chrcterize the deteriortion of PCCP. This pper presents preliminry results on the comprison of different models for the response of impct test for the purpose of evluting PCCP. Keywords: impct test, prestressed concrete cylinder pipe, system identifiction, feture extrction.. Introduction Prestressed concrete cylinder pipe (PCCP) is widely used throughout the world. In the USA nd Cnd, there re n estimted 30,000 miles of this product instlled []. The instlled PCCP will undergo vrious deteriortion stges nd there re numer of resons tht cuse the filure of PCCP pipelines. The deteriortion my include the corrosion nd rekge of wires, loss of wire prestress, delmintion of the outer mortr, delmintion of steel cylinder nd concrete core interfce, crck growth nd strength loss of concrete core. The finl stge comes the ctstrophic filure [2]. Non-destructive inspection/testing (NDI/NDT) techniques provide tools for pipe inspection nd condition ssessment [3]. Different technicl solutions hve een proposed so fr. However, none of them cn revel ll the informtion out the pipe t ll stges. The comintion of multiple NDI techniques could e potentil solution. Impct test, which is lso known s impulse response test, implements fst evlution of PCCP structures nd hs een pplied to lrge concrete structure, like floor sls, pvements, ridge decks, etc. [4, 5] The impct test uses ruer-tipped hmmer to send low-strin impct propgting stress wves to the PCCP. The response of the PCCP is mesured y ccelerometers ttched to the pipe surfce nd is chrcterized y trnsfer function, which descries dynmic system with the rtio of response nd impct force spectrum. When ny discontinuities (crcks/flws) re present in the pipe, there will e n ssocited reduction in spectrl mplitude [6]. Therefore, the trnsfer function contins the informtion relted to the structures. However, the use of such informtion for quntittive nlysis or chrcteriztion of PCCP hs not een reported so fr. In this study, we evluted different system identifiction pproches to model the response of PCCP to the impulse generted y ruer-tipped hmmer. The system prmeters determined y the dynmic model cn e used chrcterize pipe condition. Different models re compred sed on the ccurcy. Preliminry experimentl results re presented.

2 2. Impct Test for PCCP The impct test mesures the response of the tested mteril to the impct. A 98cm long PCCP segment s shown in Figure ws used nd the setup for the impct test is illustrted. The inside dimeter of the PCCP segment is out 42cm. Four ccelerometers were plced t sttions A, B, C, nd D. The impct force ws pplied to the edge of pipe. Three different impct loctions re mrked in Figure with numers, 2, nd 3. A WveSurfer oscilloscope ws used to record the impct force nd the redings from the four ccelerometers. The smpling rte in the following experiments ws set s 5ks/s. Figure. The impct test of PCCP. 3. Modeling with System Identifiction Approches Dynmic models corresponding to the four loctions (A to D) cn e uilt from the mesured dt with system identifiction pproches. Four models were considered in this study. These include ) liner model, 2) uto-regressive exogenous input model, 3) lck-ox stte-spce model, nd 4) Hmmerstein-Wiener Model. The detiled theoreticl descriptions of the these methods re ville in the literture [7]. 3. Liner Model Using Steiglite-McBride Itertion The first model is to find n IIR (infinite impulse response) filter to descrie the time-domin impulse response. This prmetric model is implemented with Steiglitz-McBride itertion lgorithm, which minimizes the error etween the predicted output nd the oserved output [8]. The trnsfer function is written s: H ( z) B = A ( z) ( z) = () + ( 2) z + L+ ( n + ) z () + ( 2) z + L+ ( n + ) z where () i nd () i re the corresponding coefficient ( i =,2, L, + ; j =,2, L, + ) of B ( z) nd A ( z). The coefficients of this trnsfer function cn e used to model the response of the test. In our ppliction, we set = 4 nd = 3 respectively. 3.2 Auto-Regressive Exogenous Input Model Prmetric modeling is to minimize the model's simulted output nd the mesured output. A prmetric model cn e expressed with difference equtions. Auto-Regressive exogenous input (ARX) model is commonly used for modeling dynmic systems [7]. The eqution for ARX cn e written s: y () t + y( t ) + + y( t n ) = u( t n ) + + u( t n n + ) e( t) n k L n k + L (2) ()

3 where y () t is the output signl t time t ; ( t ) u n k is the input signl t time nk e is the noise; n nd n re the model prmeters; n nd n indicte the order of the respective polynomils nd n k is time dely from input to output. Eqution (2) cn e written s: ()() z y t B()( z u t n + ) e() t t ; ( t) A = k + (3) where there re: A ( z n ) z z = + + L+ n B (4) ( z n ) z z = + L+ n (5) A lest-squres method tht uses QR-fctoriztion for overdetermined liner equtions is pplied to estimte the prmeters of the ARX model [7]. The e ( t) is ssumed to e white noise. In the experiment, n nd n were set s 4 nd 3 respectively. 3.3 Blck-Box Stte-Spce Models In stte-spce model, system is chrcterized with stte vriles in set of first-order differentil equtions. The generl stte-spce model structure is: ( t ) = Ax() t + Bu() t Ke() t x + + (6) y () t Cx() t + Du( t) + e( t) where y () t represents the output t time t, u ( t) represents the input, ( t) () t = (7) x is the stte vlue, nd e is white noise. The mtrices A, B, C, D, nd K re the stte-spce mtrices. A nonitertive suspce method is used to estimte the stte-spce model [7]. The order of the model ws estimted s four. 3.4 Hmmerstein-Wiener Model A Hmmerstein-Wiener (HW) model consists of one or two sttic nonliner locks nd liner lock s illustrted in Figure 2 [7]. Figure 2. The digrm of Hmmerstein-Wiener model. The HW model is descried y the equtions elow: () t f ( u() t ) B () ( q) t w() t F( q) () t h( x() t ) w = (8) x = (9) y = (0)

4 where the input nd output re ( t) correspond to the input nd output nonlinerities. ( t) F ( q) re polynomils in the ckwrd shift opertor [0]. u nd ( t) w nd x ( t) re internl vriles. ( q) y respectively. Nonliner function f nd h B nd 4. Experimentl Results In this study, we used the dt sets otined t the 90º (loction ) with smpling rte of 5kHz. The pulse pplied to the PCCP nd its spectrum re shown in Figure 3. The test ws pplied twice. The first set of the dt ws used to estimte the models while the second set of dt ws used to vlidte the models. () Time-domin plot. () Spectrum of (). Figure 3. The pulse pplied to PCCP t loction (). Figure 4 shows the echo signl nd spectrum plot t loction B. It is oserved from Figure 4() tht pek hppens t 30Hz. This is from the pipe support [9]. Therefore, FIR (finite impulse response) high-pss filter is designed to filter the echo signl. The cutoff frequency is set t 200Hz. The filtered signl nd its spectrum plot re given in Figure 4(c) nd 4(d) respectively. The filtered signl is used in model estimtion. We used the lgorithms presented in section 3, which re implemented in Mtl nd its system identifiction tooloxes to uild the models from mesurement dt. Two sets of mesured dt cquired t loction B were used. The percentge of the output vrition is computed s [0] : ( yˆ y ) 2 i i i fit( %) = 00 ( ) () 2 y i i yi where y i is the i th mesured vlue nd ŷ i is the i th computed vlue from the model. The verge of the mesurement is y. A perfect model gives result of 00 %. Tle shows the results of four selected models nd Figure 5 gives the corresponding outputs of the models. The Hmmerstein-Wiener model chieved the est result.

5 () Time-domin response. () Spectrum of (). (c) High-pss filtered time-domin response. (d) Spectrum of (c). Figure 4. The impct test results cquired t loction (B). As illustrted in Figure 2, there re two non-liner locks in HW model. In the experiment, we used ded-zone nd sturtion nonlinerity estimtor for the input nd output respectively. However, the sturtion is not ovious in the ctul response in Figure 5(), lthough such configurtion gives etter result in term of the output vrition. The output vrition my not e the only criterion to evlute the performnce of the proposed models. Tle. The evlution of the estimted models with fitting rte. SI method Liner model ARX model Blck-ox stte spce model Hmmerstein- Wiener model Fit (%)

6 () Time-domin response of the second test. () The simulted outputs from different models. Figure 5. Originl response () nd model outputs ().

7 5. Summry In this pper, we presented the results of pplying system identifiction pproches to model the impct test of PCCP. Among the selected models, Hmmerstein-Wiener model chieved the est result. The deteriortion of PCCP is complicted nd vries t different stges. The cquired response signl is ffected y numer of fctors even in lortory environment. The model prmeters my reflect the deteriortion t different stges. The most prominent fctor needs to e identified. How system prmeters chnge with the deteriortion is not cler yet. A strightforwrd method to identify the deteriortion of PCCP is through compring the signture with reference. To fully chrcterize the condition of PCCP, multiple-site modeling remins topic for our future reserch. Reference: [] W. Worthington. "Perspective on Prestressed Concrete Cylinder Pipe," Jnury, 2008; [2] B. J. Mergels, D. L. Atherton, nd X. Kong, NDE Inspection of PCCP Using Remote Field Eddy Current Trnsformer Coupling, in Proceedings of ASCE Pipeline Conference: Advnces in Pipeline Engineering nd Construction, Sn Diego, Cliforni, USA, 200, pp [3] B. Rjni, nd Y. Kleiner, Non-destructive Inspection Techniques to Determine Structurl Distress Indictors in Wter Mins, in Proceedings of Evlution nd Control of Wter Loss in Urn Wter Networks, Vlenci, Spin, 2004, pp [4] W. D. Zhu, nd B. H. Emory, On Simple Impct Test Method for Accurte Mesurement of Mteril Properties, Journl of Sound nd Virtion, vol. 287, pp , [5] Y. H. Zheng, K. E. Ng, nd J. Wei, "Evlution of Concrete Structures y Advnced Nondestructive Test Methods-Impct Echo Test, Impulse Response Test nd Rdr Survey." [6] C. C. Ferrro, Advnced Nondestructive Monitoring nd Evlution of Dmge in Concrete Mterils, Mster Thesis, University of Florid, [7] L. Ljung, System Identifiction: Theory for the User, Englewood Cliffs, New Jersey: Prentice-Hll, Inc., 987. [8] K. Steiglitz, nd L. E. McBride, A Technique for the Identifiction of Liner Systems, IEEE Trnsctions on Automtic Control, vol. 0, pp , Octoer, 965. [9] A. Wng, Z. Liu, nd D. Krys, PCCP Impct Test Report, Technicl Report, Institute for Reserch in Construction, Ntionl Reserch Council Cnd, Ottw, Ontrio, Cnd, [0] L. Ljung, "System Identifiction Toolox 7 User's Guide," The MthWorks, 2007.