27ƒ 6A Á 2007 11œ pp. 869 ~ 879 gj p ª gj p t q w : (2) œ Simulation Parameters for Surface Wave Propagation on Concrete: (2) Artificial Intelligence Engine and Estimation of Concrete Material Properties ½ yá z Á Á Kim, Jae HongÁKwak, Hyo-GyoungÁShin, Sung WooÁLee, Bang Yeon Abstract Artificial intelligence algorithm using database makes the estimation system without complication of mathematically based formulation. Therefore artificial intelligence algorithm such as soft computing methods can substitute the finite element analysis for time-consuming forward analysis and also build an inverse analysis engine to estimate the model parameters for measured surface wave. This paper shows the application of artificial neural network and genetic algorithm, which estimate the simulating parameters for surface wave. Furthermore, the smart system for estimating concrete properties such as modulus of elasticity and compressive strength was constructed and validated. Keywords : nondestructive evaluation, artificial neural network, genetic algorithm, simulation l» d l w w yƒ ƒ w œ š w w. gj p t q l vp fuq» w, w ¼ w w š, w t q x k gj p p w w ƒ w. vp fuq» œ š w, t q qx w, x ew ƒ w. ù ƒ t q qx w gj p w p l w w š, q sƒ l y w y w. w : q sƒ, œ, š, 1. zy z» (infrastructure) w w ww ƒ» x k gj p w l w. x w q (nondestructive inspection) w (rebound method) q (ultrasonic wave velocity method), š yw š (Malohtra, 2004). ù x š, q q y w wš. gj p q w w q wš, ƒ w j x q t k q(surface acoustic wave) w p š w gj p w œ wš w. gj p t q w w y y w» w v w ƒ w š w ƒ w š w š, k ew x w (principal wavelet-component analysis, PWCA) w p (feature) w w» w. gj p š, p» z Áw w» y œw (E-mail : jhongkim@kaist.ac.kr) z Á Áw w» y œw (E-mail : khg@kaist.ac.kr) w w» y œw z (E-mail : shinsw@kaist.ac.kr) w w» y œw (E-mail : ekvm80@kaist.ac.kr) 27ƒ 6A 2007 11œ 869
w w x w gj p w œ w. gj p t q w x m w d w gj p t q qx w w q w w w., w, d t q w k qƒ w y w w w (inverse analysis) v. ù w w t q l w w w» ƒ w, vp fuq(soft computing)» w w. ³e w (mathematically based method) w š, l (database)» w vp fuq», œ š (artificial intelligence algorithm) d (Ghaboussi, 2001). w w w ƒ wù, vp fuq» w (biologically inspired model) w yw. w, w w ¼ w, l» d l y w ƒ w j ƒ w. w ¼ w w w w wš, w ƒ w œ š d l ww q. p, ù œ (artificial neural network, ANN; Russell, 2003) q sƒ w š š (Wendel, 1996; Hola, 2005). œ œ š l. yw l ƒ y, w l j» w w, œ d l w (Russell, 2003)., x l w œ š w, w v w w l y w» w x v w. ù ƒ, x w w š w x l w yw d l w., y ƒ x l w š w w w ew l w, w wš, w d l wš w. w d l w, d gj p t q qx wš w w., d w d gj p w, q sƒ w d l y g w. ù ƒ, w w gj p w, k q gj p z (ACI 228, 2003) w z gj p q sƒ l wš w. 2. l œ w v w ew l ƒ w t q w w w, gj p t q qx(waveform) wš., ³ w gj p p w t q p š w w w wwš, (PWCA) p w l w. 1, ƒ w w 6 (t c ), (ρ), k (E), s (v), (η 1 ), (η 2 ) (x) w w w (FEA) (PWCA) ww, t q w 9 (k=1~3) (u k ), f (s k ), (c k ) w., w l w 16 (attribute), ƒ g (record) w w e w ww ƒw. l g ƒ l š w» w le (Monte-Carlo) w w (Haldar, 2000)., w ü 6 (t c, ρ, E, v, ç 1, ç 2 ) w ƒ (x) w 1 w e, t q ƒ 9 (u 1, s 1, c 1, u 2, s 2, c 2, u 3, s 3, c 3 ) l ƒ., w š w., (x) t q d x ƒ l 20 cm ü wwš, ¼ (1 cm) e j 20 ƒ w. 1 w w w gj p m (ρ) 1800~2800 kg/m 3, k (E) 10~60 GPa, s (v) 0.15~0.25, (η 1 ) 0~2.7 10 +4, (η 2 ) 1. t q ƒ w ew 870
0~6.3 10 7 y ƒƒ w (Neville, 1996). w, ƒ w gj p t (t c ) (steel ball) ù w š w 15~50 µsec w (Sansalone, 1997). w y m w w w l w. 3. d l 3.1 t q x» l w vpfuq š w, w w w œ w, w w k t q p w œ w ƒ w. d l w» w, t q x» m w l w w. t q x k q(elastic wave) d w Shin (2007), Popovics (1998), Wu (1995) w» d»», 2 w.» ƒ w gj p w w k q(transient elastic wave) j, x w. w, k q t q t l t q w q ü, w q t q p w ¾» w. š w ƒ q mw w ¾ w mƒ v w., d t q ƒ q w ƒ q wš,» q z w v w. 2 t q x» ƒ w w gj p t q d ww y k, w x ww. x ƒ ƒ l w (l=5 cm, d=5 cm) g w d., e w w t q (u k ), f (s k ), j»(c k ) x w» w ƒ l ƒ v w. x w, š w w (contact). x ƒ w d 2. t q d x» 3. vj w p j» w. w, w š k q m z û, t q w., vj(peak)ƒ ù z w w» w, (PWCA) w vj(k=1) (time of flight, u 1 ) q (scale, s 1 ) š wš w ( 3 )., m (conventional) p (trigger) w w (source) l y ƒ w. w w» w d w, t q w. q q q(rayleigh wave) t q(contaminated surface wave) l yw q (phase velocity) w» w w y» v w (Park, 2001). ù q ƒw q w š, d t q t q w (PWCA) w w p (feature extraction) w. w vj (V 1 ) q ƒ (group velocity) w š (maximum energy velocity) w. 3.2 l t q d x mw d w, vj w f t q l v w., ƒ l (x)ƒ 5cm, 10cm l w (query) ww vj V 1 =d/(u 1B u 1A ) e f S A =s 1A S B = s 1B w. (t c, ρ, E, v, η 1, η 2 ) w l (subdatabase) w, œ š w w l w., l» w œ (stability) y w» w, w w l w w. le (Monte-Carlo 27ƒ 6A 2007 11œ 871
t 1. v w l features V 1 S A S B t c ρ E v η 1 η 2 550 160 10 1180 1820 650 550 1890 510 1990 2000 190 550 1000 160 1990 2000 150 t 2. p w p- features V 1 S A S B t c ρ E v η 1 η 2 1.8e-09 1.4e-34 0.00 1.8e-02 0.32 1.1e-07 0.00 0.11 3.5e-07 0.66 0.13 4.9e-35 0.00 1.7e-03 1.0e-25 0.50 0.11 4.6e-92 w, t- (t-test) mw w p- (p-value) w w., p- 0.1 j ƒ m ùk ü (Devore, 2003). t 2, vj l (V 1 ) 5 (t c, ρ, E, η 1, η 2 ), f (S A ) 3 (t c, E, η 2 ), f (S B ) 4 (t c, ρ, E, η 2 ) y w. w, t 1 y w ƒ wš l ƒ 1000 w š., le l 2,000 w w m w q. 4. l ƒ y simulation) ƒ k l (correlation coefficient) w. y 10%», v w l w. w, x w q ù y w 3.3 w œ t 2 k, ƒ (y = V 1, S A, or S B ) dw œ ƒ ƒ w (The MathWorks, 2000a)., œ 5 v s (feed-forward) d (multiple-layer network, MLP)» Levenberg- Marquardt š w w g. (1) t x d w d(hidden layer) k p (tangent-sigmoid) yw (f tansig ) w š, w d ƒ e(w, b) d(output layer) ƒ e(ω, β) w d w. 5. v s d 872
7. ƒ œ 1 (output node, n o =1). 6. œ w yx ( ) = Ω f tansing ( Wx + b) + β d w ƒƒ œ w g 10z (10-fold cross validation) w w w(training set) x w(test set) 6 w. œ wš, w(overfitting) vw» w, (hidden node) x w ƒ w wš w., w (n h )ƒ ƒƒ 9, 5, 5 œ ƒƒ w., 5 (t c, ρ, E, η 1, η 2 ) vj (V 1 ) d w œ 5 (input node, n i =5) 9 (n h =9), š (1) 3.4 w œ (t c, ρ, E, v, η 1, η 2 ) (V 1, S A, S B ) l w, w w œ š ƒ w., w w w, w (y = t c, ρ, E, v, η 1, or η 2 ) dw œ w (n i =3). 7 œ w (coefficient of determination, R) txw, w ƒ œ wì w. w z (regression model) 1.0 w, (V 1, S A, S B ) d w œ w š q w. š (t c ), k (E), (η 2 ) š., t- y w (η 1 ) m, k dw œ. w, (ρ) s (v) d w œ 0.9.» (many-to-one), s w ƒ ù, yƒ j w., w w œ dw (t c ), k (E), (η 2 ), ƒ y., p mw t q w q w y w.,» y w w w 99%, 45%, k 95%, s 34%, 14%, 96% ƒ w. 3.5 w y š t q w w œ w w ƒ w v ƒ. t q (η 1 ) w, (ρ) s 27ƒ 6A 2007 11œ 873
(v) d t q ƒ w yƒ v w. 8 š w s y w., z (offspring) w qy k(roulettewheel selection), (scattered crossover), ³ s (Gaussian mutation) w (The MathWorks, 2005). š w œ w x yw t q l ƒ w.», x w w w ww, w ¼ yƒ x ƒ w. w (V 1 ) f (S A, S B ) d œ w w w., w (2) -s³- (root-mean-squared error, RMSE) w. erf( ρ, v) 4. x 8. s w y = sim exp V 1 V 1 ---------------------------- 2 S sim S exp -------------------------- A A exp exp V 1 S A 2 S sim S exp 2 + + -------------------------- B B S B exp gj p d l w ww t q x ƒ (L:, M: m, H: š )» t q x, x(dynamic test) x(static test) w z k w. ƒ t q x w x (40 cm 40 cm 15 cm) 1 t œ (φ15 cm 30 cm) 7 w gj p x z x w, t œ w d w t 3. gj p t œ type f c [MPa] E c [GPa] L M H 19.9 32.0 53.0 24.4 31.1 36.2 (2) 9. gj p t q x y, (ASTM C 39) k (ASTM C 469). 2» x t q x ww. xƒ (miniature accelerometer, PCB353B15) w w d y, y e(signal conditioner, PCB480B21) gv(oscilloscope, TDS2022) w ful w. t q d x ƒ w x (repeatability) y w ƒ w (Sansalone, 1997), w œ» w e(air-shot gun) w, w (steel ball) ùw w w x y w t q d x y g (Shin, 2007). d t q y 9 w w y(cwt using gaus1 wavelet with dt=1e-7) mw y ww (The MathWorks, 2000b), w w w y k w w. w, w x p w. vj t 4. gj p t q x type V 1 [m/s] S A S B L1 L2 L3 M1 M2 M3 H1 H2 H3 2024 2000 2008 2262 2283 2262 2500 2475 2451 45 50 45 36 39 37 41 39 41 49 50 47 41 44 43 43 41 45 874
t 5. œ w type t c [µs] E [GPa] η 2 L1 L2 L3 M1 M2 M3 H1 H2 H3 31.10 32.53 31.96 23.08 24.86 22.53 28.73 27.81 26.43 26.59 28.55 27.26 32.66 33.56 32.05 43.23 42.25 39.93 1.718e-7 4.283e-8 3.981e-8 1.276e-7 1.496e-7 1.866e-7 4.253e-8 2.720e-8 1.776e-7 w, t 4 vj l (V 1 ) f (S A, S B ) x w d l k., ƒ t q x w t q x wš w. 4.1 t q x (V 1, S A, S B ) ƒ š œ m w (t c, E, η 2 ) w. t 4 x k t 5. t 6. š w type ρ [kg/m 3 ] v erf(ρ, v) L1 L2 L3 M1 M2 M3 H1 H2 H3 2223 2478 2260 2368 2391 2392 2263 2268 2469 0.248 0.159 0.248 0.151 0.150 0.151 0.245 0.246 0.154 0.10492 0.12264 0.00839 0.03327 0.04001 0.02559 0.03600 0.02379 0.00952 w, œ d ƒ (ρ, v) š w w w. t 6, s, š w w., w wš š w s r ƒ w. t q qx w s ƒ û, w (erf) s j w». y y w» w, t 5 t 6 10. gj p t q 27ƒ 6A 2007 11œ 875
w w ww, x d t q qx L3, M3, H3 w w.» (η 1 ) t q qx w, 0 ƒ w., x w ƒ ƒ ƒ ƒ w» (normalization),» (A) vj» w. 10» t q qx q y w y w. p, w» qx x ƒ ew y w. vj m z x y» w (noise) q. 4.2 x x k ƒ x yw gj p x p w, q gj p k (dynamic modulus of elasticity) x mw d w w k (chord modulus) ƒ. k w (Neville, 1996). E c = 0.83E d (3.1) E c = 1.25E d 19 10 9 E c = 1.04E d 4.1 10 9 E c = 11. k k 1.4 0.11E d ρ (3.2) (3.3) (3.4)» k k w 11., t 3 d k (ø), m (ÿ), š (ý) gj p w t q x ww w t 5 k w. t q x mw k d w w š, p (3.1) (3.3)» yw d š. 12. gj p d w œ w 876
13. gj p d 4.3 gj p d gj p x p tw, w» p. k (4) š (ACI 318, 2002). E c = 43ρ 1.5 f c (3) (4) w, k w (5). f c ( 0.83E d ) 2 = ---------------------- 43 2 ρ 3 ( 1.25E d 19 10 9 ) 2 f c = ---------------------------------------------- 43 2 ρ 3 ( 1.04E d 4.1 10 9 ) 2 f c = ------------------------------------------------ 43 2 ρ 3 f c 1.4 ( 0.11E d ρ ) 2 = -------------------------------- 43 2 ρ 3 (4) (5.1) (5.2) (5.3) (5.4) t q x k dw w œ w» w, ƒ w l v w. w, t q x» w l (t c, ρ, E, v, η 1, η 2 ) (V 1, S A, S B ). l ƒƒ (5.1)~(5.4) w, (f c ) (V 1, S A, S B ) l w. l w, ƒ œ w y x w» ƒ w (n h ) 4, 7, 5, 3 w., ƒ œ (R) 0.989, 0.999, 0.994, 0.977 w d y w. œ w dw ƒ x w 13. gj p d w t q x w š, p 3 y w 1 w d w k w q. š, 1» gj p dw w œ w. 5. gj p t q, gj p p üsw, gj p t q d w gj p p dw. gj p t q qx w l», gj p dw y (accuracy) (stability) y w œ w. œ w, ƒ x t q d mw gj p k dw x w w. œ š mw 27ƒ 6A 2007 11œ 877
y w ü, d l w. 1. ew» l, ƒ w le ww l ƒƒ ƒ w., œ š l s. 2. t q x» k x d w vj l f (V 1, S A, S B ) w, œ w w w l (t c, ρ, E, v, η 1, η 2, & V 1, S A, S B ) w. 3. œ w l k y, œ l p y y wš, y w w l w. p, x l w w, ew l w l t w w. 4. œ w w w w, p (V 1, S A, S B ) w ƒ š dw. w, w l w w œ w, (t c ), k (E), (η 2 ) ƒ š dw. 5. œ w d gj p t q qx w š w yw š, w w w x qx w y w. 6. d x mw d w gj p k w, q sƒ w d l y wš d w œ w. gj p t q ƒ 5cm d w 1e-7 gaus1 w y vj l (V 1 ) ƒ f (S A, S B ) w, œ w gj p ƒƒ dw., -1 l +1 ey š, x=f mapping (<V 1 S A S B > T ) w min(v 1, S A, S B )=(1160.1 m/s, 22, 24) max(v 1, S A, S B )=(3676.5 m/s, 82, 97) w., k p yw (f tansig ) eyw (f mapping ). f tansig () t = f mapping () t = 1 2 ----------------- 1 ----------------- 1 1 e 2t 1 + 1 e 2t 2 + 2( t 1 t 1mix, ) ----------------------------- 1 t 1max, t l, min T 2( t 2 t 2min, ) ------------------------------ 1 t 2max, t 2min, T (1) : t c =f mapping 1 (y tc (x)) with t c,min =15.02e-6 sec & t c,max =49.98e-6 sec y tc ( x) = Ω tc f tansig ( W tc x+ b tc ) + β tc W tc 0.5414 4.1400 4.4129 1.5576 0.1500 1.6221 0.5145 3.8193 3.9595 106.24 29.318 286.82 = 2.0133 1.3483 2.8575 b tc 1.5536 0.2129 0.2007 1.5560 0.1499 0.0115 1.0047 14.632 28.641 0.4851 3.4844 3.4918 T Ω tc 66.085 29461 138.77 0.0865 = 0.3792 β tc = { 0.2368} 18.065 20.327 0.1760 74.352 0.9341 1.8845 0.9149 20.432 = 0.0875 1.2731 1.3071 5.8808 0.8905 (2) k : E=f mapping 1 (y E (x)) with E min =10.04e+9 Pa & E max =59.97e+9 Pa y E ( x) = Ω E f tansing ( W E x+ b E ) + β E 1.3702 0.5182 0.5590 1.6492 W E = b E = 1.4618 0.5321 0.5729 1.6078 T 168.54 Ω E = β E = { 28.035} 139.29 (3) : η 2 =f mapping 1 (y ç2 (x)) with η 2,min =2.437e-10 & η 2,max =6.289e-7 y η2 ( x) = Ω η2 f tansig ( W η2 x+ b η2 ) + β η2 W η2 1.7551 4.9308 2.7243 5.9217 3.9336 4.8092 5.7641 3.5941 5.0052 207.05 74.797 581.63 = 7.8861 232.21 130.63 b η2 1.8551 0.1039 4.5798 16.975 127.13 152.32 31.858 457.86 569.86 40.934 80.915 159.91 T Ω η2 0.5004 25.426 25.918 0.2144 = 0.1643 β η2 = { 0.0779} 0.7539 0.1640 0.1538 0.1920 0.5284 3.0902 2.9941 147.12 = 76.013 1.2504 11.44 87.997 15.640 (4) : f c =f mapping 1 (y fc (x)) with f c,min =1.748e+6 Pa & f c,max =219.0e+6 Pa 878
y fc ( x) = Ω fc f tansig ( W fc x+ b fc ) + β fc 71.302 21.974 70.984 48.870 W 0.8974 1.4686 1.5322 0.7864 fc = b fc = 97.837 112.83 177.23 84.399 0.8710 1.3733 1.4364 0.8754 T Ω fc 5.2293 = 17.373 0.0704 β fc = { 2.0123} 21.645 m w» (05 w C19) w w. š x ACI Committee 228 (2003) In-Place Methods to Estimate Concrete Strength, ACI 228.1R-03, American Concrete Institute. ACI Committee 318 (2002) Building Code Requirements for Structural Concrete and Commentary, ACI 318-02, American Concrete Institute. American Society for Testing and Materials (2002) Standard Test Method for Static Modulus of Elasticity and Poisson s Ratio of Concrete in Compression, ASTM C 469-02, ASTM. American Society for Testing and Materials (2005) Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens, ASTM C 39-05, ASTM. Devore, J.L. (2003) Probability and Statistics for Engineering and the Sciences, 6 th ed., Duxbury press. Ghaboussi, J. (2001) Biologically inspired soft computing methods in structural mechanics and engineering, Structural Engineering and Mechanics, Vol. 11, No. 5, pp. 485-502. Haldar, A. and Mahadevan, S. (2000) Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, Inc. Hola, J. and Schabowicz, K. (2005) New technique of nondestructive assessment of concrete strength using artificial intelligence, NDT&E International, Vol. 38, pp. 251-259. Malohtra, V.M. and Carino, N.J. (2004) Handbook on Nondestructive Testing of Concrete, 2 nd ed., CRC Press. Neville, A.M. (1996) Properties of Concrete, 4 th ed., Willey. Park, H.C. and Kim D.-S. (2001) Evaluation of the dispersive phase and group velocities using harmonic wavelet transform, NDT&E International, Vol. 34, pp. 457-467. Popovics, J.S., Song, W., Achenbach, J.D., Lee, J.H., and Andre, R.F. (1998) One-sided stress wave velocity measurement in concrete, Journal of Engineering Mechanics, ASCE, Vol. 124, No. 12, pp. 1346-1353. Russell, S. and Norvig, P. (2003) Artificial Intelligence: A Modern Approach, 2 nd ed., Pearson Education, Inc. Sansalone, M.J. and Streett, W.B. (1997) Impact-echo: Nondestructive Evaluation of Concrete, Bullbrier press. Shin, S.W., Popovics, J.S., Yun, C.-B., and Kim, J.H. (2007) Improved rayleigh wave velocity measurement for nondestructive early-age concrete monitoring, Research in Nondestructive Evaluation, Vol. 18, pp 45-68. The MathWorks, Inc. (2005) Genetic Algorithm and Direct Search Toolbox User s Guide, For Use with MATLAB, Version 2. The MathWorks, Inc. (2000a) Neural Network Toolbox User s Guide, For Use with MATLAB, Version 4. The MathWorks, Inc. (2000b) Wavelet Toolbox User s Guide, For Use with MATLAB, Version 3. Wendel, R. and Dual, J. (1996) Application of neural networks to quantitative nondestructive evaluation, Ultrasonics, Vol. 34, pp. 461-465. Wu, T.-T., Fang, J.-S., Liu, G.-Y., and Kuo, M.-K. (1995) Determination of elastic constants of a concrete specimen using transient elastic waves, Journal of the Acoustical Society of America, Vol. 98, No. 4, pp. 2142-2148. ( : 2006.8.28/ : 2007.5.13/ : 2007.9.20) 27ƒ 6A 2007 11œ 879