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1 27ƒ 6A Á œ 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 ( z Á Áw w» y œw ( w w» y œw z ( w w» y œw ( 27ƒ 6A œ 869

2 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~ , (η 2 ) 1. t q ƒ w ew 870

3 0~ 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 œ 871

4 t 1. v w l features V 1 S A S B t c ρ E v η 1 η t 2. p w p- features V 1 S A S B t c ρ E v η 1 η 2 1.8e e e e e e e e e-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

5 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 œ 873

6 (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 S sim S exp A A exp exp V 1 S A 2 S sim S exp 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 (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 H

7 t 5. œ w type t c [µs] E [GPa] η 2 L1 L2 L3 M1 M2 M3 H1 H2 H e e e e e e e e e-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 H 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 gj p t q 27ƒ 6A œ 875

8 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 E c = 1.04E d E c = 11. k k E 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

9 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 = ρ 3 ( 1.25E d ) 2 f c = ρ 3 ( 1.04E d ) 2 f c = ρ 3 f c 1.4 ( 0.11E d ρ ) 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, 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 œ 877

10 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 )=( m/s, 22, 24) max(v 1, S A, S B )=( m/s, 82, 97) w., k p yw (f tansig ) eyw (f mapping ). f tansig () t = f mapping () t = e 2t e 2t 2 + 2( t 1 t 1mix, ) t 1max, t l, min T 2( t 2 t 2min, ) 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 = b tc T Ω tc = β tc = { } = (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 W E = b E = T Ω E = β E = { } (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 η = b η T Ω η = β η2 = { } = (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

11 y fc ( x) = Ω fc f tansig ( W fc x+ b fc ) + β fc W fc = b fc = T Ω fc = β fc = { } 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 , 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 , 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 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 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 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 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 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 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 ( : / : / : ) 27ƒ 6A œ 879

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