Modal Strain Energy Decomposition Method for Damage Detection of an Offshore Structure Using Modal Testing Information

Transcription

1 Thrd Chnese-German Jont Symposum on Coastal and Ocean Engneerng Natonal Cheng Kung Unversty, Tanan November 8-16, 2006 Modal Stran Energy Decomposton Method for Damage Detecton of an Offshore Structure Usng Modal Testng Informaton Huaun L*, Shuqng Wang and Hezhen Yang Insttute of Coastal and Offshore Engneerng, Ocean Unversty of Chna, Qngdao Abstract A newly derved damage locaton algorthm s proposed to predct locaton of damage n offshore structures usng changes n mode shapes from modal testng. Ths method decomposes elemental modal stran energy nto two parts, and defnes two damage ndcators: axal damage ndcator and transverse damage ndcator. Analyzng the ont nformaton of the two damage ndcators can localze damage elements. In order to valdate the damage detecton method, a physcal platform model was manufactured and several damage cases were smulated. Results demonstrates that the proposed method s effectve for the structural damage detecton and acheves satsfactory precson. 1 Introducton Offshore structures, durng ther servce lfe, contnually accumulate damage that results from the acton of varous envronmental forces. The only way to ensure the safety of human lfe and to reduce the loss of wealth s to detect the exstence and locaton of sgnfcant damage on the structure (Rytter, 1993). Structural damage detecton based on vbraton measurements holds promse for the global nondestructve damage detecton of structures. Doeblng et al. (1998) present a thorough revew of the vbraton-based damage dentfcaton methods. Many researchers provde varous damage detecton technques based on modal parameters. But most of them have some lmtatons n practce. For example, some methods need mass normalzed mode shapes; some methods need complete mode parameters (ncludng structural rotatonal degree of freedoms, hgh modal parameters), or some methods need the envronmental loadng. A damage ndex method base on modal stran energy was developed by Stubbs et al. (1995) and had been successfully appled to beam-type (one-dmensonal) structures for damage localzaton. However, ts applcatons to two- and three-dmensonal frame type structures were shown to be not as promsng (Farrar and Jauregu, 1996). To avod these shortcomngs of the methods mentoned

2 above, an effectve damage localzaton method, modal stran energy decomposton (MSED) method, s developed by Yang et al. (2004) for three-dmensonal frame structures. The MSED method defnes two damage ndcators, axal damage ndcator and transverse damage ndcator, for each member. Analyzng the ont nformaton of the two damage ndcators greatly mproves the accuracy of localzng damage elements. The appealng features of the modal stran energy decomposton method are: (1) t requres only a few ncomplete mode shapes dentfed from damaged and undamaged structures under ambent exctaton whch don't nclude structural rotatonal degree of freedoms (DoFs), and (2) t can locate local damages n the 3-D frame structures, such as offshore platforms. For valdatng the damage detecton method, a physcal platform model was manufactured and several damage cases ncludng sngle damage locaton and double damage locatons were smulated. Modal stran energy decomposton method was appled to localze the damages. Results demonstrates that the proposed method s effectve for the structural damage detecton and acheves satsfactory precson. 2 Modal Stran Energy Decomposton Method In ths paper, the structural modal stran energy was assgned nto two parts: One s axal modal stran energy; the other s flexural modal stran energy. In order to detect damage locaton n the offshore platform, two damage ndcators were defned; axal modal stran energy change can be obtaned as followng: [( ) ] NM * T c * * T c * T c [ Φ k Φ + Φ K Φ Φ K Φ ( ) ] T = T c T c * c Φ Φ + Φ Φ Φ Φ * 1 k K K c β = =1, 2, e (1) And flexural modal stran energy change s gven as: [( ) ] NM * T f * * T f * T f [ Φ k Φ + Φ K Φ Φ K Φ ( ) ] T = T f T f * f Φ Φ + Φ Φ Φ Φ * 1 k K K f β = =1, 2, e (2) * where Φ, Φ are the structural undamaged mode shapes and damaged mode shapes, respectvely. k c s the element stffness, whch contans structural compresson nformaton, only; k f s the element stffness, whch contans structural flexuosty nformaton only; and NM s the dentfed mode shapes. Two normalzed damage localzaton ndcators: axal modal stran energy change rato (Axal damage Indcator) s obtaned as follows: c Z c c c ( β β ) σ = (3) β Flexural modal stran energy change rato (Transverse damage ndcator) s obtaned as follows:

3 f Z f f f ( β β ) σ β = (4) c f where β, β represent the mean of the damage ndces, and σ c β, represent the standard devaton of the damage ndces. f σ β 3 Verfcaton Usng Modal Testng Data 3-1 Descrpton of the Offshore Platform Model The structure studed here s a acket-type offshore platform model, as shown n Fg.1. The platform model s a welded-steel space frame wth four prmary legs, braced wth horzontal and dagonal members. All the members are welded wth steel ppes except that the top deck s a steel plate (deck). The essental geometrcal and materal propertes of the frame structure are gven below. Young s modulus E s a constant equal to Pa for all members. The prmary legs of the frst story of the model had a dameter of 18 mm wth ts ppe thckness 2.5mm. The prmary legs of other three stores of the model had a dameter of 14 mm wth ts ppe thckness 2.5mm. All the horzontal braces had a dameter of 10mm(thckness 2mm). All the dagonal braces n vertcal plane had a dameter 8mm(thckness 1.5mm) and all the dagonal braces n horzontal planes are sold bar wth dameter 10mm. The deck s a steel plate of 20mm thckness. Other geometrcal dmensons are shown n fgure Expermental Set-up and Modal Testng Totally 32 accelerometers are nstalled to montor the whole physcal model, wth each ont two sensors to record the response n x and y drectons, respectvely. The model s fxed to concrete foundaton at the bottom and excted by an mpact hammer whch horzontally hts the center of the platform deck. Frst tests are performed on the undamaged structure. Then the tests are repeated n the same way for the damaged structure after some structural member(s) s/are broken. Damages were smulated n the way as shown n Fg.3. Damage occurs when the bolts and metal spacer are removed. When refttng the spacer and settlng the screws, damage dsappear. Throughout the test, the samplng frequency s 500Hz. Several damage scenaros are smulated n the tests, as lsted n table 1. The damage scenaros nclude sngle damage cases and double damage cases, damaged dagonal braces n dfferent levels and n dfferent drectons. As stated n secton 2, damage detecton based on modal stran energy requres the stffness matrx of each element of the undamaged structure. Accordng to the specfcatons of the platform structure, numercal model of the tested structure s modeled by fnte element method, as shown n fgure 2. And each element was assgned wth a number.

4 Fg. 1 Physcal model under test spacer Fg. 2 Descrpton of the model brace bolt Fg. 3 damage smulaton

5 3-3 System Identfcaton Egensystem realzaton algorthm wth natural exctaton technque was verfed to be effectve for modal dentfcaton based on output-only responses(wang and L, 2005) and was used to extract modal frequences and mode shapes of the undamaged and damaged structure. The frst two modal frequences of the undamaged structure and other damage cases are lsted n table 2. The frst mode vbrates domnantly n y (short-span) drecton and 2nd mode domnantly n x (long-span) drecton. Table 1 Damage cases of the model and the frst two modal frequences Damage cases Damaged Frequences (Hz) element 1st mode 2nd mode Undamaged FEM Undamaged physcal model Damage case 1 brace Damage case 2 brace Damage case 3 brace Damage case 4 brace 39 brace Damage Locaton Results Applyng the damage detecton procedure of the modal stran energy decomposton method usng the frst two dentfed mode shapes, the damage detecton for each damage case s shown n fgure 4 to fgure 7, respectvely. Damage cases 1 to 3 nvestgate the damage detecton for sngle damage locaton. For damage case 1, the damage member s a dagonal brace 30 n the fourth story n the long-span drecton. The results are shown n Fg.4. The top panel of Fg.4 s the axal damage ndcator and the bottom panel s the transverse damage ndcator. From the axal damage ndcator, t can be obvously seen that element 30 s damaged. The transverse ndcator proves the above concluson by ndcatng vertcal elements 2 and 3 are affected by true damaged dagonal brace 30. In damage case 2, the damaged member s the dagonal brace 34 n the thrd story n short-span drecton and the damage member s the dagonal brace n the frst story n long-span drecton n damage case 3. The results are shown n Fg.5 and Fg.6. Same concluson can be drawn as from damage case 1.

6 Damage case 4 nvestgates the damage detecton of double damage locatons and result s shown n fgure 7. The damaged locatons are dagonal brace 39 of floor 2 n long-span drecton and dagonal brace 34 of floor 3 n short-span drecton. From fgure 7, one can see that modal stran energy decomposton method can localze the damage locatons correctly. Fg. 4 Damage case1: brace 30 s damaged Fg. 5 Damage case2: brace 34 s damaged Fg. 6 Damage case3: brace 43 s damaged Fg. 7 Damage case4: brace 34 and 39 are damaged 4 Concludng Remarks Modal stran energy decomposton method for detectng damages of an offshore acket structures s nvestgated. Ths newly proposed damage localzaton algorthm defnes two damage ndces: axal damage ndcator and transverse damage ndcator, for each member based on the change of modal stran energy

7 assocated wth structural elements before and after damage occurred.. Analyzng the ont nformaton of the two damage ndcators greatly mproves the accuracy of localzng damage elements. For valdatng the damage detecton method, a physcal platform model was manufactured and several damage cases ncludng sngle damage locaton and double damage locatons were smulated by the physcal model. Modal stran energy decomposton method was appled to localze the damages. In applyng the procedure, only the frst two dentfed modes are used for damage localzaton. And partal nformaton, wth each node (ont) two dentfed components are utlzed. Results demonstrates that the proposed method s effectve for the structural damage detecton and acheves satsfactory precson. 5 References Doeblng, S.W., C.R. Farrar, M.B. Prme and D.W. Shevtz. A Revew of Damage Identfcaton Methods that Examne Changes n Dynamc Propertes, Shock and Vbraton Dgest, 30 (2), pp , Farrar, C.R. and D.V. Jauregu. Damage Detecton Algorthms Appled to Expermental and Numercal Modal Data from the I-40 Brdge, Los Alamos Natonal Laboratory Report, LA MS, Rytter, A.. Vbraton Based Inspecton of Cvl Engneerng Structures, Ph. D. Dssertaton, Department of Buldng Technology and Structural Engneerng, Aalborg Unversty, Denmark, Stubbs N., J.T. Km and C.R. Farrar. Feld Verfcaton of a Nondestructve Damage Localzaton and Severty Estmaton Algorthm, Proc. of IMAC, Connectcut, USA, Socety of Expermental Mechancs, pp , Wang Shuqng and Huaun L. Output-based Modal Parameters Identfcaton of a Three Dmensonal Structure, Proceedngs of the Second Internatonal Structural Health Montorng of Intellgent Infrastructure, Vol.2, , Yang H.Z. and H.J. L. Modal Parameter Identfcaton of Offshore Platform under Ambent Exctaton, Hgh Technology Letters, 10(1), pp.80-84, Yang H.Z. and H.J. L. Damage Localzaton of Offshore Platform under Ambent Exctaton, Chna Ocean Engneerng, 17(4), pp , 2003.

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