Summary of PhD thesis: Development and application of signal processing methods for crack diagnosis of bar structures

The objective of the thesis: Study the effect of cracks on the dynamic characteristics of the structure, study the applicability of the time-frequency signal processing method in detecting cracks. Application and development the processing time-frequency oscillation signals methods for cracks detection.

VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY o0o NGUYEN VAN QUANG DEVELOPMENT AND APPLICATION OF SIGNAL PROCESSING METHODS FOR CRACK DIAGNOSIS OF BAR STRUCTURES Major: Engineering Mechanics Code: 9520101 SUMMARY OF PhD THESIS Hanoi – 2018 The thesis has been completed at: Vietnam Academy of Science and Technology Graduate University of Science and Technology Supervisor: Assoc Prof Dr Nguyen Viet Khoa Reviewer 1: Prof Dr Hoang Xuan Luong Reviewer 2: Assoc Prof Dr Luong Xuan Binh Reviewer 3: Assoc Prof Dr Nguyen Phong Dien Thesis is defended before the State level Thesis Assessment Council held at: Graduate University of Science and Technology - Vietnam Academy of Science and Technology At ……… on …………………………………………… Hardcopy of the thesis can be found at: + Library of Graduate University of Science and Technology + National Library of Vietnam List of the Author’s publications Khoa Viet Nguyen, Quang Van Nguyen Time-frequency spectrum method for monitoring the sudden crack of a column structure occurred in earthquake shaking duration Proceeding of the International Symposium Mechanics and Control 2011, p 158-172 Khoa Viet Nguyen, Quang Van Nguyen Wavelet based technique for detection of a sudden crack of a beam-like bridge during earthquake excitation International Conference on Engineering Mechanics and Automation ICEMA August 2012, Hanoi, Vietnam, p 87-95 Nguyễn Việt Khoa, Nguyễn Văn Quang, Trần Thanh Hải, Cao Văn Mai, Đào Như Mai Giám sát vết nứt thở dầm phương pháp phân tích wavelet: nghiên cứu lý thuyết thực nghiệm Hội nghị Cơ học toàn quốc lần thứ 9, 2012, p 539-548 Khoa Viet Nguyen, Hai Thanh Tran, Mai Van Cao, Quang Van Nguyen, Mai Nhu Dao Experimental study for monitoring a sudden crack of beam under ground excitation Hội nghị Cơ họ V r n i n ng oàn uốc lần thứ 11, 2013, p 605-614 Khoa Viet Nguyen, Quang Van Nguyen Element stiffness index distribution method for multi-cracks detection of a beamlike structure Advances in Structural Engineering 2016, Vol 19(7) 1077-1091 Khoa Viet Nguyen, Quang Van Nguyen Free vibration of a cracked double-beam carrying a concentrated mass Vietnam Journal of Mechanics, VAST, Vol.38, No.4 (2016), pp 279293 Khoa Viet Nguyen, Quang Van Nguyen, Kien Dinh Nguyen, Mai Van Cao, Thao Thi Bich Dao Numerical and experimental studies for crack detection of a beam-like structure using element stiffness index distribution method Vietnam Journal of Mechanics, VAST, Vol.39, No.3 (2017), pp 203-214 INTRODUCTION Crack detection methods based on oscillating signals are usually based on two main factors: the dynamical characteristics of the structure and the oscillating signal processing methods In practice, the change in dynamical characteristics of the structure caused by the crack is very small and difficult to detect directly from the oscillating measurement signal Therefore, in order to detect these minor changes, modern signal processing methods are given, which is the method of signal processing in time-frequency domains These methods include the Short-time Fourier Transform (STFT), the Wavelet Transform (WT) v.v These methods will analyze signals in two time and frequency domains When using these methods, the signals over time will be represented in the frequency domain while the time information is retained Therefore, time-frequency methods will be useful for analyzing small or distorted variations in the oscillation signal caused by the crack The objective of the thesis  Study the effect of cracks on the dynamic characteristics of the structure  Study the applicability of the time-frequency signal processing method in detecting cracks  Application and development the processing time-frequency oscillation signals methods for cracks detection Study method  The dynamic characteristics of cracked structures, such as frequencies, mode shapes will be calculated and studied by finite element method  The time-frequency signal processing method will be applied to analyze the simulated vibration signals of the cracked structure  Develop an oscillating signal processing method to detect changes in element stiffness to detect the crack  Carry out some experiments to verify the effectiveness of the methods New findings of the dissertation  The application of wavelet spectral methods for sudden cracks detection  The application of wavelet analysis for cracks detection based on the effect of cracks and concentrated mass  Proposed a new method using the "Element stiffness index distribution method" for crack detection of the structure In this method, the element stiffness index distribution is calculated directly from the oscillation signal Structure of the thesis The contents of the thesis include the introduction, the conclusion, and chapters: Chapter 1: An overview Presents an overview of the world's research on cracks detection methods based on structural dynamics, signal-processing methods in time-frequency domain for analysis and crack detection Chapter 2: Theoretical basic Provides a theoretical basic of structural dynamics with cracks Introduce cracks model of 2-D and 3-D beams Chapter 3: Theory of oscillating signal processing methods Presentation of theoretical basis of signal processing methods in time-frequency domains and presents an element stiffness index distribution method for crack detection of the structure Chapter 4: Application of oscillating signal processing methods in some problems Presents the applications of time-frequency methods and an element stiffness index distribution method to detect cracks in different structures Chapter 5: Experimental verification Presents some experiments to verify the methods developed and applied in the thesis Conclusion: presents the results of the thesis and some issues that need to be implemented in the future CHAPTER AN OVERVIEW 1.1 Diagnostic problem We can use direct or indirect methods to detect damage in the structure Direct methods include visual observation, film shooting, or remove the structural details for inspection Indirect method is the response singnal analyzing method of the structure under external impact to detect the structural damage In indirect methods, vibration methods are developed and applied in the world as well as in Vietnam These methods can be divided into two main groups: the method based on structural dynamics parameter and the method based on oscillation data processing 1.2 Methods of structural damage detection based on structural dynamics parameter The existence of damage in the structure leads to changes in the frequencies and shape modes Therefore, the structural characteristics of the damaged structure will contain information about the existence, location and level of damage In order to detect structural damage, it is essential to study the dynamics of the structure 1.3 Wavelet analysis method to detect structural damage The change in frequency is the most interest parameter for damage tracking because it is a global parameter of structure By conventional approach, the natural frequency can be extracted by Fourier transform However, the information of the time when the frequency changed is lost in this transform Fortunately, there is another approach which can analyse the frequency change while the information of time is still kept called time-frequency analysis Recently, some time-frequency based methods have been applied wildly for SHM such as Short Time Fourier transform (STFT), Wigner-Ville Transform (WVT), Auto Regressive (AR), Moving Average (MA), Auto Regressive Moving Average, and Wavelet Transform (WT) [58] Among these methods, the WT has emerged as an effective method for tracking the change in natural frequency of structures CHAPTER THEORETICAL BASIC In order to analyze the dynamical characteristics of damaged structures, the thesis will use finite element method because it can analyze complicated structures which analytical method is difficult to perform So in this chapter, we will present the theoretical basis of finite element method for solving the damaged dynamics problem 2.2 Finite element models for 2D and 3D beam with crack 2.2.1 2D beam with crack It is assumed that the cracks only affect the stiffness, not affect the mass and damping coefficient of the beam An element stiffness matrix of a cracked element can be obtained as following: W (0)  EI l   M  Pz  dz  EI  P 2l   MPl  M l    The additional energy due to the crack can be written as: a  K I2  K II2 1    K III2  (1) W  b    E  E  da  (2.1) (2.4) The generic component of the flexibility matrix C~ of the intact element can be calculated as: cij(0)   2W (0) , P1  P, P2  M ; Pi Pj i, j  1, (2.6) The additional flexibility coefficient is: cij(1)   2W (1) , P1  P, P2  M ; Pi Pj The total flexibility coefficient is: cij  cij(0)  cij(1) i, j  1, (2.7) (2.8) By the principle of virtual work the stiffness matrix of the cracked element can be expressed as: K c  TT C 1T (2.11) 2.2.2 3D beam with crack The total compliance C of the cracked element is the sum of the compliance of the intact element and the overall additional compliance due to crack: cij  cij(o)  cij(1) (2.14) The components of the compliance of an intact element can be calculated from Castingliano’s theorem: cij(0)   2W (0) ; i, j  6, Pi Pj (2.15) and the components of the local additional: cij(1)   2W (1) ; i, j  Pi Pj (2.16) Where W(0) is the elastic strain energy of the intact element and can be expressed as follows: W (0)   P12 l  P22 l  P32 l P2 l P6 l P2 P6 l P32 l P5 l P3 P5l P4 l              AE GA GA 3EI z EI z EI z 3EI y EI y EI y GI  Where W(1) is the additional strain energy due to crack [116]:         K Ii     K IIi      K IIIi   E       A 2 W (1)     dA  (2.19) The stiffness matrix of the cracked element can be obtained as follows: K c  TT C1T (2.36) 2.3 Equation of structural by finite element method In finite element model the governing equation of a beam-like structure can be written as follows [118]: My(t )  Cy(t )  Ky(t )  NT f (t )  f(t ); f   NTe f e dx, f   TeT f Le (2.37) e M, C, K are structural mass, damping, and stiffness matrices, T respectively; f the excitation force; N is the transposition of the 20 b Multi-crack detection of a beam  Noise-free signals In this section, two cracks are made at the locations of L/3 and 2L/3 corresponding to the 10th and 20th elements The measurement is first assumed to be noise free Figure 4.16 presents the element stiffness index distributions with five levels of crack depth As can be seen from this figure, there are two peaks in the distribution at the cracked elements as expected When the crack depth increases, the heights of the peaks also increase a) b) c) d) e) Fig 4.16 Reconstructed element stiffness index distribution, noise 0%: a) crack depth 10%, b) crack depth 20%, c) crack depth 30%, d) crack depth 40%, and e) crack depth 50% 21 Fig 4.17 The height of the two peaks versus crack depth, without noise  Noisy signals a) b) c) d) e) Fig 4.18 Reconstructed element stiffness index distribution: a) crack depth 10%, noise 1%; b) crack depth 20%, noise 2%; c) crack depth 30%, noise 4%; d) crack depth 40%, noise 6%; e) crack depth 50%, noise 10% 22 Fig 4.19 The height of the first peak versus crack depth, with and without measurement noise Fig 4.20 The height of the second peak versus crack depth, with and without measurement noise 4.3.2 Multi-crack detection of a frame In order to give a more solid evidence of the proposed method, the frame consisting of two vertical columns with the height of m and one horizontal bar with length of m in the X–Z plane as depicted in Figure 4.21 is analyzed The frame is divided by 70 frame elements with the cross section of 0.04m x 0.04m in finite element model Two cracks are made at 10th and 20th elements in the left column Since the frame element has 12 DOFs, the stiffness matrix of a cracked element is adopted from Nguyen (2014) The 23 dynamic response of the frame is calculated by finite element method Fig 4.21 The frame model in the X–Z plane Fig 4.22 Reconstructed element stiffness index distribution of the left column, noise 0% Fig 4.23 Reconstructed element stiffness index distribution of the left column: a) crack depth 10%, noise 1%; b) crack depth 20%, noise 2%; c) crack depth 30%, noise 4%; d) crack depth 40%, noise 6%; e) crack depth 50%, noise 10% 24 The simulation results show that there are two clear peaks in the element stiffness index distribution of the left column at the cracked elements as presented in Figures 4.22 and 4.23 in the cases without and with measurement noise However, as can be seen from these figures, the first peak which is close to the fixed end of the column is more significant than the second peak which is close to the free end of the column This implies that the crack close to the fixed end can be detected more efficiently Fig 4.24 The height of the first peak versus crack depth, with and without measurement noise 4.3.3 Crack detection of a high slender structure A numerical example of a slender symmetric structure acted at the middle point by the force in the X-direction as presented in Fig 4.25 is investigated The frequency response functions in the X-direction are obtained along the structure 25 Measurement points Force position Crack position Fig 4.25 The high slender structure model This structure consists of four columns and braced elements with the dimensions of 0.25m × 0.25m × 3.6m The columns and braced elements of this structure are modelled as frame elements in the finite element analysis The cross section of column and braced elements are 0.02m × 0.02m and 0.02m × 0.002m, respectively The material properties of the elements are: mass density ρ = 7855 kg/m3; modulus of elasticity E=2.1x1011 N/m2 The number of elements used in this simulation is 240 Each column is divided by 36 elements It is assumed that there is a crack located at the 17th element in column #1 Here, the elements in column #1 are numbered ascendantly from the bottom to the top of the structure 26 e) Fig 4.26 Reconstructed element stiffness index distribution, element #17 is cracked: a) crack depth 10%; b) crack depth 20%; c) crack depth 30%; d) crack depth 40%; e) crack depth 50% The stiffness matrix of the cracked element is adopted from [36] Five levels of the crack depth ranging from 10% to 50% are investigated With this configuration of the force and the measurement points, the slender symmetric structure can be considered equivalently as a cantilever beam-like structure and the proposed method is then applied for crack detection Fig 4.27 The height of the first peak versus crack depth 27 4.3.4 Conclusion In this thesis, a method using ‘‘element stiffness index distribution’’ for single-crack and multi-crack detections of a beamlike structure is presented the global stiffness matrix is reconstructed directly from FRFs, not from the mode shapes to avoid some limitation of the measured mode shapes Any change in the stiffness of an element will lead to a change in the element stiffness index of that element By monitoring the change in the element stiffness index distribution, the location of the crack is detected The existence of cracks is detected by significant peaks in the element stiffness index distribution and the crack positions are determined by the locations of these peaks The cracks with depths as small as 10% of the beam height can be detected by the proposed method 28 CHAPTER EXPERIMENTAL VERIFICATION In Chapter 4, three diagnostic problems were identified in order to detect cracks occurring in the structure The numerical results were simulated and analyzed based on the modern oscillator signal processing method and showed good results However, in practice measurement results are always affected by measurement noise Therefore, to verify the applicability of the developed methods and its application in this thesis, the author conducted some experiments 5.1 Detection a sudden crack of beam by wavelet method In this work the ground excitation is generated by the vibration table using earthquake spectrum as can be seen from Fig 5.1 Parameters of the beam are: Mass density is 7855 kg/m3; modulus of elasticity E=2.1x1011 N/m2; L=1.2 m; b=0.06 m; h=0.01 m The excitation duration is T=16 s The crack is appeared at around T/2 s Five levels of the crack from 10% to 50% were examined Fig 5.1 The cracked beam on the vibration table 29 Simultation Experiment a) b) c) d) 30 Simultatio Experiment e) Fig 5.3 IFs of the beam: a) Crack depth 10%; b) crack depth 20%; c) crack depth 30%; d) crack depth 40%; e) crack depth 50% a) b) Fig 5.4 Relation between df and crack depth a) Simulation; b) Experiment 5.2 Crack detection of a high slender structure using element stiffness index distribution method In order to justify the application of the proposed method in practice, a symmetric steel structure was made in the laboratory of the Institute of Mechanics, Vietnam Academy of Science and Technology as seen in Fig 5.5 The global dimensions of the structure are 0.25m x 0.25m x 3.6m This structure consists of columns connected rigidly together by 144 braced elements The cross section of column and braced elements are 0.02m x 0.02m and 0.02m x 0.002m, respectively The vibration instrument system 31 consists of the Bruel & Kjaer Pulse instrument for measuring vibration data and Pulse Labshop software for analysing frequency response functions The crack was made by a saw at the 17th element in column #1 Five levels of the crack from zero to 50% have been made In this experiment, the frequency response functions were measured by using one hammer and one vibration transducer The force was applied at a fixed node while the vibration transducer moved along column #1 Column #1 is divided by 36 equal elements The frequency response functions were obtained at 36 nodes along column #1 The element stiffness matrix index distribution was then established from these 36 measured frequency response functions by the proposed method a) b) Fig 5.5 Experiment in the laboratory of the Institute of Mechanics-Vietnam Academy of Science and Technology: a) The steel high slender structure; b) Crack was made by a saw The experimental results show that there are clear peaks in the element stiffness index distributions of column #1 at the 17th 32 element with different crack depths as presented in Fig 5.7 The significant peak in the element stiffness index distribution explains that there is a change in the stiffness of the 17th element which is the Element stiffness index distribution cracked element 0.8 0.6 dh 0.4 0.2 0 10 20 30 Element number 40 e) Fig 5.7 Reconstructed element stiffness index distribution, element #17 is cracked: a) crack depth 10%; b) crack depth 20%; c) crack depth 30%; d) crack depth 40%; e) crack depth 50% Fig 5.8 The height of the first peak versus crack depth 33 5.3 Conclusion Chapter presents the results of two experiments: Experimental study for monitoring a sudden crack of beam, using the IF frequency extracted from the wavelet energy spectrum Experiment study for crack detection of frame by an element stiffness index distribution method To compare theories with experiments, it show that the simulation results based on these method are well matched with the experimental results 34 CONCLUSION The thesis aims to develop and apply modern signal processing methods for the diagnosis problems The signal processing methods based on spectrum analysis in frequency domain and wavelet analysis in time-frequency domains Conclusion of thesis New findings of the dissertation:  First proposed an application of wavelet spectral method for sudden cracks detection problem  First proposed an application of wavelet analysis for cracks detection problem which based on the influence of the concentrated mass and cracks  Proposed an element stiffness index distribution for crack detection in the structure The global stiffness matrices reconstructed directly from FRFs The limitations of the thesis, and the work studys in the future  The thesis only uses wavelet method to detect cracks for simple beams Therefore, the proposed method based on wavelet analysis needs to be studied for more complex structures in order to evaluate the applicability of these methods in practice  An element stiffness index distribution method has good results for both beam and frame structures, however, this method only applies to symmetrical structures Beam or column elements contain cracks are assumed that they have a constant cross section Thus, structure has unsymmetrical and section change, is needed to study in practice  Experimental verification for cracks detection method of beam structure with concentrated mass has not been conducted So, this is a study needs to be followed by the thesis ... of the structure  Study the applicability of the time-frequency signal processing method in detecting cracks  Application and development the processing time-frequency oscillation signals methods. .. oscillating signal processing methods Presentation of theoretical basis of signal processing methods in time-frequency domains and presents an element stiffness index distribution method for crack. .. for crack detection of the structure Chapter 4: Application of oscillating signal processing methods in some problems Presents the applications of time-frequency methods and an element stiffness