Identification of Multiple Cracks of Cantilever Beam
CHAPTER 8 Analysis & Description of Experimental
8.2 Systematic experimental procedure
The experimental investigation has been performed on the cracked and non-cracked cantilever beams of layered composite and structural steel to verify the robustness of the results derived from theoretical, numerical and various AI techniques. The cracks at various locations and different depths are introduced in the specimen with the help of wire cut EDM for structural steel beam and for layered composite by putting the slips during the fabrication of composite beam. The test specimens have been clamped one by one of each material in the vibrating table as shown in figure 8.1. The test specimen are excited by signal generator at desirable signal and power amplifier is used for amplify the signal. The specimens have been excited at their first three consecutive modes of vibration and corresponding vibration response (natural frequency and mode shape) received by Deltatron accelerometer by suitable positioning of accelerometer and tuning the vibration shaker at the corresponding resonance frequencies. The vibration analyzer examined the vibration signal received from intact and cracked cantilever beam and displayed in the vibration indicator loaded with the Pulse labshop software. Vibration analyzer is connected with Pulse labshop software with the PCMCIA card. The snapshot of various instruments used in experimental test shown in figures 8.2(a) to 8.2(h).
Figure 8.2(a) Delta Tron Accelerometer
Figure 8.2(b) PCMCIA card
Figure 8.2(c) Vibration analyzer
Figure 8.2(d) Vibration indicator imbedded with PULSE lap Shop software
Figure 8.2(e) Signal generator
Figure 8.2(f) Power amplifier
Figure 8.2(g) Vibration Shaker
Figure 8.2(h) Concrete foundation with specimen
8.3 Results and discussion
This section depicts the analysis of results derived from experimental investigation.
The intact and cracked beams with various crack locations and different crack depths have been examined in experimental bed to get vibration response. This is used to verify the robustness of results obtained from various techniques discussed in the previous chapters. A comparison and verification of the results derived from theoretical model for multiple cracks beam with orientation of cracks (β1=0.25, β2=0.5, ψ1=0.1667 and ψ2=0.5) are shown in chapter 3 and It is plotted with results of experimental examination in the figures 3.13 to 3.15 (for composite) and figures 3.16 to 3.18 (for structural steel). The results derived from theoretical and experimental observation are displayed in tabular form with first three modal parameters (natural frequencies and mode shapes) and relative crack location and crack depth in the table 3.1 and table 3.2 for composite beam and steel bream respectively. Good agreement between the results is observed. The total percentage of deviation of the theoretical analysis is 3.8% for composite beam and 4.4% for structural steel. The results for first three consecutive mode shapes are obtained from numerical analysis for multiple cracks beam with orientation of cracks (β1=0.25, β2=0.5, ψ1=0.1667 and ψ2=0.5) in chapter 4. It is plotted with corresponding mode shapes derived from theoretical and experimental diagnosis for cracked composite beam and have been shown in figures 4.2a-4.2c. Similarly graph plotted for structural steel has been shown in figures 4.4a to 4.4c. The results for relative first crack depth and crack position and relative second crack depth and crack position are derived from theoretical, numerical and
experimental examination corresponding to relative 1st, 2nd & 3rd natural frequencies and mode shapes. And it is presented in table 4.2 and table 4.4 for composite and steel beam respectively. The total percentages of deviation of numerical analysis are 3.10% for composite beam and 3.50% for structural steel. In chapter 5, the results derived from various fuzzy models (Triangular, Gaussian and Trapezoidal) and experimental test have been compared in table 5.4 for composite beam and likewise table 5.5 presents the comparison of results obtained from various method for structural steel. The total percentage of deviation of results for triangular fuzzy model is 8.1%, for Gaussian fuzzy model is 4.6%, for Trapezoidal fuzzy model is 7.4% for the case of composite beam.
Similarly for structural steel, total percentage of deviation of results for triangular fuzzy model is 7.5%, for Gaussian fuzzy model is 4.3 %, for Trapezoidal fuzzy model is 6.8%.
In chapter 6 presents discussion about various neural models. The results derived from BPNN, RBFNN and KSOM model compared with experimental analysis results and has been presented in tables 6.1 and 6.3 for composite beam and steel beam respectively. The percentage of total deviation for BPNN is 4.9%, for RBFNN is 4.6% and for KSOM is 5.4%for composite beam. Similarly for the structural steel beam the total percentage of deviation for BPNN is 5.7%, for RBFNN is 4.3% and for KSOM is 6.21%. The comparison of results derived from various hybrid fuzzy-neuro systems have been displayed in tables 7.1, 7.2 and 7.3 for composite beam. After the study of results, it is observed that Gaussian BPNN, Gaussian RBFNN and Gaussian fuzzy-KSOM hybrid system provides least deviation in the results. A similar pattern is observed for structural steel. The comparison of results obtained from various hybrid models have been presented in tables 7.5, 7.6 and 7.7. A close proximity is found between the results.
CHAPTER 9 Results and Discussion
9.1 Introduction
This chapter describes the systematic analysis of performance of various techniques used for identification of multiple damages of cantilever beams cited in the above chapters.
The vibration responses of faulty structures have been used for development of damage assessment tool. Various techniques are discussed in current dissertation for assessment of multiple damages of cantilever beams. These techniques are: theoretical method (chapter 3), Finite element method (chapter 4), fuzzy logic system (chapter 5), and artificial neural network (chapter 6), hybrid fuzzy-neuro methods (chapter 7) and experimental investigation (chapter 8).