Analysis of Adaptive Fuzzy Technique for Multiple Crack Diagnosis of Faulty Beam Using Vibration Signatures

Table 3

Comparison of results between fuzzy Gaussian controller, numerical FEM analysis, and experimental setup.

Relative first natural frequency “fnf”	Relative second natural frequency “snf”	Relative third natural frequency “tnf”	Average relative first mode shape difference “fmd”	Average relative second mode shape difference “smd”	Average relative third mode shape difference “tmd”	Fuzzy Gaussian controller relative 1st crack depth “rcd1,” 1st crack location “rcl1,” 2nd crack depth “rcd2,” 2nd crack location “rcl2”				FEM relative 1^st crack depth “rcd1,” 1^st crack location “rcl1,” 2nd crack depth “rcd2,” 2nd crack location “rcl2”				Numerical relative 1^st crack depth “rcd1,” 1st crack location “rcl1,” 2nd crack depth “rcd2,” 2nd crack location “rcl2”				Experimental relative 1^st crack depth “rcd1,” 1st crack location “rcl1,” 2nd crack depth “rcd2,” 2nd crack location “rcl2”
						rcd1	rcl1	rcd2	rcl2	rcd1	rcl1	rcd2	rcl2	rcd1	rcl1	rcd2	rcl2	rcd1	rcl1	rcd2	rcl2
0.9987	0.9993	0.9996	0.0092	0.0027	0.0036	0.163	0.123	0.24	0.373	0.163	0.123	0.24	0.373	0.160	0.120	0.21	0.37	0.169	0.128	0.27	0.377
0.9968	0.9996	0.9992	0.0002	0.9712	0.2259	0.331	0.123	0.415	0.49	0.330	0.121	0.414	0.48	0.327	0.119	0.409	0.48	0.336	0.129	0.420	0.52
0.9924	0.9986	0.9995	0.0149	0.01	0.0826	0.413	0.124	0.330	0.875	0.412	0.122	0.329	0.873	0.408	0.118	0.326	0.87	0.419	0.127	0.336	0.879
0.9983	0.9997	0.9986	0.002	0.0034	0.0809	0.164	0.25	0.25	0.5	0.162	0.23	0.24	0.49	0.158	0.23	0.24	0.48	0.169	0.29	0.27	0.53
0.9980	0.9964	0.9883	0.0023	0.0333	0.0132	0.25	0.25	0.414	0.76	0.24	0.24	0.413	0.74	0.22	0.23	0.41	0.73	0.29	0.29	0.418	0.79
0.9992	0.9977	0.9975	0.3721	0.3416	0.2614	0.415	0.25	0.165	0.51	0.414	0.24	0.163	0.49	0.411	0.23	0.159	0.47	0.419	0.28	0.170	0.54
0.9852	0.9985	0.9864	0.0149	0.0201	0.0122	0.50	0.25	0.25	0.73	0.48	0.23	0.25	0.74	0.47	0.24	0.25	0.74	0.53	0.29	0.28	0.77
0.9994	0.9965	0.9968	0.0012	0.0013	0.0082	0.165	0.374	0.24	0.623	0.163	0.373	0.24	0.622	0.159	0.37	0.22	0.621	0.171	0.379	0.29	0.627
0.9985	0.9850	0.9885	0.0064	0.0083	0.0287	0.332	0.374	0.49	0.624	0.331	0.374	0.49	0.623	0.329	0.373	0.49	0.620	0.338	0.379	0.53	0.628
0.9991	0.99641	0.9994	0.0049	0.0032	0.0148	0.414	0.374	0.25	0.625	0.413	0.373	0.24	0.624	0.411	0.37	0.23	0.623	0.419	0.378	0.28	0.629