Advances in Fuzzy Systems

Research Article

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

Table 1

Description of fuzzy linguistic terms.


Membership functions name	Linguistic terms	Description and range of the linguistic terms

L1F1, L1F2, L1F3, L1F4	fnf_{1 to 4}	Low ranges of relative natural frequency for first mode of vibration in descending order, respectively.
M1F1, M1F2	fnf_5, 6	Medium ranges of relative natural frequency for first mode of vibration in ascending order, respectively.
H1F1, H1F2, H1F3, H1F4	fnf_{7 to 10}	Higher ranges of relative natural frequency for first mode of vibration in ascending order, respectively.
L2F1, L2F2, L2F3, L2F4	snf_{1 to 4}	Low ranges of relative natural frequency for second mode of vibration in descending order, respectively.
M2F1, M2F2	snf_5, 6	Medium ranges of relative natural frequency for second mode of vibration in ascending order, respectively.
H2F1, H2F2, H2F3, H2F4	snf_{7 to 10}	Higher ranges of relative natural frequencies for second mode of vibration in ascending order, respectively.
L3F1, L3F2, L3F3, L3F4	tnf_{1 to 4}	Low ranges of relative natural frequencies for third mode of vibration in descending order, respectively.
M3F1, M3F2	tnf_5, 6	Medium ranges of relative natural frequencies for third mode of vibration in ascending order, respectively.
H3F1, H3F2, H3F3, H3F4	tnf_{7 to 10}	Higher ranges of relative natural frequencies for third mode of vibration in ascending order, respectively.
S1M1, S1M2, S1M3, S1M4	fmd_{1 to 4}	Small ranges of first relative mode shape difference in descending order, respectively.
M1M1, M1M2	fmd_5, 6	Medium ranges of first relative mode shape difference in ascending order, respectively.
H1M1, H1M2, H1M3, H1M4	fmd_{7 to 10}	Higher ranges of first relative mode shape difference in ascending order, respectively.
S2M1, S2M2, S2M3, S2M4	smd_{1 to 4}	Small ranges of second relative mode shape difference in descending order, respectively.
M2M1, M2M2	smd_5, 6	Medium ranges of second relative mode shape difference in ascending order, respectively.
H2M1, H2M2, H2M3, H2M4	smd_{7 to 10}	Higher ranges of second relative mode shape difference in ascending order, respectively.
S3M1, S3M2, S3M3, S3M4	tmd_{1 to 4}	Small ranges of third relative mode shape difference in descending order, respectively.
M3M1, M3M2	tmd_5, 6	Medium ranges of third relative mode shape difference in ascending order, respectively.
H3M1, H3M2, H3M3, H3M4	tmd_{7 to 10}	Higher ranges of third relative mode shape difference in ascending order, respectively.
S1L1, S1L2,…, S1L22	rcl1_{1 to 22}	Small ranges of relative crack location in descending order, respectively.
M1L1, M1L2	rcl1_23, 24	Medium ranges of relative crack location in ascending order, respectively.
B1L1, B1L2,…, B1L22	rcl1_{25 to 46}	Bigger ranges of relative crack location in ascending order, respectively.
S1D1, S1D2,…, S1D9	rcd1_{1 to 9}	Small ranges of relative crack depth in descending order, respectively.
M1D	rcd1₁₀	Medium relative crack depth.
L1D1, L1D2,…, L1D9	rcd1_{11 to 19}	Larger ranges of relative crack depth in ascending order, respectively.
S2L1, S2L2,…, S2L22	rcl2_{1 to 22}	Small ranges of relative crack location in descending order, respectively.
M2L1, M2L2	rcl2_23, 24	Medium ranges of relative crack location in ascending order, respectively.
B2L1, B2L2,…, B2L22	rcl2_{25 to 46}	Bigger ranges of relative crack location in ascending order, respectively.
S2D1, S2D2,…, S2D9	rcd2_{1 to 9}	Small ranges of relative crack depth in descending order, respectively.
M2D	rcd2₁₀	Medium relative crack depth.
L2D1, L2D2,…, L2D9	rcd2_{11 to 19}	Larger ranges of relative crack depth in ascending order, respectively.