Damage Detection on Steel Truss Bridges Using Modal Based Methods

Dita Kamarul Fitriyah; Budi Suswanto; Heppy Kristijanto; Ahmad Basshofi Habieb; Djoko Irawan

doi:10.2478/cee-2026-0093

Damage Detection on Steel Truss Bridges Using Modal Based Methods

Civil and Environmental Engineering

AHEAD OF PRINT

By: Dita Kamarul Fitriyah, Budi Suswanto, Heppy Kristijanto, Ahmad Basshofi Habieb and Djoko Irawan

Open Access

|Apr 2026

Figures & Tables

Damage scenarios modelled in the experiment

Table 1:

Models and damage scenario

Models	Damage scenario	Damage location
Intact	-	-
Dmg-CC	Cutting diagonal members	L/2 (0.5 L)
Dmg-BC	Buckling diagonal members	L/2 (0.5 L)
Dmg-EC	Missing diagonal members	L/2 (0.5 L)
Dmg-CE	Cutting diagonal members	L/5 (0.2 L)
Dmg-BE	Buckling diagonal members	L/5 (0.2 L)
Dmg-EE	Missing diagonal members	L/5 (0.2 L)

Rembun Bridge after collapsing due to severe corrosion on the bottom chord (right)

The diagonal member at the end was struck by a vehicle

Table 2:

Section properties

Members	Section properties [mm]
End post	L 30×30×3
Upper chord	2L 40×40×4
Lower chord	2L 40×40×4
Diagonal members	L 30×30×3
Portal strut	L 30×30×3
Strut	L 30×30×3
Girder	L 50×50×5

Geometry of the steel frame bridge specimen

Finite element model and modal displacement of the Dmg-CC structure

Experimental simulation of mid-span diagonal member damage (Dmg-CC)

Curvature index of each method on the DMG-CC model

Table 3:

Comparison of modal damage index accuracy for mid-span diagonal cutting damage (Dmg-CC)

Modal parameter	Squared displacement difference (unitless)											SSE	MSE	RMSE
	0.0L	0.1L	0.2L	0.3L	0.4L	0.5L	0.6L	0.7L	0.8L	0.9L	1.0L
MSIi	0.00	0.00	0.03	0.09	0.38	0.02	0.12	0.30	0.27	0.23	0.00	1.44	0.13	0.36
MSSi	0.00	0.00	0.00	0.00	0.00	0.00	0.07	0.00	0.00	0.00	0.00	0.08	0.01	0.08
MSCi	0.00	0.00	0.00	0.00	0.36	0.00	0.05	0.02	0.01	0.03	0.00	0.48	0.04	0.21
MSCSi	0.00	0.00	0.00	0.02	0.22	0.02	0.09	0.13	0.05	0.01	0.00	0.53	0.05	0.22

Finite element model and modal displacement of the dmg-BC structure

Experimental simulation of mid-span diagonal member damage (Dmg-BC)

Curvature index of each method on the DMG-BC model

Table 4:

Comparison of modal Damage Index Accuracy for Mid-Span Buckling Damage Model (Dmg-BC)

Modal parameter	Squared displacement difference (unitless)											SSE	MSE	RMSE
	0.0L	0.1L	0.2L	0.3L	0.4L	0.5L	0.6L	0.7L	0.8L	0.9L	1.0L
MSIi	0.00	0.00	0.01	0.04	0.09	0.26	0.17	0.44	0.10	0.04	0.00	1.16	0.11	0.32
MSSi	0.00	0.00	0.00	0.01	0.01	0.00	0.25	0.00	0.02	0.01	0.00	0.29	0.03	0.16
MSCi	0.00	0.00	0.14	0.03	0.01	0.02	0.45	0.02	0.14	0.00	0.00	0.81	0.07	0.27
MSCSi	0.00	0.00	0.00	0.05	0.29	0.06	0.31	0.30	0.02	0.00	0.00	1.03	0.09	0.31

Finite element model and modal displacement of the Dmg-EC structure

Experimental simulation of mid-span diagonal member damage (Dmg-EC)

Curvature index of each method on the DMG-EC model

Table 5:

Comparison of modal damage index accuracy for mid-span diagonal member removal (Dmg-EC)

Modal parameter	Squared displacement difference (unitless)											SSE	MSE	RMSE
	0.0L	0.1L	0.2L	0.3L	0.4L	0.5L	0.6L	0.7L	0.8L	0.9L	1.0L
MSIi	0.00	0.00	0.00	0.07	0.07	0.55	0.03	0.67	0.22	0.04	0.00	1.66	0.15	0.39
MSSi	0.00	0.00	0.00	0.00	0.08	0.00	0.18	0.14	0.01	0.02	0.00	0.43	0.04	0.20
MSCi	0.00	0.00	0.12	0.13	0.00	0.11	0.50	0.15	0.03	0.01	0.00	1.06	0.10	0.31
MSCSi	0.00	0.00	0.00	0.00	0.18	0.39	0.11	0.45	0.06	0.00	0.00	1.25	0.11	0.34

Finite element model and modal displacement of the Dmg-CE structure

Experimental simulation of diagonal member damage at 1/5 of the span (Dmg-CE)

Curvature index of each method on the DMG-CE model

Table 6:

Accuracy comparison of modal damage indices for 1/5-span diagonal cutting damage (Dmg-CE)

Modal parameter	Squared displacement difference (unitless)											SSE	MSE	RMSE
	0.0L	0.1L	0.2L	0.3L	0.4L	0.5L	0.6L	0.7L	0.8L	0.9L	1.0L
MSIi	0.00	0.00	0.01	0.03	0.11	0.10	0.05	0.01	0.11	0.07	0.00	0.50	0.05	0.21
MSSi	0.00	0.00	0.00	0.01	0.00	0.05	0.01	0.03	0.00	0.00	0.00	0.11	0.01	0.10
MSCi	0.00	0.00	0.00	0.00	0.02	0.00	0.03	0.02	0.04	0.03	0.00	0.13	0.01	0.11
MSCSi	0.00	0.00	0.00	0.00	0.04	0.11	0.03	0.07	0.01	0.00	0.00	0.27	0.02	0.16

Finite element model and modal displacement of the dmg-BE structure

Experimental simulation of diagonal member damage at 1/5 of the span (Dmg-BE)

Curvature index of each method on the DMG-BE model

Table 7:

Accuracy comparison of modal damage indices for 1/5-span diagonal buckling damage (Dmg-BE)

Modal parameter	Squared displacement difference (unitless)											SSE	MSE	RMSE
	0.0L	0.1L	0.2L	0.3L	0.4L	0.5L	0.6L	0.7L	0.8L	0.9L	1.0L
MSIi	0.00	0.00	0.01	0.06	0.00	0.00	0.01	0.01	0.12	0.06	0.00	0.27	0.02	0.16
MSSi	0.00	0.01	0.05	0.01	0.00	0.01	0.00	0.00	0.00	0.01	0.00	0.08	0.01	0.09
MSCi	0.00	0.00	0.02	0.14	0.00	0.00	0.02	0.02	0.00	0.01	0.00	0.21	0.02	0.14
MSCSi	0.00	0.00	0.02	0.14	0.02	0.00	0.00	0.04	0.01	0.00	0.00	0.23	0.02	0.14

Finite element model and modal displacement of the dmg-EE structure

Experimental simulation of diagonal member damage at 1/5 of the span (Dmg-EE)

Table 8:

Accuracy comparison of modal damage indices for 1/5-span diagonal member removal damage (Dmg-EE)

Modal parameter	Squared displacement difference (unitless)											SSE	MSE	RMSE
	0.0L	0.1L	0.2L	0.3L	0.4L	0.5L	0.6L	0.7L	0.8L	0.9L	1.0L
MSIi	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.01	0.06	0.04	0.00	0.13	0.01	0.11
MSSi	0.00	0.00	0.00	0.00	0.00	0.01	0.00	0.00	0.00	0.00	0.00	0.02	0.00	0.04
MSCi	0.00	0.00	0.00	0.00	0.00	0.00	0.02	0.02	0.01	0.01	0.00	0.06	0.01	0.08
MSCSi	0.00	0.00	0.01	0.03	0.02	0.00	0.00	0.04	0.00	0.00	0.00	0.11	0.01	0.10

References

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DOI: https://doi.org/10.2478/cee-2026-0093 | Journal eISSN: 2199-6512 (formerly 1336-5835) | Journal ISSN: 1336-5835

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Language: English

Submitted on: Oct 27, 2025

Accepted on: Feb 25, 2026

Published on: Apr 21, 2026

Published by: University of Žilina

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

SHMS,

Related subjects:

Business and economics,

Business management,

Industries,

Environmental management

© 2026 Dita Kamarul Fitriyah, Budi Suswanto, Heppy Kristijanto, Ahmad Basshofi Habieb, Djoko Irawan, published by University of Žilina
This work is licensed under the Creative Commons Attribution 4.0 License.

AHEAD OF PRINT

Damage Detection on Steel Truss Bridges Using Modal Based Methods

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