Reasonable and effective quantification of the spatial uncertainty of bridge parameters is a prerequisite for structural reliability analysis and design. However, it is usually difficult to measure the uncertainty of actual bridge parameters directly. In this paper, a method is proposed to estimate the spatial uncertainty interval field of bridge parameters based on the measured dynamic characteristic data. Firstly, a non-probabilistic ellipsoid model for describing the uncertainty of bridge dynamic characteristics is established based on a small number of test samples. Secondly, the interval field of bridge parameters with the spatial uncertainty is parameterized, and a parameterized finite element model is established to calculate the ellipsoid model. Then, the interval field parameters are optimized iteratively to match the computational ellipsoid model and the measured ellipsoid model, and a realistic interval field of the bridge parameters with spatial uncertainty is constructed accordingly. Finally, the effectiveness and superiority of the proposed method are verified by experimental and numerical cases, and the influence of interval field parameters and the number of dynamic characteristics is investigated. The results indicate that the proposed method can reasonably and practically construct an interval field of bridge parameters based on a small amount of measured dynamic characteristic data.
AlhaddadRJoHJeongJH, et al. (2025) Impact load identification by training a convolutional neural network (CNN) with physics-based simulator under uncertainty. Advances in Structural Engineering, in press.
2.
ChaparroBMThuillierSMenezesLF, et al. (2008) Material parameters identification: gradient-based, genetic and hybrid optimization algorithms. Computational Materials Science44(2): 339–346.
3.
ChoiCKYooHH (2017) Stochastic inverse method to identify parameter random fields in a structure. Structural and Multidisciplinary Optimization54(6): 1557–1571.
4.
FaesMMoensD (2017) Identification and quantification of spatial interval uncertainty in numerical models. Computers and Structures192: 16–33.
5.
FaesMMoensD (2020) On auto‐ and cross‐interdependence in interval field finite element analysis. International Journal for Numerical Methods in Engineering121(9): 2033–2050.
6.
FaesMGRBroggiMSpanosPD, et al. (2022) Elucidating appealing features of differentiable auto-correlation functions: a study on the modified exponential kernel. Probabilistic Engineering Mechanics69: 103269.
7.
GillPEMurrayWSaundersMA (2001) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Journal on Optimization12(4): 979–1006.
8.
HouZYHuSLWangW (2025) Interpretable machine learning models for predicting probabilistic axial buckling strength of steel circular hollow section members considering discreteness of geometries and material. Advances in Structural Engineering28(5): 828–844.
9.
HuJQiuZ (2010) Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty. Applied Mathematical Modelling34: 725–734.
10.
HuangFSavaAAdjallahKH, et al. (2021) Fuzzy model identification based on mixture distribution analysis for bearings remaining useful life estimation using small training data set. Mechanical Systems And Signal Processing148: 107173.
11.
JayalakshmiVRaoARM (2017) Simultaneous identification of damage and input dynamic force on the structure for structural health monitoring. Structural and Multidisciplinary Optimization55: 2211–2238.
12.
JiangCHanXLiuGR (2007) Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Computer Methods in Applied Mechanics and Engineering196(49–52): 4791–4800.
13.
JiangCBiRGLuGY, et al. (2013) Structural reliability analysis using non-probabilistic convex model. Computer Methods in Applied Mechanics and Engineering254: 83–98.
14.
JiangCNiBYHanX, et al. (2014) Non-probabilistic convex model process: a new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems. Computer Methods in Applied Mechanics and Engineering268: 656–676.
15.
KangZZhangW (2016) Construction and application of an ellipsoidal convex model using a semi-definite programming formulation from measured data. Computer Methods in Applied Mechanics and Engineering300: 461–489.
16.
KhachiyanLG (1996) Rounding of polytopes in the real number model of computation. Mathematics of Operations Research21: 307–320.
17.
KimTLeeGYounBD (2019) Uncertainty characterization under measurement errors using maximum likelihood estimation: cantilever beam end-to-end UQ test problem. Structural and Multidisciplinary Optimization59: 323–333.
18.
LiYLHeWYRenWX, et al. (2024) Bridge dynamic response analysis considering the spatial dependency of uncertainty parameters. Computers and Structures301: 107424.
19.
LoiolaBROrlandeHRBDulikravichGS (2020) Approximate Bayesian computation applied to the identification of thermal damage of biological tissues due to laser irradiation. International Journal of Thermal Sciences151: 106243.
20.
LüHYangKHuangX, et al. (2022) Uncertainty and correlation propagation analysis of powertrain mounting systems based on multi-ellipsoid convex model. Mechanical Systems And Signal Processing173: 109058.
21.
MoensDMunckMDDesmetW, et al. (2011) Numerical dynamic analysis of uncertain mechanical structures based on interval fields. In: BelyaevAKLangleyRS (eds) IUTAM symposium on the vibration analysis of structures with uncertainties. Netherlands: Springer, 71–83.
22.
NiBYJiangC (2020) Interval field model and interval finite element analysis. Computer Methods in Applied Mechanics and Engineering360: 112713.
23.
SofiAMuscolinoG (2015) Static analysis of Euler–Bernoulli beams with interval Young’s modulus. Computers and Structures156: 72–82.
24.
SofiARomeoEBarreraO, et al. (2019) An interval finite element method for the analysis of structures with spatially varying uncertainties. Advances in Engineering Software128: 1–19.
25.
TaoJChenJ (2003) Experimental study on the spatial variability of concrete by the core test and rebound hammer test. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part A: Civil Engineering9(4): 04023029.
26.
VerhaegheWDesmetWVandepitteD, et al. (2013) Interval fields to represent uncertainty on the output side of a static FE analysis. Computer Methods in Applied Mechanics and Engineering260: 50–62.
27.
WangC (2019) Evidence-theory-based uncertain parameter identification method for mechanical systems with imprecise information. Computer Methods in Applied Mechanics and Engineering351: 281–296.
28.
WangLChenZYangG (2020) An interval uncertainty analysis method for structural response bounds using feedforward neural network differentiation. Applied Mathematical Modelling82: 449–468.
29.
WuDGaoW (2017) Uncertain static plane stress analysis with interval fields. International Journal for Numerical Methods in Engineering110(13): 1272–1300.
30.
XiaBWangL (2018) Non-probabilistic interval process analysis of time-varying uncertain structures. Engineering Structures175(15): 101–112.
31.
YangSLiuBLiF (2022) Estimations of the elastic moduli of concrete at different temperatures and humidities by mesomechanics methods. Case Studies in Construction Materials17: e01254.
32.
ZhangYQMiyamoriYMikamiS, et al. (2019) Vibration‐based structural state identification by a 1‐dimensional convolutional neural network. Computer-Aided Civil and Infrastructure Engineering34(9): 822–839.
33.
ZhaoMYYanWJYuenKV, et al. (2021) Non-probabilistic uncertainty quantification for dynamic characterization functions using complex ratio interval arithmetic operation of multidimensional parallelepiped model. Mechanical Systems And Signal Processing156: 107559.
