Statics-Based Model-Free Damage Detection under Uncertainties Using Modal Interval Analysis

Abstract

Deterministic damage detection methods often fail in practical applications due to ever-present uncertainties. Moreover, vibration-based model updating strategies are easily affected by measurement noises and could encounter ill-conditioning problems during inverse solutions. On this account, a model-free method has been proposed combining modal interval analyses with static measurements. Structural geometrical dimensions, material parameters and external loads are expressed by interval variables representing uncertainties. Mechanical formulas for static responses are then extended to their interval forms, which are subsequently solved using classic interval and modal interval analyses. The analytical interval envelopes of static responses such as deflections and strains are defined by the interval solutions, and damage can be detected when the measured responses intersect the envelopes. By this approach, potential damage can be found in a fast and rough way without any inverse solution process such as model updating. The proposed method has been verified against both numerical and experimental reinforced concrete beams whose strains were taken as the desirable responses. It was found that the strain envelopes provided by modal interval analysis were narrower than those by classic interval analysis. Modal interval analysis effectively avoids the phenomenon of interval overestimation. In addition, the intersection point also identifies the current external load, providing a loading alarm for structures.

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements

“…The system under consideration is a single-degree-of-freedom system, as depicted in Figure 9, where the viscoelastic element is described using the Maxwell model. The presented method requires the equations of motion to be formulated in a way that describes the relationship between the central value of the parameter and its uncertainties, as outlined in Equation (31). In the case of the Kelvin model, as discussed in the previous section, achieving this is relatively straightforward.…”

“…Interval analysis finds broad application when dealing with uncertain design parameters, extending to other problems related to the analysis of structural behavior under dynamic loads. In [29] by Sofi et al, it was applied to analyze the reliability of systems with viscoelastic dampers; in [30] by Wang et al, it was applied to assess the reliability of systems with active vibration control; and in [31], Fang and Huang utilized it in the analysis of structural damage detection involving various types of uncertainties.…”

“…Advantage: they can be applied when probability distribution is lacking; disadvantages: operations are computationally expensive and results may be less precise than with probabilistic methods.  Methods based on interval analysis [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][23][24][25][26][27][28][29][30][31]35,[42][43][44], where parameters are modeled as intervals. Advantages: they consider the range in which the parameter changes without knowing its exact distribution, allow for the relatively easy determination of the lower and upper bounds of the response function, and are relatively easy to code; disadvantage: the obtained results may be overestimated.…”

A Novel Hybrid Whale-Chimp Optimization Algorithm for Structural Damage Detection

“…Step 3: Update the population position according to the size of random value p and correlation coefficient vector A. If p < 0.5 and |A| ≥ 1, the random search mechanism is used for updating the population position according to Equation (13). If p < 0.5 and |A| < 1, the chimp individuals update their population positions with the traditional ChOA according to Equation (5).…”

“…Boumechra [12] proposed a strategy to identify structural damage based on the deflection change of bridges to update the finite element model. Fang and Huang [13] introduced a model-free structural damage detection method using static measurement data and modal interval analysis to detect damage. Liu et al [14] presented a method for structural damage detection of statically loaded structures based on the change of internal force and displacement of the finite element model.…”