Damage Identification in Beam-Type Structures Using Pseudo Strain Energy Density and Grey Relation Coefficient

Based on pseudo strain energy density (PSED) and grey relation coefficient (GRC), an index is proposed to locate the damage of beam-type structures in time-domain. The genetic algorithm (GA) is utilized to identify the structural damage severity of confirmed damaged locations. Furthermore, a systematic damage identification program based on GA is developed on MATLAB platform. ANSYS is employed to conduct the finite element analysis of complicated civil engineering structures, which is embedded with interface technique. The two-step damage identification is verified by a finite element model of Xinxingtang Highway Bridge and a laboratory beam model based on polyvinylidens fluoride (PVDF). The bridge model was constructed with 57 girder segments, and simulated with 58 measurement points. The damaged segments were located accurately by GRC index regardless of damage extents and noise levels. With stiffness reduction factors of detected segments as variables, the GA program evolved for 150 generations in 6 h and identified the damage extent with the maximum errors of 1% and 3% corresponding to the noise to signal ratios of 0 and 5%, respectively. In contrast, the common GA-based method without using GRC index evolved for 600 generations in 24 h, but failed to obtain satisfactory results. In the laboratory test, PVDF patches were used as dynamic strain sensors, and the damage locations were identified due to the fact that GRC indexes of points near damaged elements were smaller than 0.6 while those of others were larger than 0.6. The GA-based damage quantification was also consistent with the value of crack depth in the beam model.

Structural damage identification using test static data based on grey system theory

A new structural damage identification method using limited test static displacement based on grey system theory is proposed in this paper. The grey relation coefficient of displacement curvature is defined and used to locate damage in the structure, and an iterative estimation scheme for solving nonlinear optimization programming problems based on the quadratic programming technique is used to identify the damage magnitude. A numerical example of a cantilever beam with single or multiple damages is used to examine the capability of the proposed grey-theory-based method to localize and identify damages. The factors of meas-urement noise and incomplete test data are also discussed. The numerical results showed that the damage in the structure can be localized correctly through using the grey-related coefficient of displacement curvature, and the damage magnitude can be iden-tified with a high degree of accuracy, regardless of the number of measured displacement nodes. This proposed method only requires limited static test data, which is easily available in practice, and has wide applications in structural damage detection.

Evaluation of measurement uncertainty based on grey system theory for small samples from an unknown distribution

To evaluate measurement uncertainty for small sample size and measurement data from an unknown distribution, we propose a grey evaluation method of measurement uncertainty based on the grey relation coefficient. The uncertainty of measurement is analyzed using grey system theory, and the defects of the grey evaluation model of measurement uncertainty (GEMU) are studied. We then establish an improved grey evaluation model of measurement uncertainty (IGEMU). Simulations show that the precision of IGEMU is greater than that of GEMU, and that sample size has only a small effect on the precision of IGEVU. In particular, IGEMU is applied to evaluating measurement uncertainty for small sample size and measurement data from an unknown distribution. The measurement uncertainty of total profile deviation, which is measured by the CNC gear measuring center, can be evaluated by a combination of IGEMU and the Monte Carlo method.

Optimizing soil dissolved organic matter extraction by grey relational analysis

Dissolved organic matter(DOM)in soil plays an important role in the fate and transport o f contaminants.It is typically composed of many compounds,but the effect of different extraction factors on the abundance of different DOM components is unknown.In this study,DOM was extracted from three soils(paddy field,vegetable field and forest soils)with various extraction time,liquid to solid ratios(LSRs).extractant types,and extractant concentrations.The LSR had a significant effect on DOM content,which increased by 0.5-4.0 times among the three soils when LSR increased from 2:1 to 10:1(P<0.05).Dissolved organic matter content increased by 4%-53%when extraction time increased from 10 to 300 min(P<0.05).Extractant concentration had different effects on DOM content depending on the extractant.Higher concentrations of KC1 promoted DOM extraction,while higher concentrations o f KH2PO4 inhibited DOM extraction.Therefore,grey relational analysis was used to further quantitatively evaluate the effect of extraction time,LSR,and extractant concentration on DOM,using KC1 as an extractant.For the paddy field and forest soils,the impact of these three factors on DOM extraction efficiency was in the following order:KC1 concentration>LSR>extraction time.However,the effect was different for the vegetable field soil:LSR>extraction time>KCI concentration.Taking all these factors into account,1.50 mol L^-1 KC1 and an LSR of 10:1 with a shaking time of 300 min was recommended as the most appropriate method for soil DOM extraction.