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.

Relationship between Housing Price and Land Price Based on Grey Relational Analysis

In recent Years, China＇s real estate market has been rapid developed, and real estate has become a hot spot of consumption and investment. In some large and medium-sized cities there has been a rapid rise in housing prices. The rapid rise in housing prices has led to difficulties in the purchase of houses in some cities and towns, and this phenomenon has aroused the attention and con- cern of all walks of life. Housing is the basic human life needs. Housing problem is not only an economic problem, but also a social problem. The relationship between house price and land price and the effective control of housing prices have become the focus of government and scholars. Thus, grey relational analysis is used to ana- lyze the relationship between housing prices and land prices, and the grey relational coefficients are calculated.

On grey relation projection model based on projection pursuit

Multidimensional grey relation projection value can be synthesized as one-dimensional projection value by using projection pursuit model. The larger the projection value is,the better the model. Thus,according to the projection value,the best one can be chosen from the model aggregation. Because projection pursuit modeling based on accelerating genetic algorithm can simplify the implementation procedure of the projection pursuit technique and overcome its complex calculation as well as the difficulty in implementing its program,a new method can be obtained for choosing the best grey relation projection model based on the projection pursuit technique.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

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 and Driving Force Analysis of Marine Sustainable Development based on the Grey Relational Model and Path Analysis

With the rapid development of the marine economy,the demand for marine resources development and the pressure on marine environmental protection are gradually increasing.It is critical to evaluate and analyze the driving forces of marine sustainable development in order to promote the coordinated development of the marine economy,resources and environment.Taking Jiangsu Province of China as an example,this paper constructs an evaluation index system for marine sustainable development from the three aspects of marine economy,resources and environment,and calculates the weight of the variation coefficient for each indicator.Based on the grey relational model,the average value of the relational degree,calculated by the average value method of correlation coefficients and the weighting method,is then used to evaluate the status of marine sustainable development in this province.The comprehensive index model is used to analyze the dynamic trend of the evolution of marine sustainable development.The driving forces of marine sustainable development are analyzed by the path analysis method combined with the average values of the grey relational degree for each indicator.This analysis found that the marine sustainable development in 2016 and 2012 was good,the situation in 2007 was bad,and the remaining years were intermediate.Compared with the previous years,the optimal conditions of 2008 and 2012 were obvious.The main driving factors of marine sustainable development are cargo throughput of coastal ports,economic losses caused by storm surges in coastal areas,the area of marine nature reserves in coastal areas,coastal wind power generation capacity,and marine biodiversity.

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.

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.

Factors influencing methane diffusion behaviors in micro-nano coal pores: a comprehensive study

Gas diffusion in the coal matrix plays a significant role in forecasting the production performance of coalbed methane(CBM)wells.To better understand methane diffusion behavior,a systematic study was performed on various rank coals with vitrinite reflectance(Ro,m)ranging from 0.46%to 2.79%.Multiple experiments,including coal petrographic analysis,field emission scanning electron microscopy(FESEM),low-temperature N2 adsorption/desorption,and mercury intrusion porosimetry(MIP),were conducted to quantitatively characterize the multiscale micro-nano pore system in different rank coals,which showed that the pore structure of coals exhibited a multimodal pore size and volume distribution.Isothermal adsorption-diffusion experiments using the volumetric method were also performed to understand the methane diffusion characteristics in the micro-nano pores of the coal reservoir.The applicability of the multiporous diffusion model is verified,and methane diffusion in the multi-scale pores of coal reservoirs exhibits the characteristics of early fast diffusion,transitional diffusion in the medium term,and slow diffusion in the later period.In addition,the factors affecting methane diffusion in coals were systematically analyzed,and gray relational analysis(GRA)was employed to analyze and identify the importance of these factors on methane diffusion.The results show the impact ranking of factors,in order from the most important to the least:particle size>moisture>surface area>pore volume>pressure>coal rank>temperature in all of three diffusion stages.These findings are helpful for forecasting production performance and enhancing the production efficiency of CBM.