Damage Identification Of Beam Structures Based On Flexibility Matrix And Information Entropy

As an indispensable part of the national modern transportation system,bridge is an essential part of supporting the high-quality development of national economy.In the process of long-term service of the bridge,it will be affected by the harsh natural environment,vehicle overload,and maintenance conditions,which will lead to local stiffness degradation even losing of overall stability.If the local damage is not accurately identified and the corresponding reinforcement measures are taken,the collapse of the bridge will cause serious economic losses and adverse social impact.The state has attached great importance to the construction of bridge health monitoring system and the establishment of bridge health records,so it is of great practical significance to find a damage identification index with strong adaptability to structural types,accurate identification of damage occurrence,convenient on-site operation and good economy property.Flexibility matrix is a kind of promising damage identification index in practical application because of its high sensitivity to damage,simple calculation and easy programming implementation,and each value in the matrix has a clear physical meaning.In this paper,the dynamic flexibility matrix based on dynamic test and the static flexibility matrix based on static test are used respectively.Two damage identification methods are proposed based on information entropy theory.Using finite element simulationn and an experiment to verify the effectiveness of these indicators.The work of this paper mainly includes:(1)In order to identify the damage of the structure without prior information,combining the characteristics of information entropy and generalized flexibility curvature in structural damage identification,a method based on the interpolation curve of generalized flexibility curvature entropy is proposed.By calculating the generalized flexibility curvature entropy index,the damage location is carried out according to the index mutation.Different numerical interpolation methods are used to calculate the entropy points of the damage area,and the polynomial is used to fit the undamaged curve to obtain the functional relationship between the damage area and the damage degree,so as to carry out the quantitative damage research.The results show that the method is accurate in damage location and good in quantitative effect when the signalto-noise ratio is above 50 d B,so the proposed index has good anti-noise ability.(2)Based on the static test data before and after structural damage,combined with the definition of flexibility matrix,the static response equation is constructed,and the minimum rank restriction is imposed on the structural flexibility disturbance matrix.The equation of the minimum rank solution of the static flexibility matrix is derived in detail,and the minimum rank flexibility matrix after structural damage is obtained.Combined with the information entropy formula,the minimum rank flexibility entropy index is proposed Finally,different levels of noise are applied to the static test data to study the influence of measurement error.The results show that the structural damage location and relative damage degree can still be identified stably within 3% error of displacement data.(3)In order to verify the feasibility of the minimum rank flexibility index in practical application,aluminum box section simply supported beam is used as the experimental object.The structure damage is simulated by cutting grooves,three groups of static loads are applied respectively,the displacement data are collected by laser displacement meter,and the minimum rank flexibility entropy index is calculated by using the experimental data.The experimental results show that the minimum rank flexibility entropy index proposed in this paper can mutate at the damage location,and the larger the damage is,the larger the mutation value is,which can judge the relative damage degree of the element.