Research On Dynamic Damage Identification Method Of Stochastic Structure Based On Fractional Statistical Moment

Due to the impact of harsh environments such as corrosion,earthquakes,and typhoons,civil engineering structures face problems of performance degradation after being built and operating for a certain period of time.Therefore,the research and application of structural damage detection methods based on vibration theory in evaluating the function and safety of civil engineering structures have attracted extensive attention.However,damage detection and diagnosis of civil engineering structures is still a challenging task.Current damage detection methods are either insensitive to local structural damage or sensitive to measurement noise.In addition,the uncertainty of a large amount of information is inherently related to the damage detection of civil engineering structures,which limits the successful application of most deterministic damage detection methods.In response to this problem,this paper establishes a framework in which,considering the uncertainty of measurement,structure and external excitation,a random method based on cubic normal transformation is proposed to detect the damage of the building structure.The main research work includes:(1)For the first time,a method of damage detection based on fractional statistical moments(FSMBDD)under the excitation of Gaussian white noise is proposed.The sensitivity of different structural response types and different orders of statistical moments to structural damage is discussed.The damage detection formula based on the complete quadratic term combination method(CQC)to calculate the structural response statistical moment is derived.The impact of measurement noise on damage detection is determined.Using genetic algorithm,the new damage index and the proposed FSMBDD method are extended to multi-degree-of-freedom systems.As a numerical study,the method is applied to single-layer and multi-layer shear-type structures considering measurement noise.The calculation results show that under noisy and no-noise conditions,the recognition error of the fractional 46/9 moment proposed in this paper is smaller than that of the fourth-order integer moment.And the size of the small recognition error in genetic algorithm optimization and least squares optimization is studied.The research results show that the recognition error of genetic algorithm in damage recognition is smaller than the least squares optimization error.It is also proved that the 46/9-order displacement statistical moment based on the interlayer displacement can better identify the location and severity of various failure modes of the shear wall structure.In addition,a significant advantage of the FSMBDD method is that it is not only sensitive to local structural damage,but also insensitive to measurement noise.(2)For the application of actual engineering structures,the generalized FSMBDD method is proposed from the following two aspects: 1)calculation method of structural response;2)type and location of external excitation.By using the fast virtual excitation method to calculate the structural response,as long as the Gaussian distribution is satisfied,the FSMBDD method has a wider applicability to the building structure under any random excitation.A large number of numerical examples have verified the feasibility and effectiveness of the generalized SMBDD method.For multi-degreeof-freedom shear wall structures under colored noise excitation at different locations,the efficiency of different structural response calculation methods for FSMBDD method to identify structural damage was studied.This paper also studies the influence of measurement noise on the quality of recognition results,and analyzes the influence of measurement noise on external excitation and measurement response under all set damage conditions.The numerical analysis results show that the use of the fast virtual excitation method to calculate the structural response is the most efficient in identifying structural damage with the FSMBDD method,and the damage location and severity can still be effectively identified under various damage situations.(3)Aiming at the inevitable random parameters or uncertainties of civil structures,a random damage detection method based on the generalized FSMBDD method is proposed.The proposed random damage detection method based on cubic positive transformation can not only locate the structural damage,but also can identify the severity of the damage without requiring a large amount of calculation,and can also handle Gaussian and non-Gaussian random parameters.(4)A new algorithm for random damage detection method is proposed.A new damage index was used to identify the damage location and damage severity,and then a numerical simulation of a shear wall structure was conducted to verify the effectiveness of the method.The damping ratio of the shear tower is selected as the random parameter of the normal distribution,and three damage conditions are studied,including single damage conditions and multiple damage conditions.The numerical analysis results show that,when considering the uncertainty or random parameters,this method can better identify the damage location and damage severity of the random parameter building structure,and the algorithm is simple and the recognition efficiency is high.The research content of this paper includes the application of FSMBDD method and random damage detection method.A large number of numerical and experimental studies have shown that the FSMBDD method is not only sensitive to local damage to the structure,but also insensitive to measurement noise.Random damage detection methods can identify damage to structural uncertainties or random parameters.