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Online damage detection based on cointegration of frequencies under influence of environmental temperature
Abstract
Structure frequency, which is always regarded as damage detection feature for its more convenient testability and higher measurement precision, is also susceptible to environmental and operational variations. The variations lead to frequency sequence non-stationary and make much disturbances for actual structure health monitoring and damage detection. So cointegration method in econometrics is introduced to deal with the non-stationary problem by the linear combination of non-stationary variables, thus the non-stationary problem for structure damage detection feature caused by environmental factor variation is transformed to stationary problem. At first, ADF (augmented Dickey-Fuller) test and EG (Engle-Granger) test are detailedly introduced to check non-stationary order of the feature sequence and calculate the cointegration coefficients. Next, the cointegration relationship between frequency sequences is verified using a simple supported beam and online damage detection procedure based on cointegration of frequency under the influence of environmental temperature is introduced. At last, the validity and robustness of the proposed method are illustrated through a prestressed concrete beam and a simple supported steel bridge.
... A multinomial combination of non-linear signals was applied to the non-linear cointegration method. Diao et al. (2017) took the first-order coefficients of the auto regressive (AR) model based on the structural acceleration response data as a cointegrated variable to remove the temperature and mass effects on structural damage detection; Liang et al. (2014) took the natural frequency as a cointegrated variable. Although the EMI technique has been widely used for SHM and damage detection in recent years, the application of cointegration for EMI signatures is rarely reported. ...
Electromechanical impedance technique has been widely used in the area of structural health monitoring. However, both damage and variation in environmental temperature can cause the changes in electromechanical impedance signature, which may cause false damage diagnosis. The temperature effect on the electromechanical impedance-based method has been one of its main drawbacks in practical application. This article proposes a new approach based on cointegration to eliminate temperature interference in the electromechanical impedance technique. The augmented Dickey–Fuller test is used to analyze the stationary characteristics of the time series and determine the degree of non-stationarity. The Johansen test is used to obtain the cointegrating residuals instead of the direct electromechanical impedance responses for damage detection. The proposed method is verified on the undamaged and damaged steel plates with the consideration of environmental temperature variations. The damage detection was based on the electromechanical impedance technique in which the peak frequency is chosen as a cointegrated variable. The experimental results show that the cointegration method can remove the temperature effect on the electromechanical impedance responses, and the cointegrating residuals are effective indices to indicate the occurrence of damage.
Changes of damage feature caused by structural damage are often masked by the changes caused by environmental variations (temperature, mass), resulting in the failure of vibration based damage identification methods. In this paper, the coefficients of AR model in time series and cointegration in econometrics are used to identify the damage of offshore platform in changing environmental variations (temperature, mass). Firstly, the AR model is used to fit the structural acceleration response from different nodes of the offshore platform pre and post damage, and the first-order AR coefficient is selected as cointegration variable. Secondly, the cointegration procedure is applied to the variables from different nodes and the cointegration residuals are taken as the damage indicators. Finally, the X-bar control chart is employed to identify the damage of structure. The results of numerical simulation and shaking table model test of a five-floor steel offshore platform verify the effectiveness of the proposed method.
Time-varying environmental and operational conditions such as temperature and external loading may often mask subtle structural changes caused by damage and have to be removed for successful structural damage identification. In the paper, a symplectic geometry spectrum analysis method is employed to decompose a time series into the sum of a small number of independent and interpretable components, in which one can determine which components are caused by external influences. The symplectic geometry spectrum analysis method is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. One excellent advantage of the method is that it can deal with nonlinear time series which is inherently rooted in structural damage due to crack opening and closing. Numerical simulation shows that the method is promising to detect structural damage in the presence of environmental and operational variations.
Before structural health monitoring (SHM) technologies can be reliably implemented on structures outside laboratory conditions the problem of environmental variability in monitored features must be first addressed. Structures that are subjected to changin environmental or operational conditions will often exhibit inherently non-stationary dynamic and quasi-static responses, whic can mask any changes caused by the occurrence of damage. The current work introduces the concept of cointegration, a tool for the analysis of non-stationary time series, as a promising new approach for dealing with the problem of environmenta variation in monitored features. If two or more monitored variables from an SHM system are cointegrated, then some linea combination of them will be a stationary residual purged of the common trends in the original dataset. The stationary residua created from the cointegration procedure can be used as a damage-sensitive feature that is independent of the normal environmenta and operational conditions.
The necessity and the urgency to conduct safety assessment, health monitoring and damage diagnosis in civil engineering are introduced. The concepts, theories and methods are presented systematically. Several key issues related to health monitoring, such as optimal sensor placement, damage identification and newly emerging optical fiber sensors etc. are emphasized. Finally this paper points out future studies and application efforts in these aspects.
The robustness of the damage indicator with respect to changing environmental conditions is of particular importance. Temperature as well as damage can change the dynamic behaviour of a structure. If the detection method is not able to separate different effects coming from changing environmental conditions or damage, this will lead to a great amount of false alarms. In the present paper a smart structure concept is presented that is able to perform a self-diagnosis. The work carried out here is focussed on the detection of small delaminations in composite materials and a high reliability of the damage indicator with respect to temperature effects. A residual vector is defined that is based on an orthogonality relation between a so-called Hankel matrix computed of the actual structural response and a left kernel space determined for a reference state related to the undamaged structure. The basic mathematical framework is the Subspace Identification Method developed by Basseville and co-workers. The method is modified and combined with a smart structure technique, where the system is excited with random noise by an integrated actuator and the system's vibration response and temperature is measured. However, this requires that the structure is equipped with a sensor network and actuation devices and an "artificial brain" which processes all the measurement information and which is able to make a decision on the structures health conditions. Results are presented for two different CFRP plates.
The response of bridges exposed to thermal environment conditions is studied. Analytical methods are developed to obtain temperature distributions and the maximum bridge temperature ranges. Thermoelastic analysis is conducted to obtain the temperature induced movements and the associated stresses in bridges. Parametric studies are conducted for different bridge geometries, temperature distributions, and support conditions. A field test is conducted on a bridge to verify the analytical models. The analysis suggests that concrete bridges sometimes are designed for smaller temperature ranges and corresponding thermal movements than may be expected in practice. The analysis suggests that steel bridges with composite concrete decks sometimes are designed for larger temperature ranges and thermal movements than may be expected at many locations in the United States. Skew and curved bridges often exhibit magnitude and direction of movement that is different than commonly expected. Additional guidelines and recommendations are provided regarding the analysis required to accurately predict thermal movements and the placement of bearings and expansion joints. This study will help engineers better understand thermal movements and stresses developed in bridges.