Undamaged Elements Research Articles

On determining structural wall layout during the adaptive reuse process of historic masonry buildings

Defining modifications to a building’s layout during the adaptive reuse of historic masonry buildings can be challenging since the existing structural grid constrains the transformations to be performed. This paper proposes a novel methodology for exploring modifications to a structural wall layout during the adaptive reuse process of historic buildings. The primary objective is to redefine structural wall arrangements to accommodate new openings and/or cuts in existing structural elements, offering designers flexibility in spatial arrangement modifications. Considering that existing buildings are subjected to damage, an evolutionary approach is used to define which wall segments can be removed from the existing layout, according to a multi-objective function that targets minimizing the presence of damaged elements and maximizing the presence of undamaged elements in the design, in addition to minimizing the building’s eccentricity. The problem considers structural constraints based on the compressive capacity and minimum length of shear components. A computational strategy based on Genetic Algorithm is conceptualized as a tool for deriving potential layout solutions that adhere to structural requirements while facilitating the incorporation of new openings. By systematically evolving potential solutions over multiple generations, the algorithm navigates the design space to pinpoint areas within the original shear layout where material can be removed while respecting the given structural constraints. The methodology’s validity is demonstrated through a case study situated in a UNESCO World Heritage Site, providing evidence of the practical application and success of the genetic algorithm approach in real-world scenarios. The findings presented in this paper contribute to the convergence of structural engineering and architectural preservation, offering a systematic and efficient means of determining structural wall layouts for the adaptive reuse of historic masonry buildings. Integrating computational techniques into the adaptive reuse process holds transformative potential, establishing a robust framework for sustainable urban development that honors and enhances the historical fabric of our built environment.

Accelerometer Mass Loading Study Based on a Damage Identification Method using Fundamental Laws in Closed Systems

Many civil engineering structures can be evaluated as closed systems in which additional mass spatial distribution can change within the system in terms of the fundamental continuity and energy equations. Considering the heavy hours of traffic, it can be assumed that the position of the vehicle mass on the bridge is variable, but the total mass remains constant. This study aims to show that the damage to the closed systems can be successfully estimated by using a damage indicator that is valid for systems with constant mass distribution. In the analytical study, a 100-element 200 degree of freedom fixed-free beam is investigated and the assessment of the damage position is verified numerically and the validity of the parameter is examined in an experimental study. Except for the piece at the free end of the beam; It has been determined that the damage indicator calculated on the damaged elements is 60 times larger than the damage indicator calculated at the undamaged elements. In the elements at the free end of the beam; it was observed that this ratio is between 6 and 40 depending on the mass of the accelerometer. Therefore, a criterion for accelerometer mass and damage indicator is proposed.

An Adaptive Sparse Regularization Method for Response Covariance-Based Structural Damage Detection

Structural damage detection is usually an ill-posed inverse problem due to the contamination of measurement noise and model error in structural health monitoring. To deal with the ill-posed damage detection problem, l2-regularization is widely used. However, l2-regularization tends to provide nonsparse solutions and distribute identified damage to many undamaged elements, potentially leading to false alarms. Therefore, an adaptive sparse regularization method is proposed, which considers spatially sparse damage as a prior constraint since structural damage often occurs in some locations with stiffness reduction at the sparse elements out of the large total number of elements in an entire structure. First, a response covariance-based convex cost function is established by incorporating an l1-regularized term and an adaptive regularization factor to formulate the sparse regularization-based damage detection problem. Then, optimal sensor placement is conducted to determine the optimal measurement locations where the acceleration responses are adopted for computing the response covariance-based damage index and cost function. Further, the predictor-corrector primal-dual path-following approach, an efficient and robust convex optimization algorithm, is applied to search for solutions to the damage detection problem. Finally, a comparison study with the Tikhonov regularization-based damage detection method is conducted to examine the performance of the proposed adaptive sparse regularization-based method by using an overhanging beam model subjected to different damage scenarios and noise levels. The numerical study demonstrates that the proposed method can effectively and accurately identify damage under multiple damage scenarios with various noise levels, and it outperforms the Tikhonov regularization-based method in terms of high accuracy and few false alarms. The analyses on time consumption, adaptiveness of the sparse regularization factor, model-error resistance, and sensor number influence are conducted for further discussions of the proposed method.

Locating damages of space trusses by combining cross-model modal strain energy and wavelet transform

To effectively locate damages of a space truss which usually has hundreds of elements, a new damage index is proposed by combining the cross-model modal strain energy (CMSE) and the wavelet transform (WT). Firstly, the novel CMSE are introduced to construct the damage index CMSEI. It is noted that the traditional modal strain energy (MSE) is calculated based only on mode shapes of the same model, i.e., the undamaged structure or the damaged structure. In contrast, the CMSE is computed by simultaneously utilizing mode shapes from two different models, i.e., both undamaged and damaged structures. Secondly, the WT is further conducted on the space-domain sequence composed of elemental values of the CMSEI, with high-frequency detail coefficients extracted to form the new damage index WT_CMSEI. Finally, damages are located for the elements with outstanding values of the WT_CMSEI. A space truss with as many as 504 elements is numerically analyzed. Results show that the proposed WT_CMSEI can better indicate damage locations than widely used indexes based on traditional MSE. It presents high robustness to resist the influences of noise, and can effectively decrease the disturbances from other undamaged elements. This study provides a potential application of the WT_CMSEI in damage localization for large-scale space trusses which have many elements.

Защита короткой сети руднотермических печей

Protection against short circuits between buses tubes in short networks of ore-thermal furnaces is provided by means of electrical insulation. Failure of the insulation leads to an arc, and then to the complete destruction of the expensive bus tube package. Disconnection fault in the elements of a short network cause overheating of undamaged elements. Currently, emergency modes of operation of a short network are determined with indirect signs. It is impossible to use current protection for this purpose because of the existing restrictions on the number of current transformers and the place for their placement. The authors developed a current protection of short networks of ore-thermal furnaces from electrical damage on a single magnetic current transformer. The proposed protection is simple in design, it is able to identify breaks in the elements of a short network and protect them from short circuits. The location of the magnetic current transformer relative to the bus tube package is determined based on the simulation of the magnetic field. The article describes a method for simulating the components of the magnetic field of a bus tube package, which allows us to model them in operational and emergency modes with an error of no more than 10%.

Damage detection of cylindrical shells based on Sander's theory and model updating using incomplete modal data considering random noises

In this paper, a new system of damage detection equations for damage identification of cylindrical shells is developed based on classic finite element method, incomplete noisy modal data and model updating. Classic finite element technique in conjunction with Sander's thin shell theory is deployed in order to construct the finite element model of cylindrical shells and compute vibration data. To overcome the difficulty of incomplete data, “system equivalent reduction expansion process” (SEREP) method is applied to find a proper complete approximation of incomplete modal data. The proposed system is usually ill-posed due to noisy data and ill-conditioned system derived from the model updating process. To tackle this issue, a constraint as a regularization parameter is employed in model updating problem to differentiate potentially damaged elements and undamaged elements. This constraint is imposed on the model updating process by defining a Reduction Index (RI) and forcing severities of undamaged elements to tend to zero. Furthermore, the presented system is non-square and large depending on the number of structural unknowns. For these reasons, Biconjugate gradient (BCG) method along with an appropriate preconditioner are employed to solve the system of equations. Not only does the preconditioner stabilize the solution against numerical errors and inaccuracies caused by noisy data, but also it alters the system to a square one. Numerical studies are performed to demonstrate the efficiency of the presented method. Moreover, a statistical analysis is carried out to evaluate the effect of different sequences of random noises on the damage detection results. Findings show that the proposed method is capable of detecting the severities and sites of damages for cylindrical shells in the presence of noisy data.

Acute Lethal Toxicity Test of Cd2 + Against Gambusia (Gambusia affinis) and Influence on Protease Activity

Cadmium the form of undamaged elements but can change shape to different compounds. The low concentrations of toxic cadmium for all life, including plants, fish, birds, mammals (including humans), and microorganisms. The purpose of this research is to know the value of LC50-96 hours Cd2+ on test biota. The test biota was Gambusia fish (Gambusia affinis), the test biota can represented the actual state of the environment. The study was divided into two stages, namely preliminary test and acute lethal toxicity (LC50-96 hours), each treatment repeated three times. Acute lethal toxicity test data were analyzed probit. The results showed that the value of LC50-96 hours Cd2+ to fish gambusia was 0.03 ppm. While in the protease activity of cadmium exposed preliminary fish increased activity from the control fish.

An experimental study of the feasibility of phase‐based video magnification for damage detection and localisation in operational deflection shapes

AbstractOptical measurements from high‐speed, high‐definition video recordings can be used to define the full‐field dynamics of a structure. By comparing the dynamic responses resulting from both damaged and undamaged elements, structural health monitoring can be carried out, similarly as with mounted transducers. Unlike the physical sensors, which provide point‐wise measurements and a limited number of output channels, high‐quality video recording allows very spatially dense information. Moreover, video acquisition is a noncontact technique. This guarantees that any anomaly in the dynamic behaviour can be more easily correlated to damage and not to added mass or stiffness due to the installed sensors.However, in real‐life scenarios, the vibrations due to environmental input are often so small that they are indistinguishable from measurement noise if conventional image‐based techniques are applied. In order to improve the signal‐to‐noise ratio in low‐amplitude measurements, phase‐based motion magnification has been recently proposed.This study intends to show that model‐based structural health monitoring can be performed on modal data and time histories processed with phase‐based motion magnification, whereas unamplified vibrations would be too small for being successfully exploited. All the experiments were performed on a multidamaged box beam with different damage sizes and angles.

Application of the vibration method for damage identification of a beam with a variable cross-sectional area

The subject of the paper is an application of the non-destructive vibration method for identifying the location of two cracks occurring in a beam. The vibration method is based on knowledge of a certain number of vibration frequencies of an undamaged element and the knowledge of the same number of vibration frequencies of an element with a defect. The analyzed beam, with a variable cross-sectional area, has been described according to the Bernoulli-Euler theory. To determine the values of free vibration frequencies the analytical solution, with the help of the Green’s function method, has been used.

Numerical Studies on the Failure Process of Heterogeneous Brittle Rocks or Rock-Like Materials under Uniaxial Compression.

In rocks or rock-like materials, the constituents, e.g. quartz, calcite and biotite, as well as the microdefects have considerably different mechanical properties that make such materials heterogeneous at different degrees. The failure of materials subjected to external loads is a cracking process accompanied with stress redistribution due to material heterogeneity. However, the latter cannot be observed from the experiments in laboratory directly. In this study, the cracking and stress features during uniaxial compression process are numerically studied based on a presented approach. A plastic strain dependent strength model is implemented into the continuous numerical tool—Fast Lagrangian Analysis of Continua in three Dimensions (FLAC3D), and the Gaussian statistical function is adopted to depict the heterogeneity of mechanical parameters including elastic modulus, friction angle, cohesion and tensile strength. The mean parameter μ and the coefficient of variance (hcv, the ratio of mean parameter to standard deviation) in the function are used to define the mean value and heterogeneity degree of the parameters, respectively. The results show that this numerical approach can perfectly capture the general features of brittle materials including fracturing process, AE events as well as stress-strain curves. Furthermore, the local stress disturbance is analyzed and the crack initiation stress threshold is identified based on the AE events process and stress-strain curves. It is shown that the stress concentration always appears in the undamaged elements near the boundary of damaged sites. The peak stress and crack initiation stress are both heterogeneity dependent, i.e., a linear relation exists between the two stress thresholds and hcv. The range of hcv is suggested as 0.12 to 0.21 for most rocks. The stress concentration degree is represented by a stress concentration factor and found also heterogeneity dominant. Finally, it is found that there exists a consistent tendency between the local stress difference and the AE events process.

Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements

It is difficult to establish a constitutive model of damage for rock materials due to the complex meso-mechanism of the rock deterioration process. In this paper, by analysis of the damage mechanism, the reason for the existence of a rock damage threshold is explained and we conclude that damaged rock elements of micro scale can still bear stress. The correlation between damaged and undamaged elements is examined in relation to stress distribution. Rocks under different initial conditions can be defined as undamaged materials with different properties, to avoid the issue of the solution of the undamaged condition and to simplify the damage model. On the basis of the Mohr-Coulomb criterion and theories of continuum damage and statistical mechanics, a constitutive model of rock materials affected by the load-bearing capacity of damaged elements under triaxial compression is established. Compared with previous experimental data and theoretical results, we show that this model can reflect the stress-strain relationship of the whole process of rock failure. In particular, the description of the strain softening stage after peak strength is proved to be more reasonable. Programming of the constitutive model applied to stability analysis of the Qingdao subway station is achieved by secondary development of FLAC3D. The computing results compare very well with field monitoring data, indicating that the constitutive model of damaged rock can reflect the deterioration effect of weathered rock at the site. This constitutive model of rock damage may provide a useful reference for practical application.

Statistical evaluation of characteristic SDDLV-induced stress resultants to discriminate between undamaged and damaged elements

The stochastic dynamic damage location vector (SDDLV) method utilizes the vectors from the kernel of a damaged-induced transfer function matrix change to localize damages in a structure. The kernel vectors associated with the lowest singular values are converted into static pseudo-loads and applied alternately to an undamaged reference model with known stiffness matrix, hereby, theoretically, yielding characteristic stress resultants approaching zero in the damaged elements. At present, the discrimination between potentially damaged elements and undamaged ones is typically conducted on the basis of modified characteristic stress resultants, which are compared to a pre-defined tolerance value, without any thorough statistical evaluation. In the present paper, it is tested whether three widely-used statistical pattern-recognition-based damage-detection methods can provide an effective statistical evaluation of the characteristic stress resultants, hence facilitating general discrimination between damaged and undamaged elements. The three detection methods in question enable outlier analysis on the basis of, respectively, Euclidian distance, Hotelling's T2 statistics, and Mahalanobis distance. The study of the applicability of these methods is based on experimentally obtained accelerations of a cantilevered residential-sized wind turbine blade subjected to an unmeasured multi-impulse load. The characteristic stress resultants are derived by applying the static pseudo-loads to a representative finite element (FE) model of the actual blade.

Damage detection for beam-like structures using the normalized curvature of a uniform load surface

This paper presents a new vibration-based damage detection method for beam-like structures that uses the normalized uniform load surface (NULS) curvature obtained by modal flexibility. Analytical studies on the NULS curvature method for beam-like structures, which follow Bernoulli–Euler beam theory, have shown that changes in NULS curvature only occur at damaged elements and not at intact ones because the internal forces induced by damage only act on the damaged elements and not on the undamaged elements. Therefore, computing the changes in NULS curvature set indicating only damaged elements at a normalized level is central to the approach. Also, a damage index is proposed based on outlier analysis to account for measurement noise. In order to confirm the feasibility of the proposed method, a cantilever beam and a simply supported beam were numerically investigated for two damage scenarios by using modal parameters obtained by eigenvalue analysis and simulations of an impact test using MATLAB/Simulink. The results showed that the proposed method could accurately localize multiple damage locations as well as single damage locations without any false-positive or false-negative detections. For comparison, damage detection was also conducted using the uniform load surface (ULS) curvature method and the mode shape curvature method. The ULS curvature method clearly identified single damage locations but some missed multiple damage locations. For the mode shape curvature method, it was shown that the false-positive and false-negative detections were performed at several damaged or undamaged locations. The comparison showed that the proposed detection method can more effectively identify single and multiple damage locations than the other two methods. In conclusion, the proposed method performed better in detecting damages than the other two methods in terms of sensitivity to damage regardless of location and robustness against noisy signals generated from calculating the mode shape curvature.

A direct algebraic method to calculate the sensitivity of element modal strain energy

The sensitivity study of modal strain energy (MSE) is of primary importance for its extensive applications in structural damage detection and health monitoring fields. In this paper, the first-order sensitivity formulae of the element MSE for a real symmetric undamped system are derived based on the algebraic eigensensitivity method. The formulae are simple and compact having the desirable properties of preserving the band and symmetry structures of the stiffness and mass matrices. Three types of analysis have been investigated on the first-order sensitivity of element MSE via a numerical parametric studies: the sensitivity to structural geometric and physical parameters, the sensitivity to structural parameter variation due to damage, and the effect of noise on the element MSE sensitivities. It is demonstrated that the element MSE is more sensitive to the geometrical parameters than the physical parameters. The fact that the element MSE change in a damaged element is larger than that of any other undamaged element is not always true for the higher modes. The sensitivity of element MSE for the lower modes is less affected by noise than that for the higher modes and therefore it will be the most likely to indicate the structural damage. Copyright © 2009 John Wiley & Sons, Ltd.

Substructuring Technique for Damage Detection Using Statistical Multi-Stage Artificial Neural Network

Artificial Neural networks (ANN) have been proven in many studies to be able to efficiently detect damage from vibration measurements. Their capability to recognize patterns and to handle non-linear and non-unique problems provides an advantage over traditional mathematical methods in correlating the vibration data to damage location and severity. However, one shortcoming of ANN is they require enormous computational effort and sometimes prohibitive time and computer memory for training a reliable ANN model, especially when structures with many degrees of freedom are involved. Therefore, in most cases, rather large elements are used in the structure model to reduce the degrees of freedom. This results in the structural vibration properties not being sensitive to small damage in a large element. As a result, direct application of ANN to detecting damage in a large civil engineering structures is not feasible. In this study, a multi-stage ANN incorporating a probability method is proposed to tackle this problem. Through this method, a structure is divided into several substructures, and each substructure is assessed independently. In each subsequent stage, only the damaged substructures are analyzed, and eventually the location and severity of small structural damage can be detected. This approach greatly reduces the computational time and the required computer memory. Moreover, a probabilistic method is also used to include the uncertainties in vibration frequencies and mode shapes in damage detection analysis. It is found that this method reduces the uncertainty effect in frequencies due to duplication error in the multi-stage ANN model and reduces the uncertainty effect in mode shapes due to the damage in other substructures. The developed approach is applied to detect damage in numerically simulated and laboratory tested concrete slab. The results demonstrate that the proposed method can detect small damage with a higher level of confidence, and the undamaged elements are less likely to be falsely detected.

Adaptive Tikhonov regularization for damage detection based on nonlinear model updating

This paper presents an adaptive regularization approach for solving the nonlinear model updating inverse problem. The discrimination of possible damaged elements and undamaged elements is done from results obtained in previous iterations via a new side condition which aims at (a) to limit the local change in damaged structural elements in each iteration; and (b) to force the variation of other undamaged elements close to zero. A thirty-one bar plane truss structure with multiple damages is studied. Results obtained from the proposed method are greatly improved over those obtained from the traditional Tikhonov regularization even with large noise contamination in the measurements.

Damage detection in jacket type offshore platforms using modal strain energy

Structural damage detection, damage localization and severity estimation of jacket platforms, based on calculating modal strain energy is presented in this paper. In the structure, damage often causes a loss of stiffness in some elements, so modal parameters; mode shapes and natural frequencies, in the damaged structure are different from the undamaged state. Geometrical location of damage is detected by computing modal strain energy change ratio (MSECR) for each structural element, which elements with higher MSECR are suspected to be damaged. For each suspected damaged element, by computing cross-modal strain energy (CMSE), damage severity as the stiffness reduction factor -that represented the ratios between the element stiffness changes to the undamaged element stiffness- is estimated. Numerical studies are demonstrated for a three dimensional, single bay, four stories frame of the existing jacket platform, based on the synthetic data that generated from finite element model. It is observed that this method can be used for damage detection of this kind of structures.

Multiple-Criterion Method for Determining Structural Damage

A new multiple-criterion updating method that minimizes the Euclidean norm of the error vector obtained by adding the normalized eigenproblem equation and equation of motion with equal weighting functions is proposed. The method is applied to detecting damage in structures and is tested on an unsymmetrical H-shaped structure. It is found that the multiple-criterion updating method predicts the presence, the position, and the extent of damage. The multiple-criterion method is compared to the frequency-response function method and the modal property-based method by using the coordinate modal assurance criterion and the modal assurance criterion. The multiple-criterion method was found to give better results than the other two methods. This is because it was better able to detect damage on the structure than the modal property method (which failed to detect multiple-damage cases) and gave results that were less noisy, i.e., less updating to undamaged elements, than the frequency-response method.