Damage In Truss Structures Research Articles

Study on Damage Inference of Parker Trusses Based on Bayesian Principles

The assessment of the health condition and safety of engineering structures is currently a research focus in the field of civil engineering. The traditional deterministic model for damage recognition is limited by the fine reading of field inspections and the accuracy of experts, resulting in a low recognition rate. Structural damage identification methods that consider uncertainty have been developed due to modelling errors, observation noise, system time variability, and other factors that lead to uncertainty. This study focuses on the Parker truss structure, and a two-dimensional planar finite element model is established by setting various key parameters such as prior distribution, stiffness, modulus of elasticity, node distribution, and external loading. The model is updated using the Bayesian updating principle. This principle is then combined with the finite element model. Opensees software is used for programming, and the Monte Carlo random sampling technique is used for structural damage inference. The study results demonstrate that the method can accurately identify the damage level of Parker truss structures with high robustness. The method can be of reference significance and practical value for identifying damage in truss structures.

A procedure to estimate the Minimum Observable Damage in truss structures using vibration-based Structural Health Monitoring systems

In this work, we propose a procedure to estimate the Minimum Observable Damage (MOD) by a vibration-based Structural Health Monitoring (SHM) system. The MOD is defined as the smallest damage size that can be detected by an SHM system with given Probability of Detection (POD) and Probability of False Alarm (PFA). To this purpose, the MOD is computed by exploiting the Receiver Operating Characteristic (ROC) analysis, once a damage index (DI) built on monitoring data/features is defined. In particular, the MOD is defined as the damage intensity corresponding to an area under the ROC curve of 95%. The proposed idea is discussed by utilizing pseudo-experimental data generated via numerical simulations for undamaged and damaged structures. In the developed simulations, environmental uncertainties and measurement noises are considered. As case studies, we consider truss structures and use modal data, namely frequencies of vibrations and mode shapes, to build the DIs. Using the dataset of DIs, the ROC methodology is exploited to establish the probability of detecting certain damage over the probability of false alarms. For a given DI, results are provided in terms of MOD for each structural element of the truss structure considering one damaged element at a time. By establishing a relation between modal data, damage size, and POD/PFA, the proposed approach can assess the quality of the adopted DI, thus supporting the initial design of an SHM system.

Damage Detection of Truss Structures by Reduction of Degrees of Freedom Using the Serep Method

Damage detection of bridge structures during their operating lifetime is essential. In this paper, two approaches, All Degrees of Freedom and Reduction of the Degrees of Freedom methods, are used to detect the damages in structures. The first method considers All Degrees of Freedom of the structure and the second method, Reduction of the Degrees of Freedom. Since the sensors are installed only on a few degrees of freedom, the responses are available for some of them. The Degrees of Freedom must be reduced and System Equivalent Reduction Expansion Process method is one of the most efficient ways to solve the problem. This research aimed to identify the damage of structures using the Modal Strain Energy method by reducing the structural degree of freedom. Two standard examples are used and the results compared to different damage cases to examine the efficiency of the mentioned method. The results illustrated the proper performance of the Reduction of the Degrees of Freedom method to identify the damage in truss structures. By increasing the number of modes, Reduction of the Degrees of Freedom method detects considerably more accurate the damaged elements, especially when the noise is considered. Also, based on the outcomes to identify damaged elements, it is possible to consider more modes instead of more sensors.

The Researches on Damage Detection Method for Truss Structures

This paper presents an effective method to detect damage in truss structures. Numerical simulation and experimental analysis were carried out on a damaged truss structure under instantaneous excitation. The ideal excitation point and appropriate hammering method were determined to extract time domain signals under two working conditions. The frequency response function and principal component analysis were used for data processing, and the angle between the frequency response function vectors was selected as a damage index to ascertain the location of a damaged bar in the truss structure. In the numerical simulation, the time domain signal of all nodes was extracted to determine the location of the damaged bar. In the experimental analysis, the time domain signal of a portion of the nodes was extracted on the basis of an optimal sensor placement method based on the node strain energy coefficient. The results of the numerical simulation and experimental analysis showed that the damage detection method based on the frequency response function and principal component analysis could locate the damaged bar accurately.

Truss structure damage identification using residual force vector and genetic algorithm

In this paper, damage detection has been introduced as an optimization problem and a two-step method has been proposed that can detect the location and severity of damage in truss structures precisely and reduce the volume of computations considerably. In the first step, using the residual force vector concept, the suspected damaged members are detected which will result in a reduction in the number of variables and hence a decrease in the search space dimensions. In the second step, the precise location and severity of damage in the members are identified using the genetic algorithm and the results of the first step. Considering the reduced search space, the algorithm can find the optimal points (i.e. the solution for the damage detection problem) with less computation cost. In this step, the Efficient Correlation Based Index (ECBI), that considers the structure\'s first few frequencies in both damaged and healthy states, is used as the objective function and some examples have been provided to check the efficiency of the proposed method; results have shown that the method is innovatively capable of detecting damage in truss structures.

Detection of damage in truss structures using Simplified Dolphin Echolocation algorithm based on modal data

Nowadays, there are two classes of methods for damage detection in structures consisting of static and dynamic. The dynamic methods are based on studying the changes in structure\'s dynamic characteristics. The theoretical basis of this method is that damage causes changes in dynamic characteristics of structures. The dynamic methods are divided into two categories: signal based and modal based. The modal based methods utilize the modal properties consisting of natural frequencies, modal damping and mode shapes. As the modal properties are sensitive to changes in the structure, these can be used for detecting the damages. In this study, using dynamic method and modal based approach (natural frequencies and mode shapes), the objective function is formulated. Then, detection of damages of truss structures is addressed by using Simplified Dolphin Echolocation algorithm and solving inverse optimization problem. Many scenarios are used to simulate the damages. To demonstrate the ability of the algorithm, different truss structures with several multiple elements scenarios are tested using a few runs. The influence of the two different levels of noise in the modal data for these scenarios is also considered. The last example of this article is investigated using a different mutation. This mutation obtains the exact answer with fewer loops and population by limited computational effort.

Damage identification of truss structures based on force method and free vibration analysis

The improved structural analysis is presented to determine the sites and extents of multiple damages of truss structures. The algorithm uses the mathematical programming of the finite element technique based on the force method and the free vibration analysis. The equilibrium matrix is generated through the finite element analysis, while the compatibility matrix is obtained directly using the force–displacement relations and the singular value decomposition technique. The governing equations with the element nodal forces as variables are presented by combining the equilibrium and compatibility matrices with the force–displacement relations. Next, the genetic algorithm is used to properly identify the sites and extents of multiple damage cases in truss structures. In order to verify the accuracy and superiority of the proposed damage detection technique, numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and genetic algorithm can provide a reliable tool to accurately and efficiently identify the multiple damages of truss structures.

Improved Computational Framework for Efficient Bayesian Probabilistic Inference of Damage in Truss Structures Based on Vibration Measurements

This paper presents a computationally efficient Bayesian inference framework and its application to infer damage in truss bridges. The novelty of the proposed framework for reducing the computational burden of Bayesian inference of structural damage lies in ( a) the revised transitional Markov chain Monte Carlo algorithm for efficiently drawing statistical samples of damage indexes and ( b) the likelihood function in the frequency domain based on modal properties that could be derived from the stochastic subspace identification. Other special features of the proposed framework include ( a) explicitly modeling complexities of truss joints for allowing identification of truss joint damage and the assessment of its associated uncertainties and ( b) incorporating the structural finite element model into the probabilistic inference computational environment through the program application interface. Those improvements make new contributions to the field of damage identification for truss bridges, leading to the practical application of Bayesian inference of the large amounts of potential damage not only in truss members but also in truss joints. The applicability and efficiency of the proposed framework are illustrated and examined by using numerical simulation of a damaged prototype truss structure. Simulation results indicate that the proposed approach has the potential capacity for determining the extent and location of large amounts of truss damage and the probabilistic characteristics. Finally, the limitation of this study and the future research need for practical application of the proposed probabilistic framework are discussed.

Mixed Integer Nonlinear Least-Squares Problem for Damage Detection in Truss Structures

We present a mixed integer nonlinear least-squares problem for identifying damage in truss structures from their measured response. In detecting damage based on parameter estimation, the number of unknown parameters is often less than that of measurements, which gives rise to nonunique solutions. To overcome the difficulty, we formulate damage detection as a mixed integer nonlinear least-squares problem, where the subset of unknown parameters is sought that best represents damaged sites. To solve the problem, we present four heuristic algorithms based on the greedy algorithm. One is its direct application. The other three select the near-optimal subsets more efficiently by linearizing the error function, by applying the line search, and by grouping unknown parameters. We assess the performance of these algorithms along with conventional regularization methods through numerical experiments, where many synthetic damage cases are tested. The effect of modeling and measurement errors on the estimate is also studied. We found from the numerical experiments that the linearization-based approach was more efficient than the direct application while the two methods gave reasonably accurate estimates.