Substructure Damage Identification Based on Model Updating of Frequency Response Function

To research the dynamic response of a new type of dedicated transmission for a hybrid electric vehicle, a detailed dynamics model should be built. However, a model with too many degrees of freedom has a negative effect on controller design, which means the detailed model should be simplified. In this paper, two dynamic models are established. One is an original and detailed powertrain dynamics model (ODPDM), which can capture the transient response, and it is validated that the ODPDM can be used to accurately describe the real vehicle in some specific operating conditions. The other is a simplified torsional vibration dynamics model to study the torsional vibration characteristics of the hybrid electric vehicle. Compared with the full-order model, which is based on the ODPDM, the simplified model has a very similar vibration in low frequency. This study provides a basis for further vibration control of the hybrid powertrain during the process of a driving-mode switch.

A dynamic condensation method with free interface substructuring

Structural damage identification is the core of Structural health monitoring system. The paper points out existing damage identification methods and analysis the application status and disadvantages of various methods. The research hotspots are summarized on considering the statistical identification method under uncertainty and the environmental impact of damage identification methods. Aiming at the characters of bridge engineering, the paper points out that a four-in-one multi-system damage identification method is the develop direction for bridge structural damage identification, which is established based on construction, load testing, health monitoring and manual inspection.

A method of damage identification of piles was established by using vibration characteristics. The approach focused on the application of the element strain energy and sensitive modals. A damage identification equation of piles was deduced using the structural vibration equation. The equation contained three major factors: change rate of element modal strain energy, damage factor of pile, and sensitivity factor of modal damage. The sensitive modals of damage identification were selected by using sensitivity factor of modal damage firstly. Subsequently, the indexes for early-warning of pile damage were established by applying the change rate of strain energy. Then the technology of computational analysis of wavelet transform was used to damage identification for pile. The identification of small damage of pile was completely achieved, including the location of damage and the extent of damage. In the process of identifying the extent of damage of pile, the equation of damage identification was used in many times. Finally, a stadium project was used as an example to demonstrate the effectiveness of the proposed method of damage identification for piles. The correctness and practicability of the proposed method were verified by comparing the results of damage identification with that of low strain test. The research provided a new way for damage identification of piles.

Guidelines for seismic performance evaluation of existing structures have been published by FEMA and the European Commission. Additionally, these organizations have presented frameworks for strengthening the resilience of society and industry. These frameworks require countermeasures for early recovery after natural disasters. For rapid post-earthquake recovery, it is necessary to assess the structural integrity and implement repairs. To achieve this, the utilization of structural health monitoring is essential. In structural damage assessment, loads and response displacements are important physical quantities, but these are difficult to obtain directly from structures. Therefore, in structural health monitoring, structural integrity is evaluated using measured accelerations. However, the superposition of uncertainties related to seismic motion and structures can sometimes complicate the setting of thresholds for structural integrity evaluation. To detect structural anomalies caused by earthquakes rapidly and with high accuracy, structural health monitoring methods incorporating deep learning have begun to be researched. Additionally, by extracting features from measured data using deep learning, prior setting of evaluation thresholds becomes unnecessary. Generally, training deep learning models requires large amounts of training data. However, since it is difficult to acquire anomaly data from existing structures, seismic response analysis is utilized. Typically, to represent real phenomena, analytical models require many degrees of freedom. In frequency domain response analysis, the frequency response function is defined as the ratio of the Fourier spectra of the structural seismic response to the seismic motion. By modeling the frequency response function, the seismic response of structures can be calculated. In this paper, we develop a method to calculate structural seismic responses by modeling the frequency response function with an AR model. This eliminates the need to set parameters such as degrees of freedom, mass, and stiffness of the analytical model. Furthermore, we propose a structural health monitoring method that uses this approach for training deep learning models. Verification of this method using experimental data from a full-scale steel building demonstrated that anomaly detection was possible from limited observational data only.

본 연구에서는 축소모델을 기반으로 비행체 날개를 최적화하는 기법을 제안한다. 잘 구축된 축소모델은 고유치 문제나 동적 해석 시 정확한 해석결과를 제공하며, 최적화 과정에서 필요한 민감도 계산에서도 정확한 결과를 제공할 수 있다. 이러한 축소모델은 모드기반으로 구축되는 축소차수모델(Reduce Order Model)과 자유도기반으로 구축되는 축소시스템(Reduced System)으로 구분되는데, 본 연구에서 사용하는 자유도 기반 축소시스템은 구조물의 거동에 지배적인 자유도를 적절히 선정하는 것이 중요하므로, 이를 위하여 기존 연구에서 신뢰성이 검증된 2단계 축소방법을 사용하였고, IRS(Improved Reduced System)에 의해 최종시스템을 구축하였다. 수치예제에서 최적화 과정에서 계산되는 등가응력, 고유치 및 설계민감도는 모두 축소시스템 기반으로 구해지며, 축소시스템을 통해 구속조건을 잘 만족하면서 목적함수에 대한 최적 결과를 얻을 수 있음을 보인다. The present study proposes the optimization of wing structure base on reduced model which assures the solution accuracy and computational efficiency. Well-constructed reduced model assures the accurate result in the eigenvalue problem, dynamic analysis or sensitivity of design optimization. Reduced system is classified into the reduce-order model based on structural modes and the reduced system based on degrees of freedom. Because this study uses the reduced system based on degrees of freedom, it is important to select the dominant degrees of freedom properly. For this work, robust selection method, two-level selection scheme, is employed and IRS(Improved Reduced System) is applied to construct the final reduced system. In the optimization process based on the reduced system, all of the equivalent stress, eigenvalue and design sensitivities are calculated from the reduced system. Through a numerical example, it is shown that the present optimization methodology based on the reduction method can provide an optimal results for objective function satisfying constraint condition.

Recently, the robot with many links and degrees of freedoms is actively produced. Generally, the robot that has many degrees of freedoms owns many redundant joints. So we make a suggestion for using redundant joints effectively. The paper proposes using redundant joint as a counter weight. We make a trajectory in momentum space, and we use Fourier Basis Algorism as the method for an optimization. This trajectory generating method has an effect on reducing a driving energy for throwing motion.

A method of structural damage identification using harmonic excitation force is presented. It considers the effects of both measurement and modelling errors in the baseline finite element model. Damage that accompanies changes in structural parameters can be estimated for a damaged structure from the change between measured vibration responses and ones calculated from the analytical model of the intact structure. In practice, modelling errors exist in the analytical model due to material and geometric uncertainties and a reduction in the degrees of freedom as well as measurement errors, making identification difficult. To surmount these problems, bootstrap hypothesis testing, which enables statistical judgment without information about these errors, was introduced. The method was validated by numerical simulation using a three-dimensional frame structure and real vibration data for a three-storey steel frame structure. Copyright © 2005 John Wiley & Sons, Ltd.

Structural damage identification is essentially an inverse problem. Ill-posedness is a common obstacle encountered in solving such an inverse problem, especially in the context of a sensitivity-based model updating for damage identification. Tikhonov regularization, also termed as ℓ2-norm regularization, is a common approach to handle the ill-posedness problem and yields an acceptable and smooth solution. Tikhonov regularization enjoys a more popular application as its explicit solution, computational efficiency, and convenience for implementation. However, as the ℓ2-norm term promotes smoothness, the solution is sometimes over smoothed, especially in the case that the sensor number is limited. On the other side, the solution of the inverse problem bears sparse properties because typically, only a small number of components of the structure are damaged in comparison with the whole structure. In this regard, this paper proposes an alternative way, sparse regularization, or specifically ℓ1-norm regularization, to handle the ill-posedness problem in response sensitivity-based damage identification. The motivation and implementation of sparse regularization are firstly introduced, and the differences with Tikhonov regularization are highlighted. Reweighting sparse regularization is adopted to enhance the sparsity in the solution. Simulation studies on a planar frame and a simply supported overhanging beam show that the sparse regularization exhibits certain superiority over Tikhonov regularization as less false-positive errors exist in damage identification results. The experimental result of the overhanging beam further demonstrates the effectiveness and superiorities of the sparse regularization in response sensitivity-based damage identification. Copyright © 2015 John Wiley & Sons, Ltd.

In this thesis, we present a dynamical systems approach to adaptive controllers for locomotion control. The approach is based on a rigorous mathematical framework using nonlinear dynamical systems and is inspired by theories of self-organization. Nonlinear dynamical systems such as coupled oscillators are an interesting approach for the on-line generation of trajectories for robots with many degrees of freedom (e.g. legged locomotion). However, designing a nonlinear dynamical system to satisfy a given specification and goal is not an easy task, and, hitherto no methodology exists to approach this problem in a unified way. Nature presents us with satisfactory solutions for the coordination of many degrees of freedom. One central feature observed in biological subjects is the ability of the neural systems to exploit natural dynamics of the body to achieve efficient locomotion. In order to be able to exploit the body properties, adaptive mechanisms must be at work. Recent work has pointed out the importance of the mechanical system for efficient locomotion. Even more interestingly, such well suited mechanical systems do not need complicated control. Yet, in robotics, in most approaches, adaptive mechanisms are either missing or they are not based on a rigorous framework, i.e. they are based on heuristics and ad-hoc approaches. Over the last three decades there has been enormous progress in describing movement coordination with the help of Synergetic approaches. This has led to the formulation of a theoretical framework: the theory of dynamic patterns. This framework is mathematically rigorous and at the same time fully operational. However, it does not provide any guidelines for synthetic approaches as needed for the engineering of robots with many degrees of freedom, nor does it directly help to explain adaptive systems. We will show how we can extend the theoretical framework to build adaptive systems. For this purpose, we propose the use of multi-scale dynamical systems. The basic idea behind multi-scale dynamical systems is that a given dynamical system gets extended by additional slow dynamics of its parameters, i.e. some of the parameters become state variables. The advantages of the framework of multi-scale dynamical systems for adaptive controllers are 1) fully dynamic description, 2) no separation of learning algorithm and learning substrate, 3) no separation of learning trials or time windows, 4) mathematically rigorous, 5) low dimensional systems. However, in order to fully exploit the framework important questions have to be solved. Most importantly, methodologies for designing the feedback loops have to be found and important theoretical questions about stability and convergence properties of the devised systems have to be answered. In order to tackle this challenge, we first introduce an engineering view on designing nonlinear dynamical systems and especially oscillators. We will highlight the important differences and freedom that this engineering view introduces as opposed to a modeling one. We then apply this approach by first proposing a very simple adaptive toy-system, consisting of a dynamical system coupled to a spring-mass system. Due to its spring-mass dynamics, this system contains clear natural dynamics in the form of resonant frequencies. We propose a prototype adaptive multi-scale system, the adaptive frequency oscillator, which is able to adapt its intrinsic frequency to the resonant frequency of the body dynamics. After a small sidetrack to show that we can use adaptive frequency oscillators also for other applications than for adaptive controllers, namely for frequency analysis, we then come back to further investigation of the adaptive controller. We apply the same controller concept to a simple spring-mass hopper system. The spring-mass system consists of a body with two legs attached by rotational joints. The legs contain spring-damper elements. Finally, we present results of the implementation of the controller on a real robot, the experimental robot PUPPY II. This robot is a under-actuated robot with spring dynamics in the knee joints. It will be shown, that due to the appropriate simplification and concentration on relevant features in the toy-system the controller concepts works without a fundamental change on all systems from the toy system up to the real robot.

Structural nonlinear damage identification based on Bayesian optimization GNAR/GARCH model and its experimental study

This article presents data collected in support of research on damage identification in a composite plate, using low-frequency vibration measurements. The data consist of the Frequency Response Functions (FRFs) of a square plate, measured using an impact hammer and accelerometers, as an alternative to ultrasonic measurements. The plate is instrumented with 7 accelerometers, and a dense grid of candidate damage locations is defined. First, a set of baseline FRFs is collected by measuring the responses to hammer excitations at all grid points. Then, 6 damage identification scenarios are considered, and for each scenario, a set of FRFs is collected by measuring the responses to hammer excitations at the 7 accelerometer locations. Added masses are glued to the plate to reproduce the scattering effect of damage. This provides a convenient academic example for a wide range of topics in the field of structural dynamics and serves as a first proof-of-concept exercise for damage identification research. In addition, it allows to validate different approaches and benchmark their performance, thereby contributing a reference test case to adequately compare methods against one another.

Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties. The algorithms make use of a finite-element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite-element model. In this work, the concept of the minimum rank perturbation theory (MRPT) is adopted to determine the damage extent on the mass properties of an undamped structure. In addition, the MRPT is extended to the case of proportionall y damped structures. For proportionally damped structures, the MRPT is used to find the damage extent in any two of the three structural property matrices (mass, damping, or stiffness). Finally, illustrative case studies using both numerical and actual experimental data are presented. HE advent of the Space Shuttle has prompted considerable attention to the design and control of large space structures. Due to the large size and complexity of envisioned structures, as well as the use of advanced materials to reduce structural weight, it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs. From experience gained in the machinery health monitoring field, one would expect the vibration signature of the structure, either frequency response functions and/or modal parameters, to provide useful information in determining the location and extent of structural damage. Assume that a refined finite element model (FEM) of the structure has been developed before damage has occurred. By refined, we mean that the measured and analytical modal properties are in agreement. Next, assume that at a later date some form of structural damage has occurred. If significant, the damage will result in a change in the structures modal parameters. The question is: can the discrepancy between the original FEM modal properties and postdamage modal properties be used to ascertain structural damage? Most prior work in damage detection has used the general framework of FEM refinement (system identification) in the development of damage assessment algorithms. The motivation behind the development of FEM refinement techniques is based on the need to validate engineering FEMs before their acceptance as the basis for final design analysis. The standard problem has been to seek a refined FEM that is as close to the original FEM and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation. A considerable amount of work in this area has been

A simplified Nonlinear Sway-Rocking model for evaluation of seismic response of structures on shallow foundations

Damage identification methods using finite element methods need a long computational time for large and complex structures. In this paper, we develop an effective damage identification method for large truss structures containing multiple damaged truss members using a successive iteration method of bounding domain and a domain decomposition finite element technique. The subdomains of truss structures which contain damaged truss members are first determined by a flexibility method. The subdomains are subdivided into smaller subdomains using a successive iteration method of bounding domain, and finally the damaged truss members are identified. By conducting the damage identification for a large three-dimensional truss structure, it is recognized that the damaged truss members and their residual stiffnesses can be identified precisely and the present damage identification method can reduce the computational time.