K. Zhou

Component Mode Synthesis Order-Reduction for Dynamic Analysis of Structure Modeled With NURBS Finite Element

Nonuniform rational B-splines (NURBS) finite element has advantages in analyzing the structure with curved surface geometry. In this research, we develop a component mode synthesis (CMS) based order-reduction technique which can be applied to large-scale NURBS finite element dynamic analysis. In particular, we establish a new substructure division scheme. The underlying idea is to optimally construct interface between adjacent substructures that can maximize the geometry consistency between the original structure and the divided substructures and at the meantime facilitate the compatibility conditions needed in mode synthesis. Case studies are carried out to validate the performance of the order-reduction formulation.

Adaptive Damage Detection Using Tunable Piezoelectric Admittance Sensor and Intelligent Inference

The piezoelectric impedance/admittance-based damage detection has been recognized to be sensitive to small-sized damage due to its high frequency measurement capability. Recently, a new class of admittance-based damage detection schemes has been proposed, in which the piezoelectric transducer is integrated with a tunable inductive circuitry. The present research focuses on exploiting the tunable nature of the piezoelectric admittance sensor for the effective identification of damage. In particular, we incorporate the Bayesian inference network into the damage detection process which can intelligently guide the accurate identification of damage location and severity by taking full advantage of the baseline model and measurement as well as the online measurement. As the tunable sensor can provide greatly enriched measurement information, the Bayesian inference can adequately utilize such information and furthermore directly and continuously update the structural model until the model prediction matches with the measurement results. This new approach takes into account the model uncertainty, measurement error, and incompleteness of measurements. Extensive numerical analyses and experimental studies are carried out on a panel structure for methodology demonstration and validation.Copyright

Efficient model updating using Bayesian probabilistic framework based on measured vibratory response

Currently, the deviation between the model and an actual structure is generally identified through a so-called model updating process, in which a set of experimental measurement of structural dynamic response is used in combination with the model prediction to facilitate an inverse analysis that is usually deterministic. In reality, however, structural properties, such as mass and stiffness, are inevitably subject to variation/uncertainties. As such, the identification of property variations in a probabilistic manner can truly reveal the underlying physical characteristics of the structure involved. In this research, we adopt the Bayesian probabilistic framework to conduct stochastic model updating using measured vibratory response. Furthermore, this paper proposes an efficient scheme to facilitate such procedures by incorporating the Gaussian process and Markov Chain Monte Carlo (MCMC) into the Bayesian framework. The feasibility of this presented methodology is validated by case studies.

Vibration analysis of structure with uncertainty using two- level Gaussian processes and Bayesian inference

Vibration analysis of structure with uncertainty is computationally costly, especially when the finite element model involved has high dimensionality. In this research a combination of two-level Gaussian processes and Bayesian inference is employed to facilitate the development of an efficient and accurate probabilistic order-reduced model. We first employ the two-level Gaussian processes emulator to integrate together small amount of high- fidelity data from full-scale finite element analysis and large amount of low-fidelity data from order-reduced component mode synthesis (CMS) model to improve the response variation prediction. We then utilize the improved response variation prediction on modal characteristics to update the CMS model in the probabilistic sense. The effectiveness of this method is demonstrated through a case study.

Structural damage identification using piezoelectric impedance and Bayesian inference

Structural damage identification is a challenging subject in the structural health monitoring research. The piezoelectric impedance-based damage identification, which usually utilizes the matrix inverse-based optimization, may in theory identify the damage location and damage severity. However, the sensitivity matrix is oftentimes ill-conditioned in practice, since the number of unknowns may far exceed the useful measurements/inputs. In this research, a new method based on intelligent inference framework for damage identification is presented. Bayesian inference is used to directly predict damage location and severity using impedance measurement through forward prediction and comparison. Gaussian process is employed to enrich the forward analysis result, thereby reducing computational cost. Case study is carried out to illustrate the identification performance.

Efficient Uncertainty Quantification in Structural Dynamic Analysis Using Two-Level Gaussian Processes

Uncertainty quantification is an important aspect in structural dynamic analysis. Since practical structures are complex and oftentimes need to be characterized by large-scale finite element models, component mode synthesis (CMS) method is widely adopted for order-reduced modeling. Even with the model order-reduction, the computational cost for uncertainty quantification can still be prohibitive. In this research, we utilize a two-level Gaussian process emulation to achieve rapid sampling and response prediction under uncertainty, in which the low- and high-fidelity data extracted from CMS and full-scale finite element model are incorporated in an integral manner. The possible bias of low-fidelity data is then corrected through high-fidelity data. For the purpose of reducing the emulation runs, we further employ Bayesian inference approach to calibrate the order-reduced model in a probabilistic manner conditioned on multiple predicted response distributions of concern. Case studies are carried out to validate the effectiveness of proposed methodology.Copyright

Design modification of cyclically periodic structure using Gaussian process

Cyclically periodic structures, such as blade-disk assembly in turbo-machinery, are widely used in engineering practice. While these structures are generally designed to be periodic with identical substructures, it is well-known that small random uncertainties exist among substructures which in certain cases may cause drastic change in the dynamic responses, a phenomenon known as vibration localization. Previous studies have illustrated that the introduction of small design modifications, i.e., intentional mistuning, may alleviate such vibration localization. The design objective here thus is to identify proper deign modification that can reduce the response variation under uncertainties. In this research, we first develop a perturbation-based approach to efficiently quantify the variation of forced response of a periodic structure, without and with the design modification, under uncertainties. We then propose a Gaussian process emulation which enables us to evaluate the objective function over the design space by using only a small number of design candidates. The combination of these algorithms allows us to perform effective design modification to minimize the response variation in nearly periodic structures.

Perturbing Structural Design Towards Minimizing Variation in Vibratory Response

Real structures are always subject to uncertainties due to material imperfection, machining tolerance, and assemblage error, etc. These uncertainties lead to variations in structural vibratory responses. In order to reduce the likelihood of unexpected failures in structures, we need to minimize the response variations, which is the underlying idea of robust design. In this paper, we present an inverse sensitivity-based algorithm that allows us to tailor the structural design such that, under the same level of uncertainties, the response variations can be effectively reduced. We first develop a direct relation between the structural uncertainties and the response variations including the means and variances. We then formulate an optimal identification algorithm that will yield design perturbation to minimize the response variances while maintaining the mean values. Case analyses are carried out to validate the validity and efficiency of the new algorithm.Copyright

Rapid identification of structural properties based on mass response method

This paper presents a new methodology that is built upon existing hardware such as shaker force generator and accelerometers that are both portable and convenient to use for a variety of civil and mechanical structures. Our key idea is to use a moving load that is placed successively at a number of locations on the structure, and measure the corresponding frequency responses. These frequency response measurements will then be used to extract the structural properties. Our new methodology so called mass response method enables the direct extraction of the equivalent stiffness and mass of the critical members of a structure without using a priori information of the structure. A number of case studies are carried out to demonstrate the accuracy and efficiency of its usage in structural health monitoring applications. Furthermore, the uncertainty introduces to this methodology is also investigated and discussed.

Towards Alleviating Vibration Response Variation Based on Reduced Order Modeling and Analysis

Periodic structures generally consist of spatially repetitive substructures, which are very common in industrial applications such as turbo-machinery bladed disks. The dynamic responses of these structures are very sensitive to variations in geometry and material properties. Previous studies have shown that, when the substructure-to-substructure coupling is weak, even small variations (referred to as mistuning) among the substructures can cause drastic different in the vibratory response of a periodic structure. The goal of this research is to analyze the variation propagation from substructural properties to the dynamic response of the integral structure, and then inversely identify the design perturbation needed to reduce the response anomaly when such anomaly exceeds the allowable threshold. An order-reduced modeling approach is formulated to facilitate the efficient analysis of vibratory response of the integral structure, and several design perturbations are evaluated in order to reduce the response variations in an example periodic structure.Copyright