Structural Dynamic Systems Research Articles

A general two-phase Markov chain Monte Carlo approach for constrained design optimization: Application to stochastic structural optimization

This contribution presents a general approach for solving structural design problems formulated as a class of nonlinear constrained optimization problems. A Two-Phase approach based on Bayesian model updating is considered for obtaining the optimal designs. Phase I generates samples (designs) uniformly distributed over the feasible design space, while Phase II obtains a set of designs lying in the vicinity of the optimal solution set. The equivalent model updating problem is solved by the transitional Markov chain Monte Carlo method. The proposed constraint-handling approach is direct and does not require special constraint-handling techniques. The population-based stochastic optimization algorithm generates a set of nearly optimal solutions uniformly distributed over the vicinity of the optimal solution set. The set of optimal solutions provides valuable sensitivity information. In addition, the proposed scheme is a useful tool for exploration of complex feasible design spaces. The general approach is applied to an important class of problems. Specifically, reliability-based design optimization of structural dynamical systems under stochastic excitation. Numerical examples are presented to evaluate the effectiveness of the proposed design scheme.

Novel sparseness-inducing dual Kalman filter and its application to tracking time-varying spatially-sparse structural stiffness changes and inputs

While the theory of Bayesian system identification provides a probabilistic means for reliably and robustly inferring models of a dynamic system and their parameters based on measured dynamic response, exploiting sparseness during online tracking of changing model parameters is not well understood. The focus in this study is to implement the dual Kalman filter for real-time Bayesian sequential state and parameter identification based on noisy sensor signals while incorporating sparse Bayesian learning to impose sparse model parameter changes from their initial reference values. We also want out model to be able to capture the evolution of sparse model parameter changes between two successive time instants. To this end, we present a hierarchical Bayesian model for tracking the joint posterior distribution of the state and model parameter vectors for a monitored dynamical system, where the two afore-mentioned sparseness constraints (sparse changes from reference values and with time) are also effectively incorporated for each time. We show our stochastic model of the structural dynamical system can be represented as a coupled conditionally-linear Gaussian state space model for the state and model parameter vectors, leading to some interesting analytical properties of the method that allow quantities of interest to be calculated in real time by using Kalman filtering equations. The parameters for the measurement and state prediction errors are learned solely from the available data up to the current time and so our method resolves the well-known instability problem in Kalman filtering due to arbitrary assignment of the error-distribution parameters. Finally, two illustrative applications are presented, one for identification of stiffness degradation and the other for input time–history identification where both are based on noisy dynamic response measurements from a structure.

Efficient seismic reliability analysis of non-linear structures under non-stationary ground motions

The seismic reliability assessment (SRA) of complex nonlinear structures which possess structural and seismic uncertainty is an open challenge for academics and practical engineers. This paper proposes an improved maximum entropy method (IMEM) for the SRA of nonlinear structures. Non-stationary ground motions are first generated via a random-function-based spectral representation method. High-dimensional random variables in the ground motion simulation are then converted into two basic random variables as the high-dimensional probability space is reduced to a low-dimensional probability space. A two-step IMEM constrained with fractional moments is deployed to estimate the extreme value distribution (EVD) of the nonlinear structural dynamic system. An improved Latin hypercube sampling approach is also established to calculate the fractional moments of the complex nonlinear dynamic system. The first-passage probability of the structural nonlinear seismic response can be computed conveniently by a numerical integration using the EVD. Two numerical examples, 1) a three-story nonlinear shear frame structure and 2) a real-world high-pier continuous rigid frame bridge model, both of which exhibit strong nonlinearity under seismic action, are analyzed to show that the proposed method is efficient and accurate.

Chatter reliability prediction of side milling aero-engine blisk

Reliability analysis of a dynamic structural system is applied to predict chatter of side milling system for machining blisk. Chatter reliability is defined as the probability of stability for processing. A reliability model of chatter was developed to forecast chatter vibration of side milling, where structure parameters and spindle speed are regarded as random variables and chatter frequency is considered as intermediate variable. The first-order second-moment method was used to work out the side milling system reliability model. Reliability lobe diagram (RLD) was applied to distinguish reliable regions of chatter instead of stability lobe diagram (SLD). One example is used to validate the effectiveness of the proposed method and compare with the Monte Carlo method. The results of the two approaches were consistent. Chatter reliability and RLD could be used to determine the probability of stability of side milling.

Drive comfort and safety evaluation for vortex-induced vibration of a suspension bridge based on monitoring data

Vortex-induced vibration (VIV) caused by wind excitation can seriously affect traffic comfort and safety. Therefore, reasonable control measures in the initial stage of VIV shall be formulated by the bridge management department to ensure the safety of passing vehicles. In this paper monitoring data of VIV of a suspension bridge from 2013 to 2017 were analyzed and the characteristics of structural vibration response factors such as wind parameters and Energy Concentration Coefficient (ECC) of VIV were studied. A dynamic monitoring model which used for VIV prediction was established based on the massive data collected by the existing structural health monitoring system and dynamic monitoring system of VIV installed on the bridge which is located in the East China Sea. The data measured in 2017 by the anemometers and acceleration sensors from dynamic monitoring system was taken as input to simulate the prediction process of VIV. The warning mechanism of VIV with 5 levels and corresponding measures were proposed. Results show that the root mean square (RMS) value of acceleration and ECC can be used as further criteria for judging the occurrence of VIV. The comprehensive decision method and trend analysis method can be used for VIV judgment. The recognition rate of the occurrence VIV is 88.00% and 93.24% by the comprehensive decision method and trend analysis method respectively, based on the dynamic monitoring model. The dynamic monitoring model for VIV can be adopted to timely predict VIV, and can be effectively applied in practical engineering.

Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information

Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference. Equivalently, the expected information entropy of the posterior of the model parameters is minimized over all possible sensor configurations for a given sensor budget. In the context of structural dynamical systems, this minimization is computationally expensive because of the large number of possible sensor configurations. Here, a very efficient convex relaxation scheme is presented to determine informative and possibly optimal solutions to the problem, thereby bypassing the necessity for an exhaustive, and often infeasible, combinatorial search. The key idea is to relax the binary sensor location vector so that its components corresponding to all possible sensor locations lie in the unit interval. Then, the optimization over this vector is a convex problem that can be efficiently solved. This method always yields a unique solution for the relaxed problem, which is often binary and therefore the optimal solution to the original problem. When not binary, the relaxed solution is often suggestive of what the optimal solution for the original problem is. An illustrative example using a 50‐story shear building model subject to sinusoidal ground motion is presented, including a case where there are over 47 trillion possible sensor configurations. The solutions and computational effort are compared with greedy and heuristic methods.

Data-driven identification of reliable sensor species to predict regime shifts in ecological networks.

Signals of critical slowing down are useful for predicting impending transitions in ecosystems. However, in a system with complex interacting components not all components provide the same quality of information to detect system-wide transitions. Identifying the best indicator species in complex ecosystems is a challenging task when a model of the system is not available. In this paper, we propose a data-driven approach to rank the elements of a spatially distributed ecosystem based on their reliability in providing early-warning signals of critical transitions. The proposed method is rooted in experimental modal analysis techniques traditionally used to identify structural dynamical systems. We show that one could use natural system fluctuations and the system responses to small perturbations to reveal the slowest direction of the system dynamics and identify indicator regions that are best suited for detecting abrupt transitions in a network of interacting components. The approach is applied to several ecosystems to demonstrate how it successfully ranks regions based on their reliability to provide early-warning signals of regime shifts. The significance of identifying the indicator species and the challenges associated with ranking nodes in networks of interacting components are also discussed.

Physical Characteristics of Section Coal and Rock Pillars Under Roof Shock Disturbances From Goaf

The stability of rock strata structure is closely related to its response physical characteristics under external shock disturbance. The roof shock disturbance from goaf is usually one of the important factors of causing coal and rock pillars instability. It is necessary to study the dynamic physical characteristics of coal and rock pillars under roof shock disturbance from goaf. The dynamic structural system model of elastic-plastic finite element was established for the formation of surrounding rock and coal pillars in a deep stope. And the response physical characteristics of coal pillars with different widths were analyzed, under the roof shock disturbance intensity and frequency from goaf. The natural vibration characteristics of the stope model were calculated and the first ten orders natural frequencies were extracted. Calculations indicated that the vertical displacement and the plastic zone occupation ratio of the coal pillar increased with the increase of the shock disturbance intensity, decreased with the increase of the shock disturbance frequency, and decreased with the increase of the coal pillar width. The influence of the vertical deformation and the plastic zone occupation ratio of the coal pillar under shock disturbance frequency was more obvious compared with that of shock disturbance intensity, especially at low frequency. The closer the shock disturbance frequency was to the natural frequency of the model, the larger the plastic zone of coal pillars was, which the bearing capacity of coal pillar decreased significantly. It is significant that more attention should be paied to monitoring the frequency of roof shock disturbance signal when design coal pillars width in the coal mine.

Convolutive PD controller for hybrid improvement of dynamic structural systems

Passively controlled structural systems may be exhibiting scarce capability in resisting dynamic solicitations under adverse special or unexpected conditions. Improvements of the overall performance of the passive system may be obtained when introducing supplemental corrective control actions, possibly coupling different technologic solutions and moving to mixed systems. In the paper the performance of a base isolation system is increased by embedding in the control layout an additional passive/active device, commanded by a newly designed control algorithm. The main novelty lays in the overall control system, which is regarded and completely newly designed as a whole rather than coupling already existing separated control systems, which are usually adopted and forced to comply with each other, thus realizing full complementarity. The proposed approach is aimed at further improving the reliability of the control system, ensuring its functionality even when unexpected adverse conditions occur, causing ineffectiveness of the main system.

THE INFLUENCE OF HUMAN MOVEMENT ON THE FORMATION OF ADAPTIVE ARCHITECTURE

Adaptive architecture relates to buildings that are specially designed to adapt to their inhabitants and their environments and in order to design a biologically adaptive system, we can observe how living creatures in nature are constantly adapting to various external and internal stimuli can be a great source of inspiration. The issue is not just how to create a system capable of change but also how to look for quality change and determine the incentive to adapt. The research deals with the possibilities of transforming spaces by using the human body as an active tool, and the research aims to design and build an effective dynamic structural system that can be applied on an architectural scale and integrate them all into creating a new adaptive system that allows us to envision a new way to design, build and experiment with architecture in a dynamic way. The main objective was to address the possibility of a mutual transition between the user and the architectural component so that the architecture can adapt to the user, as the user adapts to the architecture. Motivation is the desire to engage with the psychological benefits of an environment that can respond and thus empathize with human emotions through its ability to adapt to the user. The adaptive affiliations of kinematic structures have been discussed in architectural research for more than a decade, and these issues have proven their effectiveness in the development of kinematic, responsive and adaptive structures and their contribution to an “intelligent architecture”. A wide range of strategies have also been used in building the mechanisms of complex kinematic and robotic systems to achieve convertibility and adaptability in engineering and architecture. One of the major contributions to this research is the exploration of how the physical environment can alter its shape to accommodate various spatial displays based on the user's body movement. The main focus is on the relationship among materials, shape and reactive control systems and the intent is to create a scenario where the user can move and the structure interacts without any physical contact. , the language of soft form transformation and interaction control technology will provide new possibilities for enriching human-environment interactions.

An adaptive scheme for reliability-based global design optimization: A Markov chain Monte Carlo approach

The reliability-based design of structural dynamic systems under stochastic excitation is presented. The design problem is formulated in terms of the global minimization of the system failure probability. The corresponding optimization problem is solved by an effective stochastic simulation scheme based on the transitional Markov chain Monte Carlo method. Although the scheme is quite general, is computationally very demanding due to the large number of reliability analyses required during the design process. To cope with this difficulty, an advanced simulation technique is combined with an adaptive surrogate model for estimating the failure probabilities. In particular, a kriging meta-model is selected in the present formulation. The algorithm generates a set of nearly optimal solutions uniformly distributed over a neighborhood of the optimal solution set. Such set can be used for exploration of the global sensitivity of the system reliability. Several illustrative examples are presented to investigate the applicability and effectiveness of the proposed design scheme.

Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties

Surrogate models enable efficient propagation of uncertainties in computationally demanding models of physical systems. We employ surrogate models that draw upon polynomial bases to model the stochastic response of structural dynamics systems. In linear structural dynamics problems, the system response can be described by the frequency response function. It is well known that standard polynomial chaos expansions of the frequency response present slow convergence around system eigenfrequencies, due to the highly nonlinear nature of the frequency response for low damping. To overcome this issue, we develop a rational approximation that expresses the system response as a rational of two polynomials with complex coefficients. To estimate the latter, we propose a regression approach that is non-intrusive and can be easily coupled with existing deterministic solvers. We demonstrate the effectiveness of the proposed method with two examples, a two-degree-of-freedom system and a finite element model of a cross laminated timber plate.

On the application of Gaussian process latent force models for joint input-state-parameter estimation: With a view to Bayesian operational identification

The problem of identifying dynamic structural systems is of key interest to modern engineering practice and is often a first step in an analysis chain, such as validation of computer models or structural health monitoring. While this topic has been well covered for tests conducted in a laboratory setting, identification of full-scale structures in place remains challenging. Additionally, during in service assessment, it is often not possible to measure the loading that a given structure is subjected to; this could be due to practical limitations or cost. Current solutions to this problem revolve around assumptions regarding the nature of the load a structure is subject to; almost exclusively this is assumed to be a white Gaussian noise. However, in many cases this assumption is insufficient and can lead to biased results in system identification. This current work presents a model which attempts the system identification task (in terms of the parametric estimation) in conjunction with estimation of the inputs to the system and the latent states—the displacements and velocities of the system. Within this paper, a Bayesian framework is presented for rigorous uncertainty quantification over both the system parameters and the unknown input signal. A Gaussian process latent force model allows a flexible Bayesian prior to be placed over the unknown forcing signal, which in conjunction with the state-space representation, allows fully Bayesian inference over the complete dynamic system and the unknown inputs.

A novel recursive modal parameter estimator for operational time-varying structural dynamic systems based on least squares support vector machine and time series model

Modal parameters are practically important for vibration control, structural dynamic design, health monitoring, etc. Presently, the commonly used recursive modal parameter estimators are generally based on the empirical risk minimization principle, and thus can result in overfitting problem easily. This paper presents a novel recursive modal parameter estimator for operational linear time-varying structures based on least squares support vector machine (LSSVM) and vector time-dependent autoregressive moving average model. A sliding-window forgetting mechanism is adapted to fix computational complexity of each update step and enhance tracking capability of the proposed estimator. A numerical example and a laboratory experiment are performed to demonstrate that the proposed structural risk minimization principle based estimator is robust to model structure and its computational complexities are independent of the dimension of output measurements comparing with the existing recursive extended least squares estimator.

Accelerating the convergence of AFETI partitioned analysis of heterogeneous structural dynamical systems

Variationally based algorithms for the partitioned solution of structural mechanics problems are presented. Two key features of the present algorithms are the judicious application of the d’Alembert-Lagrange principal equations and the use of dominant substructural deformation modes. The paper includes three developments:1. Variational derivation of AFETI parallel solution methods.2. One-level and two-level AFETI implicit transient analysis algorithms with coarse problem included in the projector and based on free floating rigid body modes.3. A new AFETI implicit transient solution algorithm derived by constraining the interface equilibrium equations with the floating and dominant deformational modes.In addition to variational derivations of solution algorithms, the present paper is strived to offer new physical and/or numerical insight as each of variational derivational steps is succinctly explained. Performance evaluations of the algorithms described herein are presented.

The Integrated Test Analysis Process for Structural Dynamic Systems

Abstract Over the past 60 years, the U.S. aerospace community has developed, refined, and standardized an integrated approach to structural dynamic model verification and validation. One name for t...

Numerical analysis on flutter of Busemann-type supersonic biplane airfoil

The Busemann-type supersonic biplane can effectively reduce the wave drag through shock interference effect between airfoils. However, considering the elastic property of the wing structure, the vibration of the wings can cause the shock oscillation between the biplane, which may result in relative aeroelastic problems of the wing. In this research, fluid–structure interaction characteristics of the Busemann-type supersonic biplane at its design condition have been studied. A theoretical two-dimensional structure model has been established to consider the main elastic characteristics of the wing structure. Coupled with unsteady Navier–Stokes equations, the fluid–structure dynamic system of the supersonic biplane is studied through the two-way computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling method. The biplane system has been simulated at its design Mach number with different nondimensional velocities. Different initial disturbance has been applied to excite the system and the effects of the position of the mass center on the system’s aeroelastic stability is also discussed. The results reveal that the stability of the airfoil in supersonic biplane system is decreased compared with that of the airfoil isolated in supersonic flow and such stability reduction effect should be given due attention in practical design.

On the statistical mechanics of structural vibration

The analysis of the structural dynamics of a complex engineering structure has much in common with the subject of statistical mechanics. Both are concerned with the analysis of large systems in the presence of various sources of randomness, and both are concerned with the possibility of emergent laws that might be used to provide a simplified approach to the analysis of the system. The aim of the present work is to apply a number of the concepts of statistical mechanics to structural dynamic systems in order to provide new insights into the system behaviour under various conditions. The work is foundational, in that it is based on employing the fundamental equations of motion of the system in conjunction with various definitions of entropy, and no recourse is made to emergent laws that are accepted in thermodynamics. The analysis covers closed (undamped and unforced) and open (forced and damped) systems, linear and nonlinear systems, and both single systems and coupled systems. The fact that the system itself can be random leads to a number of results that differ from those found in classical statistical mechanics, where the initial conditions might be considered to be random but the Hamiltonian is taken to be well defined. For example, the occurrence of a stationary state in a closed system normally requires nonlinearity and coarse-graining of the statistical distribution, but neither condition is required for a random system. For coupled systems it is shown that under certain conditions both Statistical Energy Analysis (SEA) and Transient Statistical Energy Analysis (TSEA) are emergent laws, and insights are gained as to the validity of these laws. The analysis is supported by a number of numerical examples to illustrate key points.

Seismic Performance Levels of a Large Underground Subway Station in Different Soil Foundations

ABSTRACT With the soil constitutive model developed for the dynamic large deformation of soft soil, a finite element model was constructed to simulate the soil–underground structure static and dynamic coupling interaction system, in which the dynamic contact between soil and underground structure and the dynamic damage of reinforced concrete were considered. The seismic performance and damage mechanism of the large underground subway station in different soil foundations were investigated and evaluated in detail. It was proven that the interaction mechanism between the soil and underground structure would change with the type of soil foundation and the peak acceleration of input ground motion, which can be evaluated by the interaction coefficient between the soils and underground structure. At the same time, some regulations on the seismic performance of underground structure in China code are already unsuitable for evaluating the seismic performance of a large underground subway station in the soft soil foundation or subjected to a strong earthquake, which should be investigate by the specialized time–history analysis method instead. In this study, five seismic performance levels were firstly defined by the inter-storey drift angle of underground structure and corresponding earthquake damage states.

Direct probability integral method for stochastic response analysis of static and dynamic structural systems

This paper proposes a unified and efficient direct probability integral method (DPIM) to calculate the probability density function (PDF) of responses for linear and nonlinear stochastic structures under static and dynamic loads. Firstly, based on the principle of probability conservation, the probability density integral equation (PDIE) equivalent to the probability density differential equation is derived for stochastic system. We highlight that, for time dependent stochastic system the PDIE is satisfied at each time instant. Secondly, the novel DPIM is proposed to solve PDIE directly by means of the point selection technique based on generalized F discrepancy and the smoothing of Dirac delta function. Moreover, the difference and connection among the DPIM, the existing probability density evolution method and probability transformation method are examined. Finally, four typical examples for stochastic response analysis, including the linear and nonlinear systems subjected to static and dynamic loads, demonstrate the high computational efficiency and accuracy of proposed DPIM.