Structural Dynamic Systems Research Articles

Preface special issue on structural dynamical systems

Preface special issue on structural dynamical systems

A long short-term memory based deep learning algorithm for seismic response uncertainty quantification

The application of metamodeling technique to overcome computational challenge of Monte Carlo simulation (MCS) technique for response uncertainty quantification under stochastic earthquake load is a difficult task due to the high-dimensional nature of stochastic load. Recent developments in the sequential models for forecasting and prediction have opened a new avenue in this regard. Various deep learning algorithms, particularly the convolutional neural network and recurrent neural network are quite suitable for response uncertainty quantification of nonlinear stochastic dynamic system. However, most of the existing studies consider stochastic load as the only source of uncertainty assuming the parameters characterizing a structure as deterministic. The present study proposes a long short-term memory (LSTM) based deep learning algorithm for seismic response uncertainty quantification by duly addressing both the stochastic nature of dynamic load and structural system parameter uncertainty. The functional application program interface feature of Keras that allows layers sharing to form more complex model is explored to form a response approximation model. It incorporates more than one input source i.e., stochastic dynamic excitation sequence as well as structural system parameter uncertainty. The proposed algorithm is elucidated through two numerical examples i.e., a proof-of-concept example and one realistic structural engineering problem by considering the direct MCS based results as the benchmark. The results of accuracy matrices, regression analysis results, comparison of seismic response statistics and reliability results with the results of direct MCS technique clearly revealed the enhanced prediction capability of the proposed LSTM model.

System reliability analyses of static and dynamic structures via direct probability integral method

Structural system reliability analysis is of important significance for evaluating the safety of structures with many components. Since a structural system can be acted by static or dynamic load, a unified and efficient method is required to assess the system reliability of static or dynamic load induced structures. In this study, the direct probability integral method (DPIM) is proposed to uniformly attack system reliability problems of static and dynamic structures. Firstly, the static and first-passage dynamic reliability formulas of the series, parallel and mixed systems are established by the joint probability density function (PDF) of multiple performance functions. Based on the probability density integral equation (PDIE) of performance functions, the DPIM is proposed along the two approaches, i.e., DPIM-S and DPIM-H. The former computes the system reliability using the PDF of extreme value mapping of performance functions, which is obtained by smoothing Dirac delta function. In the latter, the system reliability formulas with Heaviside function are analytically derived by the PDIE of multiple performance functions. Specially, the role of smoothing of Dirac delta function in DPIM for stochastic response and reliability analyses is revealed. Finally, five typical examples, including two mathematical examples and three static and dynamic structural systems, demonstrate high efficiency and accuracy of the DPIM for system reliability computation. Because of omitting the smoothing of Dirac delta function, the DPIM-H takes less CPU time for solving system reliabilities of static and dynamic structures than DPIM-S, while the DPIM-S has a significant advantage of obtaining the PDF of performance function.

Highly precise and efficient solution strategy for linear heat conduction and structural dynamics

AbstractTime‐dependent parabolic and hyperbolic equations are widely encountered in practical engineering. Accurate and fast solution methods for such equations have always attracted attention. To reach this aim, this article proposes a strategy to construct highly precise and efficient time integration methods (TIMs) for linear heat conduction and structural dynamic systems. In the proposed strategy, an integrated amplification matrix of a TIM is created to precisely transfer the free responses of the previous step, and the Gauss–Legendre quadrature is employed to precisely compute the forced responses of the current step. To reduce computational cost and rounding error, a 2m algorithm and a method of storing incremental matrix are applied in the construction of the integrated matrix. Moreover, the L‐stable backward difference formula for heat conduction and the generalized trapezoidal rule for structural dynamics, which is A‐stable and has controllable dissipation, are utilized to conduct this strategy. Numerical experiments validate that compared with some existing TIMs, the TIMs generated by the proposed strategy enjoy advantages both in precision and efficiency.

Recovering tractor stability from an intensive rollover with a momentum flywheel and active steering: System formulation and scale-model verification

As a representative type of off-road vehicle, agricultural wheeled tractors are driven under varied and complicated road conditions such as plowed and hilly fields. Active control is the essential technique to solve tractor rollover accidents which have been identified as the most fatal incident along with agricultural mechanization. The aim of this study is to provide active correction of tractor attitude in emergency cases by combing a single-axis momentum flywheel system and active steering system. In this study, the time-varying structural nonlinear vehicle dynamic system and its subsystems are formulated during transitions among tractor states under road stimulation. By exploring the phased mutation mechanism of tractor stability, the corresponding stability criteria are proposed. The coordinated tractor safety control strategy was verified using parametric studies in a simulation and scale-model experiments. The results indicated the effective and robust control of tractor safety regarding the independent and integrated active control systems. The proposed approach is expected to provide a theoretical basis and technical support for advanced driver assistance systems applied to future intelligent agricultural vehicles.

Relational Dynamics of Treatment Behavior Among Individuals with Tuberculosis in High-Income Countries: A Scoping Review.

Although tuberculosis (TB) incidence has significantly declined in high-income, low-incidence (HILI) countries, challenges remain in managing TB in vulnerable populations who may struggle to stay on anti-TB treatment (ATT). Factors associated with non-adherence to ATT are well documented; however, adherence is often narrowly conceived as a fixed binary variable that places emphasis on individual agency and the act of taking medicines, rather than on the demands of being on treatment more broadly. Further, the mechanisms through which documented factors act upon the experience of being on treatment are poorly understood. Adopting a relational approach that emphasizes the embeddedness of individuals within dynamic social, structural, and health systems contexts, this scoping review aims to synthesize qualitative evidence on experiences of being on ATT and mechanisms through which socio-ecological factors influence adherence in HILI countries. Six electronic databases were searched for peer-reviewed literature published in English between January 1990 and May 2020. Additional studies were obtained by searching references of included studies. Narrative synthesis was used to analyze qualitative data extracted from included studies. Of 28 included studies, the majority (86%) reported on health systems factors, followed by personal characteristics (82%), structural influences (61%), social factors (57%), and treatment-related factors (50%). Included studies highlighted three points that underpin a relational approach to ATT behavior: 1) individual motivation and capacity to take ATT is dynamic and intertwined with, rather than separate from, social, health systems, and structural factors; 2) individuals’ pre-existing experiences of health-seeking influence their views on treatment and their ability to commit to long-term regular medicine-taking; and 3) social, cultural, and political contexts play an important role in mediating how specific factors work to support or hinder ATT adherence behavior in different settings. Based on our analysis, we suggest that person-centered clinical management of tuberculosis should 1) acknowledge the ways in which ATT both disrupts and is managed within the everyday lives of individuals with TB; 2) appreciate that individuals' circumstances and the support and resources they can access may change over the course of treatment; and 3) display sensitivity towards context-specific social and cultural norms affecting individual and collective experiences of being on ATT.

Identification of Dynamic Models by Using Metaheuristic Algorithms

A modified versions of metaheuristic algorithms are presented to compare their performance in identifying the structural dynamic systems. Genetic algorithm, biogeography based optimization algorithm, ant colony optimization algorithm and artificial bee colony algorithm are heuristic algorithms that have robustness and ease of implementation with simple structure. Different algorithms were selected some from evolution algorithms and other from swarm algorithms to boost the equilibrium of global searches and local searches, to compare the performance and investigate the applicability of proposed algorithms to system identification; three cases are suggested under different conditions concerning data availability, different noise rate and previous familiarity of parameters. Simulation results show these proposed algorithms produce excellent parameter estimation, even with little measurements and a high noise rate.

Stability analysis of discretized structure systems based on the complex network with dynamics of time‐varying stiffness

The stability analysis of dynamic continuous structural system (DCSS) has often been investigated by discretizing it into several low‐dimensional elements. The integrated results of all elements are employed to describe the whole dynamic behavior of DCSS. In this paper, DCSS is regarded as the complex dynamic network with the discretized elements as the dynamic nodes and the time‐varying stiffness as the dynamic link relations between them, by which the DCSS can be regarded to be the large‐scale system composed of the node subsystem (NS) and link subsystem (LS). Therefore, the dynamic model of DCSS is proposed as the combination of dynamic equations of NS and LS, in which their state variables are coupled mutually. By using the model, this paper investigates the stability of DCSS. The research results show that the state variables of NS and LS are uniformly ultimately bounded (UUB) associated with the synthesized coupling terms in LS. Finally, the simulation example is utilized to demonstrate the validity of method in this paper.

An improved Bayesian collocation method for steady-state response analysis of structural dynamic systems with large interval uncertainties

This paper presents an improved Bayesian collocation method (IBCM) for steady-state response analysis of structural dynamic systems with large interval uncertainties. The main task of interval analysis is to search the extrema of steady-state response within the parametric intervals, so that the response bounds can be obtained. However, interval analysis problems with large parametric uncertainties are usually highly nonlinear. Thus, to improve efficiency and accuracy for nonlinear interval analysis, the IBCM executes a bi-directional global optimization process by using a sequential Gaussian process surrogate model. In this method, IBCM constructs crude surrogate models based on Gaussian process. Then a bi-directional sampling strategy is proposed to guide to search the extrema within the parametric interval. Meanwhile, the surrogate model will also be refined. A decayed weight function is presented to balance exploration and exploitation in highly nonlinear cases. The above process repeats until it converges. The interval of steady-state response can be calculated with low computational cost according to the refined Gaussian process surrogate model. The feasibility and validity of the IBCM are demonstrated by numerical examples and engineering applications.

The scaling of nonlinear structural dynamic systems

A new scaling theory has appeared in the recent literature that has the potential to transform current approaches to scaled experimentation. The new theory introduces new similitude rules that hitherto did not exist and significantly extends the classical definition of similitude underpinned by dimensional analysis. Each new similitude rule is tied to the number of scaled experiments, and in theoretical terms there is no limit to the number of scaled experiments involved.The focus of this paper is on one and two scaled experiments applied to nonlinear structural dynamics, which is a field of study and application that gives rise to significant difficulties for scaled experimentation. The highly nonlinear behaviour common to these systems means that only very precise scaled-model designs can feasibly achieve acceptable outcomes. It is shown in the paper how the new exact similitude rules provided by the new theory deliver the precision necessary for mathematically exact replication of behaviours. It is demonstrated further how the limited scope provided by a single scaled experiment can be significantly extended by application of two properly designed scaled experiments. Through the analysis of carefully selected structural systems of one and two degrees of freedom involving nonlinear springs, dashpots and friction, the benefits of two scaled experiments are demonstrable for a range of loading conditions. Exact similitude for two scaled experiments is confirmed providing exact replication of behaviours with conformity recorded over long timescales.

An enhanced indirect video-based measurement procedure for dynamic structural system identification applications

A video-based indirect sensing procedure for dynamic identification purposes is presented. To overcome major limitations of video-based methods in real on-site measurements, a novel three step pre-modification, magnification, post-modification process is developed. This process includes revision of the initial input video record in order to delete disturbing objects, utilizing a magnification method to filter the frequency content of the monitored motion and using a revision step for elimination of noises generated during magnification process. Finally, a set of digital signal and image processing analyses are performed on the modified video using virtual visual sensor technology. Based on the results of this research, motion signals of the monitored object are detected. The proposed approach has been used for identification of dynamic characteristics of two historic masonry minarets in Istanbul. Results shows that the proposed procedure is able to assess the dynamic characteristics of the monitored structure with a high-level of accuracy.

Transient Flutter Stability Analysis of Structural Mistuned Blisk by Energy Growth Method

Abstract Blisks suffer from flutter, a self-sustained vibration caused by aerodynamic coupled forces. This instability could cause serious damage to the blades and the machine. Flutter stability is usually analyzed based on the eigenvalue method in the aspect of the linear structural dynamic system, which transforms a dynamics stability analysis into a point of equilibrium in an infinite time scale. However, in reality, most of the blisk vibrations arise on a finite time horizon. The transient vibration amplification may cause serious damage. This paper proposes a transient flutter stability analysis method in a finite time for structural mistuned blisk based on the energy growth method. First, two common blisk models coupled aerodynamic force with different complexity are built and are all expressed in the state space representation. A novel energy growth method is then employed to analyze the transient stability and to find the maximum energy growth of the models. The optimal initial condition which leads to the maximum energy growth is obtained. A new flutter stability criterion is developed to consider the transient stability based on the energy growth method and the infinite time stability based on the eigenvalue method. The new transient stability method is verified by two numerical studies. It is found that the structural mistuned blisk model which is traditionally predicted stable still has a transient instability in a finite time due to the non-normal property of the dynamic state matrix.

Iterative Rational Krylov Algorithms for model reduction of a class of constrained structural dynamic system with Engineering applications

<p style='text-indent:20px;'>This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody dynamics, mechatronics and many other branches of sciences and technologies. By deflecting the algebraic equations the second-order index-3 system can be altered into an equivalent standard second-order system. This can be done by projecting the system onto the null space of the constraint matrix. However, creating the projector is computationally expensive and it yields huge bottleneck during the implementation. This paper shows how to find a reduce order model without projecting the system onto the null space of the constraint matrix explicitly. To show the efficiency of the theoretical works we apply them to several data of second-order index-3 models and experimental resultants are discussed in the paper.</p>

Vision-based modal parameter identification for bridges using a novel holographic visual sensor

Noncontact monitoring using holography can be quite useful in vision-based structural health monitoring owing to its advantages in terms of data visualization and real-time applications. Aimed at exploring the potential of vision-based sensors for structural health monitoring in more general applications, this paper has developed the holographic visual sensor (HVS) with a vision-based modal parameter identification method. This strategy is an extension of the current vision-based techniques and holography. Based on the newly introduced spatial and temporal sequence data measured by HVS, the vision-based modal parameter identification method was proposed and applied to structural health monitoring for the first time. Accordingly, the feature point set describing the geometric morphology of the structural holography and the time-state-space mathematical model of the structural dynamics system was constructed. In this way, the mechanical behavior characteristics could be extracted from serial transient holographic responses following excitation, and the structural modal parameters were then calculated and quantitatively analyzed. Laboratory experiments and field tests were employed for validation based on the comparison between the results determined by the proposed HVS and those determined by conventional, high-precision contact sensors. The developed HVS and identification algorithms were able to visually collect and identify modal parameters at a higher data resolution and provide smoother modal shapes. The proposed method can thus be used to complement and improve existing computer-vision-based measurement techniques and damage detection.

On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression

This paper presents the use of spike-and-slab (SS) priors for discovering governing differential equations of motion of nonlinear structural dynamic systems. The problem of discovering governing equations is cast as that of selecting relevant variables from a predetermined dictionary of basis functions and solved via sparse Bayesian linear regression. The SS priors, which belong to a class of discrete-mixture priors and are known for their strong sparsifying (or shrinkage) properties, are employed to induce sparse solutions and select relevant variables. Three different variants of SS priors are explored for performing Bayesian equation discovery. As the posteriors with SS priors are analytically intractable, a Markov chain Monte Carlo (MCMC)-based Gibbs sampler is employed for drawing posterior samples of the model parameters; the posterior samples are used for basis function selection and parameter estimation in equation discovery. The proposed algorithm has been applied to four systems of engineering interest, which include a baseline linear system, and systems with cubic stiffness, quadratic viscous damping, and Coulomb damping. The results demonstrate the effectiveness of the SS priors in identifying the presence and type of nonlinearity in the system. Additionally, comparisons with the Sparse Bayesian (SBL) – that uses a Student’s-t prior – indicate that the SS priors can achieve better model selection consistency, reduce false discoveries, and derive models that have superior predictive accuracy. Finally, the Silverbox experimental benchmark is used to validate the proposed methodology.

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

AbstractAn Iterative Flexibility‐based Component Mode Synthesis (IF‐CMS) is presented for the model reduction of partitioned structural dynamic systems via localized Lagrange multipliers. A distinct IF‐CMS feature is the inclusion of hierarchical residual flexibility at each iteration, resulting in considerably improved accuracy compared with the classical Craig–Bampton (CB) CMS method. The present IF‐CMS method does not increase the number of substructural modes during the hierarchical iteration process. In particular, to alleviate ill‐conditioning during the iteration steps, the proposed IF‐CMS method adopts the so‐called (qd, , ub)‐formulation by condensing Lagrange multipliers from the original F‐CMS method. The performance of the proposed method is evaluated through numerical examples, which illustrates improved accuracy over existing CMS methods.

Reduced-order modeling of nonlinear structural dynamical systems via element-wise stiffness evaluation procedure combined with hyper-reduction

In nonlinear analysis, performing iterative inverse calculation and nonlinear system construction procedures incurs expensive computational costs. This paper presents an element-wise stiffness evaluation procedure combined with hyper-reduction reduced-order modeling (HE-STEP ROM) method. The proposed approach constructs a non-intrusive reduced-order model based on an element-wise stiffness evaluation procedure (E-STEP) and hyper-reduction methods. Because the E-STEP evaluates nonlinear stiffness coefficients element-by-element using cubic polynomial, numerous number of polynomial variables are required. The number of variables directly affects the computational efficiency of the online and offline stages. Therefore, to enhance efficiency of the online/offline stages, the proposed method employs hyper-reduction method. By applying hyper-reduction, the full stiffness coefficients are approximated from the stiffness coefficients evaluated at a few sampling points. Subsequently, the number of polynomial equations and variables is prominently reduced, and the efficiency of the reduced system increases. The efficiency and accuracy of the proposed approach are validated via several structural dynamic problems with geometric and material nonlinearities.

Multilevel Decomposition Framework for Reliability Assessment of Assembled Stochastic Linear Structural Systems

AbstractTo reduce the computational cost of assembled stochastic linear structural dynamic systems, a three-staged reduced order model-based framework for forward uncertainty propagation was develo...

Solving ARGESIM Benchmark C21 ’State Events and Structural-dynamic Systems’ with Simulink

Solving ARGESIM Benchmark C21 ’State Events and Structural-dynamic Systems’ with Simulink

Machine learning based digital twin for dynamical systems with multiple time-scales

Digital twin technology has a huge potential for widespread applications in different industrial sectors such as infrastructure, aerospace, and automotive. However, practical adoptions of this technology have been slower, mainly due to a lack of application-specific details. Here we focus on a digital twin framework for linear single-degree-of-freedom structural dynamic systems evolving in two different operational time scales in addition to its intrinsic dynamic time-scale. Our approach strategically separates into two components – (a) a physics-based nominal model for data processing and response predictions, and (b) a data-driven machine learning model for the time-evolution of the system parameters. The physics-based nominal model is system-specific and selected based on the problem under consideration. On the other hand, the data-driven machine learning model is generic. For tracking the multi-timescale evolution of the system parameters, we propose to exploit a mixture of experts as the data-driven model. Within the mixture of experts model, Gaussian Process (GP) is used as the expert model. The primary idea is to let each expert track the evolution of the system parameters at a single time-scale. For learning the hyperparameters of the ‘mixture of experts using GP’, an efficient framework that exploits expectation-maximization and sequential Monte Carlo sampler is used. Performance of the digital twin is illustrated on a multi-timescale dynamical system with stiffness and/or mass variations. The digital twin is found to be robust and yields reasonably accurate results. One exciting feature of the proposed digital twin is its capability to provide reasonable predictions at future time-steps. Aspects related to the data quality and data quantity are also investigated.