Uncertainties In Structural Parameters Research Articles

Robust eigenvalue-clustering in a specified circular region for linear uncertain discrete singular systems with state delay

In this paper, the robust eigenvalue-clustering in a specified circular region problem (i.e., the robust D-stability problem) of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside a specified circular region, a new sufficient condition is proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle of the z-plane, the proposed criterion will become the stability robustness criterion. The presented criterion is mathematically proved to be less conservative than the existing ones reported very recently in the literature.

LMI optimization approach on robustness and H∞ control analysis for observer-based control of uncertain systems

This paper investigates the observer-based controls for a class of dynamic linear systems with structural parameter uncertainties. Two issues are mainly concerned with LMI optimization techniques: the first regards the robustness analysis of the observer-based control systems without disturbance inputs and the other is the H ∞ control when involving disturbance inputs. A numerical example is given to illustrate the main contribution of this paper.

Natural frequency and mode shape analysis of structures with uncertainty

Two methods called random factor method (RFM) and interval factor method (IFM) for the natural frequency and mode shape analysis of truss structures with uncertain parameters are presented in this paper. Using the RFM, the structural physical parameters and geometry can be considered as random variables. The structural stiffness and mass matrices can then, respectively, be described by the product of two parts corresponding to the random factors and the deterministic matrix. The structural natural frequencies, mode shapes and random response can be expressed as the function of the random factors. By means of the random variable's algebra synthesis method, the computational expressions for the mean value and standard deviation of natural frequencies and mode shapes are derived from the Rayleigh quotient. Using the IFM, the structural parameters can be considered as interval variables and the computational expressions for the lower and upper bounds of the natural frequency and mode shape are derived by means of the interval operations. The effect of uncertainty of individual structural parameters on structural dynamic characteristics, and the comparison of structural natural frequency and mode shape using the RFM and IFM are demonstrated by truss structures.

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

In this paper, the regional eigenvalue-clustering robustness problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside certain specified regions, two new sufficient conditions are proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle, the proposed criteria will become the stability robustness criteria. For the case of eigenvalue clustering in a specified circular region, one proposed sufficient condition is mathematically proved to be less conservative than those reported very recently in the literature. Another new sufficient condition is also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties holds the properties of regularity, causality, and eigenvalue clustering in a specified region. An example is given to demonstrate the applicability of the proposed sufficient conditions.

SYSTEM IDENTIFICATION OF PHOTOSENSITISER UPTAKE KINETICS IN PHOTODYNAMIC THERAPY

This study presents the contributions of system identification techniques to the experimental modelling of photosensitiser uptake kinetics in photodynamic therapy. The experimental framework is limited to one cancer cell line (HT29-A4), one photosensitiser (Chlorin e6), one photosensitiser dose (5μg · ml–1), four albumin rates in a monolayer culture and eight measurements between 1h and 24h. Issues associated with this experimental modelling study are the deficiency of measurement points, low signal-to-noise ratios and 'poor' excitation signals (step signals). This paper deals with model structure selection, parameter estimation and parameter uncertainty description by probabilistic confidence regions. Moreover, an explicit relationship between the static gain of the estimated model and the albumin rate of the culture medium has been established.

ROBUST STATIC OUTPUT FEEDBACK ℋ∞ CONTROL OF A CLASS OF STOCHASTIC HYBRID SYSTEMS IN NOISY ENVIRONMENT: LMI FORMULATION

In this paper, we address the robust static output feedback control problem of continuous time active fault tolerant control system with Markovian parameters (AFTCSMP) subject to structured parameter uncertainties, in noisy environnement. We will first derive a necessary and sufficient condition for the robust internal exponential stability in the mean square of the uncertain AFTCSMP in terms of nonlinear matrix inequalities. Then, an LMI relaxation scheme is presented to eliminate the nonlinearities, yielding a new easily tractable sufficient condition. Having obtained this result, we can move on the control problem and write the robust output feedback ℋ∞ control problem of the uncertain continuous time AFTCSMP in terms of an LMI optimization problem. The convex approach naturally leads to powerful numerical algorithms to solve these problematic. A numerical example is presented to illustrate the theoretical results.

Robust controllability for linear uncertain descriptor systems

In this paper, under assumptions that the linear nominal descriptor system is regular and controllable, some sufficient conditions are proposed to preserve the assumed properties when both structured (elemental) and unstructured (norm-bounded) parameter uncertainties are added into the nominal descriptor system. Besides, another sufficient conditions are also presented to preserve the assumed properties for a class of linear descriptor systems having structured uncertainties in the structure information matrix as well as having both structured and unstructured parameter uncertainties in the system matrix and the input matrix simultaneously. The corresponding results for the dual observability robustness problems are straightforward extensions. Three numerical examples are given to illustrate the applications of the proposed sufficient conditions, and it is shown that the proposed sufficient conditions could be less conservative than the existing ones reported recently in the literature.

Probabilistic shear-lag analysis of structures using Systematic RSM

In the shear-lag analysis of structures deterministic procedure is insufficient to provide complete information. Probabilistic analysis is a holistic approach for analyzing shear-lag effects considering uncertainties in structural parameters. This paper proposes an efficient and accurate algorithm to analyze shear-lag effects of structures with parameter uncertainties. The proposed algorithm integrated the advantages of the response surface method (RSM), finite element method (FEM) and Monte Carlo simulation (MCS). Uncertainties in the structural parameters can be taken into account in this algorithm. The algorithm is verified using independently generated finite element data. The proposed algorithm is then used to analyze the shear-lag effects of a simply supported beam with parameter uncertainties. The results show that the proposed algorithm based on the central composite design is the most promising one in view of its accuracy and efficiency. Finally, a parametric study was conducted to investigate the effect of each of the random variables on the statistical moment of structural stress response.

Robust D-stability analysis for linear uncertain discrete singular systems with state delay

In this work, by using the maximum modulus principle and the spectral radii of matrices, a new robust D-stability (i.e., robust eigenvalue clustering in a specified circular region) condition is proposed to ensure that, for all admissible structured parameter uncertainties, the linear discrete singular system with state delay is regular, causal and D-stable. The proposed criterion is mathematically proved to be less conservative than the existing one reported very recently.

Reliability-based shape optimization of structures undergoing fluid–structure interaction phenomena

Fluid–structure interaction phenomena are often roughly approximated when the stochastic nature of a system is considered in the design optimization process, leading to potentially significant epistemic uncertainty. In this paper, after reviewing the state-of-the-art methods in robust and reliability-based design optimization of problems undergoing fluid–structure interaction phenomena, a computational framework is presented that integrates a high-fidelity aeroelastic model into reliability-based design optimization. The design optimization problem is formulated pursuant to the reliability index and performance measure approaches. The system reliability is evaluated by a first-order reliability analysis method. The steady-state aeroelastic problem is described by a three-field formulation and solved by a staggered procedure, coupling a potentially detailed structural finite element model and a finite volume discretization of the Euler flow. The design and imperfection sensitivities are computed by evaluating the analytically derived direct and adjoint coupled aeroelastic sensitivity equations. The computational framework is verified by the optimization of three-dimensional wing structures. The lift-to-drag ratio is maximized, subject to stress constraints, by varying shape, thickness, and material properties. Uncertainties in structural parameters, including design parameters, operating conditions, and modeling uncertainties are considered. The results demonstrate the need for reliability-based optimization methods, for the design of structures undergoing fluid–structure interaction phenomena, and the applicability of the proposed framework to realistic design problems. Comparing the optimization results for different levels of uncertainty shows the importance of accounting for uncertainties in a quantitative manner.

Predictive uncertainty of a nearshore bed evolution model

Predictions of nearshore depth evolution using process-based numerical simulation models contain inherent uncertainties owing to model structural deficiencies, measurement errors, and parameter uncertainty. This paper quantifies the parameter-induced predictive uncertainty of the cross-shore depth evolution model Unibest-TC by applying the Bayesian Generalised Likelihood Uncertainty Estimation methodology to modelling depth evolution at Egmond aan Zee (Netherlands). This methodology works with multiple sets of parameter values sampled uniformly in feasible parameter space and assigns a likelihood value to each parameter set. Acceptable simulations (i.e., based on parameter sets with a nonzero likelihood) were found for a wide range of parameter values owing to parameter interdependence and insensitivity. The 95% uncertainty prediction interval of bed levels after the 33 days prediction period was largest (0.5–1 m) near the sandbar crests that characterize the Egmond depth profile, reducing to near-zero values in the sandbar troughs and the offshore area. The prediction interval built up during storms (when sediment transport rates are largest) and remained the same or even reduced slightly during less-energetic conditions. The prediction uncertainty ranges bracket the observations near the inner-bar crest, its seaward flank, and at the seaward flank of the outer bar, suggesting that elsewhere model structural errors (and, potentially, measurement errors) dominate over parameter errors. The interdependence and the non-Gaussian marginal posterior distribution functions of the free model parameters cast doubt on the ability of commonly applied multivariate normal distribution functions to estimate parameter uncertainty.

1516 区間連立一次方程式の領域分割型解法に関する研究(OS17 変動-バラツキを考慮した設計手法および設計例II)

The uncertainties of structural system parameters given by the intervals are studied within the finite element formulation to determine the sharp bounds of the displacement response. Direct approach in which the ordinary real arithmetic is simply replaced with the corresponding interval arithmetic gives extremely overestimated solution of intervals. This problem is called independent problem of interval arithmetic. In order to avoid the overestimation, an approach based on the bracketing of the solution set by subdivided interval boxes is proposed. Validation of this method is tested to the analysis of truss structural systems with uncertainties in nodal coordinates.

Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

This paper investigates the stability robustness of linear output feedback systems with both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties as well as delayed perturbations by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, two new sufficient conditions are proposed for ensuring that the linear output feedback systems with delayed perturbations as well as both time-varying structured and unstructured parameter uncertainties are asymptotically stable. The corresponding stable region, that is obtained by using the proposed sufficient conditions, in the parameter space is not necessarily symmetric with respect to the origin of the parameter space. Two numerical examples are given to illustrate the application of the presented sufficient conditions, and for the case of only considering both the delayed perturbations and time-varying structured parameter uncertainties, it can be shown that the results proposed in this paper are better than the existing one reported in the literature.

Application of the spatial wavelet transform and Bayesian approach to the crack detection of a partially obstructed beam

This paper presents a crack detection method for partially obstructed beams, which develops from the spatial wavelet transform and the Bayesian approach. The objective of this method is to estimate the location and extent of a crack on the obstruction area where vibration responses are not available. In the numerical simulations, it is assumed that except for those on the obstructed area, all displacement responses are available. Measurement noises and structural parameter uncertainties are also considered in the simulation model. The displacement responses of the beam are first transformed using the spatial wavelet method. Based on the wavelet-transformed displacement responses, the probability densities of different crack locations and extents are calculated using the Bayesian approach. Finally, the crack location and extent with the highest probability are identified. From the numerical results, it is demonstrated that the proposed method is capable of identifying a crack on an obstructed area of a beam-structure, even when measurement noises and structural parameter uncertainties exist.

Design of Reduced-Order Robust Controllers for Smart Structural Systems

This paper presents a method of designing reducedorder robust controllers for smart structural systems. We consider two kinds of uncertainties in the structural systems, norm bounded unstructured uncertainty and the variations of structural parameters. The smart structure with lead zirconate titanate (PZT) sensors and actuators is represented by a high order analytical model. Model error due to the uncertainties in structural parameters is modeled by parametric uncertainty in natural frequencies and damping ratios. By generalizing balanced truncation method for uncertain system, the high order model with uncertainties is reduced to a low order model with preserved parametric uncertainty. Based on linear matrix inequalities (LMIs) and Popov criterion, a robust controller is designed to suppress the lowfrequency vibrations caused by external disturbances and to guarantee the stability and performance of the closed-loop system under uncertainties. The order of the controller is further reduced by a frequency weighted model reduction method using LMI. The procedure was experimentally tested on a smart structural test article.

Convex models and interval analysis method to predict the effect of uncertain-but-bounded parameters on the buckling of composite structures

A new, non-probabilistic, set-theoretical models, that is interval analysis method is developed in this study to predict the variability or uncertainty in buckling loads of composite structures resulting from the unavoidable scatter in structural parameters. By mathematically analyzing and proving, the width of the upper and lower bounds on the critical buckling loads calculated by the interval analysis method is sharper than those that are obtained by convex models method, moreover, the interval analysis method has less computational cost than convex models method. Comparison between convex models and interval analysis method is performanced through numerical examples. For the specific cases considered, the results of numerical examples indicate that uncertainties in structural parameters have significant effect on the critical buckling loads of composite structures.

Stability robustness of linear output feedback systems with both time-varying structured and unstructured uncertainties as well as actuator saturation

This paper investigates the stability robustness of linear output feedback systems with actuator saturation as well as both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the linear output feedback systems with actuator saturation as well as both time-varying structured and unstructured parameter uncertainties are robustly stable. A numerical example is given to illustrate the application of the presented sufficient condition.

D-stability robustness for linear discrete uncertain singular systems with delayed perturbations

In this paper, the robust D-stability problem (i.e. the robust eigenvalue-clustering in a specified circular region problem) of linear discrete singular systems with both structured (elemental) parameter uncertainties and delayed perturbations is investigated. Under the assumptions that the linear discrete nominal singular system is regular and causal, and has all its finite eigenvalues lying inside a specified circular region, by using the maximum modulus principle and the spectral radius of matrices, a new sufficient condition is proposed to preserve the assumed properties when both structured parameter uncertainties and delayed perturbations are added into the linear discrete nominal singular system. When all the finite eigenvalues lie inside the unit circle of the z-plane, the proposed criterion will become the stability robustness criterion. The proposed criterion is mathematically proved and numerically shown, respectively, to be less conservative than the existing ones reported recently.

Regional Eigenvalue-Clustering Robustness Analysis for Linear Discrete Time-Delay Systems with Both Structured and Unstructured Parameter Uncertainties

In this paper, the problem of the regional eigenvalue-clustering robustness analysis for linear discrete time-delay systems with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties is investigated. Under the assumption that all the eigenvalues of a linear nominal discrete time-delay system lie within a specified region, a new sufficient condition is proposed to preserve the assumed property when both the structured (elemental) and the unstructured (norm-bounded) parameter uncertainties are added into the linear nominal discrete time-delay system. No restriction is imposed on the shapes of the specified region. When all the eigenvalues are just required to locate inside the unit circle, the proposed criterion will become the robust stability criterion. For the case that the linear discrete time-delay system only subjects to structured (elemental) parameter uncertainties, by two illustrative examples, the presented sufficient condition is shown to be less conservative than the existing one reported recently in the literature.

Quadratic stabilisation with H∞-norm bound of non-linear discrete-time uncertain systems with bounded control

The paper addresses the problem of quadratic stabilisability with H ∞-norm bound of uncertain discrete-time control-affine systems by norm-bounded controls. Both structured parameter uncertainties and unstructured exogenous disturbances are taken into account. The given definition of quadratic stabilisability is a generalisation of that used for linear systems so far. A necessary condition of the stabilisability is formulated. A state feedback control satisfying an a priori constraint is proposed for the solution of the formulated H ∞ problem. The proposed method may be applicable even in such cases when the linearisation technique cannot be used.