Covering relations and Lyapunov condition for topological conjugacy

In this paper, we study stability of non-autonomous discrete dynamical systems. For a two-sided non-autonomous systems with covering relations determined by a transition matrix A, we show that any small C⁰ perturbed system has a sequence of compact invariant sets restricted to which the system is topologically semi-conjugate to σ_A, the two-sided subshift of finite type induced by A. Together with Lyapunov condition of good rate, the semi-conjugacy will become conjugacy. Moreover, if the Lyapunov condition is strict and has perfect rate, then any small C¹ perturbed systems is topological conjugate to σ_A. We also study topological chaos of one-sided systems and systems with limit functions. Lack of hyperbolicity and the time dependence of the rate prevent us from applying classical hyperbolic results or earlier works for autonomous systems: cone condition and Lyapunov function. Two examples are provided to demonstrate the existence of a non-trivial, non-hyperbolic invariant and essential of controlling rate.     

Evolution systems of measures for stochastic flows

A new concept of an evolution system of measures for stochastic flows is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for asymptotically compact stochastic flows is obtained. For a white noise stochastic flow, there exists a one to one correspondence between evolution systems of measures for a stochastic flow and evolution systems of measures for the associated Markov transition semigroup. As an application, an alternative approach for evolution systems of measures of 2D stochastic Navier–Stokes equations with a time-periodic forcing term is presented.     

A computational comparison of cyclical and non-cyclical control for stochastic production-inventory systems

Cyclical production planning is popular in real-life because of its organisational benefits. We study the application and performance of cyclical production planning in a complex stochastic production-inventory system with job shop routings. We propose a decision-support system that allows computing cost efficient cyclical production plans. Insights on the applicability and performance of cyclical production planning are obtained from an extensive simulation study in which the cyclical approach is compared with a state-of-the-art non-cyclical approach.     

Centre manifolds for infinite dimensional random dynamical systems

Stochastic centre manifolds theory are crucial in modelling the dynamical behaviour of complex systems under stochastic influences. The existence of stochastic centre manifolds for infinite dimensional random dynamical systems is shown under the assumption of exponential trichotomy. The theory provides a support for the discretisations of nonlinear stochastic partial differential equations with space–time white noise.     

Transfer operators for contractive Markov systems and stochastic stability of the invariant measure

We consider contractive Markov systems, a generalization due to Werner of iterated function systems that contract on average. We study a transfer operator for such systems and determine an appropriate function space on which this operator acts quasi-compactly and has good spectral perturbation properties. We discuss how these results apply to the stochastic stability of the invariant measure.     

Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation

A hybrid Subset Simulation approach is proposed for reliability estimation for general dynamical systems subject to stochastic excitation. This new stochastic simulation approach combines the advantages of the two previously proposed Subset Simulation methods, Subset Simulation with Markov Chain Monte Carlo (MCMC) algorithm and Subset Simulation with splitting. The new method employs the MCMC algorithm before reaching an intermediate failure level and splitting after reaching the level to exploit the causality of dynamical systems. The statistical properties of the failure probability estimators are derived. Two examples are presented to demonstrate the effectiveness of the new approach and to compare with the previous two Subset Simulation methods. The results show that the new method is robust to the choice of proposal distribution for the MCMC algorithm and to the intermediate failure events selected for Subset Simulation.     

Fuzzy covariance control for a class of continuous perturbed nonlinear stochastic systems

Abstract

This paper addresses the analysis and design of a fuzzy controller for a class of continuous perturbed nonlinear stochastic systems. The nonlinear systems are modeled by the Takagi‐Sugeno (T‐S) fuzzy models. The conventional LMI‐based fuzzy control method is inconvenient for directly assigning the common positive definite covariance matrix. Hence, this paper tries to develop a useful methodology to allow designers to assign a common positive definite covariance matrix for the closed‐loop system. Applying the theory of covariance control, a fuzzy controller is developed to achieve the stable conditions for the assigned common positive definite covariance matrix. Finally, a numerical example is given to demonstrate the usefulness of the proposed approach.     

Discrete-event stochastic systems with correlated inputs: Modeling and performance evaluation

In the majority of the previous works on discrete-event stochastic systems, they have been assumed to have independent input processes. However, in many applications, these input processes can be highly correlated. Furthermore, the performance measures of the systems with correlated inputs can be significantly different from those with independent inputs. In this paper, we provide an overview on some commonly used methods for modeling correlated input processes, and we discuss the difficulties and possible future research topics in the study of discrete-event stochastic systems with correlated inputs.     

Direct control method for improving stability and reliability of nonlinear stochastic dynamical systems

Optimal control for improving the stability and reliability of nonlinear stochastic dynamical systems is of great significance for enhancing system performances. However, it has not been adequately investigated because the evaluation indicators for stability (e.g. maximal Lyapunov exponent) and for reliability (e.g. mean first-passage time) cannot be explicitly expressed as the functions of system states. Here, a unified procedure is established to derive optimal control strategies for improving system stability and reliability, in which a physical intuition-inspired separation technique is adopted to split feedback control forces into conservative components and dissipative components, the stochastic averaging is then utilized to express the evaluation indicators of performances of controlled system, the optimal control strategies are finally derived by minimizing the performance indexes constituted by the sigmoid function of maximal Lyapunov exponent (for stability-based control)/the reciprocal of mean first-passage time (for reliability-based control), and the mean value of quadratic form of control force. The unified procedure converts the original functional extreme problem of optimal control into an extremum value problem of multivariable function which can be solved by optimization algorithms. A numerical example is worked out to illustrate the efficacy of the optimal control strategies for enhancing system performance.     

Some aspects of chaotic and stochastic dynamics for structural systems

In this paper, the bifurcation behaviour of an externally excited four-dimensional nonlinear system is examined. Throughout this paper, a two-degree-of-freedom shallow arch structure under either a periodic or a stochastic excitation will be considered. For the case when the excitation is periodic, the local and global behaviour is examined in the presence of principalsubharmonic resonance and1:2 internal resonance. The method of averaging is used to obtain the first order approximation of the response of the system under resonant conditions. A standard Melnikov type perturbation method is used to show analytically that the system may exhibit chaotic dynamics in the sense of Smale horseshoe for the 1:2 internal resonance case in the absence of dissipation. In the case of stochastic excitation, the stability of the stationary solution is examined by determining themaximal Lyapunov exponent andmoment Lyapunov exponent in terms of system parameters. An asymptotic method is used to obtain explicit expressions for various exponents in the presence of weak dissipation and noise intensity. These quantities provide almost-sure stability boundaries in parameter space. When the system parameters lie outside these boundaries, it is essential to understand the nonlinear behaviour. The method of stochastic averaging is applied to obtain a set of approximate Itô equations which are then examined to describe the local bifurcation behaviour.     

Simulations and experiments of stochastic characteristics for collective short fatigue cracks in steels

ABSTRACT Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.     

Optimising installation (R,Q) policies in distribution networks with stochastic lead times: a comparative analysis of guaranteed- and stochastic service models

This paper studies two modelling approaches to the multi-echelon inventory optimisation problem in a distribution network with stochastic demands and lead times. It compares the performance of a novel guaranteed-service model (GSM), using an installation (R, Q) inventory control policy, with a stochastic service model (SSM) considering ordering, holding and flexibility costs. From both cycle service level and fill rate perspectives, our numerical analysis of the 1-warehouse 2-retailer network shows that cost difference between both models is driven by the internal service level at the warehouse. The GSM outperforms the SSM for over 80% of the simulated instances and realises an average total cost improvement of approximately 10%. This analysis goes against earlier results that showed a relatively low-cost difference between the two approaches, and demonstrates that it is worthwhile to evaluate competing models for multi-echelon inventory optimisation in real-world supply chains with batch ordering and variable lead times.     

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme.     

Multi-agent systems applications in manufacturing systems and supply chain management: a review paper

This paper offers a review of the development and use of multi-agent modelling techniques and simulations in the context of manufacturing systems and supply chain management (SCM). The objective of the paper is twofold. First, it presents a comprehensive literature review of current multi-agent systems (MAS) research applications in the field of manufacturing systems and SCM. Second, it aims to identify and evaluate some key issues involved in using MAS methods to model and simulate manufacturing systems. A variety of different MAS applications are reviewed in three different classified research areas: production design and development, production planning and control, and SCM. In presenting a detailed taxonomy of MAS applications, the paper describes MAS application domains from five different perspectives. The review suggests the MAS approach represents a feasible framework for designing and analysing real-time manufacturing operations, since the approach is capable of modelling different levels of agent behaviour and dynamical interactions. The paper also highlights a number of key issues which have to be taken into account in attempting to design MAS-based research paradigms for future applications in manufacturing systems.     

Physics-integrated deep learning for uncertainty quantification and reliability estimation of nonlinear dynamical systems

Assumptions and approximations made while analyzing any physical system induce modeling uncertainty, which, if left unchecked, can result in the erroneous analysis of the system under consideration. Additionally, the discrepancy in the exact knowledge of system parameters can further result in deviation from the ground truth. This paper explores Physics-integrated Variational Auto-Encoder (PVAE) to account for modeling and parametric uncertainties in partially known nonlinear dynamical systems. The PVAE under consideration has three main parts: encoder, latent space, and decoder. The complete PVAE architecture is employed during the training stage of the machine learning model, while only the decoder is used to make the final predictions. The encoder determines the correct parameter values for the known part of the model (in the form of a known ODE). The decoder is augmented with an ODE solver that solves the known part of the system and the estimated discrepancy together to reconstruct the measurements. To test the efficacy of the PVAE architecture, three case studies are carried out, each presenting unique challenges. The probability density functions obtained for the various systems’ responses demonstrate the efficacy of the PVAE architecture. Furthermore, reliability analysis has been carried out, and the results produced have been compared against those obtained from a multi-layered, densely connected forward neural network.     

Adaptive reduced order modeling for nonlinear dynamical systems through a new a posteriori error estimator: Application to uncertainty quantification

Multiquery problems such as uncertainty quantification (UQ), optimization of a dynamical system require solving a differential equation at multiple parameter values. Therefore, for large systems, the computational cost becomes prohibitive. This issue can be addressed by using a cheaper reduced order model (ROM) instead. However, the ROM entails error in the solution due to approximation in a lower dimensional subspace. Moreover, the ROM lacks robustness over a wide range of parameter values. To address these issues, first, an upper bound on the norm of the state transition matrix is derived. This bound, along with the residual in the governing equation, are then used to develop an error estimator for general nonlinear dynamical systems. Furthermore, this error estimator is used in conjunction with the modified greedy search algorithm proposed by Hossain and Ghosh (Int J Numer Methods Eng, 2018;116(12-13): 741-758) to adaptively construct a robust proper orthogonal decomposition-based ROM. This adaptive ROM is subsequently deployed for UQ by invoking it in a statistical simulation. Two numerical studies: (i) viscous Burgers' equation and (ii) beam on nonlinear Winkler foundation, showed an improved accuracy of the error estimator compared to the current literature. A significant computational speed-up in UQ is achieved.     

Optimal method for changing the number of kanbans in the e -Kanban system and its applications

The Toyota Motor Corporation has recently developed a new kanban system called ‘e-Kanban’, which is a parts ordering information system that operates within the communications network established between Toyota and its suppliers. One of the goals for developing the e-Kanban system was to introduce an efficient means for properly changing the number of kanbans once the required number has been calculated, as changing the number of kanbans in the kanban system directly affects the order quantity. Consequently, it is very important to monitor carefully and control changes in the number of kanbans. The paper investigates and proposes an effective method for changing the number of kanbans using the e-Kanban system. Applying this method to three problems, it is shown that the e-Kanban system can be implemented more efficiently and effectively than the original kanban system.     

用于微机电系统的类金刚石膜制备及表征

采用等离子体源离子注入和电子回旋共振-微波等离子体辅助化学气相沉积技术相结合的方法在Si衬底上制备出了性能良好的类金刚石膜.通过共聚焦Raman光谱验证了薄膜的类金刚石特性,用原子力显微镜、微摩擦计和扫描电镜等对薄膜的表面形貌、摩擦系数和耐磨损性能进行了表征和测量.结果表明,用离子注入法制备过渡层大大提高了DLC膜与衬底的结合强度,薄膜的表面比较光滑,粗糙度大约为0.198 nm,具有较低的摩擦系数(0.1～0.15),具有较好的耐磨损性能.     

Design of polymeric nanoparticles and its applications as drug delivery systems for acne treatment

Objective: The aim of this study was to evaluate a formulation made of poly(lactide-co-glycolide) (PLGA) nanoparticles containing azelaic acid for potential acne treatment.

Methods: Azelaic acid-loaded PLGA nanoparticles were prepared by spontaneous emulsification processes using poloxamer 188 as stabilizer. Several manufacturing parameters such as stirring rate, concentration of stabilizer and different recovery methods were investigated. Nanoparticles were evaluated in terms of size, zeta potential, encapsulation efficiency, release kinetics and permeation kinetics in vitro. Furthermore, in vitro toxicological studies were performed in Saccharomyces cerevisiae model.

Results: The results showed that by adjusting some formulation conditions it was possible to obtain nanoparticles with high loading and a controlled drug release. Freeze-dried recovery altered the nanoparticles structure by enhancing porous structures and mannitol was required to control the mean particle size. The centrifugation recovery was found to be the best approach to nanoparticles recovery. Similar toxicity profiles were observed for both drug-free and azelaic acid-loaded nanoparticles, with concentration-dependent decreases in cell viability.

Conclusion: These results indicate a potential formulation for controlled release delivery of azelaic acid to the follicular unit.