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The purpose of this paper is to provide an overview of the major reliability issues of microelectromechanical systems (MEMS) under mechanical and environmental loading conditions. Furthermore, a comprehensive study on the nonlinear behavior of silicon MEMS devices is presented and different aspects of this phenomenon are discussed.

Regarding the reliability investigations, the most important failure aspects affecting the proper operation of the MEMS components with focus on those caused by environmental and mechanical loads are reviewed. These studies include failures due to fatigue loads, mechanical vibration, mechanical shock, humidity, temperature and particulate contamination. In addition, the influence of squeeze film air damping on the dynamic response of MEMS devices is briefly discussed. A further subject of this paper is discussion of studies on the nonlinearity of silicon MEMS. For this purpose, after a description of the basic principles of nonlinearity, the consequences of nonlinear phenomena such as frequency shift, hysteresis and harmonic generation and their effects on the device performance are reviewed. Special attention is paid to the mode coupling effect between the resonant modes as a result of energy transfer because of the nonlinearity of silicon. For a better understanding of these effects, the nonlinear behavior of silicon is demonstrated by using the example of Si cantilever beams.

It is shown that environmental and mechanical loads can influence on proper operation of the MEMS components and lead to early fracture. In addition, it is demonstrated that nonlinearity modifies dynamic response and leads to new phenomena such as frequency shift and mode coupling. Finally, some ideas are given as possible future areas of research works.

This is a review paper and aimed to review the latest manuscripts published in the field of reliability and nonlinearity of the MEMS structures.

The purpose of this paper is to first, test for nonlinearity in Local Indian Exchange Traded Funds (ETFs) listed at NSE, India – NIFTYBEES, JUNIORBEES, BANKBEES, PSUBANKBEES, and INFRABEES – using a battery of nonlinearity tests; second, to ascertain, using both metric and topological approaches, the adequacy of appropriate AR-GARCH models when it comes to capturing all of the nonlinearity in Indian ETFs; and third, to test for chaos in Indian ETFs.

To start with, a battery of tests such as and limited to McLeod Li test, Engle's LM test, Tsay F-test, Hinich Bispectrum Test and Hinich Bicorrelation test were employed to test for nonlinearity in Indian ETFs. Subsequently, the nature of nonlinearity in all the ETFs was systematically investigated by subjecting the ETF data sets to a metric (BDS test) and a topological test (close returns tests) at different stages of the model-building process. Finally, Lyapunov Exponent test was employed to test for chaos in Indian ETFs.

Test outcomes pertaining to a battery of nonlinearity tests indicate prevalence of nonlinearity amidst all ETFs except for INFRABEES. BDS test outcomes at the different stages of the model-building process indicated high sensitivity of the test outcomes to choice of embedding dimension, threshold value and residual transformations. Close returns test outcomes indicated that, but for BANKBEES, all of the nonlinearity in Indian ETFs could be captured by appropriate GARCH models. Finally, chaos was found to be absent in any of the ETFs considered for this study.

The collective take-way from this study is threefold in nature. First, in light of the many limitations of the BDS test, topological approaches such as close-returns test offer a better avenue to test for adequacy of AR-GARCH models in explaining the nature of nonlinearity in asset price movements. Second, adequacy of AR-GARCH models in capturing all of the nonlinearity in NIFTYBEES, JUNIORBEES, PSUBANKBEES, and INFRABEES, as indicated by close-returns test findings, is a reflection of multiplicative nature of nonlinearity in these five ETFs. Third, persistence of nonlinearity in AR-GARCH filtered standardized residuals of BANKBEES, coupled with the absence of chaos in any of the ETFs considered for this study, brings to light the possibility of existence of additive nonlinearity in conjunction with multiplicative nonlinearity.

This is possibly the first study that systematically investigates the nature of nonlinearity in Indian ETFs and ascertains the adequacy of AR-GARCH models when it comes to capturing all of the nonlinearity in Indian ETFs using a topological approach.

This study seeks to explore the nature of a data‐generating process for four dollar exchange rates.

Using a discrete parametric modeling approach, an efficient test statistic was computed for nonlinearity in terms of variance of the residuals of the linear and nonlinear autoregressive models by Akaike Information Criterion, and a surrogate data analysis was conducted.

It shows that a nonlinear autoregressive model outperforms a linear stochastic model in certain subsamples of baht, pound, ringgit, and yen dollar exchange rates. However, when the test statistics using different model orders and the data for the entire samples are estimated, it appears that the nonlinear model has a better performance than the linear model in fitting Thai and Malaysian currencies. The nonlinear model performs better than the linear model in the case of the UK pound in two thirds of the models, but the linear models completely outperform the nonlinear models for the yen data.

More financial and economic time series will be explored to employ the methodology used in the study, and tests for possible presence of nonlinear deterministic dynamics (chaos) in the exchange rates series will be conducted based on the present findings in further study.

These findings suggest that the assumption of linear stochastic process as the underlying dynamics for all currencies examined in this study may not be justifiable.

To the best of the authors' knowledge, this study is the first attempt to use the test statistic based on the information‐theoretical method in testing nonlinearity in financial and economic time series.

The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy.

The proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel.

Implementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method.

The proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.

Doppler-Bearing Tracking (DBT) is commonly used in target tracking applications for the underwater environment using the Hull-Mounted Sensor (HMS). It is an important and challenging problem in an underwater environment.

The system nonlinearity in an underwater environment increases due to several reasons such as the type of measurements taken, the speeds of target and observer, environmental conditions, number of sensors considered for measurements and so on. Degrees of nonlinearity (DoNL) for these problems are analyzed using a proposed measure of nonlinearity (MoNL) for state estimation.

In this research, the authors analyzed MoNL for state estimation and computed the conditional MoNL (normalized) using different filtering algorithms where measurements are obtained from a single sensor array (i.e. HMS). MoNL is implemented to find out the system nonlinearity for different filtering algorithms and identified how much nonlinear the system is, that is, to measure nonlinearity of a problem.

Algorithms are evaluated for various scenarios with different angles on the target bow (ATB) in Monte-Carlo simulation. Computation of root mean squared (RMS) errors in position and velocity is carried out to assess the state estimation accuracy using MATLAB.

The purpose of this paper is to develop a new criterion for the exponential stability and

_∞ performance of state-space digital filters under the influence of any combination of quantization/overflow nonlinearities.

The proposed criterion uses the

_∞ approach that is suitable for the design of discrete system in the presence of external disturbance. Analysis and synthesis in an

_∞ setting is advantageous as it proposes effective disturbance attenuation, less sensitivity to uncertainties and many practical applications.

The criterion not only guarantees exponential stability but also reduces the effect of external interference. A numerical example demonstrating the effectiveness of the proposed method is given.

The main result of the paper is reported for the first time and it is useful to ensure the stability of digital filters in the presence of external disturbance and any combination of quantization/overflow nonlinearities.