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The purpose of this paper is to support total productive maintenance implementers by providing a roadmap for autonomous maintenance (AM) preparation phase.

The authors use the axiomatic design (AD) methodology with lean philosophy as a paradigm.

This is an exploratory research to find the most important factors in AM preparation phase. A decoupled AD design ensures an effective usage of training within industry (TWI) and the introduction of standardized work (SW). TWI provides value in importance it assigns to leaders, with its “train the trainers” approach and in preparing a training program. Besides being an effective training method, TWI job instruction (TWI JI) provides needed information infrastructure to front load operators SW and equipment trainings.

Although AD, TWI and lean artifacts are generally field proven, the research is limited due to the lack of an industrial application.

In many real-life projects, companies do not know where to start and how to proceed, which leads to costly iterations. The proposed roadmap minimizes iterations and increases the chance of project success.

The authors apply AD for the first time to AM preparation phase despite it is used in the analysis of lean manufacturing. AD permits to structure holistically the most relevant lean manufacturing solutions to obtain a risk free roadmap. TWI has emerged as a training infrastructure; TWI JI-based operator SW training and the adaptation of JI structure to equipment training are original additions.

Nowadays, the event detection is so important in gathering news from social media. Indeed, it is widely employed by journalists to generate early alerts of reported stories. In order to incorporate available data on social media into a news story, journalists must manually process, compile and verify the news content within a very short time span. Despite its utility and importance, this process is time-consuming and labor-intensive for media organizations. Because of the afore-mentioned reason and as social media provides an essential source of data used as a support for professional journalists, the purpose of this paper is to propose the citizen clustering technique which allows the community of journalists and media professionals to document news during crises.

The authors develop, in this study, an approach for natural hazard events news detection and danger citizen’ groups clustering based on three major steps. In the first stage, the authors present a pipeline of several natural language processing tasks: event trigger detection, applied to recuperate potential event triggers; named entity recognition, used for the detection and recognition of event participants related to the extracted event triggers; and, ultimately, a dependency analysis between all the extracted data. Analyzing the ambiguity and the vagueness of similarity of news plays a key role in event detection. This issue was ignored in traditional event detection techniques. To this end, in the second step of our approach, the authors apply fuzzy sets techniques on these extracted events to enhance the clustering quality and remove the vagueness of the extracted information. Then, the defined degree of citizens’ danger is injected as input to the introduced citizens clustering method in order to detect citizens’ communities with close disaster degrees.

Empirical results indicate that homogeneous and compact citizen’ clusters can be detected using the suggested event detection method. It can also be observed that event news can be analyzed efficiently using the fuzzy theory. In addition, the proposed visualization process plays a crucial role in data journalism, as it is used to analyze event news, as well as in the final presentation of detected danger citizens’ clusters.

The introduced citizens clustering method is profitable for journalists and editors to better judge the veracity of social media content, navigate the overwhelming, identify eyewitnesses and contextualize the event. The empirical analysis results illustrate the efficiency of the developed method for both real and artificial networks.

To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough examination of the historical milieu preceding the Adomian decomposition method.

Develops a theoretical background of the Adomian decomposition method under the auspices of the Cauchy‐Kovalevskaya theorem of existence and uniqueness for solution of differential equations. Beginning from the concepts of a parametrized Taylor expansion series as previously introduced in the Murray‐Miller theorem based on analytic parameters, and the Banach‐space analog of the Taylor expansion series about a function instead of a constant as briefly discussed by Cherruault et al., the Adomian decompositions series and the series of Adomian polynomials are found to be a uniformly convergent series of analytic functions for the solution u and the nonlinear composite function f(u). To derive the unifying formula for the family of classes of Adomian polynomials, the author develops the novel notion of a sequence of parametrized partial sums as defined by truncation operators, acting upon infinite series, which induce these parametrized sums for simple discard rules and appropriate decomposition parameters. Thus, the defining algorithm of the Adomian polynomials is the difference of these consecutive parametrized partial sums.

The four classes of Adomian polynomials are shown to belong to a common family of decomposition series, which admit solution by recursion, and are derived from one unifying formula. The series of Adomian polynomials and hence the solution as computed as an Adomian decomposition series are shown to be uniformly convergent. Furthermore, the limiting value of the mth Adomian polynomial approaches zero as the index m approaches infinity for the prerequisites of the Cauchy‐Kovalevskaya theorem. The novel truncation operators as governed by discard rules are analogous to an ideal low‐pass filter, where the decomposition parameters represent the cut‐off frequency for rearranging a uniformly convergent series so as to induce the parametrized partial sums.

This paper unifies the notion of the family of Adomian polynomials for solving nonlinear differential equations. Further it presents the new notion of parametrized partial sums as a tool for rearranging a uniformly convergent series. It offers a deeper understanding of the elegant and powerful Adomian decomposition method for solving nonlinear ordinary and partial differential equations, which are of paramount importance in modeling natural phenomena and man‐made device performance parameters.

L. Gǎvruţa (2012) introduced a special kind of frames, named K-frames, where K is an operator, in Hilbert spaces, which is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative K-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative K-atomic decompositions in Banach spaces. Also some results on the existence of approximative K-atomic decompositions are obtained. We discuss several methods to construct approximative K-atomic decomposition for Banach Spaces. Further, approximative _d-frame and approximative _d-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative _d-Bessel sequence and approximative _d-frame give rise to a bounded operator with respect to which there is an approximative K-atomic decomposition. Example and counter example are provided to support our concept. Finally, a possible application is given.

This paper aims to explore a new way to extract the fault feature of a rolling bearing signal on the basis of a combinatorial method.

By combining local mean decomposition (LMD) with Teager energy operator, a new feature-extraction method of a rolling bearing fault signal was proposed, called the LMD–Teager transform method. The principles and steps of method are presented, and the physical meaning of the time–frequency power spectrum and marginal spectrum is discussed. On the basis of comparison with the fast Fourier transform method, a simulated non-stationary signal was processed to verify the effect of the new method. Meanwhile, an analysis was conducted by using the recorded vibration signals which include inner race, out race and bearing ball fault signal.

The results show that the proposed method is more suitable for the non-stationary fault signal because the LMD–Teager transform method breaks through the difficulty of the Fourier transform method that can process only the stationary signal. The new method can extract more useful information and can provide better analysis accuracy and resolution compared with the traditional Fourier method.

Combining the advantage of the local mean decomposition and the Teager energy operator, the LMD–Teager method suits the nature of the fault signal. A marginal spectrum obtained from the LMD–Teager method minimizes the estimation bias brought about by the non-stationarity of the fault signal. So, the LMD–Teager transform has better analysis accuracy and resolution than the traditional Fourier method, which provides a good alternative for fault diagnosis of the rolling bearing.

The purpose of this paper is to present a geometric approach to the problem of dimensional reduction. To derive (3 + 1) D formulations of 4D field problems in the relativistic theory of electromagnetism, as well as 2D formulations of 3D field problems with continuous symmetries.

The framework of differential‐form calculus on manifolds is used. The formalism can thus be applied in arbitrary dimension, and with Minkowskian or Euclidean metrics alike.

The splitting of operators leads to dimensionally reduced versions of Maxwell's equations and constitutive laws. In the metric‐incompatible case, the decomposition of the Hodge operator yields additional terms that can be treated like a magnetization and polarization of empty space. With this concept, the authors are able to solve Schiff's paradox without use of coordinates.

The present formalism can be used to generate concise formulations of complex field problems. The differential‐form formulation can be readily translated into the language of discrete fields and operators, and is thus amenable to numerical field calculation.

The approach is an evolution of recent work, striving for a generalization of different approaches, and deliberately avoiding a mix of paradigms.

The purpose of this paper is to propose the Laplace Adomian Decomposition Method (LADM) for studying the nonlinear temperature and thermal stress analysis of annular fins with time-dependent boundary condition.

The nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root is studied by the LADM. The radiation effect is considered. The convective heat transfer coefficient is considered as a temperature function.

The proposed solution method is helpful in overcoming the computational bottleneck commonly encountered in industry and in academia. The results show that the circumferential stress at the root of the fin will be important in the fatigue analysis.

This study presents an effective solution method to analyze the nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root by using LADM.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

This paper proposes a unified original general framework, designed to theoretically develop and to extremely easily implement elastoplastic constitutive laws defined in the so called two-invariants space, both in small and finite strain regime.

A general return mapping algorithm is proposed, and particularly a standard procedure is developed to compute the two algorithmic tangent operators, required to solve the Newton–Raphson scheme at the local and global level and thus cast the elastoplastic algorithm within a FEM code.

This work demonstrates that the proposed procedure is fully general and can be applied whatever is the elastic law, the yield surface, the plastic potential function and the hardening law. Several numerical examples are reported, not only to demonstrate the accuracy and robustness of the algorithm, but also explain how to use this general algorithm also in other applications.

The proposed algorithm and its numerical implementation into a FEM code is new and original. The usefulness and the value of the algorithm is twofold: (1) it can be implemented in a small and finite strain simulation FEM code, in order to handle different types of constitutive laws in the same modular way, thus fully leveraging on modern object-oriented coding approach; (2) it can be used as a framework to develop (and then to implement) new constitutive models, since the researcher can simply define the relevant functions (and its main derivatives) and automatically get the numerical algorithm.

This study aims to present a highly efficient operator-splitting finite element method for the nonlinear two-dimensional/three-dimensional (2D/3D) Allen–Cahn (AC) equation which describes the anti-phase domain coarsening in a binary alloy. This method is presented to overcome the higher storage requirements, computational complexity and the nonlinear term in numerical computation for the 2D/3D AC equation.

In each time interval, the authors first split the original equation into a heat equation and a nonlinear equation. Then, they split the high-dimensional heat equation into a series of one-dimensional (1D) heat equations. By solving each 1D subproblem, the authors obtain a numerical solution for heat equation and take it as an initial for the nonlinear equation, which is solved analytically.

The authors show that the proposed method is unconditionally stable. Finally, various numerical experiments are presented to confirm the high accuracy and efficiency of this method.

A new operator-splitting method is presented for solving the 2D/3D parabolic equation. The 2D/3D parabolic equation is split into a sequence of 1D parabolic equations. In comparison with standard finite element method, the present method can save much central processing unit time. Stability analysis and error estimates are derived and numerical results are presented to support the theoretical analysis.