In this paper, we propose a novel inductor-free chaotic circuit by using two locally active memristors (LAMs), a capacitor, and a DC bias. These two LAMs are the current-controlled and voltage-controlled type, respectively, exhibiting S-type and N-type DC V-I (voltage-current) characteristics. Only when the two LAMs are both operated in the negative differential resistance (NDR) regions, may the periodical and chaotic dynamic behaviors appear in the proposed circuit. This may be because the local activity contributes to the generation of complexity. With different initial conditions, the coexisting attractors are observed in the circuit, which is analyzed through the equilibrium points and phase portraits. Finally, physical circuit realizations of the inductor-free chaotic circuit are presented, including the S-type and N-type memristor emulators. Both simulation and experimental results demonstrate the feasibility of the proposed chaotic circuit.

To improve the computational efficiency of the time-dependent failure probability (TDFP) to system with dynamic loads, materials degeneration and other time-varying factors, a two-phase adaptive Kriging model-based importance sampling (IS) method is proposed. The main contribution of this article is that a single Kriging model is established and adaptively refined to gradually approach the optimal IS probability density function (PDF) and estimate TDFP in two sequential phases. In the first phase, a generally approximate IS PDF is constructed by Kriging model based on its prediction characteristic and subsequently updated until convergence. Then, a simple rejection sampling technique is used to robustly generate IS samples for the estimation of TDFP. In the second phase, current Kriging model is subsequently refined for accurately identifying the classification of the IS samples generated in the last phase. Finally, the TDFP can be estimated using the products obtained in the above two phases. As the IS PDF established by Kriging model is used for directly approximating the optimal one, the proposed method has the capacity to deal with the complicated problem containing multiple failure regions. Additionally, since IS procedure can dramatically improve the sampling efficiency, the proposed method is an effective technique to the time-consuming TDFP analysis problems.

For reliability analysis of complex structures with time-consuming implicit performance functions, the computational cost required by direct sampling methods is usually unaffordable for engineering applications. However, the adaptive metamodel embedded in sampling methods can significantly improve reliability analysis efficiency. Therefore, a new metamodel-based directional importance sampling method (Meta-DIS-AK) is proposed for reliability analysis in this article. The main novelty of Meta-DIS-AK is constructing the quasi-optimal DIS density (DIS-D) by the Kriging model and giving a simple rejection sampling algorithm for accurately extracting DIS-D samples. By the constructed quasi-optimal DIS-D, the failure probability is transformed into a two-step estimation of augmented failure probability and a correction item. The updating of the first step is designed to ensure that the constructed DIS-D is well approaching to theoretical optimal DIS-D and obtain augmented failure probability estimation, and the second step updating can guarantee the accuracy of correction item estimation. Meta-DIS-AK not only overcomes the difficulties of constructing DIS-D and extracting importance direction vector samples in the existing DIS but also inherits the advantages of DIS in dealing with high-dimensional and small failure probability problems. Compared with the existing efficient sampling methods combined with AK, the results of the examples fully verify the accuracy and efficiency of the proposed Meta-DIS-AK.

This article proposes a new compact model and presents a circuit-theoretical analysis for a third-order memristive neuromorphic element fabricated by Kumar et al. The proposed model mainly consists of a box-shaped resistor model and a simplified piecewise-linear memristor model. Since the dynamic behavior of the box-shaped hysteresis in the quasistatic current–voltage curve is mostly unexplored, we first extract the box-shaped resistor model and construct its oscillators. The coordinate system shifting method and dynamic route analysis method are used to reveal the operating mechanism of boxshaped resistor-based oscillators. Both the theoretical analysis and simulation verification indicate that the box-shaped hysteresis characteristic facilitates the generation of neuromorphic action potentials. The proposed new compact model not only captures quasi-static characteristics but also includes dynamic behaviors, such as action potential, periodic spiking, and periodic bursting. The influences of the model parameters are further investigated to reveal the mechanism of the neuromorphic behaviors in the box-shaped hysteresis and positive differential resistance regions. Simulation results manifest the feasibility of the proposed model and the correctness of the presented analysis methods, which pave the way to the optimized design of memristive devices and the research of neuromorphic dynamics.

A fuzzy first-order and second moment (FFOSM) method is proposed to efficiently estimate time-independent and time-dependent failure credibility in the presence of fuzzy uncertainty. For the time-independent linear performance function with independently, regularly, and identically distributed fuzzy inputs, the analytical relationship is first derived between the failure credibility and fuzzy safety index, and the relation form is established between fuzzy safety index and fuzzy first two moments of the performance function. Second, in the standard space of fuzzy inputs, the minimum infinite norm distance from the coordinate origin to the linear limit state surface is analytically derived, and the point with the smallest infinite norm distance located on the limit state surface is defined as the fuzzy design point. Based on this definition, the geometric and physical meanings are explained for the fuzzy safety index and fuzzy design point, and the FFOSM method for time-independent failure credibility analysis is established for both linear and nonlinear performance function. Third, for time-dependent performance functions, the equivalence is proved between time-dependent fuzzy safety index and the minimum value of transient fuzzy safety indices, on which the iteration steps of the FFOSM method is designed for time-dependent fuzzy safety index and failure credibility estimation. Since the proposed FFOSM method is an approximately analytical approach, it has higher efficiency than the fuzzy simulation method and the cut level optimization method. Finally, the effectiveness and applicability of the proposed method are demonstrated by different examples.

The global reliability sensitivity index (GRSI) can measure the effect of model input variable on the failure probability of the structure and provide guidance for the reliability-based design optimization. In this paper, to efficiently estimate the GRSI, an equivalent form of the GRSI is derived by elaborative combination of Bayes' theorem and the law of total expectation in the successive intervals without overlapping, and it not only makes the total computational cost independent of the dimensionality of model inputs, but also avoids approximating the probability density function approximation used in the existing Bayes' theorem based global reliability sensitivity analysis. For further improving the efficiency of estimating the GRSI by the equivalent form, two algorithms are presented by nesting the adaptive Kriging (AK) into Monte Carlo simulation (MCS) and importance sampling (IS), respectively, which are abbreviated as AK-MCS and AK-IS. Results of one numerical example and four engineering applications show that the number of model evaluations by the AK-IS is less than 2% of that by direct IS, and the model evaluation number by AK-MCS is less than 4% of that by direct MCS under the convergent condition. The results illustrate that the proposed methods for estimating the GRSI are practical for engineering applications.