Reliability analysis of subsea pipelines under spatially varying ground motions by using subset simulation

A computational framework is presented to calculate the reliability of subsea pipelines subjected to a random earthquake. This framework takes full account of the physical features of pipelines and the earthquake, and also retains high computing precision and efficiency. The pipeline and the seabed are modelled as a Timoshenko beam and a Winkler foundation, respectively, while the unilateral contact effect between them is considered. The random earthquake is described by its power spectrum density function and its spatial variation is considered. After suitable discretizations in the spatial domain by the finite element method and the time domain by the Newmark integration method, the dynamic unilateral contact problem is derived as a linear complementarity problem (LCP). Subset Simulation (SS), which is an advanced Monte Carlo simulation approach, is used to estimate the reliability of pipelines. By means of numerical examples, the accuracy and robustness of SS are demonstrated by comparing with the direct Monte Carlo simulation (DMCS). Then a sensitivity analysis of the reliability and a failure analysis are performed to identify the influential system parameters. Finally, failure probabilities of subsea pipelines are assessed for three typical cases, namely, with and without the unilateral contact effect, with different grades of spatial variations and with different free spans. The influences of these effects or parameters on the reliability are discussed qualitatively

A Matrix Approach for Constructing Quadratic APN Functions

We find a one to one correspondence between quadratic APN functions without linear or constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On $\mathbb{F}_{2^7}$, we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which is 20 times more than the known ones. Before this paper, there are only 23 classes of CCZ-inequivalent APN functions on $\mathbb{F}_{2^{8}}$ have been found. With our method, we have found more than 2000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still increasing quickly

Constructing differential 4-uniform permutations from know ones

It is observed that exchanging two values of a function over ${\mathbb F}_{2^n}$, its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential $4$-uniform over ${\mathbb F}_{2^6}$ whose number of the pairs of input and output differences with differential $4$-uniform is $54$, less than $63$, which provides a solution for an open problem proposed by Berger et al. \cite{ber}. Moreover, for the inverse function over $\mathbb{F}_{2^n}$ ($n$ even), various possible differential uniformities are completely determined after its two values are exchanged. As a consequence, we get some highly nonlinear permutations with differential uniformity $4$ which are CCZ-inequivalent to the inverse function on $\mathbb{F}_{2^n}$

An uncertain computational model for random vibration analysis of subsea pipelines subjected to spatially varying ground motions

Based on a nonparametric modelling approach, this paper presents a random vibration analysis of a subsea pipeline subjected to spatially varying ground motions. The earthquake-induced ground motions are modelled as nonstationary random processes and their spatial variations are considered. The modelling uncertainties of the subsea pipeline are taken into account using a random matrix theory, while the unilateral contact relationship between the pipeline and seabed is also considered. Thus, an uncertain computational model for the subsea pipeline subjected to a random earthquake is established, and the corresponding solutions are calculated using Monte Carlo simulation (MCS). In order to highlight the contribution of the unilateral contact effect to random responses of pipelines, comparative studies are performed between the unilateral and permanent contact models. In numerical examples, the possible convergence problems in the present computational model are firstly studied to determine the optimal numbers of reduced modes and MCS samples. Then influences of the randomness in the earthquake and modelling uncertainties in the pipeline are investigated qualitatively through three representative cases. The different propagations of randomness and modelling uncertainties in the unilateral and permanent models are also examined and discussed. It is concluded that the randomness of the earthquake and modelling uncertainties of the pipeline have significant influences on the statistical characteristics of earthquake responses of the pipeline

Learning Transferable Adversarial Examples via Ghost Networks

Recent development of adversarial attacks has proven that ensemble-based methods outperform traditional, non-ensemble ones in black-box attack. However, as it is computationally prohibitive to acquire a family of diverse models, these methods achieve inferior performance constrained by the limited number of models to be ensembled. In this paper, we propose Ghost Networks to improve the transferability of adversarial examples. The critical principle of ghost networks is to apply feature-level perturbations to an existing model to potentially create a huge set of diverse models. After that, models are subsequently fused by longitudinal ensemble. Extensive experimental results suggest that the number of networks is essential for improving the transferability of adversarial examples, but it is less necessary to independently train different networks and ensemble them in an intensive aggregation way. Instead, our work can be used as a computationally cheap and easily applied plug-in to improve adversarial approaches both in single-model and multi-model attack, compatible with residual and non-residual networks. By reproducing the NeurIPS 2017 adversarial competition, our method outperforms the No.1 attack submission by a large margin, demonstrating its effectiveness and efficiency. Code is available at https://github.com/LiYingwei/ghost-network.Comment: To appear in AAAI-2

Random vibration analysis of axially compressed cylindrical shells under turbulent boundary layer in a symplectic system

A random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer (TBL) is presented in the symplectic duality system. By expressing the cross power spectral density (PSD) of the TBL as a Fourier series in the axial and circumferential directions, the problem of structures excited by a random distributed pressure due to the TBL is reduced to solving the harmonic response function, which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude. The governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system, and then a symplectic eigenproblem is formed by using the method of separation of variables. Expanding the excitation vector and unknown state vector in symplectic space, decoupled governing equations are derived, and then the analytical solution can be obtained. In contrast to the modal decomposition method (MDM), the present method is formulated in the symplectic duality system and does not need modal truncation, and hence the computations are of high precision and efficiency. In numerical examples, harmonic response functions for the axially compressed cylindrical shell are studied, and a comparison is made with the MDM to verify the present method. Then, the random responses of the shell to the TBL are obtained by the present method, and the convergence problems induced by Fourier series expansion are discussed. Finally, influences of the axial compression on random responses are investigated