This paper presents a perturbative analysis of bifurcation pressure of 2D corroded rings characterized by locally thinned regions under external pressure by asymptotically analyzing the Timoshenko differential equation and parametric analysis. First, for the case of one corrosion region, we formulate regular perturbative solution separately for anti-symmetric bifurcation and symmetric bifurcation cases. Concise formulation is presented by introducing a corrosion severity parameter and perturbative solution is presented. Second, we present a detailed analysis for the case where corrosion region has small angular extent by converting it into a singular perturbative problem and conduct various asymptotic analyses to illustrate the interesting interlacing behaviors. The derived explicit formula explains some numerical observation by Fatt in literature. Third, we conduct parametric analysis for the case of two interacting corrosion regions by classifying it into two cases: symmetric corrosion case and non-symmetric corrosion case. Finally, we present asymptotical analysis to investigate the extremely corroded case and show by Prufer transformation that anti-symmetric bifurcation pressure decreases when the distance of two corrosion regions is increasing. This paper serves to enhance the understanding of the collapse pressure of subsea pipes with local thickness reduction.
Digital audio tampering detection can be used to verify the authenticity of digital audio. However, most current methods use standard electronic network frequency (ENF) databases for visual comparison analysis of ENF continuity of digital audio or perform feature extraction for classification by machine learning methods. ENF databases are usually tricky to obtain, visual methods have weak feature representation, and machine learning methods have more information loss in features, resulting in low detection accuracy. This paper proposes a fusion method of shallow and deep features to fully use ENF information by exploiting the complementary nature of features at different levels to more accurately describe the changes in inconsistency produced by tampering operations to raw digital audio. Firstly, the audio signal is band-pass filtered to obtain the ENF component. Then, the discrete Fourier transform (DFT) and Hilbert transform are performed to obtain the phase and instantaneous frequency of the ENF component. Secondly, the mean value of the sequence variation is used as the shallow feature; the feature matrix obtained by framing and reshaping of the ENF sequence is used as the input of the convolutional neural network; the characteristics of the fitted coefficients are obtained by curve fitting. Then, the local details of ENF are obtained from the feature matrix by the convolutional neural network, and the global information of ENF is obtained by fitting coefficient features through deep neural network (DNN). The depth features of ENF are composed of ENF global information and local information together. The shallow and deep features are fused using an attention mechanism to give greater weights to features useful for classification and suppress invalid features. Finally, the tampered audio is detected by downscaling and fitting with a DNN containing two fully connected layers, and classification is performed using a Softmax layer. The method achieves 97.03% accuracy on three classic databases: Carioca 1, Carioca 2, and New Spanish. In addition, we have achieved an accuracy of 88.31% on the newly constructed database GAUDI-DI. Experimental results show that the proposed method is superior to the state-of-the-art method.
This paper proposes an audio tampering detection method based on the ENF phase and BI-LSTM network from the perspective of temporal feature representation learning. First, the ENF phase is obtained by discrete Fourier transform of ENF component in audio. Second, the ENF phase is divided into frames to obtain ENF phase sequence characterization, and each frame is represented as the change information of the ENF phase in a period. Then, the BI-LSTM neural network is used to train and output the state of each time step, and the difference information between real audio and tampered audio is obtained. Finally, these differences were fitted and dimensionally reduced by the fully connected network and classified by the Softmax classifier. Experimental results show that the performance of this method is better than the state-of-the-art approaches.
P91-type steel is widely used for the high-temperature pipe work components in advanced power plants. The creep behavior of the P91-type steel has been studied by many researchers during the past years. Since it is well known that the creep behavior of P91-type steel cannot be satisfactorily described by a simple, Arrhenius-type, power-law constitutive model. While Norton-Bailey creep is a deviatoric temperature-dependent creep model, furbished with a time-hardening creep model, which is the most common model for modeling primary and secondary creep together, and Kachanov-Rabotnov creep damage theory described with Norton creep model can be used to model tertiary creep. Both of them based on Norton creep constitutive equation. In this paper, based on the Norton-Bailey creep law and Kachanov-Rabotnov creep damage theory, a new combined constitutive model has been developed, in which the creep and damage function are both considered as nonlinear variables. The damage parameters in the model have clear physical meaning and can be determined from the benchmark experiment. The results indicated that this combined damage model was applicable to describe the full damage evolution for P91-type steel.
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