Explicit solutions to vertical and horizontal displacements are derived for large deformation of a cantilever beam under point load at the free end by an improved homotopy analysis method (IHAM). Quadratic and cubic nonlinear differential equations are adopted to construct more proficient nonlinear equations for vertical and horizontal displacements respectively combined with their currently available nonlinear displacement equations. Higher-order nonlinear iterative homotopy equations are established to solve the vertical and horizontal displacements by combining simultaneous equations of the constructed nonlinear equations and the auxiliary linear equations. The convergence range of vertical displacement is extended by the homotopy-Páde approximation. The explicit solutions to the vertical and horizontal displacements are in favorable agreements with the respective exact solutions. The convergence ranges for a relative error of 1% by the improved homotopy analysis method for vertical and horizontal displacements increases by 60% and 7%, respectively. These explicit formulas are helpful in practical engineering design for very slender structures, such as high-rise buildings and long bridges.
Deep learning (DL) models have been shown to be vulnerable to recent backdoor attacks. A backdoored model behaves normally for inputs containing no attacker-secretlychosen trigger and maliciously for inputs with the trigger. To date, backdoor attacks and countermeasures mainly focus on classification tasks, in particular, image classification. Most of these backdoor attacks have been implemented in the digital world with digital triggers. Besides the classification tasks, object detection systems are also designed to identify the location of an object, which is a fundamental basis for various computer vision tasks. However, there is no investigation and understanding of the backdoor vulnerability of the object detector, even in the digital world with digital triggers.For the first time, this work demonstrates that existing object detectors are inherently susceptible to physical backdoor attacks, thus revealing severe real-world security threats, e.g., when malicious cloaking is abused. We use a natural T-shirt bought from a market as a trigger to enable the cloaking effect-the person bounding-box disappears in front of the object detector. We show that such a backdoor can be implanted from two widely exploitable attack scenarios into the object detector, which is outsourced or fine-tuned through a pretrained model. We have extensively evaluated three popular object detection algorithms: anchor-based Yolo-V3, Yolo-V4, and anchor-free CenterNet. Building upon 19 videos (about 11,800 frames in total) shot in real-world scenes, we confirm that the backdoor attack is robust against various factors: movement, distance, angle, nonrigid deformation, and lighting. Specifically, the attack success rate (ASR) in most videos is 100% or close to it, while the clean data accuracy of the backdoored model is the same as its clean counterpart. The latter implies that it is infeasible to detect the backdoor behavior merely through a validation set. The averaged ASR still remains sufficiently high to be 78% in the transfer learning attack scenarios evaluated on CenterNet. The comprehensive demo video (up to 5 minutes) is available at https://youtu.be/Q3HOF4OobbY.
An improved homotopy analysis method (IHAM) is proposed to solve the nonlinear differential equation, especially for the case when nonlinearity is strong in this paper. As an application, the method was used to derive explicit solutions to the rotation angle of a cantilever beam under point load at the free end. Compared with the traditional homotopy method, the derivation includes two steps. A new nonlinear differential equation is firstly constructed based on the current nonlinear differential equation of the rotation angle and the auxiliary quadratic nonlinear differential equation. In the second step, a high-order non-linear iterative homotopy differential equation is established based on the new non-linear differential equation and the auxiliary linear differential equation. The analytical solution to the rotation angle is then derived by solving this high-order homotopy equation. In addition, the convergence range can be extended significantly by the homotopy–Páde approximation. Compared with the traditional homotopy analysis method, the current improved method not only speeds up the convergence of the solution, but also enlarges the convergence range. For the large deflection problem of beams, the new solution for the rotation angle is more approachable to the engineering designers than the implicit exact solution by the Euler–Bernoulli law. It should have significant practical applications in the design of long bridges or high-rise buildings to minimize the potential error due to the extreme length of the beam-like structures.
Abs~act :The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance ( SIHB ) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.
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