Nonlinear Frame Research Articles

Linguistic response surface methodology approach to measure the quality of nonlinear frame‐pixel and bit place‐based video steganography

AbstractSteganography refers to the practice of hiding sensitive information inside seemingly unrelated data sets. Steganography in the video is one of the best methods available for hiding data without compromising the film's appearance. For improved security and compatibility, the traditional system uses different video steganography techniques with linear or precise positions. Traditional linear video steganography practices face vulnerability, a lack of security, limited embedding options, and inadequate compatibility. Here nonlinear frame(s) and pixel positions based information hiding techniques have been developed to overwhelm the following. Both the nonlinear frame positions and nonlinear pixel positions are selected for the video‐based steganography. In the beginning, the nonlinear frame positions are selected through the key and the key may be with any prescribed range and alphanumeric characters. A single or more frames may be selected through the key and that entirely depends upon the corresponding run‐through. Then the nonlinear pixel and bit positions are also selected through a similar key. The proposed method is also compared with some former techniques and gives a magnificent result. Furthermore, a security analysis of the suggested algorithm has also been conducted using the differential attack method. To validate the suggested method and ensure that it is accurate, the author of this article made use of a very specific and innovative methodology known as the linguistic response surface methodology (LRSM). This model is framed based on achieving a few steganography assessment measures like PSNR, SSIM, and MSE metric values after incorporating hidden text in various nonlinear frames' nonlinear pixel locations of the video. The analysis of the variance using LRSM for PSNR, SSIM, and MSE response reveals very substantial results with confirmation.

An efficient model for 3D analysis of steel frames exposed to fire

The paper presents a nonlinear concentrated plasticity frame element for advanced analysis of steel frames exposed to elevated temperatures. The element extends the formulation based on the generalized plasticity material model that was successfully applied to the analysis of steel and composite structures. It considers the material's nonlinear behavior, temperature-induced loading, strength and stiffness degradation typical for structures under fire conditions. The nonlinear geometry is taken into account with the corotational formulation. Because of the generalized plasticity relations adoption, the element can describe the gradual yielding of cross sections. At the same time, the implemented return mapping algorithm ensures the element's high computational efficiency. The governing element equations, selection of parameters and computer implementation are discussed in the paper, followed by element validation through the number of experimental data examples and other numerical models. The comparative analysis demonstrated the element's versatility and capability to accurately predict the structural response of steel frame structures exposed to fire.

Convergence of non-linear diagonal frame filtering for regularizing inverse problems

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization techniques have been proposed. In particular, the use of filtered diagonal frame decompositions (DFDs) has proven to be effective and computationally efficient. However, existing convergence analysis applies only to linear filters and a few non-linear filters such as soft thresholding. In this paper, we analyze filtered DFDs with general non-linear filters. In particular, our results generalize singular value decomposition-based spectral filtering from linear to non-linear filters as a special case. As a first approach, we establish a connection between non-linear diagonal frame filtering and variational regularization, allowing us to use results from variational regularization to derive the convergence of non-linear spectral filtering. In the second approach, as our main theoretical results, we relax the assumptions involved in the variational case while still deriving convergence. Furthermore, we discuss connections between non-linear filtering and plug-and-play regularization and explore potential benefits of this relationship.

Nonlinear dynamic collapse analysis of space semi-rigid frames using finite particle method

Based on the finite particle method, this work presents a general numerical method to perform the nonlinear dynamic collapse analysis of space semi-rigid structures. A space connection element composed of two particles and six zero-length springs is proposed to simulate the space semi-rigid connection. Geometrical nonlinearity is addressed through fictitious motion, while material and connection behavior nonlinearities are captured by updating the element stiffness matrix and the connection stiffness matrix, respectively. Member and connection fracture models are convenient for simulating fracture behaviors during collapse processes. To verify the effectiveness of the proposed method, the numerical results are compared with those from previous studies, and energy conversion analyses are adopted. The analysis results indicate that only member fractures occur at beam ends in the rigid and linear semi-rigid frames, while only connection fractures occur at beam ends in the nonlinear semi-rigid frame.

The damping problem in non-linear viscoelastic frames under varying temperature

A theoretical consideration of the damping problem in frame engineering structures made of functionally graded materials with non-linear viscoelastic behaviour is carried-out. The frames studied are under external mechanical load and varying temperature. In particular, damping in a two-legged frame with supports on different levels is analyzed. The frame is subjected to a cyclic side load with simultaneous variation of the temperature. The material of the frame is functionally graded in the thickness direction. Thus, the material properties change smoothly along the thickness. Equilibrium equations are used for determining the curvature and the neutral axis coordinates in the members of the frame structure. The damping energy density is integrated in the volume of the frame members in order to find-out the damping energy in the whole frame structure. A parametric investigation is performed by using the solution of the damping energy in order to clarify the influence of various factors (the frame geometry, loading, etc.) on the damping phenomenon at different temperatures.

NVH numerical analysis of the mounting layout of hydrostatic transmissions in continuously variable transmissions

The present work proposes a numerical approach to model the dynamic behavior of the mounting layout of hydrostatic transmissions in continuously variable transmissions for off-road vehicles. The methodology takes advantage of a finite element model constituted by a rigid body, representing the hydrostatic transmission, connected to the overall transmission frame through a combination of torsional couplings, rolling-element bearings and brackets, considered as flexible components. Bearings, in particular, are substituted with nonlinear springs, while brackets and frames are 3D meshed according to the actual geometry of the system. The model allows to estimate the frequency dependent forces applied on the frame in reference to the loads generated within the hydrostatic transmission. The method is applied on a case study, showing that the torsional joints play a relevant role on the overall NVH behavior of the system and their kinematic characteristics should be carefully defined to tune the loads transmitted on the transmission frame.

A conditional extreme value distribution method for dynamic reliability analysis of stochastic structures

An efficient post-processing simulation method is proposed to estimate small failure probabilities of stochastic dynamic structures involving the inherent randomness of structural physical-geometrical parameters and external excitations. To extract a small failure probability, the proposed method introduces an intermediate event to represent the realizations of extreme structural response in the tail of distribution. With the aid of this intermediate event, structural failure probability is reformulated as a product of the event’s occurrence probability and the conditional exceedance probability of extreme response when the event occurs. The latter corresponds to a distribution of extreme response under the condition of the intermediate event, referred to as the conditional extreme value distribution (CEVD). Accordingly, the proposed method is termed the CEVD method. To reconstruct the CEVD, a truncated shifted generalized lognormal distribution model is employed. Bayesian estimation method is utilized to determine the two shape parameters of this model based on the samples of both original extreme value distribution and CEVD, where the CEVD samples are generated by Markov chain Monte Carlo sampling. The efficiency and accuracy of the proposed method are demonstrated through two numerical examples considering seismic reliability analyses of a 10-story nonlinear frame and a soil-foundation-structure interaction system.

Guided Deep Learning Manifold Linearization of Porous Media Flow Equations

Summary Integrated reservoir studies for performance prediction and decision-making processes are computationally expensive. In this paper, we develop a novel linearization approach to reduce the computational burden of intensive reservoir simulation execution. We achieve this by introducing two novel components: (1) augmention of the state-space to yield a bilinear system and (2) an autoencoder based on a deep neural network to linearize physics reservoir equations in a reduced manifold using a Koopman operator. Recognizing that reservoir simulators execute expensive Newton-Raphson iterations after each timestep to solve the nonlinearities of the physical model, we propose “lifting” the physics to a more amenable manifold where the model behaves close to a linear system, similar to the Koopman theory, thus avoiding the iteration step. We use autoencoder deep neural networks with specific loss functions and structure to transform the nonlinear equation and frame it as a bilinear system with constant matrices over time. In such a way, it forces the states (pressures and saturations) to evolve in time by simple matrix multiplications in the lifted manifold. We also adopt a “guided” training approach, which is performed in three steps: (1) We initially train the autoencoder, (2) then we use a “conventional” model order reduction (MOR) as an initializer for the final (3) full training, when we use reservoir knowledge to improve and to lead the results to physically meaningful output. Many simulation studies exhibit extremely nonlinear and multiscale behavior, which can be difficult to model and control. Koopman operators can be shown to represent any dynamical system through linear dynamics. We applied this new framework to a 2D two-phase (oil and water) reservoir subject to a waterflooding plan with three wells (one injector and two producers) with speedups around 100 times faster and accuracy in the order of 1% to 3% on the pressure and saturation predictions. It is worthwhile noting that this method is a nonintrusive data-driven method because it does not need access to the reservoir simulation internal structure; thus, it is easily applied to commercial reservoir simulators and is also extendable to other studies. In addition, an extra benefit of this framework is to enable the plethora of well-developed tools for MOR of linear systems. To the authors’ knowledge, this is the first work that uses the Koopman operator for linearizing the system with controls. As with any MOR method, this can be directly applied to a well-control optimization problem and well-placement studies with low computational cost in the prediction step and good accuracy.

Optical quantum hydrostatic electromagnetic microplates according to non-linear heat frame

Optical quantum hydrostatic electromagnetic microplates according to non-linear heat frame

Simplified frame models to simulate the in-plane load–displacement response of multi-story, perforated, partially grouted masonry walls

Equivalent frame models can be considered a relatively simple alternative in modeling masonry shear walls. Therefore, this study employed linear and non-linear frame models to simulate the in-plane load–displacement response of multi-story, perforated, partially grouted masonry walls. Different configurations of linear frame models were assessed for replicating the initial lateral stiffness of the walls: additional involvement of seismic performance factors (SPFs) and ultimate top drift limits enabled assessment of prediction of an idealized load–displacement response. Also, a new non-linear frame model approach was further evaluated to simulate the actual load–displacement response of the walls. Results indicated that including rigid offsets on the horizontal and vertical elements of the portal frame model resulted in a lateral stiffness and internal loads closest to that of experimental walls. It was possible to reproduce the idealized lateral response of the walls using the initial lateral stiffness of the linear models associated with adequate SPFs and ultimate top drifts. The idealized curves better matched the actual response when the lateral stiffness of the linear models was closer to that of the reference walls. An imposed ultimate drift higher than the actual amplified the estimation of the lateral load capacity and vice-versa, using all the approaches assessed. Values of 0.4% and 0.2% for the ultimate top drifts proved to be reasonable options for the cases in which the walls were submitted to a pre-compression of 0.04 fm′ and 0.2 fm′, respectively. Furthermore, the proposed non-linear braced frame model could predict the envelope curves of the experimental walls up to the peak load but did not present the expected strength degradation in the post-peak stage. Model BF could represent the distribution of loads between the elements only in the linear phase. It is necessary to make further adjustments to this model to account for the interaction between axial load and moment in the strength capacity of the flexural plastic hinges without compromising numerical convergence.

Physics-enhanced machine learning-based optimization of tuned mass damper parameters for seismically-excited buildings

Optimal design of tuned mass damper (TMD) parameters should be implemented before device installation to achieve the desired vibration reduction effects for tall and quite slender buildings. Although various optimization algorithms have been developed for searching TMD parameters, there has been very limited exploration of machine learning-based optimization approach in this domain. In this paper, two machine learning-based algorithms are proposed to optimize the natural frequency and damping ratio of a TMD device for seismically excited building. The first algorithm investigates the single-objective optimization of a TMD parameters on a linear building structure. It is based on physics-enhanced generative and adversarial network (GAN) architecture. A generative network randomly generates the primary TMD parameters within the specified parameter ranges, while an adversarial network guides the evolution of parameters to acquire updated parameters, a physical evaluation network assesses the performance of the updated and primary parameters, subsequently providing training data for both the generated network and adversarial network. Furthermore, a second physics-enhanced machine learning algorithm is proposed for the multi-objective optimization of a TMD parameters on a nonlinear building structure under various seismic excitations. The physical evaluation network is extended to consider multiple objective functions, in which the multiple objective functions are integrated through a kind of decomposition scheme, i.e., weighted sum approach. Then, a better set of parameters can be determined and a Pareto optimal solution is obtained. To verify the effectiveness of the two proposed algorithms, single-objective optimization of a TMD parameters for a linear shear-type structure under seismic excitation and a multiple-objectives optimization of a TMD parameters for a seismically excited nonlinear moment-resisting frame (MRF) are conducted and the optimizations are validated by comparing with those by the conventional particle swarm optimization (PSO) approach.

Earthquake data augmentation using wavelet transform for training deep learning based surrogate models of nonlinear structures

Machine learning methods have gained traction in the civil engineering community for analysis of civil infrastructures. A major field of application is in development of surrogate models for non-linear dynamic analysis for civil infrastructures. These data-driven models generally consist of a large number of parameters which need to be estimated from available data. However, due to limited availability of data in the field of earthquake engineering, often, it is difficult to develop stable models that can predict structural response by taking into account both material and earthquake uncertainty. To this end, the authors propose a discrete wavelet transform (DWT) enabled surrogate modeling framework for prediction of nonlinear structural response while accounting for material and earthquake uncertainty. DWT is used for earthquake data augmentation and feature extraction, which, along with constitutive material parameters, are used to train a deep neural network (DNN). It is shown that DWT can efficiently augment existing small earthquake datasets while the DNN can capture the non-linear structural response. The framework is validated by applying it to successfully predict structural response of 3DOF nonlinear spring–mass–damper system and non-linear three-story steel moment-resisting frame for unseen earthquakes with a median error less than 12%.

Reliability Evaluation of a Nonlinear Frame Structure under Explosive Ground Motions Generated by Dimension-Reduction Method

In the present study, a stochastic model of explosive ground motions applying the dimension-reduction method is proposed, and the reliability evaluation of a nonlinear frame structure under such excitations is realized by means of the probability density evolution method and an equivalent extreme-value-based reliability evaluation strategy. Firstly, the evolutionary power spectrum density function of the explosive ground motions is modeled by respectively identifying the normalized total energy distribution function and the frequency total energy distribution function on the basis of the measured motion records. In addition, an exponential model is constructed to forecast the seismic characteristics of the explosive ground motions based on the given distance to the explosive source and the charge quantity. Then, the representative samples of the explosive ground motions are simulated using the dimension-reduction method. The simulation results show that the generated acceleration samples have significant seismic characteristics of the explosive ground motions, and the accuracy is verified by comparing the second-order statistics with the sample set and the corresponding targets. Due to the fact that the probabilities of the representative samples simulated by the dimension-reduction method can compose a comprehensive probability set, it contributes to the refined dynamic response analysis and reliability evaluation of complex structures combining with the probability density evolution method. The accurate dynamic response analysis and reliability evaluation of a nonlinear frame structure illustrates the effectiveness of the proposed model and the dimension-reduction method for simulating the explosive ground motions. The numerical results demonstrate that the explosive ground motions have a substantial effect on the nonlinear behavior and the security of engineering structures.

Dynamic reliability analysis of structures under nonstationary stochastic excitations using tail-modified extreme value distribution

In practical engineering, it is usually necessary to compute the small first-passage probability of dynamic systems exposed to nonstationary stochastic excitations. However, it is still a challenging problem to efficiently estimate the super-small failure probability using an approximate extreme value distribution (EVD) based on a small number of simulated samples. In this study, a novel EVD model is proposed to describe the probability distribution of the structural extreme response induced by nonstationary stochastic excitations. This EVD model consists of two parts: the main body is modeled by a truncated-shifted generalized lognormal distribution, and a monotonic exponential model is proposed to fit the tail region. Besides that, a criterion for determining the breakpoint between the main body and tail region is proposed, which ensures the non-negativity and normativity of the proposed EVD model and allows the EVD to be reconstructed accurately and efficiently, particularly in its tail region. In this regard, the corresponding first passage probabilities under different thresholds can be straightly evaluated. The precision and completeness of the proposed EVD model are investigated using two numerical examples that consider linear and nonlinear frame structures subjected to nonstationary ground motion accelerations. The results show that the proposed model is in excellent agreement with the results of Monte Carlo simulation, even when the failure probability is very small.

Antiferromagnetic viscosity model for electromotive microscale with second type nonlinear heat frame

In this paper, we construct second type frame affiliated with the nonlinear heat system. This work is an important study to present a spacelike Landau–Lifshitz second type [Formula: see text] viscosity model. Then, we introduce antiferromagnetic spacelike Landau–Lifshitz second type [Formula: see text] viscosity model electromotive nonlinear heat microscales. Also, we obtain optical magnetic spacelike second type [Formula: see text] microscales in Minkowski space. Finally, we design antiferromagnetic viscosity model for optical Landau–Lifshitz second type [Formula: see text] optimistic density.

Material‐tangent‐stiffness‐proportional viscous damping for nonlinear geometric inelastic frame analysis

AbstractThis work presents a stiffness‐proportional viscous damping model based on the material component of the total tangent stiffness matrix. It is developed for nonlinear geometric inelastic frame analysis and implemented with distributed plasticity formulations. The use of a corotational approach allows isolating the nonlinear effects arising from material and geometric sources, hence allowing to preclude the contribution of the latter to simulate non‐modelled sources of energy dissipation. Following the presentation of the theoretical framework and a discussion on the physical meaningfulness of the proposed approach, several illustrative case studies are presented. The first is based on the damped free vibration response of a slender cantilever with elastic response, whereas the second addresses the seismic behavior of an inelastic reinforced concrete cantilever column. Comparisons with the total‐tangent‐stiffness‐proportional approach showcase the advantages of the current proposal.

A Response Spectrum Method for Base-Isolated Structures with Equivalent Base Excitations

Base isolation is an effective seismic design strategy that has received considerable attention in recent decades. This research is dedicated to developing a response spectrum method (RSM) for analysis of base-isolated structures under seismic excitation. A novel analytical model consisting of a linear superstructure under equivalent base excitations is proposed in the present study. To determine the response spectra corresponding to the base excitations, termed as the base response spectra, a sufficient number of samples of base excitations comprising base responses need to be obtained through time-history analysis of the nonlinear base-isolated structure in conjunction with the Monte Carlo simulation (MCS). To improve the efficiency for each sample analysis, the recently proposed explicit time-domain method (ETDM) is utilized for fast analysis of the base acceleration and velocity responses with a dimension-reduced iteration scheme. Once the base response spectra are obtained, the mean peak values (MPVs) of structural responses of the linear superstructure can be conveniently evaluated through the complete quadratic combination (CQC) rule. A 4-story nonlinear base-isolated frame structure was analyzed to validate the effectiveness of the proposed analytical model and the feasibility of the present approach for seismic response analysis of nonlinear base-isolated structures.

Investigation of Corroded Bond-Slip Effects for Corroded RC Columns

Steel bar corrosion is one of the most common causes of structural performance degradation for reinforced concrete (RC) columns subjected to extreme loads such as earthquakes. Due to the different characteristics of corrosion effects, a comprehensive and efficient finite element (FE) modeling approach is necessary for the performance assessment of corroded RC columns. To this end, this study provides an effective FE modeling approach using a recently developed geometrically nonlinear fiber-based frame element that considers bond-slip, allowing for explicit representation of corrosion-affected bonding. This aspect necessitates the use of an explicit material model for corroded bond-slip and its associated corroded properties. Since the existing models of corroded bonding properties in the literature were developed based on the highly scattered and limited experimental data, this study develops a new probabilistic model for corroded bonding properties based on more experimental data compiled from the literature and quantifies the prevailing uncertainties. To facilitate its use for modeling corroded RC structures, a cyclic corroded bond-slip model in an open-source FE software framework is implemented. In this paper, the FE modeling approach is first used to model two corroded RC columns tested in the literature, with comparison to the conventional modeling approach (i.e., assuming perfect bonding). The influence of corroded bonding on the static and dynamic behaviors of RC columns is further explored deterministically. Furthermore, the impact of uncertainty in corroded bonding properties on the static and dynamic behavior simulations of RC columns is examined. This work is concluded that (1) the FE modeling approach provided for corroded RC columns proves to be effective in capturing corrosion effects; and (2) corroded bonding plays an important role in simulating the behavior of corroded RC columns, and thus cannot be neglected. This is particularly true considering its associated uncertainty and its impact on the performance assessment of RC columns under severe corrosion conditions.

Efficient modeling of steel bar slippage effect in reinforced concrete structures using a newly implemented nonlinear element

In structural modeling of reinforced concrete (RC) structures, a common assumption lies in perfect bonding between steel reinforcing bars and the surrounding concrete. This paper aims to assess this assumption and investigate the need and importance of considering imperfect bonding (i.e., steel bar slippage or bond-slip) for predicting the nonlinear behavior of RC columns. To this end, an efficient finite element model capable of capturing bond-slip is required to evaluate the effect of imperfect bonding. Thus, this study first developed a geometrically nonlinear fiber-based frame element considering steel bar slippage and implemented this element in OpenSees with hybrid corotational transformation. Subsequently, using the newly developed element, the effect of imperfect bonding on the behavior of RC columns was investigated. In this regard, the role of bond-slip was studied under different scenarios, including hooked or unhooked ends of longitudinal steel bars in the anchorage area, low or high load levels, and short- or long-duration earthquake ground motions. The results reaffirm the need for prudent consideration of imperfect bonding for advanced finite element modeling of RC structures in several scenarios.

JNMR: Joint Non-linear Motion Regression for Video Frame Interpolation.

Video frame interpolation (VFI) aims to generate predictive frames by motion-warping from bidirectional references. Most examples of VFI utilize spatiotemporal semantic information to realize motion estimation and interpolation. However, due to variable acceleration, irregular movement trajectories, and camera movement in real-world cases, they can not be sufficient to deal with non-linear middle frame estimation. In this paper, we present a reformulation of the VFI as a joint non-linear motion regression (JNMR) strategy to model the complicated inter-frame motions. Specifically, the motion trajectory between the target frame and multiple reference frames is regressed by a temporal concatenation of multi-stage quadratic models. Then, a comprehensive joint distribution is constructed to connect all temporal motions. Moreover, to reserve more contextual details for joint regression, the feature learning network is devised to explore clarified feature expressions with dense skip-connection. Later, a coarse-to-fine synthesis enhancement module is utilized to learn visual dynamics at different resolutions with multi-scale textures. The experimental VFI results show the effectiveness and significant improvement of joint motion regression over the state-of-the-art methods.