Penalty Technique Research Articles

Thermo-mechanical post-buckling analysis of variable angle tow composite plate assemblies

The increasing use of composite materials for lightweight structural applications and the extended tailoring capabilities offered by variable stiffness laminates requires rapid and robust analysis tools that adequately describe the mechanical behaviour of such structures. In this work, a Rayleigh–Ritz solution for generally restrained multilayered stiffened variable angle tow plates in the post-buckling regime is presented. The plate model is based on first-order shear deformation theory and accounts for geometrical nonlinearity through von Kármán’s assumptions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to approximate the unknown displacement field. Stiffened variable angle tow plates are modeled as an assembly of plate-like elements and penalty techniques are used to enforce the displacements continuity of the assembled multidomain structure and also to apply the kinematical boundary conditions. The developed postbuckling analysis is sufficiently versatile to model a wide range of configurations and load cases for multi-component, variable angle tow, composite structures, and provide the same accuracy level as finite element analysis. The proposed solution is validated by comparison with literature and finite elements analysis and original results are presented for the thermo-mechanical post-buckling solution of multilayered stiffened variable angle tow plates. The effectiveness of the developed analysis tool for both stiffened plates and a tapered stiffened wing box is shown, with a reduced number of unknowns and simplified data preparation compared to finite element analysis.

Co-AGSA: An efficient self-adaptive approach for constrained optimization of analog IC based on the shrinking circles technique

This paper aims to take a step forward to enhance the performance of the optimization kernel of electronic design automation (EDA) tools by coping with the existing challenges in the analog circuit sizing problems. For this purpose, a novel co-evolutionary-based optimization approach, called Co-AGSA, is proposed. In the Co-AGSA, a self-adaptive penalty technique based on the concept of the co-evolution model is incorporated into a powerful optimization algorithm, named advanced gravitational search algorithm (AGSA), to efficiently solve more realistic constrained optimization problems. The performance of the Co-AGSA approach is first evaluated by solving three constrained engineering design problems. Then, the optimization capability of the Co-AGSA-based IC sizing tool is validated using three different case studies, i.e., a two-stage op-amp, a folded-cascode op-amp and a two-stage telescopic cascode amplifier, to show the applicability of the proposed approach. The results demonstrate that the Co-AGSA gives better performance compared to other approaches in terms of efficiency, accuracy and robustness.

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F-bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.

Sparse Memoryless LQR Design for Uncertain Linear Time-Delay Systems

The sparse memoryless LQR design problem is formulated for uncertain linear time-delay systems. In such a problem, the goal is to minimize a quadratic cost supplemented by sparsity-promoting term (weighted-ℓ1 in our case) subject to stability of closed-loop system under norm-bounded uncertainty. It is shown that such an optimization problem can be reformulated as a rank-constrained optimization problem which consists of convex constraints except one rank constraint. Utilizing the bi-linear rank penalty technique, the sparse memoryless LQR is designed. Numerous numerical results depict that there exists a trade-off between time-delay and sparsification quality. In addition, the larger time-delay, the poorer performance-sparsity trade-off is observed.

Three-dimensional vibration analysis of sandwich and multilayered plates with general ply stacking sequences by a spectral-sampling surface method

This paper investigates the three-dimensional (3-D) vibration characteristics of sandwich and multilayered plates with general ply stacking sequences and arbitrary restraints based on a spectral-sampling surface method. The theoretical formulation is undertaken by the 3-D theory of elasticity such that it is able to study the dynamic behavior of sandwich and multilayered plates very well, even in the presence of soft layers. Under the current framework, a set of sampling surfaces along the thickness direction of each plate layer are primarily selected and the displacements of these surfaces are chosen as basic plate variables. Consequently, vibration solutions for sandwich and multilayered plates with different thicknesses, material properties and ply stacking sequences can be derived up to desired accuracy by selecting sufficient number of sampling surfaces. In addition, the penalty technique and Lagrange multiplier method are adopted to relax the enforcement of the boundary conditions. As a result, the proposed formulation can be applied efficiently to the 3-D vibration analysis of sandwich and multilayered plates with general restraints. The final solutions are determined by a modified variational principle, in which each of the basic plate variables is approximated by the spectral method. Results show that the present method is capable of calculating highly accurate numerical results for thick sandwich and multilayered plates with general ply stacking sequences and arbitrary boundary conditions.

A New Stable Full-Wave Maxwell Solver for All Frequencies

Magnetic vector potential (MVP) formulations are widely used in the electromagnetic (EM) field computation. For problems with both inductive and capacitive effects, existing full-wave MVP formulations are mostly nonuniquely solvable, and sophisticated preconditioners are indispensable when solving these resultant linear matrix equations. To find a stable formulation with a unique solution, it is important to incorporate the necessary physics equations and the gauge condition properly. Traditional Coulomb-gauged formulation using the penalty technique does not work for edge elements, since the divergence of the edge element basis function is zero within each element. In this paper, a novel MVP formulation with Coulomb gauge for full-wave Maxwell equations using edge elements is proposed in the frequency domain. Extensive numerical examples are computed to show that the proposed formulation is stable even for tiny frequencies, which is very useful in full-wave engineering EM field computation.

A Novel Formulation With Coulomb Gauge for 3-D Magnetostatic Problems Using Edge Elements

A novel magnetic vector potential (MVP) formulation with Coulomb gauge is proposed for solving 3-D magnetostatic problems. A dummy scalar variable is introduced in the whole computation domain to impose the Coulomb gauge. Unlike traditional Coulomb-gauged formulation using the penalty technique, which works only for nodal elements approximation of the MVP, the new formulation proposed in this paper allows the use of edge element approximation of the MVP. It can avoid possible large errors at material interfaces or re-entrant corners of the problem domain when using nodal discretizations for the MVP. This formulation is easy to implement, and the resultant matrix system is symmetric with a unique solution. Both linear and nonlinear numerical examples are presented to showcase the accuracy and usefulness of the proposed method for engineering computation.

Analysis of Flow Past Oscillatory Cylinders Using a Finite Element Fixed Mesh Formulation

In this work, we propose a fixed mesh finite element formulation to solve the fluid dynamic on an Eulerian mesh dealing with immersed bodies in motion. The study is focused on the computation of the fluid dynamic forces acting on immersed bodies which strongly depend on the evolution of the vortex shedding. The frequency of vortex detachment for flow past cylinder problems can be modified when the cylinder moves, promoting the modification of the wake of vortices. Synchronization phenomena appear when the frequencies of the resulting flow pattern coincide with the frequency of the imposed body motion. To study this problem, we propose to describe the immersed body surface by a collection of markers that moves according to the imposed body motion. The markers are updated using a Lagrangian scheme. In this framework, a distinct aspect of the present work is the imposition of the body velocity as an internal immersed boundary condition for the fluid dynamic analysis. To transfer the body velocity to the fluid along the fluid–solid interface, a restriction on the flow velocity is added into the weak form of the Navier–Stokes equations by means of a penalty technique. This work encompasses the study of flows past a crossflow, streamwise, and rotational oscillating cylinders. The results are satisfactorily compared with numerical data reported in the literature, showing a proper behavior for the analysis of long-term vibrating systems at low Reynolds numbers.

Elasticity solution for vibration of 2-D curved beams with variable curvatures using a spectral-sampling surface method

Summary An accurate spectral-sampling surface method for the vibration analysis of 2-D curved beams with variable curvatures and general boundary conditions is presented. The method combines the advantages of the sampling surface method and spectral method. The formulation is based on the 2-D elasticity theory, which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced. Specifically, a set of non-equally spaced sampling surfaces parallel to the beam's middle surface are primarily collocated along the thickness direction, and the displacements of these surfaces are chosen as fundamental beam unknowns. This fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces. Each of the fundamental beam unknowns is then invariantly expanded as Chebyshev polynomials of the first kind, and the problems are stated in variational form with the aid of the penalty technique and Lagrange multipliers, which provide complete flexibility to describe any arbitrary boundary conditions. Finally, the desired solutions are obtained by the variational operation. Copyright © 2016 John Wiley & Sons, Ltd.

Diagonal-norm upwind SBP operators

High-order accurate first derivative finite difference operators are derived that naturally introduce artificial dissipation. The boundary closures are based on the diagonal-norm summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability for a large class of initial boundary value problems. These novel first derivative SBP operators have a non-central difference stencil in the interior, and come in pairs (for each order of accuracy). The resulting SBP-SAT approximations lead to fully explicit ODE systems. The accuracy and stability properties are demonstrated for linear first- and second-order hyperbolic problems in 1D, and for the compressible Euler equations in 2D. The newly derived first derivative SBP operators lead to significantly more robust and accurate numerical approximations, compared with the exclusive usage of (previously derived central) non-dissipative first derivative SBP operators.

A continuous DC programming approach for resource allocation in OFDMA/TDD wireless networks

The next generation broadband wireless networks deploys OFDM/OFDMA as the enabling technologies for broadband data transmission with QoS capabilities. Many optimization problems have arisen in the conception of such a network. This article studies an optimization problem in resource allocation. By using mathematical modeling technique we formulate the considered problem as a pure integer linear program. This problem is reformulated as a DC (Difference of Convex functions) program via an exact penalty technique. We then propose a continuous approach for its resolution. Our approach is based on DC programming and DCA (DC Algorithm). It works in a continuous domain, but provides integer solutions. To check globality of computed solutions, a global method combining DCA with a well adapted Branch-and-Bound (B&B) algorithm is investigated. Preliminary numerical results are reported to show the efficiency of the proposed method with respect to the standard Branch-and-Bound algorithm.

A modal Udwadia-Kalaba formulation for vibro-impact modelling of continuous flexible systems with intermittent contacts

Most systems consist on dynamical substructures connected at a number of constraining points. Moreover, constraints often display intermittent contact phenomena, such as arising from clearance supports. A significant difficulty when computing time-domain responses is the manner to enforce such coupling constraints. Here, we explore the Udwadia-Kalaba (U-K) formulation, which has been very seldom used in this context. By extending the basic U-K analytical framework, we address continuous flexible subsystems modelled by their unconstrained modes and coupled through the highly nonlinear intermittent point-constraints. For continuous flexible systems, a modal U-K formulation is implemented such that the constraint is applied when contact is detected at the clearance location. A crucial aspect is that constraint violations must be prevented, not only at the acceleration level, but also at the velocity and displacement levels, in order to avoid computational drift. This is achieved through a constraint violation correction method. For single gap-constraints, a convenient formulation is obtained, in which the constraint matrix is pre-computed prior to the simulation time-loop and applied whenever an intermittent contact is detected, leading to an efficient computation of vibro-impact responses. For systems with several intermittent constraints, an essential difficulty within the context of the proposed formulation is that every possible combination of contact/non-contact conditions is expressed by a different constraint matrix. A pragmatic solution is to keep track of the current system contact configuration and rebuild the constraint matrix whenever a change in the constraint state is detected. We formulate and illustrate such computational strategy, as applied to random-excited multi-supported beams with a significant number of clearance supports. Results are compared with dynamical computations performed using a classic penalty technique for enforcing the nonlinear support constraints, emphasizing the viability of the proposed technique for performing predictive analysis of flexible structures with multiple clearance supports.

Image denoising via bidirectional low rank representation with cluster adaptive dictionary

In this study, the authors propose a new image representation model that fully exploits the similarity inherent in natural images. The idea is based on an observation of similar patches. For a clean image, when a cluster of similar patches are collected to form the similar patch matrix (SPM), there exists high correlation among columns/rows of the SPM. This implies that, when the column/row vectors are linearly expressed by a dictionary, their coefficients of columns/rows should have high correlation, which leads to the coefficient matrixes of column/row representation are low-ranked. This observation inspires them to propose a novel image denoising model named bidirectional low rank representation (BiLRR) with cluster adaptive dictionary. Specifically, they use low rank penalties simultaneously on the coefficient matrixes of column and row representations to recover the correlation structure of the SPM. Meanwhile, a cluster adaptive dictionary is learned to represent each SPM so as to well preserve the fine structure of image. By applying variable splitting and penalty technique, they present an efficient alternative minimisation algorithm to solve the proposed BiLRR model. Experimental results indicate the authors’ method achieves a competitive denoising performance in comparison with state-of-the-art algorithms in terms of subjective and objective qualities.

An adaptive penalty scheme to solve constrained structural optimization problems by a Craziness based Particle Swarm Optimization

The use of Evolutionary Algorithms (EAs) to solve optimization problems has been increasing. One of the most used techniques is Particle Swarm Optimization (PSO), which is considered robust, efficient and competitive in comparison with other bio-inspired algorithms. EAs were originally designed to solve unconstrained optimization problems. However, the most significant problems, particularly those from real world optimization, present constraints. It is not trivial to define a strategy to handle constraints and, in general, penalty functions containing parameters to be set by the user and it may affect the search considerably. This paper consists of a combination of the Craziness based Particle Swarm Optimization (CRPSO) with an adaptive penalty technique, called Adaptive Penalty Method (APM), to solve constrained optimization problems. A CRPSO is adopted here in order to avoid premature convergence using a new velocity expression and an operator called “craziness velocity”. APM and its variants were applied in other EAs, originally in a Genetic Algorithm, which demonstrated its robustness. APM deals with inequality and equality constraints, and it is free of parameters to be defined by the user. In order to assess the applicability and performance of the algorithm, several structural engineering optimization problems traditionally found in the literature are used in the computational experiments.

DCA based algorithms for feature selection in multi-class support vector machine

This paper addresses the problem of feature selection for Multi-class Support Vector Machines. Two models involving the $$\ell _{0}$$ (the zero norm) and the $$\ell _{2}$$ – $$\ell _{0}$$ regularizations are considered for which two continuous approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) are investigated. The first is DC approximation via several sparse inducing functions and the second is an exact reformulation approach using penalty techniques. Twelve versions of DCA based algorithms are developed on which empirical computational experiments are fully performed. Numerical results on real-world datasets show the efficiency and the superiority of our methods versus one of the best standard algorithms on both feature selection and classification.

A Practical Approach to Traffic Engineering using an Unsplittable Multicommodity Flow Problem with QoS Constraints

The paper presents a practical approach to calculating intra-domain paths within a domain of a content-aware network (CAN) that uses source routing. This approach was used in the prototype CAN constructed as a part of the Future Internet Engineering project outcome. The calculated paths must satisfy demands for capacity (capacity for a single connection and for aggregate connections using the given path are considered distinctly) and for a number of path-additive measures like delay, loss ratio. We state a suitable variant of QoS-aware unsplittable multicommodity ow problem and present the solving algorithm. The algorithm answers to the needs of its immediate application in the constructed system: a quick return within a short and fairly predictable time, simplicity and modiability, good behavior in the absence of a feasible solution (returning approximately-feasible solutions, showing how to modify demands to retain feasibility). On the other hand, a certain level of overdimensioning of the network is explored, unlike in a typical optimization algorithm. The algorithm is a mixture of: (i) shortest path techniques, (ii) simpli ed reference-level multicriteria techniques and parametric analysis applied to aggregate the QoS criteria (iii) penalty and mutation techniques to handle the common constraints. Numerical experiments assessing various aspects of the algorithm behavior are given.

Buckling and Postbuckling of Stiffened Composite Panels with Cracks and Delaminations by Ritz Approach

A Ritz approach for the analysis of buckling and postbuckling of stiffened composite panels with through-the-thickness cracks and/or delaminations is presented. The structure is modeled as the assembly of plate elements of which the behavior is described by the first-order shear deformation theory and von Kármán’s geometric nonlinearities. Penalty techniques ensure continuity along the edges of contiguous plate elements and the enforcement of the restraints on the external boundaries. They are also used to avoid interpenetration problems. General symmetric and unsymmetric stacking sequences are considered. A computer code has been developed and used to validate the proposed method, comparing the results with literature and finite-elements solutions. Results are also presented for postbuckling of multilayered stiffened plates with through-the-thickness cracks and delaminations. The analyses carried out show the efficiency and potential of the method, which provides accuracy comparable to those of other techniques in conjunction with a reduction in the number of degrees of freedom and simplification in data preparation.

An Interior Penalty Method with C0Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

The present paper proposes and analyzes an interior penalty technique using C0-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally correct.

Estimating and testing high-dimensional mediation effects in epigenetic studies

High-dimensional DNA methylation markers may mediate pathways linking environmental exposures with health outcomes. However, there is a lack of analytical methods to identify significant mediators for high-dimensional mediation analysis. Based on sure independent screening and minimax concave penalty techniques, we use a joint significance test for mediation effect. We demonstrate its practical performance using Monte Carlo simulation studies and apply this method to investigate the extent to which DNA methylation markers mediate the causal pathway from smoking to reduced lung function in the Normative Aging Study. We identify 2 CpGs with significant mediation effects. R package, source code, and simulation study are available at https://github.com/YinanZheng/HIMA CONTACT: lei.liu@northwestern.edu.

A sparse extreme learning machine framework by continuous optimization algorithms and its application in pattern recognition

Extreme learning machine (ELM) has demonstrated great potential in machine learning owing to its simplicity, rapidity and good generalization performance. In this investigation, based on least-squares estimate (LSE) and least absolute deviation (LAD), we propose four sparse ELM formulations with zero-norm regularization to automatically choose the optimal hidden nodes. Furthermore, we develop two continuous optimization methods to solve the proposed problems respectively. The first is DC (difference of convex functions) approximation approach that approximates the zero-norm by a DC function, and the resulting optimizations are posed as DC programs. The second is an exact penalty technique for zero-norm, and the resulting problems are reformulated as DC programs, and the corresponding DCAs converge finitely. Moreover, the proposed framework is applied directly to recognize the hardness of licorice seeds using near-infrared spectral data. Experiments in different spectral regions illustrate that the proposed approaches can reduce the number of hidden nodes (or output features), while either improve or show no significant difference in generalization compared with the traditional ELM methods and support vector machine (SVM). Experiments on several benchmark data sets demonstrate that the proposed framework is competitive with the traditional approaches in generalization, but selects fewer output features.