Lagrange Parameters Research Articles

Sparse randomized policies for Markov decision processes based on Tsallis divergence regularization

This work investigates a somewhat different point of view on Markov decision processes by reinterpreting them as a randomized shortest paths problem on a bipartite graph, therefore establishing bridges with entropy-regularized reinforcement learning. The graph structure contains the set of states as “left” nodes and the set of actions as “right” nodes. In that context, the action-to-state transition probabilities are provided by the environment whereas the state-to-action probabilities correspond to the (stochastic) policy to be found. The randomized shortest paths formalism (minimizing expected cost to the goal state subject to (Shannon or Tsallis) relative entropy regularization) is then readily applied to this bipartite structure, providing a possibly sparse stochastic policy interpolating between a least-cost and a purely random policy. The algorithm computing the policy is closely related to the dual linear programming formulation of the Markov decision processes to which the relative entropy regularization term, multiplied by a scaling factor balancing exploitation and exploration (the temperature), is added. It is derived from well-known techniques of discrete optimal control, relying on costates (Lagrange parameters) backward computation. In summary, the proposed algorithm allows the design of optimal stochastic – but still sparse – policies, ranging from a purely rational to a random behavior, depending on the temperature parameter.

A FE2 shell model with periodic boundary conditions for thin and thick shells

AbstractIn this article a FE2 shell model for thin and thick shells within a first order homogenization scheme is presented. A variational formulation for the two‐scale boundary value problem and the associated finite element formulation is developed. Constraints with 5 or 9 Lagrange parameters are derived which eliminate both rigid body movements and dependencies of the shear stiffness on the size of the representative volume elements (RVEs). At the bottom and top surface of the RVEs which extend through the total thickness of the shell stress boundary conditions are present. The periodic boundary conditions at the lateral surfaces are applied in such a way that particular membrane, bending and shear modes are not restrained. This is shown by means of a homogeneous RVE. The first of all linear formulation is extended to finite strain problems introducing transformation relations for the stress resultants and the material matrix. The transformations are performed at the Gauss points on macro level. Several boundary value problems including large deformations, stability and inelasticity are computed and compared with 3D reference solutions.

Multi-objective Quantum Annealing approach for solving flexible job shop scheduling in manufacturing

Flexible Job Shop Scheduling (FJSSP) is a challenging optimization problem with multiple conflicting objectives used to model and compute real-world process scheduling tasks. In order for a manufacturing system to remain competitive, it is necessary to compute such optimization problems quickly and efficiently. The limitations of conventional optimization methods frequently stem from a delicate balance between solution quality and computation time. Consequently, a pressing need for solution algorithms arises that can effectively transcend these limitations. This paper presents a novel Quantum Annealing-based solving algorithm (QASA) for computing FJSSP, leveraging the power of Quantum Annealing combined with classical techniques. The proposed approach aims to optimize a multi-criterial FJSSP considering makespan, total workload, and job priority simultaneously. QASA employs a Hamiltonian formulation with Lagrange parameters to integrate the problem's constraints and objectives. By assigning appropriate weights to the objectives, the method allows the prioritization of certain objectives over others. To handle the computational complexity of large FJSSP instances, the problem is decomposed into smaller subproblems, and a decision logic based on bottleneck factors is employed to select critical jobs for computation combined with variable pruning techniques. To evaluate the effectiveness of the proposed approach, experiments are conducted on benchmark problems, considering makespan, total workload, and priority objectives. Therefore, QASA combining tabu search, simulated annealing, and Quantum Annealing is used for efficient computation and is compared with a classical solving algorithm (CSA) combining tabu search and simulated annealing. The results demonstrate that QASA outperforms CSA in terms of solution quality, as measured by set coverage and hypervolume ratio metrics. Furthermore, computational efficiency analysis reveals that QASA achieves superior Pareto solutions compared to the classical approach, with a reasonable increase in computation time.

Determination of Lagrange multipliers for interframe EZBC/JP2K

Interframe EZBC/JP2K has been shown to be an effective fine-grain scalable video coding system. However, its Lagrange multiplier values for motion estimation of multiple temporal levels are not specified, and must be specified by the user in the config file in order to run the program. In this paper, we investigate how to select these Lagrange parameters for optimized performance. By designing an iterative mechanism, we make it possible for the encoder to adaptively select Lagrange multipliers based on the feedback of Y-PSNR closed GOP performance. Experimental results regarding both classic test video clips and their concatenations are obtained and discussed. We also present a new analytical model for optimized Lagrange multiplier selection in terms of target Y-PSNR.

Maximum entropy copula for bivariate drought analysis

Copula functions are widely used to derive multivariate probability distributions in hydrometeorology. One of the key steps in the copula method is the derivation of marginal distributions of individual variables which can be accomplished using the principle of maximum entropy where the distribution parameters are estimated from the specified constraints. This study, investigated two drought variables (severity and duration) by coupling the principle of maximum entropy with parametric and empirical copulas. So, homogeneous climatic zones were first identified by applying the fuzzy clustering method to data from 39 synoptic stations in Iran and then drought severity and duration were determined with the standardized precipitation index. These two variables were scaled and their marginal probability distribution functions were derived using the principle of maximum entropy as well as empirically. Then, the joint probability distribution of drought severity and duration was determined using maximum entropy-copula, and parametric and empirical copulas. Thereafter, bivariate conditional return periods were determined for each homogeneous region. Results showed that 1) univariate and bivariate distributions can be obtained by maximizing entropy; 2) the dependence structure via Spearman's rho, which directly affects the Lagrange parameters of entropy copula, was a controlling factor to optimize the objective function; 3) for a given set of constraints, the maximum entropy copula is independent of the types of marginals; 4)The entropy-entropy copula (with entropy marginals) is considered a better method than alternatives, because it has a similar result to the parametric methods while it only needs to fit a single model.

A Quality-of-Experience-Aware Framework for Versatile Video Coding-Based Video Transmission

Multimedia applications have expanded and resulted in huge demands for high resolution videos in order to enhance the end user Quality of Experience (QoE). Therefore, QoE becomes a critical factor that is often addressed in design considerations of Consumer Electronics (CE) devices. Furthermore, error prone transmission conditions can influence the QoE, potentially degrading the end-user multimedia experience. Although video coding standards such as Versatile Video Coding (VVC) take potential mitigation measures to improve the bandwidth reductions, it fails to address other significant network Quality of Service (QoS) parameters that impact transmission based QoE such as transmission delay and Packet Loss Rate (PLR) in the encoding processes. In response, this paper first derives a relationship between QoE that addresses the network QoS parameters and VVC dependent parameters. Subsequently, the derived QoE model is used with the VVC encoding process to adaptively optimize Lagrange parameters as well as the quantization parameter. Extensive experiments report significant improvements to VVC Test Model (VTM) 7.0, achieving superior QoE gains over the state-of-the-art research and up to 3.41% over the anchor implementations.

Classical ground states of spin lattices

We present a generalization of the Luttinger–Tisza–Lyons–Kaplan theory of classical ground states of Bravais lattices with Heisenberg coupling to non-Bravais lattices. It consists of adding certain Lagrange parameters to the diagonal of the Fourier transformed coupling matrix analogous to the theory of the general ground state problem already published. This approach is illustrated by an application to a modified honeycomb lattice, which has exclusive three-dimensional ground states as well as a classical spin-liquid ground state for different values of the two coupling constants. Another example, the modified square lattice, shows that we can also obtain so-called incommensurable ground states by our method.

Axially-deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (IV) hfbtho (v4.0): A new version of the program

We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry for even-even nuclei. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, we added the SeaLL1 functional and improved the calculation of the Coulomb potential. Finally, we refactored the code to facilitate maintenance and future developments. New version program summaryProgram title:hfbtho v4.0CPC Library link to program files:https://doi.org/10.17632/c5g2f92by3.2Code Ocean capsule:https://codeocean.com/capsule/5389629Licensing provisions: GPLv3Programming language: Fortran 2003Journal reference of previous version: R.N. Pérez, N. Schunck, R.-D. Lasseri, C. Zhang and J. Sarich, Comput. Phys. Commun. 220 (2017) 363Does the new version supersede the previous version: YesReasons for the new version: This version adds new capabilities to restore broken symmetries and determine corresponding quantum numbers of even-even nucleiSummary of revisions:1.Angular momentum projection for even-even nuclei in a deformed basis;2.Particle number projection for even-even nuclei in the quasiparticle basis;3.Implementation of the SeaLL1 functional;4.Expansion of the Coulomb potential onto Gaussians;5.MPI-parallelization of a single hfbtho execution;6.Code refactoring.Nature of problem:hfbtho is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of hfbtho, the energy density is derived either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear superfluidity is treated at the Hartree-Fock-Bogoliubov (HFB) approximation. Constraints on the nuclear shape allow probing the potential energy surface of the nucleus as needed, e.g., for the description of shape isomers or fission. A local scale transformation of the single-particle basis in which the HFB solutions are expanded provides a tool to properly compute the structure of weakly-bound nuclei. Restoration of the rotational, particle number, and reflection symmetry for even-even nuclei enables recovering the quantum numbers that are lost at the HFB approximation.Solution method: The program uses the axial harmonic oscillator (HO) or the transformed harmonic oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the HFB Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. Lagrange parameters are used to impose constraints on HFB solutions, and their value is updated at each iteration from an approximation of the quasiparticle random phase approximation (QRPA) matrix. Symmetry restoration is implemented through standard projection techniques. Previous versions of the program were presented in [1-3].Additional comments including restrictions and unusual features: Axial and time-reversal symmetries are assumed in HFB calculations; y-simplex symmetry and even particle numbers are assumed in angular momentum projection.

Large-scale focusing joint inversion of gravity and magnetic data with Gramian constraint

SUMMARYA fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. The algorithm uses a non-linear Gramian constraint to impose correlation between the density and susceptibility of the reconstructed models. The global objective function is formulated in the space of the weighted parameters, but the Gramian constraint is implemented in the original space, and the non-linear constraint is imposed using two separate Lagrange parameters, one for each model domain. It is significant that this combined approach, using the two spaces provides more similarity between the reconstructed models. Moreover, it is shown theoretically that the gradient for the use of the unweighted space is not a scalar multiple of that used for the weighted space, and hence cannot be accounted for by adjusting the Lagrange parameters. It is assumed that the measured data are obtained on a uniform grid and that a consistent regular discretization of the volume domain is imposed. Then, the sensitivity matrices exhibit a block-Toeplitz-Toeplitz-block structure for each depth layer of the model domain, and both forward and transpose operations with the matrices can be implemented efficiently using two dimensional fast Fourier transforms. This makes it feasible to solve for large scale problems with respect to both computational costs and memory demands, and to solve the non-linear problem by applying iterative methods that rely only on matrix–vector multiplications. As such, the use of the regularized reweighted conjugate gradient algorithm, in conjunction with the structure of the sensitivity matrices, leads to a fast methodology for large-scale joint inversion of geophysical data sets. Numerical simulations demonstrate that it is possible to apply a non-linear joint inversion algorithm, with Lp-norm stabilisers, for the reconstruction of large model domains on a standard laptop computer. It is demonstrated, that while the p = 1 choice provides sparse reconstructed solutions with sharp boundaries, it is also possible to use p = 2 in order to provide smooth and blurred models. The methodology is used for inverting gravity and magnetic data obtained over an area in northwest of Mesoproterozoic St Francois Terrane, southeast of Missouri, USA.

Deep Learning and Bidirectional Optical Flow Based Viewport Predictions for 360° Video Coding

The rapid development of virtual reality applications continues to urge better compression of 360° videos owing to the large volume of content. These videos are typically converted to 2-D formats using various projection techniques in order to benefit from ad-hoc coding tools designed to support conventional 2-D video compression. Although recently emerged video coding standard, Versatile Video Coding (VVC) introduces 360° video specific coding tools, it fails to prioritize the user observed regions in 360° videos, represented by the rectilinear images called the viewports. This leads to the encoding of redundant regions in the video frames, escalating the bit rate cost of the videos. In response to this issue, this paper proposes a novel 360° video coding framework for VVC which exploits user observed viewport information to alleviate pixel redundancy in 360° videos. In this regard, bidirectional optical flow, Gaussian filter and Spherical Convolutional Neural Networks (Spherical CNN) are deployed to extract perceptual features and predict user observed viewports. By appropriately fusing the predicted viewports on the 2-D projected 360° video frames, a novel Regions of Interest (ROI) aware weightmap is developed which can be used to mask the source video and introduce adaptive changes to the Lagrange and quantization parameters in VVC. Comprehensive experiments conducted in the context of VVC Test Model (VTM) 7.0 show that the proposed framework can improve bitrate reduction, achieving an average bitrate saving of 5.85% and up to 17.15% at the same perceptual quality which is measured using Viewport Peak Signal-To-Noise Ratio (VPSNR).

Bistabilities and domain walls in weakly open quantum systems

Weakly pumped systems with approximate conservation laws can be efficiently described by (generalized) Gibbs ensembles if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the zz-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength \epsilonϵ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as \sim 1/\sqrt{\epsilon}∼1/ϵ while the density of domain walls is exponentially small in 1/\sqrt{\epsilon}1/ϵ. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.

Light element (Z=1,2) production from spontaneous ternary fission of ^{252}Cf

The yields of light elements (Z=1,2) obtained from spontaneous ternary fission of ^{252}Cf are treated within a nonequilibrium approach, and the contribution of unstable nuclei and excited bound states is taken into account. These light cluster yields may be used to probe dense matter, and to infer in-medium corrections such as Pauli blocking which is determined by the nucleon density. Continuum correlations are calculated from scattering phase shifts using the Beth-Uhlenbeck formula, and the effect of medium modification is estimated. The relevant distribution is reconstructed from the measured yields of isotopes. This describes the state of the nucleon system at scission and cluster formation, using only three Lagrange parameters which are the nonequilibrium counterparts of the temperature and chemical potentials, as defined in thermodynamic equilibrium. We concluded that a simple nuclear statistical equilibrium model neglecting continuum correlations and medium effects is not able to describe the measured distribution of H and He isotopes. Moreover, the freeze-out concept may serve as an important ingredient to the nonequilibrium approach using the relevant statistical operator concept.

Modeling the Parameter Interactions in Ranking SVM with Low-Rank Approximation

Ranking SVM, which formalizes the problem of learning a ranking model as that of learning a binary SVM on preference pairs of documents, is a state-of-the-art ranking model in information retrieval. The dual form solution of a linear Ranking SVM model can be written as a linear combination of the preference pairs, i.e., w = Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i,j)</sub> α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> -x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> ), where α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> denotes the Lagrange parameters associated with each preference pair (i,j). It is observed that there exist obvious interactions among the document pairs because two preference pairs could share a same document as their items, e.g., preference pairs (d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) and (d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) share the document d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . Thus it is natural to ask if there also exist interactions over the model parameters α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> , which may be leveraged to construct better ranking models. This paper aims to answer the question. We empirically found that there exists a low-rank structure over the rearranged Ranking SVM model parameters α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> , which indicates that the interactions do exist. Based on the discovery, we made modifications on the original Ranking SVM model by explicitly applying low-rank constraints to the Lagrange parameters, achieving two novel algorithms called Factorized Ranking SVM and Regularized Ranking SVM, respectively. Specifically, in Factorized Ranking SVM each parameter α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> is decomposed as a product of two low-dimensional vectors, i.e., α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> =〈v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ,v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> 〉, where vectors v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> correspond to document i and j, respectively; In Regularized Ranking SVM, a nuclear norm is applied to the rearranged parameters matrix for controlling its rank. Experimental results on three LETOR datasets show that both of the proposed methods can outperform state-of-the-art learning to rank models including the conventional Ranking SVM.

Relating local structures, energies, and occurrence probabilities in a two-dimensional silica network

Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring statistics, could be numerically reproduced by performing molecular dynamics simulations with an appropriately chosen 2D force field. Using a maximum entropy formulation it is shown that the probability distribution of the individual rings and triplets can be related to the ring and triplet energies, respectively, obtained from the simulations. Using additional Lagrange parameters, the correct average properties of random networks are guaranteed. In agreement with previous work, based on distributions of complementary rings and triplets, respectively, one finds a Boltzmann-type relation albeit with an effective temperature which largely deviates from the bath temperature. Furthermore, it is shown that the ring and triplet energies can be estimated based on the properties of their average inner angles. This calculation supports, on a quantitative level, the previously suggested angle mismatch theory. It suggests that correlations among adjacent rings originate from the net mismatch in the inner ring angles in a triplet of rings. By taking into account an average effect from the surrounding rings of a triplet, an even better estimate of the correlations can be provided. That approach is also applied to estimate the Aboav–Wearie parameter.

Time-dependent generalized Gibbs ensembles in open quantum systems

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which both break integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time-evolution on long time-scales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws

We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the system to a new steady state which can be approximately but efficiently described by a (generalized) Gibbs ensemble characterized by one Lagrange parameter for each conservation law. The value of those has to be determined from rate equations for conserved quantities. Remarkably, even weak perturbations can lead to large responses of conserved quantities. We present a perturbative expansion of the steady state density matrix; first we give the condition that fixes the zeroth order expression (Lagrange parameters) and then determine the higher order corrections via projections of the Liouvillian. The formalism can be applied to a wide range of problems including two-temperature models for electron-phonon systems, Bose condensates of excitons or photons or weakly perturbed integrable models. We test our formalism by studying interacting fermions coupled to non-thermal reservoirs, approximately described by a Boltzmann equation.

A layered shell element for the computation of interlaminar shear stresses and thickness normal stresses

AbstractIn this contribution a layered shell element for the computation of laminated structures is proposed. The shell kinematic is based on the Reissner‐Mindlin theory with an inextensible director field. Further a multi‐field functional is introduced including the global shell equations and additional Euler‐Lagrange equations. These Euler‐Lagrange equations enforce the correct shape of warping through the thickness and lead to continuous transverse shear stresses at layer boundaries This leads to a mixed hybrid shell element, after elimination of stresses, warping and Lagrange parameters on element level. The resulting shell element has the usual 5 or 6 degrees of freedom per node, making it possible to apply this element to complex geometrical structures. An extension of the element to compute stresses in thickness direction is shown, in order to estimate and predict interlaminar failure. The computed results show good agreement with 3D solid shell models. Numerical examples for the computation of interlaminar shear and thickness normal stresses are shown and compared to results of 3D elements. (© 2017 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Pumping approximately integrable systems

Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose–Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps.

Fault diagnosis for rotating machinery based on Local Mean Decomposition morphology filtering and Least Square Support Vector Machine

In order to improve the accuracy of fault diagnosis, a fault diagnosis method for rotating machinery based on Local Mean Decomposition (LMD) morphological filtering and Least Square Support Vector Machine(LS-SVM) is proposed. Firstly, the collected vibration signals are processed by LMD which decom poses them into a series of product function (PF) components, and PF components are carried out by method of the morphological filtering and signal recombination. Then, the feature vector is obtained from the new PF components by LMD method. Secondly, a new kernel function is proposed to improve LS-SVM, which can solve the problem of kernel function parameters selection. Further, Lagrange parameters are processed by feature weighting method, and the weighted average value of the Lagrange parameters is calculated as the threshold value of Pruning algorithm, which can solve sparsity problem in LS-SVM. Thirdly, Energy features are inputted into the new LS-SVM to recognize machinery faults according to LS-SVM parameters. Finally, the performance of the proposed method was verified by a fault diagnosis case in a rolling element bearing. The results indicated that this new method could judge and classify the multi-fault of rotating machinery quickly and effectively.

Efficient variational constitutive updates for Allen–Cahn-type phase field theory coupled to continuum mechanics

This paper deals with efficient variational constitutive updates for Allen–Cahn-type phase field theory coupled to a geometrically exact description of continuum mechanics. The starting point of the implementation is a unified variational principle: A time-continuous potential is introduced, the minimizers of which describe naturally every aspect of the aforementioned coupled model—including the homogenization assumptions defining the mechanical response of the bulk material in the diffuse interface region. With regard to these assumptions, classic models such as the one by Voigt/Taylor or the one by Reuss/Sachs are included. Additionally, more sound homogenization approaches falling into the range of rank-1 convexification are also included in the unified framework. Based on a direct discretization of this time-continuous potential in time and space, an efficient numerical finite element implementation is proposed. In order to guarantee admissible order parameters of the phase field, the unconstrained optimization problem is supplemented by respective constraints. They are implemented by means of Lagrange parameters combined with the Fischer–Burmeister NCP functions. This results in an exact fulfillment of the aforementioned constraints without considering any inequality. Several numerical examples show the predictive capabilities as well as the robustness and efficiency of the final algorithmic formulation. Furthermore, the influence of the homogenization assumption is analyzed in detail. It is shown that the choice of the homogenization assumption does influence the predicted microstructure in general. However, all models converge to the same solution in the limiting case.