Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

Necessary and Sufficient Conditions in Smooth Programming with Generalized Convexity

Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.

Criteria Condition for Generalized Diagonally Dominant Matrices

In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.

Generalized Demodulation Transform for Bearing Fault Diagnosis Under Nonstationary Conditions and Gear Noise Interferences

It is a challenging issue to detect bearing fault under nonstationary conditions and gear noise interferences. Meanwhile, the application of the traditional methods is limited by their deficiencies in the aspect of computational accuracy and e ciency, or dependence on the tachometer. Hence, a new fault diagnosis strategy is proposed to remove gear interferences and spectrum smearing phenomenon without the tachometer and angular resampling technique. In this method, the instantaneous dominant meshing multiple(IDMM) is firstly extracted from the time-frequency representation(TFR) of the raw signal, which can be used to calculate the phase functions(PF) and the frequency points(FP). Next, the resonance frequency band excited by the faulty bearing is obtained by the band-pass filter. Furthermore, based on the PFs, the generalized demodulation transform(GDT) is applied to the envelope of the filtered signal. Finally, the target bearing is diagnosed by matching the peaks in the spectra of demodulated signals with the theoretical FPs. The analysis results of simulated and experimental signal demonstrate that the proposed method is an e ective and reliable tool for bearing fault diagnosis without the tachometer and the angular resampling.

Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow

The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.

Approximate Generalized Conditional Symmetries for Perturbed Evolution Equations

The concept of approximate generalized conditional symmetry （AGCS） for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples.

Criteria Conditions for Generalized Diagonally Dominant Matrices

In this paper, some new sufficient conditions for generalized dominant matrices are given, and some results in [1] are generalized and improved.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified （C, α, p, d）-convexity

The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.

Consistency Conditions and Constraints on Generalized f(R) Gravity with Arbitrary Geometry-Matter Coupling

We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.

COMPONENTWISE CONDITION NUMBERS FOR GENERALIZED MATRIX INVERSION AND LINEAR LEAST SQUARES

We present componentwise condition numbers for the problems of MoorePenrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given.

Criteria Conditions for Generalized Diagonally Dominant Matrices

In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.

Application of generalized impedance boundary conditions to sommerfeld half-space problem

Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.

Direct and Reverse Carleson Conditions on Generalized Weighted Bergman-Orlicz Spaces

Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.

Energy Conditions and Constraints on the Generalized Non-Local Gravity Model

We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.

SOLUTION TO A PARAMETRIC EQUATION WITH GENERALIZED BOUNDARY CONDITION IN TRANSPORT THEORY

This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.