Decomposition Of Space Research Articles

Anisotropy cyclic plasticity constitutive modelling for Ni-based single-crystal superalloys based on Kelvin decomposition

Nickel-based single-crystal (SC) superalloys exhibited excellent exceptional mechanical properties at high temperatures due to the elimination of internal grain boundaries, contributed a strong orientation-dependent material response. The anisotropy of SC superalloys was modeled viscoplastically from a macroscopic viewpoint based on the Kelvin decomposition theory [1] which was a decomposition of the stress space according to the elastic matrix eigen-directions to control the viscoplastic flow by Kelvin stress decoupled from each other. Compared to the classical phenomenological macro model, the proposed model effectively captures the slip deformation mechanism of SC superalloys with the inherent ability to simulate anisotropic because of the two criterions framework controlled by Kelvin stress. Compared with others, the proposed model was able to simulate time-dependent inelastic deformation and cyclic deformation behavior under complex loading. The kinematic hardening and isotropic hardening models incorporated microscopic quantities, such as dislocation density and channel phase width, connecting the macroscopic mechanical response with the microscopic state to achieve multiscale constitutive modelling. The parameter identification and finite element implementation were conducted on a SC superalloy [2]. Simulation results demonstrated the accuracy of the proposed model in predicting deformation behavior under various orientations, rate-dependent effects, isothermal and non-isothermal cyclic deformation. Comparison with the classical anisotropic matrix macroscopic phenomenological approaches highlights the superior capability of the proposed model to simulate the orientation-dependent mechanical properties of single-crystal alloys.

Diffusion-model-based inverse problem processing for optically-measured sound field

This paper proposes a diffusion-model-based method for addressing inverse problems in optical sound-field imaging. Optical sound-field imaging, known for its high spatial resolution, measures sound by detecting small variations in the refractive index of air caused by sound but often suffers from unavoidable noise contamination. Therefore, we present a diffusion model-based approach for sound-field inverse problems, including denoising, noisy sound-field reconstruction and extrapolation. During inference, sound-field degradation is introduced into the inverse denoising process, with range-null space decomposition used as a solver to handle degradation, iteratively generating degraded sound-field information. Numerical experiments show that our method outperforms other deep-learning-based methods in denoising and reconstruction tasks, and obtains effective results in extrapolation task. The experimental results demonstrate the applicability of our model to the real world.

Direct torque control of a dual star induction generator based on a modified space vector PWM under fault conditions

Recent studies have shown that electrical systems in wind power conversion are subject to a 67 % failure rate, and conventional three-phase generators are considered to be the most sensitive to these faults. Induction generator current harmonics are a major source of torque ripples causing acoustic noise and vibrations. These ripples can progressively increase under faulty operating conditions. In six-phase machines, there is appearance of high harmonic currents in the air gap as space harmonics. Power electronic converters are also subject to faults, the most common being Short-Circuit (SC) and Open-Circuit (OC) faults. SC faults cause large peaks in the line currents, which trigger the protection devices, resulting in a complete shutdown of the production system. OC faults, on the other hand, cause imbalances in the phases, but the system remains in operation.Direct Torque Control (DTC) based on Space Vector Modulation (SVM) at constant switching frequency is an effective solution to tackle induction generator current harmonics. This paper proposes a DTC combined with a Proportional Integral Fuzzy Logic Controller (PIFLC) optimized by Particle Swarm Optimization (PSO) in order to overcome the problems of torque ripples. Furthermore, using Vector Space Decomposition (VSD) and the Modified Space Vector Pulse Width Modulation (MSVPWM) strategy, a significant reduction of harmonics in the air-gap can be achieved.Simulations were carried out under MATLAB/Simulink, and the results obtained demonstrate the superiority of the proposed DTC-PIFLC-PSO controller in terms of robustness against wind speed variations and under faulty switch conditions in the power converter of the Dual Star Induction Generator (DSIG) generator. In addition, a comparative study with the classical PI controller is presented to show the effectiveness of the DTC-PIFLC-PSO controller against faults with a significant reduction in the Total Harmonic Distortion (THD) during both faulty and non-faulty conditions.

Decomposing tensor spaces via path signatures

The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. We show that the parametrization of this variety induces a natural decomposition of the tensor space via representation theory, and connect this to the study of path invariants. We also reveal certain constraints that apply to the rank and symmetry of a signature tensor.

Bi-level optimization and integrated multiple-criteria decision making under uncertainty for structural design of insulated bearings

To address the premature failure of insulated bearings, this article proposes a design method for the structure of bearings to prolong their service life. First, a bi-level optimization model is established to determine the structural parameters of bearings considering their insulating and mechanical properties. Upper-level problems include bearing voltage ratio, porosity of insulating coatings, minimum thickness of oil film and Hertz contact area. Lower-level problems include fatigue life of bearings and adhesion of insulating coatings. Second, a non-dominated sorting genetic algorithm-III based on space decomposition and penalty-based boundary intersection (NSGA-III-SD-PBI) is designed to solve the optimization model. Third, the integrated multiple-criteria decision-making (MCDM) using the fuzzy best–worst method (BWM) and fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) is developed to determine the best structural parameters of bearings. A case study demonstrates the effectiveness and superiority of the proposed method, with fatigue life increased by 20%.

Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

Multiple Time Scales and Normal Form of Hopf Bifurcation in a Delayed Reaction–Diffusion–Advection System

In the reaction–diffusion systems, the Laplacian is usually a self-adjoint operator. Incorporating advection terms generally destroys this and yields a quite complicated decomposition of phase space in the Center Manifold Reduction (CMR) method. Considering that the Multiple Time Scales (MTS) method can be directly applied to bifurcation analysis and normal form derivation based on algebraic operations, and the computational process is relatively universal, we apply the MTS method to analyze the Hopf bifurcation problem of reaction–diffusion–advection systems with time delay. First, we introduce the MTS method for the system with a specific boundary condition, which is used to derive the normal form of Hopf bifurcation. Calculating the normal form using the MTS method can be summarized as determining the bifurcation parameters, conducting Taylor expansion based on the MTS idea, and eliminating secular terms. Then, the key coefficients in the normal form are explicitly given, which are also compared with the results obtained by the CMR method, and both methods lead to the same bifurcation results. Finally, we use the MTS method to calculate the normal form of Hopf bifurcation for a predator–prey model with mixed boundary conditions. We find that the spatially nonhomogeneous periodic solutions appear near the equilibrium in the system when the time delay exceeds the critical value, and the theoretical results are illustrated by numerical simulations.

Work domain modeling of human-automation interaction for in-vehicle automation

Automated driving systems are deployed on public roads with little empirical support for the dominant justifications of enhanced safety and enhanced productivity. Furthermore, development of automated driving systems has been piecemeal rather than systematic while research on driver-automation interaction has relied on individual analysis of accidents and on observational studies of driving behavior in a simulator or on the road. In this paper, we apply Work Domain Analysis to develop a more systematic and comprehensive model of automated driving. We use a strategy of layering the driving automation onto the resulting ion-Decomposition Space for manual driving to mimic the existing design strategy of introducing automation to take over driving functions previously the responsibility of the human driver. Our analysis shows that automation does not unequivocally supports dominant driving values. Furthermore, our analysis revealed subtle interdependencies between human and technological functions. We conclude that an ion Decomposition Space offers a systematic view of driver-automation interaction that can suggest new insights for automation design.

A Topological Distance Between Multi-Fields Based on Multi-Dimensional Persistence Diagrams.

The problem of computing topological distance between two scalar fields based on Reeb graphs or contour trees has been studied and applied successfully to various problems in topological shape matching, data analysis, and visualization. However, generalizing such results for computing distance measures between two multi-fields based on their Reeb spaces is still in its infancy. Towards this, in the current article we propose a technique to compute an effective distance measure between two multi-fields by computing a novel multi-dimensional persistence diagram (MDPD) corresponding to each of the (quantized) Reeb spaces. First, we construct a multi-dimensional Reeb graph (MDRG), which is a hierarchical decomposition of the Reeb space into a collection of Reeb graphs. The MDPD corresponding to each MDRG is then computed based on the persistence diagrams of the component Reeb graphs of the MDRG. Our distance measure extends the Wasserstein distance between two persistence diagrams of Reeb graphs to MDPDs of MDRGs. We prove that the proposed measure is a pseudo-metric and satisfies a stability property. Effectiveness of the proposed distance measure has been demonstrated in (i) shape retrieval contest data - SHREC 2010 and (ii) Pt-CO bond detection data from computational chemistry. Experimental results show that the proposed distance measure based on the Reeb spaces has more discriminating power in clustering the shapes and detecting the formation of a stable Pt-CO bond as compared to the similar measures between Reeb graphs.

Holographic phenomenology via overlapping degrees of freedom

Abstract The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.

Phase-field anisotropic damage with bond-slip model for reinforced concrete beam under the service load

Concrete, as a quasi-brittle material, undergoes a latent damage accumulation preceding macroscopic crack formation, which is further complicated by the intricate interaction between steel reinforcements and concrete in reinforced concrete (RC) structures. Traditional approaches inadequately capture these nuances, especially when it comes to the seamless transition from numerous micro cracks to a visible macro cracks. Phase-field damage theory stands out as a sophisticated tool, integrating sharp cracks into a continuous damage field representation and detailing the entire process of micro-to-macroscopic cracking evolution. In this work, a phase-field damage model that accounts for bond-slip behavior is proposed, grounded in the principle of stress space decomposition to address the inherent tension–compression anisotropy. Newton’s method with a viscosity coefficient of 0.001 enhances simulation accuracy and robustness through optimal convergence. The comparison between rigid bond and bond slip mechanisms indicates a significant difference in their impact on crack modes, revealing the necessity of considering bond slip. As the steel reinforcement ratio increases, the RC beam’s load-bearing capacity increases incrementally, concurrently exhibiting a reduction in macroscopic cracks, steel reinforcement stress, and overall damage severity. However, the comparative advantage of rigid bond in improving RC beam’s resistance against cracking begins to wane as the reinforcement proportion rises. This study thus sheds light on the nuanced interplay between bond characteristics and the cracking behavior of RC beams, providing a comprehensive and advanced perspective.

The first cohomology of lie superalgebra P̃(2) with coefficients in kac modules

Over a field of characteristic p > 2, firstly, the structure of Kac modules of Lie superalgebra P ˜ ( 2 ) and the weight space decompositions are given. Secondly, the weight-derivations of P ˜ ( 2 ) to its Kac modules are computed. Finally, the first cohomology of P ˜ ( 2 ) with coefficients in Kac modules is determined.

A parallel algorithm for reliability assessment of multi-state flow networks based on simultaneous finding of all multi-state minimal paths and performing state space decomposition

This article presents a new efficient method for reliability evaluation of two-terminal Multi-state Flow Networks (MFNs). Indirect State Space Decomposition (SSD) methods are usually more efficient than direct SSD methods. However, indirect SSD methods require searching for all d-MPs/d-MCs. The presented method requires only an MFN, a system demand requirement d, and the probability distributions of states of components as an input. The presented algorithm uses a partition technique to decompose a state space into smaller and distinct subspaces. The algorithm tries to determine a d-flow with a lower bound for each subspace. If a flow exists and it is a d-MP, the algorithm computes the probability that a capacity vector belongs to this subspace and is bounded below by the d-MP and decomposes this subspace into smaller subspaces. For all subspaces without d-MP, the presented algorithm uses parallel computations and the SSD method to compute the probability that a capacity vector belongs to this subspace and is bounded below by a d-MP. The numerical experiments show that the efficiency of the presented method improves in comparison with other indirect SSD methods if the number of available logical processes and the number of d-MPs increase.

Homotopy Theoretic Properties Of Open Books

ABSTRACT We study the homotopy groups of open books in terms of those of their pages and bindings. Under homotopy theoretic conditions on the monodromy we prove an integral decomposition result for the based loop space on an open book, and under more relaxed conditions we prove a rational loop space decomposition. The latter case allows for a rational dichotomy theorem for open books, as an extension of the classical dichotomy in rational homotopy theory. As a direct application, we show that for Milnor’s open book decomposition of an odd sphere with monodromy of finite order the induced action of the monodromy on the homology groups of its page cannot be nilpotent.

Geometric property (T) and Kazhdan projections

AbstractWe characterise Geometric Property (T) by the existence of a certain projection in the maximal uniform Roe algebra , extending the notion of Kazhdan projection for groups to the realm of metric spaces. We also describe this projection in terms of the decomposition of the metric space into coarsely connected components.

A Simplified Model Predictive Current Control Strategy for Six-phase H-bridge Inverters

Background: The double-end H-bridge inverters can realize independent control of the stator voltage in each phase and have flexible advantages of modulation and fault tolerance; thus, they are more suitable for multi-phase fault-tolerant motor drives. However, due to the increase of voltage vectors and the coupling between the electromagnetic and non-electromagnetic quantities, the normal control strategies for traditional three-phase motor drives do not work anymore. Objective: This paper aimed to propose a simplified model predictive current control strategy based on the vector space decomposition (VSD) and the vectors’ gradual simplification for the three-level six-phase H-bridge inverters. Methods: Firstly, the 729 physical variables were decomposed and mapped onto the fundamental αβ subspace, harmonic xy subspace, and the zero-sequence o1o2 subspace based on the VSD. Then, to eliminate the influence of the harmonic and zero-sequence components on the control performance and make an easy digital implementation, vectors’ simplification has been proposed based on the in-depth analysis of the relationship between the voltage vectors mapped onto different subspaces and vectors’ stratification. With the simplification method, the number of voltage vectors was simplified from 729 to 12, and then the selected voltage vectors were used in the rolling optimization of the model predictive current control (MPCC) to choose the optimal one. Finally, sufficient experiments were carried out including static and dynamic conditions, different modulation index and power factor, etc., to verify the feasibility of the proposed strategy. Results: The simulation and experimental results show that with the simplified MPCC strategy, both the static and dynamic performances are relatively good, and the THDs of the phase current under different modulations and power factors are relatively low. Conclusion: The proposed MPCC algorithm for the three-level six-phase H-bridge inverters has shown obvious improvement in solving the control problems of multi-vectors and complex redundancy issues.

Dynamic robot routing optimization: State–space decomposition for operations research-informed reinforcement learning

There is a growing interest in implementing artificial intelligence for operations research in the industrial environment. While numerous classic operations research solvers ensure optimal solutions, they often struggle with real-time dynamic objectives and environments, such as dynamic routing problems, which require periodic algorithmic recalibration. To deal with dynamic environments, deep reinforcement learning has shown great potential with its capability as a self-learning and optimizing mechanism. However, the real-world applications of reinforcement learning are relatively limited due to lengthy training time and inefficiency in high-dimensional state spaces. In this study, we introduce two methods to enhance reinforcement learning for dynamic routing optimization. The first method involves transferring knowledge from classic operations research solvers to reinforcement learning during training, which accelerates exploration and reduces lengthy training time. The second method uses a state–space decomposer to transform the high-dimensional state space into a low-dimensional latent space, which allows the reinforcement learning agent to learn efficiently in the latent space. Lastly, we demonstrate the applicability of our approach in an industrial application of an automated welding process, where our approach identifies the shortest welding pathway of an industrial robotic arm to weld a set of dynamically changing target nodes, poses and sizes. The suggested method cuts computation time by 25% to 50% compared to classic routing algorithms.

Existence and multiplicity of solutions for fractional p-Laplacian equation involving critical concave-convex nonlinearities

Abstract We investigate the following fractional p-Laplacian convex-concave problem: ( P λ ) ( − Δ ) p s u = λ | u | q − 2 u + | u | p s * − 2 u in Ω , u = 0 in R n \ Ω , $$\left({P}_{\lambda }\right) \begin{cases}\begin{aligned}\hfill {\left(-{\Delta}\right)}_{p}^{s}u& =\lambda \vert u{\vert }^{q-2}u+\vert u{\vert }^{{p}_{s}^{{\ast}}-2}u\hfill & \hfill & \quad \text{in} {\Omega},\hfill \\ \hfill u& =0 \hfill & \hfill & \quad \text{in} {\mathbb{R}}^{n}{\backslash}{\Omega},\hfill \end{aligned}\quad \hfill \end{cases}$$ where Ω is a bounded C 1,1 domain in R n ${\mathbb{R}}^{n}$ , s ∈ (0, 1), p > q > 1, n > sp, λ > 0, and p s * = n p n − s p ${p}_{s}^{{\ast}}=\frac{np}{n-sp}$ is the critical Sobolev exponent. Our analysis extends classical works (A. Ambrosetti, H. Brezis, and G. Cerami, “Combined effects of concave and convex nonlinearities in some elliptic problems,” J. Funct. Anal., vol. 122, no. 2, pp. 519–543, 1994, B. Barrios, E. Colorado, R. Servadei, and F. Soria, “A critical fractional equation with concave-convex power nonlinearities,” Ann. Inst. Henri Poincare Anal. Non Lineaire, vol. 32, no. 4, pp. 875–900, 2015, J. García Azorero, J. Manfredi, and I. Peral Alonso, “Sobolev versus Hölder local minimizer and global multiplicity for some quasilinear elliptic equations,” Commun. Contemp. Math., vol. 2, no. 3, pp. 385–404, 2000) to fractional p-Laplacian. Owing to the nonlinear and nonlocal properties of ( − Δ ) p s ${\left(-{\Delta}\right)}_{p}^{s}$ , we need to overcome many difficulties and apply notably different approaches, due to the lack of Picone identity, the stability theory, and the strong comparison principle. We show first a dichotomy result: a positive W 0 s , p ( Ω ) ${W}_{0}^{s,p}\left({\Omega}\right)$ solution of (P λ ) exists if and only if λ ∈ (0, Λ] with an extremal value Λ ∈ (0, ∞). The W 0 s , p ( Ω ) ${W}_{0}^{s,p}\left({\Omega}\right)$ regularity for the extremal solution seems to be unknown regardless of whether s = 1 or s ∈ (0, 1). When p ≥ 2, p − 1 < q < p and n > s p ( q + 1 ) q + 1 − p $n{ >}\frac{sp\left(q+1\right)}{q+1-p}$ , we get two positive solutions for (P λ ) with small λ > 0. Here the mountain pass structure is more involved than the classical situations due to the lack of explicit minimizers for the Sobolev embedding, we should proceed carefully and simultaneously the construction of mountain pass geometry and the estimate for mountain pass level. Finally, we show another new result for (P λ ) and all p > q > 1: without sign constraint, (P λ ) possesses infinitely many solutions when λ > 0 is small enough. Here we use the Z 2 ${\mathbb{Z}}_{2}$ -genus theory, based on a space decomposition for reflexible and separable Banach spaces, which has its own interest.

A novel clustering-based evolutionary algorithm with objective space decomposition for multi/many-objective optimization

The framework of decomposing a multi-objective optimization problem (MOP) into some MOPs holds considerable promise. However, its advancement is constrained by numerous elements, including the incorrect segmentation of the subspaces and the challenges in balancing convergence and diversity. To address these issues, an objective space Decomposition and Clustering-based Evolutionary Algorithm (DCEA) is proposed in this paper. Specifically, DCEA employs K-means clustering to create an appropriate mating pool for each individual without the necessity to predetermine the number of clusters. Within each mating pool, the proposed adaptive evolutionary operator is applied to produce offspring for balancing the convergence and diversity. To enhance the accuracy of partitioning, a refined environmental selection approach utilizing supplementary weight vectors is developed. Additionally, by utilizing historical clustering data, a straightforward approach to periodically adjust reference vectors for the allocation of computational resources is proposed. In experiments, both MOPs and many-objective optimization problems (MaOPs) are used to test DCEA. A total of 27 MOPs and 30 MaOPs are involved and 16 state-of-the-art algorithms are employed to compare with DCEA. Comprehensive experiments show that DCEA is an effective algorithm for solving both MOPs and MaOPs.

Multi-dimensional classification via class space fusion and comprehensive label correlations

Multi-dimensional Classification (MDC) is a new multi-output learning paradigm, where each instance in this framework is annotated with labels from multiple semantic class spaces. The vital challenge in MDC problem is how to address the heterogeneity of output space. Existing methods typically focus on the decomposition of output space, rarely consider the comprehensive fine-grained label correlations and the exploration of the intrinsic structure of the output space. And the local label correlations, which only exist within specific groups of instances, remain largely untapped in existing MDC methods. Therefore, we focus on tackling these above problems in this paper by simultaneously conducting label space fusion and considering the comprehensive label correlations to fully exploit the latent discriminative information hidden in the output space. Heuristically, we utilize low-rank representation method to achieve label space fusion to capture the intrinsic structure and implicit global correlation of label space. Then the predictive MDC model is extrapolated from the reconstructed instances equipped with the fused label space. Moreover, the topological structure information of samples is fully taken advantage of for MDC model establishment. Benefiting from these strategies, the heterogeneous label space can be fully excavated to boost the performance of MDC. Empirically, comparative experiments are conducted over several multi-dimensional benchmark data sets, and corresponding experimental results firmly illustrate that the proposed algorithm can effectively solve the MDC problem and outperform state-of-the-art methods.