Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs). First, a general class of nonlinear functions in designing FxTGFs is provided. A unified method for designing first-order FxTGFs is shown under PolyakL jasiewicz inequality assumption, a weaker condition than strong convexity. When there exist both bounded and vanishing disturbances in the gradient flow, a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented. Under the strict convexity assumption, Newton-based FxTGFs is given and further extended to solve time-varying optimization. Besides, the proposed FxTGFs are further used for solving equation-constrained optimization. Moreover, an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization. To show the effectiveness of various FxTGFs, the static regret analysis for several typical FxTGFs are also provided in detail. Finally, the proposed FxTGFs are applied to solve two network problems, i.e., the network consensus problem and solving a system linear equations, respectively, from the respective of optimization. Particularly, by choosing component-wisely sign-preserving functions, these problems can be solved in a distributed way, which extends the existing results. The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications

Formation stage and controlling factors of the paleo-uplifts in the Tarim Basin: A further discussion

AbstractVarious types of paleo-uplifts with different characteristics are developed in the Tarim Basin. Previously, there were multiple opinions on the pale-uplifts origins and structural evolution, so the oil and gas exploration ideas and deployment in the Tarim Basin were not developed smoothly. In this paper, regional seismic interpretation and structural analysis were carried out on the deep marine carbonate rocks in this basin based on the new seismic and drilling data. Then combined with the structural denudation results, the paleo-structural frameworks were reconstructed. And finally, the formation stage and main controlling factors of paleo-uplifts were discussed. It is shown that the Middle Ordovician is the key period when regional extension was converted to compression in this basin, so stratigraphic, sedimentary and structural differences occurred. Before the deposition of Yijianfang Fm in late Middle Ordovician, three carbonate paleo-uplifts (i.e., the Northern, Central and SW Tarim paleo-uplifts) begun to appear, and they were all broad-folded paleo-uplifts of nearly E–W striking and were formed at the same stage. The distribution and development of the Phanerozoic uplifts in this basin are restricted by the Northern and Southern Tarim basement pale-uplifts of nearly E–W striking which were developed during the Precambrian. It is indicated that all the three paleo-uplifts are compressional paleo-uplifts originated from the convergence of the southern plate margin based on the basement paleo-uplifts and they are all characterized by similar structural characteristics and inherited formation and evolution. The current differences of paleo-uplifts are controlled by multi-stage intense structural reformation since the Silurian. It is concluded that the oil and gas exploration potential is immense in the carbonate reservoirs of well-preserved deep paleo-structural zones in a larger area

Microstructure investigations of Pt-modified γ′-Ni3Al + γ-Ni coatings on Ni-based superalloys

The microstructure of Pt-modified γ′-Ni3Al + γ-Ni coating on CMSX-4 single-crystal superalloy has been investigated by transmission electron microscopy (TEM). Cross-sectional TEM analyses showed the presence of precipitates in the coating. This precipitate was identified as the hexagonal topologically close-packed (TCP) μ phase with lattice parameters a = 0.473 nm and c = 2.565 nm. The energy-dispersive x-ray (EDX) spectrum of the μ phase suggested a refractory element rich compound comprising the elements Re, W, and Co. Twin domains parallel to (001) were found in the μ phase. The mechanisms of the μ phase and twinning formation were discussed

Influence of Nb on the β → α″ Martensitic Phase Transformation and Properties of the Newly Designed Ti-Fe-Nb Alloys

A series of Ti-7Fe-xNb (x = 0, 1, 4, 6, 9, 11 wt.%) alloys was designed and cast to investigate the β → α″ martensitic phase transformation, β phase stability, the resulting microstructure and mechanical properties. Phase analysis revealed that only Ti-7Fe-11Nb alloy shows a single body-centred cubic β phase microstructure while the others are comprised of β and orthorhombic α″ phases. Moreover, Nb addition up to 11 wt.% enhances the stability and volume fraction of β phase in the microstructure, hence reducing the propensity of the alloy system to form α″ phase during quenching. Compressive yield strength and hardness of the alloys are (985-1847) MPa and (325-520) Hv respectively. Additionally, Ti-7Fe-11Nb possesses the lowest Young\u27s modulus (84 GPa) and the highest deformability (42% strain) among the designed alloys due to the single β phase microstructure. This high deformability is also corroborated by the large plastic deformation zone underneath the Vickers indenter. In contrast, the fractured surfaces of Ti-7Fe and Ti-7Fe-1Nb alloys after compressive tests mostly contain shallow dimples, verifying their low ductility. The good combination of mechanical properties obtained for Ti-7Fe-11Nb renders it more desirable than commonly used CP-Ti and Ti-6Al-4V materials and makes it a promising candidate for biomedical application. © 2015 Elsevier B.V. All rights reserved

Rotor retaining sleeve design for a 1.12-MW high-speed PM machine

Permanent-magnet (PM) synchronous machines (PMSMs) can provide excellent performance in terms of torque density, energy efficiency, and controllability. However, PMs on the rotor are prone to centrifugal force, which may break their physical integrity, particularly at high-speed operation. Typically, PMs are bound with carbon fiber or retained by alloy sleeves on the rotor surface. This paper is concerned with the design of a rotor retaining sleeve for a 1.12-MW 18-kr/min PM machine; its electromagnetic performance is investigated by the 2-D finite-element method (FEM). Theoretical and numerical analyses of the rotor stress are carried out. For the carbon fiber protective measure, the stresses of three PM configurations and three pole filler materials are compared in terms of operating temperature, rotor speed, retaining sleeve thickness, and interference fit. Then, a new hybrid protective measure is proposed and analyzed by the 2-D FEM for operational speeds up to 22 kr/min (1.2 times the rated speed). The rotor losses and machine temperatures with the carbon fiber retaining sleeve and the hybrid retaining sleeve are compared, and the sleeve design is refined. Two rotors using both designs are prototyped and experimentally tested to validate the effectiveness of the developed techniques for PM machines. The developed retaining sleeve makes it possible to operate megawatt PM machines at high speeds of 22 kr/min. This opens doors for many high-power high-speed applications such as turbo-generator, aerospace, and submarine motor drives

Electromagnetic design and loss calculations of a 1.12-MW high-speed permanent-magnet motor for compressor applications

Electromagnetic design of a 1.12-MW, 18 000-r/min high-speed permanent-magnet motor (HSPMM) is carried out based on the analysis of pole number, stator slot number, rotor outer diameter, air-gap length, permanent magnet material, thickness, and pole arc. The no-load and full-load performance of the HSPMM is investigated in this paper by using 2-D finite element method (FEM). In addition, the power losses in the HSPMM including core loss, winding loss, rotor eddy current loss, and air friction loss are predicted. Based on the analysis, a prototype motor is manufactured and experimentally tested to verify the machine design

Chaotic Image Encryption Based on Running-Key Related to Plaintext

In the field of chaotic image encryption, the algorithm based on correlating key with plaintext has become a new developing direction. However, for this kind of algorithm, some shortcomings in resistance to reconstruction attack, efficient utilization of chaotic resource, and reducing dynamical degradation of digital chaos are found. In order to solve these problems and further enhance the security of encryption algorithm, based on disturbance and feedback mechanism, we present a new image encryption scheme. In the running-key generation stage, by successively disturbing chaotic stream with cipher-text, the relation of running-key to plaintext is established, reconstruction attack is avoided, effective use of chaotic resource is guaranteed, and dynamical degradation of digital chaos is minimized. In the image encryption stage, by introducing random-feedback mechanism, the difficulty of breaking this scheme is increased. Comparing with the-state-of-the-art algorithms, our scheme exhibits good properties such as large key space, long key period, and extreme sensitivity to the initial key and plaintext. Therefore, it can resist brute-force, reconstruction attack, and differential attack