Reduction Of System Research Articles

Optimal allocation of reliability improvement target based on multiple correlation failures and risk uncertainty

Optimal allocation of the reliability improvement target is essential for the system optimization design. In order to solve the problems that the optimization model is with loss of generality and the validity of the optimal solution is weakened, an optimal allocation method is proposed by considering multiple correlation failures and risk uncertainty in this paper. Two new concepts are presented, such as independent failure results in basic risk, and correlation failure leads to disturbance risk. A risk assessment machinery of “actual risk = basic risk + disturbance risk” is proposed. The action mechanisms of the three correlation failures are studied based on the cooperation game theory, and the generalized risk models are given under probability measure. Considering the improvement cost, the expectation and the variance of the reduction of system risk, a multi-objective optimal allocation model is developed, which is solved by using the PSO algorithm. Finally, the proposed optimal allocation is implemented at the 2-stage NGW planetary reducer, and the results show that it is more efficient and feasible for engineering practice.

Discrete breathers and energy localization in a nonlinear honeycomb lattice.

Discrete breathers (DBs) in nonlinear lattices have attracted much attention in the past decades. In this work, we focus on the formation of DBs and their induced energy localization in the nonlinear honeycomb lattice derived from graphene. The key step is to construct a reduced system (RS) with only a few degrees of freedom, which contains one central site and its three nearest neighbors. The fixed points and periodic orbits of the RS can be obtained from the Poincaré section of the dynamics. Our main finding is that the long-running DB solution of the full honeycomb system corresponds to the periodic orbit given by one of the fixed points of RS, where the central site and its nearest neighbors vibrate inversely. When the initial condition deviates from this fixed point, the local vibration is attracted to it after a short transient process. When the initial condition is assigned to other fixed points of the RS, the initial excitation energy flows to the other part of the full system quickly, resulting in a delocalized wave propagation. Another main finding is that the long-lived DB solutions emerge only when the initial excitation energy is larger than a threshold value, above which the frequency of the DB exceeds the phonon band edge. The excitation energy generally dissipates from the local region due to the interactions between the DB and phonons near the Γ point in the dispersion relation. These results provide a holistic physical picture for the DB solutions in two-dimensional nonlinear lattices with complex potentials, which will be crucial to the understanding of energy localization in the realistic two-dimensional materials.

Conventional and Evolutionary Order Reduction Techniques for Complex Systems

Order reduction of the large-scale linear dynamic systems (LSLDSs) using stability equation technique mixed with the conventional and evolutionary techniques is presented in the paper. The reduced system (RS) is obtained by mixing the advantages of the two methods. For the conventional technique, the numerator of the RS is achieved by using the Pade approximations and improved Pade approximations, whereas the denominator is obtained by the stability equation technique (SET). For the evolutionary technique, numerator of the RS is obtained by minimizing the integral square error (ISE) between transient responses of the original and the RS using the genetic algorithm (GA), and the denominator is obtained by the stability equation method. The proposed RS retains almost all the essential properties of the original system (OS). The viability of the proposed technique is proved by comparing its time, frequency responses, time domain specifications, and ISE with the new and popular methods available in the literature.

Traditional versus improved designs for cycloidal speed reducers with a small tooth difference: The effect on dynamics

Whereas traditional cycloid reducers tend to have a one tooth difference design, a two teeth difference design is common when the transmission ratio is low (≦17). The dynamic characteristics of these small teeth difference designs, however, remain unclear. Hence, this study constructs an analytic model of system dynamics in a cycloid reducer with a small tooth difference. Specifically, taking a transmission ratio of 17 as an example, it analyzes both free-pin and fixed-pin designs to show the shortcomings of traditional designs. It then proposes a nonpin design that improves on these shortcomings, one in which the pinwheel is replaced by a cycloid internal gear. Next, adopting the theory of gearing, it constructs a mathematical model of the nonpin design with a multitooth difference and derives undercutting equations to check for the persistence of undercutting on the tooth profile. It also determines the parameter design range of nonundercutting. In an analysis of system dynamics, it then investigates twelve nonpin cases with a small tooth difference, showing the effect of the design parameters on the reducer's system dynamics. The results indicate that appropriate design parameters can indeed improve on the shortcomings of the traditional design.

Effects of long-term reduced tillage on weed infestation of pea (Pisum sativum L.)

The study evaluated weed infestation of pea (<em>Pisum sativum</em> L.) cultivated under conditions of conventional (CT), reduced (RT) and herbicide tillage (HT). It demonstrated the highest weed density per m<sup>2 </sup>in plots with the herbicide (HT) and reduced (RT) systems and significantly lower weed infestation in plots cultivated in the conventional system (CT). In addition, more weeds occurred at the third leaf stage (13/14 in BBCH scale) than at the pod development stage (73/74 BBCH) of pea. The highest biomass was produced by weeds in the herbicide system (HT), a lower one – in the reduced system (RT), and the lowest one – in the conventional system (CT). The air-dry weight of weeds depended also on pea development stage. At the pod development stage (73/74 BBCH), the air-dry weight of weeds was significantly higher than at the third leaf stage (13/14 BBCH). The tillage system was also observed to influence the species composition of weeds. This trait was also affected by the period of weed infestation assessment. At the third leaf stage of pea (13/14 BBCH), there occurred 26 weed species, including 24 annual ones. The most abundant species included: <em>Chenopodium album</em> L., <em>Stellaria media</em> (L.) Vill., <em>Capsella bursa-pastoris</em> (L.) Med., <em>Matricaria inodora</em> L., <em>Thlaspi arvense</em> L., and <em>Fallopia convolvulus</em> (L.) A. Löve. At the pod development stage (73/74 BBCH), the pea crop was colonized by 24 weed species, including 3 perennial ones. At this stage the predominant species included: <em>Avena fatua</em> L., <em>Amaranthus retroflexus</em> L., <em>Papaver rhoeas</em> L., <em>Echinochloa crus-galli</em> (L.) P.B., <em>Matricaria inodora</em> L., and <em>Galeopsis tetrahit</em> L.

Performance Enhancement of Electrical Distribution Systems with Multiple Distributed Generation Sources

The recent trends in electrical power distribution system operationand management are aimed at improving system conditions in order torender good service to the customer. Reforms in the distribution sectorhave given major scope for employment of distributed generation (DG)resources which will boost system performance. This article proposesa heuristic technique for allocation of multiple distribution generationsources in a distribution system. The allocation is determined based onoverall improvement in network performance parameters like reductionin system losses, improvement in voltage stability, improvement in volt-age profile. The hybrid of Genetic Algorithm with the proposed NetworkPerformance Enhancement Index (NPEI) along with the heuristic rulesfacilitates determination of feasible location for insertion of DG sources.A priority list is prepared with decreasing values of NPEI so that thedesigner can select most feasible locations. The developed approach istested with different test systems to ascertain its effectiveness.

Quasi-Periodic Solutions and Stability for a Weakly Damped Nonlinear Quasi-Periodic Mathieu Equation

Quasi-Periodic (QP) solutions are investigated for a weakly dampednonlinear QP Mathieu equation. A double parametric primary resonance(1:2, 1:2) is considered. To approximate QP solutions, a double multiple-scales method is applied to transform the original QP oscillator to anautonomous system performing two successive reductions. In a first step,the multiple-scales method is applied to the original equation to derive afirst reduced differential amplitude-phase system having periodiccomponents. The stability of stationary solutions of this reduced systemis analyzed. In a second step, the multiple-scales method is applied again tothe first reduced system (RS) to obtain a second autonomous differentialamplitude-phase RS. The problem for approximating QP solutions of theoriginal system is then transformed to the study of stationary regimesof the induced autonomous second RS. Explicit analytical approximationsto QP solutions are obtained and comparisons to numerical integrationare provided.

On the use of the Boussinesq equations, the reduced system, and the primitive equations for the computation of geophysical flows

Motivated in part by the mathematical problems associated with the application of open boundary conditions to the hydrostatic primitive equations (PE), Browning et al. (1990, Dyn. Atmos. Oceans , 14: 303–332) proposed the use of the reduced system (RS) of equations to replace PE for oceanographic problems. The RS are essentially the Boussinesq equations (BO) with the non-hydrostatic terms in the vertical momentum equation multiplied by a constant δ 2 ⪢ 1. This artificially alters the physics (e.g. changing the intemal-inertial wave properties) to facilitate numerical integration, but the changes are assumed to have negligible effects on the dynamics of interest. We assess the accuracy and utility of the RS (following the guidelines for the choice of δ) by comparing numerical finite difference solutions of RS, PE and BO for initial-value problems involving three-dimensional instability of an ocean front and atmospheric frontal development in a two-dimensional Eady wave. Both explicit (BO, PE) and semi-implicit (BOSI, PESI) time-difference schemes are used for the Boussinesq and primitive equations. For RS, the same explicit scheme as for BO is used where δ ⪢ 1 allows larger time steps than with the other explicit models. It is found that relative to BO solutions, the errors for RS are small but increase rapidly and monotonically with increasing δ (over a range consistent with the guidelines) and are greater than the errors for the other models. The use of BOSI allows time steps at least as large as those for RS and results in smaller errors than RS. For these problems, BOSI is the preferable model to replace PE.