An algorithm for generating optimal constrained one-stage homogenous strip cutting patterns

The cutting and stamping process is often used to divide a stock plate into items to make products. It includes two phases. A guillotine machine cuts the plate orthogonally into homogenous strips at the cutting phase; then a stamping press stamps out the items from the strips at the stamping phase. A homogenous strip contains items of the same type. A one-stage homogenous strip cutting pattern (OSHSCP) contains parallel homogenous strips of the same length. The OSHSCP is useful because it can be used independently or as elements to compose other types of cutting patterns. This article presents a dynamic programming algorithm for generating the optimal constrained OSHSCP, where the maximum demand for each item type is specified and the objective is to maximize the total value of items included in the pattern. The computational results indicate that the computation time is reasonable.     

A simple criterion to design optimal non-pharmaceutical interventions for mitigating epidemic outbreaks

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and societal costs. Here, we derive a simple and mathematically rigorous criterion for designing optimal transitory non-pharmaceutical interventions for mitigating epidemic outbreaks. We find that reducing the reproduction number below one is sufficient but not necessary. Instead, our criterion prescribes the required reduction in the reproduction number according to the desired maximum of disease prevalence and the maximum decrease of disease transmission that the interventions can achieve. We study the implications of our theoretical results for designing non-pharmaceutical interventions in 16 cities and regions during the COVID-19 pandemic. In particular, we estimate the minimal reduction of each region’s contact rate necessary to control the epidemic optimally. Our results contribute to establishing a rigorous methodology to design optimal non-pharmaceutical intervention policies for mitigating epidemic outbreaks.     

Proposal of bond criterion for hot roll bonding and its application

The aim of this work was to develop a bond criterion for laminated composites prepared by hot rolling. 7075 Al/AZ31B Mg/7075 Al laminated composites were fabricated by hot rolling at different reduction ratios and temperatures, and the hot rolling process was also simulated by finite element methods (FEM). The FEM results show that two stages existed for an option position of the interface during hot rolling, viz. the bonded interface forming period and the post-bonded period. Bonded interface would be damaged during the latter due to second tensile stress and tear stress (due to the sticking friction between the Al plates and the rollers during the rolling). A bond criterion for laminated composites fabricated by hot rolling was proposed, which includes a strain threshold and a critical bonding strength. The predicted bond results of the 7075 Al/AZ31B Mg/7075 Al laminated composite fabricated by hot rolling from the proposed bond criterion agreed with the experimental data.     

Parametric optimal control of uncertain systems under an optimistic value criterion

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.     

Do people choose an optimal response criterion in an inspection task?

In order to provide models of human behavior useful in selecting tradeoffs in function allocation of inspection systems, an experiment was performed to test five optimization models of the decision component of inspection tasks. Ten subjects examined numbers printed on computer-generated Integrated Circuit (IC) chips to decide whether to accept or reject the ICs under different conditions of defective rate and payoff. The best fitting model was a form of the Expected Utility model, modified to account for the sluggish beta phenomenon. There was a significant relationship between subjects classified as Accurate on the Matching Familiar Figures Test and subjects best fitted by the modified Expected Utility model.     

A method of generating an optimal batch monitoring plan by random sequential sampling

A method is given for generating the best plan for inspecting a batch of components on the criterion for minimum mean producer’s risk. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 12–15, October, 2007.     

动力失稳的拟静力刚度准则与能量判别准则

以可模拟非线性保守结构体系的一个计算模型为例,重点分析、对比了判别结构动力稳定性的拟静力刚度准则和能量判别准则。拟静力刚度准则依靠切线刚度非正定判定结构发生动力失稳可能导致误判。能量判别准则适用于具有屈曲后不稳定平衡路径的结构,利用屈曲后不稳定平衡路径上鞍点处的总势能作为动力失稳临界能量,结构总能量超越临界能量则判定为动力失稳。振动极值位移随荷载变化的曲线可以作为一种动力平衡路径,在接近临界荷载时,荷载的微小增量会导致结构振动极大位移显著增大,最终在临界点发生跃越失稳。     

Estimates for Polynomial Roots

Given a complex polynomial, we obtain lower bounds for the moduli of the roots outside the unit circle. Our main tool is the method of Dandelin–Graeffe, which can be used directly for polynomials with distinct absolute values of the roots. In the general case the arguments of the powers of the roots must be controlled, and we achieve this by two methods: a theorem of Dirichlet, and an argument using linear recurrent sequences. Received: July 11, 2000; revised version: August 6, 2001     

二恶英发生源的建立及其性能分析

针对如何在臭氧紫外光-滑动弧系统中建立稳定的二恶英发生源用于降解二恶英的实验系统.该发生源以医疗垃圾飞灰为对象,通过加热飞灰本身和飞灰索提液的方式使其中的二恶英在一段时间内连续挥发.结果表明,290℃时在飞灰发生源系统中,二恶英初始阶段挥发速率极快,后续的挥发速率急剧减小并趋于稳定,总挥发量仅为总量的10%,且难以再提高.相比而言索提液发生源系统挥发出的二恶英更多更稳定,但其挥发量受温度和注射速度的影响较大:当注射速度为1μL.min-1时,在300℃、400℃、500℃三个不同温度段分别为2.78%、7.88%和9.56%;当温度为500℃,注射速度为0.2 mL.min-1时,其挥发率提高到48.7%.研究还发现,注射针头与管壁的残余量是影响挥发效率的两个重要因素,当温度为500℃,载气为1000 mL.min-1,注射速度为0.2 mL.min-1时,连续进样1 h后,两者的残余量分别占注射总量的40.0%和16.7%.     

基于ICM准则法的结构动力学边界拓扑优化设计

针对结构动力学边界条件,进行了基于固有频率和振型特定要求的结构动力学边界条件优化设计研究。建立了以结构振型差的范数为目标函数,结构固有频率为约束条件的动力学边界条件设计准则。根据实际结构在设计的约束条件范围内可能变更的方案,通过不断修改设计参数,确定满足结构动力学要求的方案。采用ICM准则法对刚架边界的机翼骨架模型进行了动力学边界的拓扑优化设计,数值模拟算例验证了该方法用于动力学优化设计的可行性。     

The integrability criterion in finite elastoplasticity and its constitutive implications

Summary In traditional Eulerian rate formulation of finite elastoplasticity, an Eulerian rate equation of hypoelastic type is used as one of the basic constituents to relate the elastic part of the stretching to a stress rate. On account of the fact that the elastic-like behavior should be expected prior to yielding, the foregoing basic elastic rate equation should be exactly integrable to deliver a conventional hyperelastic stress-strain relation. Physically, it requires a consistent combination of hypoelasticity and hyperelasticity into a single Eulerian rate equation. Since this criterion is purely a physical consistency requirement and since the basic elastic rate equation involves no strain concept and allows for any stress rate in its own right, from a physical standpoint it may be of both interest and significance to know what consequences it will imply concerning the stress rate and the finite strain measure. By a simple, straightforward procedure we demonstrate in a general sense that both Hencky strain and the logarithmic rate emerge naturally as direct consequences of the foregoing criterion. This result may be regarded to reveal the physical essence behind Hencky strain and the logarithmic rate in connection with a basic physical consistency requirement in finite elastoplasticity. Constitutive implications are discussed in a few relevant respects concerning representative formulations of finite elastoplasticity.     

BoxStep methods for crew pairing problems

Crew pairing problems are often solved using column generation in a branch-and-price framework. The oscillation of dual points is the main reason which leads to instability in the standard implementation of this method. One device to deal with the problem is to use the trust-region idea to stabilize the path of dual points. Therefore, a so-called stabilized column generation with respect to control parameters is suggested to overcome this problem. In this paper we report about possible realizations of this principle and show that the performance of algorithms can be improved significantly. Three stabilizing methods are used to investigate good control parameters which contribute to the improved computation time in solving a set of crew pairing problems involving about 400 flights per week.     

Model for grain boundary sliding and its relevance to optimal structural superplasticity

Abstract

he conclusions reached based on a grain/interphase boundary sliding controlled flow model for optimal structural superplasticity are verified using experimental data from three aluminium alloy systems. Isostructural strain rate–stress relationships could be calculated very accurately using five experimentally determined, physically meaningful constants (three of which could also be calculated from theory; two fully and one partially). The true activation energy for the rate controlling boundary sliding process, the variations of the internal stress distribution arising from sliding, the stress function that is proportional to the measured isostructural isothermal strain rate, and the apparent viscosity, were calculated. It is suggested that the basic units of microscopic boundary sliding in the three aluminium alloys examined have a common structure.

MST/3077     

Failure criterion for laminated glass under impact loading and its application in finite element simulation

A failure criterion for laminated glass in case of impact is presented. The main idea of this criterion is that a critical energy threshold must be reached over a finite region before failure can occur. Afterwards crack initiation and growth is based on a local Rankine (maximum stress) criterion. The criterion was implemented in an explicit finite element solver. Different strategies for modeling laminated glass are also discussed.To calibrate the criterion and evaluate its accuracy, a wide range of experiments with plane and curved specimens of laminated glass were done. For all experiments finite element simulations were performed. The comparison between measured and simulated results shows that the criterion works very well.     

The criterion of optimal configuration of magnetic field in a thruster with closed electron drift

An integral criterion is suggested, which characterizes the configuration of magnetic field in a thruster with closed electron drift from the standpoint of efficiency of confinement of electrons in the ionization region. For the purpose of investigating the validity of the criterion, a thruster is developed with a new design of magnet system, which enables one to vary the structure of magnetic field in a wide range. The experimental investigation of the effect of magnetic field structure on the efficiency and specific impulse of plasma thruster revealed correlation between the results of application of the criterion and the parameters of efficiency of the thruster.     

A mechanism for pairing of RVB excitations

The fluctuations in the RVB order parameter over their meanfield values are considered in the BZA theory which mediate the interaction between the RVB excitations. The condition under which the effective interaction could be attractive and result in super-conductivity is investigated. The dependence of the transition temperature on the dopant concentration and the RVB order parameter is calculated.     

Polynomial chaos expansion for sensitivity analysis

In this paper, the computation of Sobol's sensitivity indices from the polynomial chaos expansion of a model output involving uncertain inputs is investigated. It is shown that when the model output is smooth with regards to the inputs, a spectral convergence of the computed sensitivity indices is achieved. However, even for smooth outputs the method is limited to a moderate number of inputs, say 10-20, as it becomes computationally too demanding to reach the convergence domain. Alternative methods (such as sampling strategies) are then more attractive. The method is also challenged when the output is non-smooth even when the number of inputs is limited.     

Minimal Homogeneous Bases for Polynomial Ideals

The minimal homogeneous basis is defined. It is shown that every minimal homogeneous basis of an ideal has the same number of elements. An algorithm for finding a minimal homogeneous basis is developed. The main idea is to modify the classical Buchbergers algorithm for finding a Gröbner basis so that a minimal homogeneous basis can be obtained as a subset of a Gröbner basis.     

An improved cuckoo search algorithm and its application in vibration fault diagnosis for a hydroelectric generating unit

This article presents an improved cuckoo search (ICS) algorithm based on the parametric adaptation mechanism and non-uniform mutation. In the ICS algorithm, the biased random walk operator is modified to take advantage of the neighbourhood information of the current solution, and then the control parameters of step size, discovery probability and scaling factor are directly integrated into the optimized problems. Meanwhile, the non-uniform mutation operation is used to adaptively tune the search step of the current optimal solution. To evaluate the feasibility and efficiency of the presented algorithm, three groups of benchmark test functions are employed to perform the validation analysis. Subsequently, to diagnose the vibration fault of a hydroelectric generating unit, a combinational model is built, which combines ICS with a back-propagation neural network (ICSBP). The experimental results indicate that ICS is competitive on the optimization problems, and the ICSBP approach can effectively improve the accuracy of vibration fault diagnosis for a hydroelectric generating unit.