Moments of conjugacy classes of binary words

For each nonempty binary word w=c₁c₂c_q, where c_i{0,1}, the nonnegative integer ∑_i=1^q (q+1−i)c_i is called the moment of w and is denoted by M(w). Let [w] denote the conjugacy class of w. Define M([w])={M(u): u[w]}, N(w)={M(u)−M(w): u[w]} and δ(w)=max{M(u)−M(v): u,v[w]}. Using these objects, we obtain equivalent conditions for a binary word to be an -word (respectively, a power of an -word). For instance, we prove that the following statements are equivalent for any binary word w with |w|2: (a) w is an -word, (b) δ(w)=|w|−1, (c) w is a cyclic balanced primitive word, (d) M([w]) is a set of |w| consecutive positive integers, (e) N(w) is a set of |w| consecutive integers and 0N(w), (f) w is primitive and [w]St.     

高精度转动惯量测量仪分析与设计

文中讨论的扭振法转动惯量测量仪,不需要测量幅值,根据振荡周期就能给出高精度的转动惯量计算结果。介绍了它的工作原理,并且详细分析了测量系统的误差,并给出了相邻周期误差的估计公式。在此基础上提出了两种数据处理方法,方法Ⅰ针对小阻尼比采用对偶时间序列误差相消,直接计算;方法Ⅱ通过计算阻尼比,把阻尼振荡周期转化为无阻尼自振周期进行转动惯量计算,放松了对阻尼比的要求,提高了计算精度。数学仿真结果表明,两种方法对测量误差都不敏感,且均可满足测量误差<±0.5%的要求。     

Optimum design of mounting components of a mass property measurement system

Measurement of inertia properties of aerospace vehicle and submarine are vital to meet the intended motion objectives. The Moment of Inertia (MOI) is calculated by measuring the frequency of free torsional oscillation of the object mounted on a nearly friction less air bearing. For getting accurate measurement and to nullify the effect of undesired vibrations, the stiffness of the different components of the mounting and fixture (torsion rod, flexure) should be maintained appropriately. The optimum design of torsion rod and flexure is based on ensuring desired natural frequencies in different modes. Initiating with an analytical approach, the actual dimensions of the components are determined based on natural frequencies obtained by finite element analysis of the components. Simulated results are verified with experimental results.     

Effect of moment of inertia on elastic stability of rectangular webs for thin-walled beams under a transverse load

So far, the equations for buckling capacity of web panels focus on thin-walled beams with very strong flanges. In this paper, elastic buckling behavior of web panels of thin-walled beams with weak flanges is further studied, aiming at a buckling coefficient formula unifying the effect of both weak and strong flanges. A new parameter, the flange-to-web ratio of moment of inertia, is proposed to characterize the effect of flanges. Then, a semi-analytical method is applied to investigate the buckling behavior of simply supported web panels, in two cases, inclusive or exclusive of effect of the moment of inertia of flanges. It is revealed that elastic buckling load, in particular, the buckling coefficient of web panel is a function of two key parameters, web aspect ratio and flange-to-web ratio of moment of inertia. Meanwhile, a finite element analysis (FEA) model allowing for the sensitivity of boundary conditions is validated by comparing with the semi-analytical solution to the case exclusive of effect of the moments of inertia of flanges. Next, numerical results are utilized to illustrate the influence of the previous parameters, which verify the increase of buckling coefficient with flange-to-web ratio of moment of inertia or the decrease of buckling coefficient with web aspect ratio. Besides, it also verifies that for the same flange-to-web ratio of moment of inertia, the buckling behavior of square web panels is closer to the uniform shear buckling than other rectangular web panels. Finally, an accurate design formula is proposed to calculate buckling coefficient of web panel.     

Effects of seismic and aerodynamic load interaction on structural dynamic response of multi-megawatt utility scale horizontal axis wind turbines

Horizontal axis wind turbines can experience significant time varying aerodynamic loads that has the potential to cause adverse effects on structural, mechanical, and power production. The progress in the wind industry has caused the construction of wind farms in areas prone to high seismic activity. With the advances in computational tools, a more realistic representation of the behavior of wind turbines should be performed. One of the simulation platforms was developed using the 5 MW NREL utility scale reference turbine model. The performed simulations will be used to evaluate the effects of aerodynamic and seismic load coupling on the power generation and structural dynamics behavior of this structure. Different turbine operational scenarios such as (i) normal operational condition with no earthquake, (ii) idling condition with the presence of seismic loads, (iii) normal operational condition with earthquake, and (iv) earthquake-induced emergency shutdown will be simulated with various loading conditions to show the differences in generated power and dynamic response. The results of this paper provide formulations for calculating generated power and design deriving parameters by considering different intensity measures. Moreover, the effects of aerodynamic damping and pitch control system are presented to shows reduction in the resulting design demand loads.     

Moment adjusted imputation for multivariate measurement error data with applications to logistic regression

In clinical studies, covariates are often measured with error due to biological fluctuations, device error and other sources. Summary statistics and regression models that are based on mis-measured data will differ from the corresponding analysis based on the “true” covariate. Statistical analysis can be adjusted for measurement error, however various methods exhibit a tradeoff between convenience and performance. Moment Adjusted Imputation (MAI) is a measurement error in a scalar latent variable that is easy to implement and performs well in a variety of settings. In practice, multiple covariates may be similarly influenced by biological fluctuations, inducing correlated, multivariate measurement error. The extension of MAI to the setting of multivariate latent variables involves unique challenges. Alternative strategies are described, including a computationally feasible option that is shown to perform well.     

Comparative analysis of discretization methods in Bayesian networks

A key step in implementing Bayesian networks (BNs) is the discretization of continuous variables. There are several mathematical methods for constructing discrete distributions, the implications of which on the resulting model has not been discussed in literature. Discretization invariably results in loss of information, and both the discretization method and the number of intervals determines the level of such loss. We designed an experiment to evaluate the impact of commonly used discretization methods and number of intervals on the developed BNs. The conditional probability tables, model predictions, and management recommendations were compared and shown to be different among models. However, none of the models did uniformly well in all comparison criteria. As we cannot justify using one discretization method against others, we recommend caution when discretization is used, and a verification process that includes evaluating alternative methods to ensure that the conclusions are not an artifact of the discretization approach.     

基于IGCT的新型固态桥式短路故障限流器

提出将带旁路电感的桥式短路故障限流器中的半控开关器件——可控硅,用大功率自关断器件——集成门极换流晶闸管（IGCT）代替,从而将整流桥的失控时间从半个周期缩短到电流信号检测时延,从而可以有效减小直流限流电感的电感量,将占据限流器体积、重量、成本主要部分的直流限流电感量缩小5／6以上。研究了在该特定电路条件下的基于IGCT的有源逆变控制方法,可以保证在采用IGCT后,桥路转入逆变工作方式和从限流器中退出时均不引起电感电流通路的阻断,因而不引起操作过电压。直流限流电感的电感量减小,有利于提高限流器动态特性,缩减由于充磁而导致波形畸变的时间。详细介绍了基于IGCT的短路故障限流器的控制策略,并进行了仿真和实验研究,结果证明了所提出的故障限流器及其控制策略的有效性和实用性。     

涤纶熔体增压泵过载保护失效分析

对涤纶熔体纺丝的增压泵易发生故障损坏,泵轴折断,扭矩限制器连接轴折断,摩擦副打滑等过载保护失效的原因进行分析,经过理论计算,得出扭矩限制器的预紧力矩值。结果表明,扭矩限制器的预紧力矩的确定参照其理论计算值,可有效地保证熔体增压泵安全,保证摩擦副在正常负载下打滑时而正常运转。