利用多项式拟合测量飞机油箱油量

飞机飞行中,测量剩余油量是关乎飞行安全的重要工作。以往采用的查表法存在存储数据量过大的问题,而插值法的计算又过于复杂,为此,提出了一种基于多项式数据拟合的油箱剩余油量测量方法,该方法通过存储多项式系数减少数据存储量,通过将多元插值计算改为多项式计算降低运算量。实验中,首先通过地面实验数据拟合获取多项式参数,再利用飞机飞行中获取的测量数据进行计算,所得结果与油箱内剩余油量的实际测量结果相比较,测量误差满足使用要求。通过理论和实验分析,在多项式拟合的阶数选择上明确了使用三阶多项式的合理性。该方法有较好的实用性,已在实践中应用。     

融合插值点优化的多项式结构宽带波束形成器设计方法

多项式结构设计方法是主瓣指向可调宽带波束形成器设计的一类重要方法。多项式结构的阶数是有限的,导致主瓣实际指向与期望指向之间存在偏差,因而影响了波束形成器的指向性指数。针对这一问题,该文提出了一种基于插值点优化的多项式结构宽带波束形成器设计方法。首先,引入多项式结构插值点处阵列响应的空间导数约束,以减小主瓣指向偏差;进而利用粒子群优化算法对多项式结构中的插值点进行优化,以充分利用插值点位置提供的自由度进一步提升多项式结构宽带波束形成器的性能。优化设计结果表明,与现有设计方法相比,该文提出的方法不仅降低了主瓣的指向偏差,同时也提高了指向性指数,有效改善了多项式结构宽带波束形成器的性能。     

多项式偏最小二乘法对非线性体系红外谱图的分析

文章利用了一种非线性模型多项式偏最小二乘法(PPLS),结合傅里叶变换红外光谱遥感技术,对大气中的五组分混合体系进行了同时分析。并与偏最小二乘法(PLS)得到的结果进行了比较,PPLS显示出较好的处理非线性数据的能力。尤其是对混合物中的苯和氯仿的预测,均方根预测误差(RMSEP)分别是0.043和0.087,用PLS预测相应的RMSEP为0.402和0.842。PPLS的这一预测精度,可以满足遥感傅里叶变换红外光谱对大气中有毒气体的实时、在线监测的需要。同时PPLS可以用较少的潜变量对变量进行解释,显示出PPLS模型的稳健性和简单化。     

On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming

This paper investigates the capabilities of several non-quadratic polynomial yield functions to model the plastic anisotropy of orthotropic sheet metal (plane stress). Fourth, sixth and eighth-order homogeneous polynomials are considered. For the computation of the coefficients of the fourth-order polynomial an improved set of analytic formulas is proposed. For sixth and eighth-order polynomials the identification uses optimization. Simple constraints on the optimization process are shown to lead to real-valued convex functions. A general method to extend the above plane stress criteria to full 3D stress states is also suggested. Besides their simplicity in formulation, it is found that polynomial yield functions are capable to model a wide range of anisotropic plastic properties (e.g., the Numisheet’93 mild steel, AA2008-T4, AA2090-T3). The yield functions have then been implemented into a commercial finite element code as constitutive subroutines. The deep drawing of square (Numisheet’93) and cylindrical (AA2090-T3) cups have been simulated. In both cases excellent agreement with experimental data is obtained. In particular, it is shown that non-quadratic polynomial yield functions can simulate cylindrical cups with six or eight ears. We close with a discussion on earing and further examples.     

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-butbounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arithmetic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation.To further reduce the overestimation caused by the "wrapping effect" of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.