Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation (KDE) and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.     

Testability evaluation using prior information of multiple sources

Testability plays an important role in improving the readiness and decreasing the lifecycle cost of equipment. Testability demonstration and evaluation is of significance in measuring such testability indexes as fault detection rate（FDR） and fault isolation rate（FIR）, which is useful to the producer in mastering the testability level and improving the testability design, and helpful to the consumer in making purchase decisions. Aiming at the problems with a small sample of testability demonstration test data（TDTD） such as low evaluation confidence and inaccurate result, a testability evaluation method is proposed based on the prior information of multiple sources and Bayes theory. Firstly, the types of prior information are analyzed. The maximum entropy method is applied to the prior information with the mean and interval estimate forms on the testability index to obtain the parameters of prior probability density function（PDF）, and the empirical Bayesian method is used to get the parameters for the prior information with a success-fail form. Then, a parametrical data consistency check method is used to check the compatibility between all the sources of prior information and TDTD. For the prior information to pass the check, the prior credibility is calculated. A mixed prior distribution is formed based on the prior PDFs and the corresponding credibility. The Bayesian posterior distribution model is acquired with the mixed prior distribution and TDTD, based on which the point and interval estimates are calculated.Finally, examples of a flying control system are used to verify the proposed method. The results show that the proposed method is feasible and effective.     

SYNTHETIC STRESS LIFE TESTING OF MECHATRONIC PRODUCTS UNDER VARIABLE STRESS SPECTRUM

Mechatronic products usually endure the variable stress spectrum when they operate in certain operational condition and environmental condition, which obey the Weibull distribution. In accordance with the features of mechatronic product, this paper analyzes the failure mode, its corresponding sensitive stress and the design principles of life testing profiles. Based on the above analyses, this paper presents a synthetic stress life testing method based on the hybrid Weibull distribution and its statistical method under variable stress spectrum to evaluate the reliability and life indices of mechatronic products. Because the mechatronic products have many characteristics such as high price, long life and small testing samples, the synthetic stress life testing method under variable load spectrum can simulate the real various spectra, decrease the life testing time and reduce the testing samples. So it is effective to carry out the life testing to mechatronic products. The application results of hydraulic pumps indicate that this method can easily handle the experimental data under variable amplitude spectrum, obtain the high precision parameters point estimation and confidence interval estimation and reduce the testing cost greatly.     

Real-time fault detection method based on belief rule base for aircraft navigation system

Real-time and accurate fault detection is essential to enhance the aircraft navigation system’s reliability and safety. The existent detection methods based on analytical model draws back at simultaneously detecting gradual and sudden faults. On account of this reason, we propose an online detection solution based on non-analytical model. In this article, the navigation system fault detection model is established based on belief rule base (BRB), where the system measuring residual and its changing rate are used as the inputs of BRB model and the fault detection function as the output. To overcome the drawbacks of current parameter optimization algorithms for BRB and achieve online update, a parameter recursive estimation algorithm is presented for online BRB detection model based on expectation maximization (EM) algorithm. Furthermore, the proposed method is verified by navigation experiment. Experimental results show that the proposed method is able to effectively realize online parameter evaluation in navigation system fault detection model. The output of the detection model can track the fault state very well, and the faults can be diagnosed in real time and accurately. In addition, the detection ability, especially in the probability of false detection, is superior to offline optimization method, and thus the system reliability has great improvement.     

Use of land＇s cooperative object to estimate UAV＇s pose for autonomous landing

The research of unmanned aerial vehicles＇（UAVs＇）autonomy navigation and landing guidance with computer vision has important signifcance.However,because of the image blurring,the position of the cooperative points cannot be obtained accurately,and the pose estimation algorithms based on the feature points have low precision.In this research,the pose estimation algorithm of UAV is proposed based on feature lines of the cooperative object for autonomous landing.This method uses the actual shape of the cooperative-target on ground and the principle of vanishing line.Roll angle is calculated from the vanishing line.Yaw angle is calculated from the location of the target in the image.Finally,the remaining extrinsic parameters are calculated by the coordinates transformation.Experimental results show that the pose estimation algorithm based on line feature has a higher precision and is more reliable than the pose estimation algorithm based on points feature.Moreover,the error of the algorithm we proposed is small enough when the UAV is near to the landing strip,and it can meet the basic requirements of UAV＇s autonomous landing.     

A fast pulse phase estimation method for X-ray pulsar signals based on epoch folding

X-ray pulsar-based navigation (XPNAV) is an attractive method for autonomous deep-space navigation in the future. The pulse phase estimation is a key task in XPNAV and its accuracy directly determines the navigation accuracy. State-of-the-art pulse phase estimation techniques either suffer from poor estimation accuracy, or involve the maximization of generally non-convex object function, thus resulting in a large computational cost. In this paper, a fast pulse phase estimation method based on epoch folding is presented. The statistical properties of the observed profile obtained through epoch folding are developed. Based on this, we recognize the joint prob-ability distribution of the observed profile as the likelihood function and utilize a fast Fourier transform-based procedure to estimate the pulse phase. Computational complexity of the proposed estimator is analyzed as well. Experimental results show that the proposed estimator significantly outperforms the currently used cross-correlation (CC) and nonlinear least squares (NLS) estima-tors, while significantly reduces the computational complexity compared with NLS and maximum likelihood (ML) estimators.     

Variational Bayesian labeled multi-Bernoulli filter with unknown sensor noise statistics

It is difficult to build accurate model for measurement noise covariance in complex back-grounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian (VB) approximation is pro-posed. The variational approximation technique is introduced to the labeled multi-Bernoulli (LMB) filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density (VB-PHD) filter and the VB cardinality balanced multi-target multi-Bernoulli (VB-CBMeMBer) filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.     

FrFT-CSWSF:Estimating cross-range velocities of ground moving targets using multistatic synthetic aperture radar

Estimating cross-range velocity is a challenging task for space-borne synthetic aperture radar（SAR）, which is important for ground moving target indication（GMTI）. Because the velocity of a target is very small compared with that of the satellite, it is difficult to correctly estimate it using a conventional monostatic platform algorithm. To overcome this problem, a novel method employing multistatic SAR is presented in this letter. The proposed hybrid method, which is based on an extended space-time model（ESTIM） of the azimuth signal, has two steps： first, a set of finite impulse response（FIR） filter banks based on a fractional Fourier transform（FrFT） is used to separate multiple targets within a range gate; second, a cross-correlation spectrum weighted subspace fitting（CSWSF） algorithm is applied to each of the separated signals in order to estimate their respective parameters. As verified through computer simulation with the constellations of Cartwheel, Pendulum and Helix, this proposed time-frequency-subspace method effectively improves the estimation precision of the cross-range velocities of multiple targets.     

Joint TDOA,FDOA and differential Doppler rate estimation: Method and its performance analysis

Considering the estimation accuracy reduction of Frequency Difference of Arrival(FDOA) caused by relative Doppler companding, a joint Time Difference of Arrival(TDOA),FDOA and differential Doppler rate estimation method is proposed and its Cramer-Rao low bound is derived in this paper.Firstly, second-order ambiguity function is utilized to reduce the dimensionality and estimate initial TDOA and differential Doppler rate.Secondly, the TDOA estimation is updated and FDOA is obtained using cross ambiguity function, in which relative Doppler companding is compensated by the existing differential Doppler rate.Thirdly, differential Doppler rate estimation is updated using cross estimator.Theoretical analysis on estimation variance and Cramer-Rao low bound shows that the final estimation of TDOA, FDOA and differential Doppler rate performs well at both low and high signal–noise ratio, although the initial estimation accuracy of TDOA and differential Doppler rate is relatively poor under low signal–noise ratio conditions.Simulation results finally verify the theoretical analysis and show that the proposed method can overcome relative Doppler companding problem and performs well for all TDOA, FDOA and differential Doppler rate estimation.     

Remaining useful life prediction based on the Wiener process for an aviation axial piston pump

An aviation hydraulic axial piston pump’s degradation from comprehensive wear is a typical gradual failure model. Accurate wear prediction is difficult as random and uncertain char-acteristics must be factored into the estimation. The internal wear status of the axial piston pump is characterized by the return oil flow based on fault mechanism analysis of the main frictional pairs in the pump. The performance degradation model is described by the Wiener process to predict the remaining useful life (RUL) of the pump. Maximum likelihood estimation (MLE) is performed by utilizing the expectation maximization (EM) algorithm to estimate the initial parameters of the Wiener process while recursive estimation is conducted utilizing the Kalman filter method to estimate the drift coefficient of the Wiener process. The RUL of the pump is then calculated accord-ing to the performance degradation model based on the Wiener process. Experimental results indi-cate that the return oil flow is a suitable characteristic for reflecting the internal wear status of the axial piston pump, and thus the Wiener process-based method may effectively predicate the RUL of the pump.     

小样本下分位数函数的Bootstrap置信区间估计

航空产品试验一般为小样本试验,为了分析小样本情况下的试验数据,结合以概率加权矩为约束条件的最大熵法和求解置信区间及置信带的Bootstrap方法,提出了一种估计小样本试验件母体分位数函数置信区间的方法。最大熵法在矩约束下能够估计样本的密度函数,而以概率加权矩为约束条件的最大熵法能够针对小样本直接给出分位数的无偏估计,无需由密度函数积分得到累积分布函数,再进行转化得到分位数函数。Bootstrap方法求解置信区间具有不依赖于数据分布的优点,具有广泛的应用范围。     

最大熵分位值估计及其对偶型优化解法

针对经典最大熵分位值估计中拉格朗日系数计算目前存在高度非线性、计算结果精度不高或有时难以收敛等问题,提出了一种对偶型 逐次寻优的方法.基于拉格朗日对偶法,推导建立了含有拉格朗日系数优化函数的对偶表达式;在此基础上,基于样本的概率权重矩约束,提出了逐次寻优算法.针对几种常见的概率分布类型和一种较为复杂的概率分布类型,采用对偶型最大熵方法和经典最大熵方法对其概率累积函数和分位值进行计算对比分析表明:对偶型最大熵分位值估计不仅具有非线性程度低、形式简单,而且对偶型 逐次寻优的方法具有比较高的计算精度,优化迭代的收敛性好等特点.      

Reliability analysis based on a novel density estimation method for structures with correlations

Estimating the Probability Density Function (PDF) of the performance function is a direct way for structural reliability analysis,and the failure probability can be easily obtained by integration in the failure domain.However,efficiently estimating the PDF is still an urgent problem to be solved.The existing fractional moment based maximum entropy has provided a very advanced method for the PDF estimation,whereas the main shortcoming is that it limits the application of the reliability analysis method only to structures with independent inputs.While in fact,structures with correlated inputs always exist in engineering,thus this paper improves the maximum entropy method,and applies the Unscented Transformation (UT) technique to compute the frac tional moments of the performance function for structures with correlations,which is a very efficient moment estimation method for models with any inputs.The proposed method can precisely estimate the probability distributions of performance functions for structures with correlations.Besides,the number of function evaluations of the proposed method in reliability analysis,which is determined by UT,is really small.Several examples are employed to illustrate the accuracy and advantages of the proposed method.     

基于样本分位数的机载燃油泵故障状态特征提取及实验研究

机载燃油泵的健康状态关系着飞行任务的完成和飞行安全,对机载燃油泵的故障状态特征提取及诊断成为亟需解决的问题。通过对机载燃油实验系统的振动与压力信号进行综合分析,提出了一种基于样本分位数的故障状态特征提取方法。首先,根据样本分位数的渐近分布定理,讨论了样本分位数的统计特性,分析了故障状态与样本分位数的对应关系,从理论上保证了该方法的可行性,在实测数据统计分析的基础上,讨论了样本容量对样本分位数稳定性的影响;其次,根据样本分位数渐近分布定理计算各故障状态的置信区间,并与Bootstrap方法得到的置信区间进行对比,结果显示,依据样本分位数渐近分布定理得到的置信区间真实可靠,为在线故障诊断提供了依据;然后,以各故障状态下提取的样本分位数为特征向量构建贝叶斯判别函数,进行故障诊断;最后依据故障诊断的正确率对传感器进行优化,结果表明,同时安装振动传感器与压力传感器可以提高故障诊断的正确率,并且只安装1个压力传感器与1个特定方向的振动传感器即可对机载燃油泵的故障状态进行完全识别。为快速准确的在线判断机载燃油泵的状态提供了理论支撑,并且可以降低工程应用中机载燃油泵监测系统的体积、功耗及复杂性。     

最大熵准则识别材料疲劳寿命分布

疲劳寿命具有很大的分散性,是工程结构设计中必须考虑的因素。为了降低主观不确定性的引入,得到更合理的疲劳寿命分布类型,提出一种用于识别疲劳寿命概率分布类型的一般计算方法。该方法首先根据疲劳试验样本信息确定疲劳寿命的前四阶统计矩;基于统计矩信息,利用最大熵准则确定疲劳寿命的概率分布类型。在基于最大熵准则识别疲劳寿命分布时,利用Lagrange乘子法求解最大熵分布。采用已有的航空铝合金2024-T351板件疲劳裂纹扩展试验数据验证所提计算方法的合理性和有效性。结果表明:所提方法能够高效地识别材料疲劳寿命分布类型,并且不局限于单峰标准分布类型。     

导弹精度评估的非参数Bootstrap方法

基于目前导弹试验的实际状况,讨论了小子样情况下精度指标的置信区间估计的非参数Bootstrap方法。介绍了Bootstrap方法的基本概念,综合比较了非参数Bootstrap抽样和参数Bootstrap抽样的特点,对基于传统百分位法的改进区间估计方法进行了简要说明,包括迭代Bootstrap方法、Bootstrap-t方法及纠偏百分位方法;最后,通过大量仿真计算初步分析了各种非参数Bootstrap区间估计方法的性能和适用范围,并给出了若干建议。     

Evaluation of aileron actuator reliability with censored data

For the purpose of enhancing reliability of aileron of Airbus new-generation A350 XWB,an evaluation of aileron reliability on the basis of maintenance data is presented in this paper.Practical maintenance data contains large number of censoring samples, information uncertainty of which makes it hard to evaluate reliability of aileron actuator.Considering that true lifetime of censoring sample has identical distribution with complete sample, if censoring sample is transformed into complete sample, conversion frequency of censoring sample can be estimated according to frequency of complete sample.On the one hand, standard life table estimation and product limit method are improved on the basis of such conversion frequency, enabling accurate estimation of various censoring samples.On the other hand, by taking such frequency as one of the weight factors and integrating variance of order statistics under standard distribution, weighted least square estimation is formed for accurately estimating various censoring samples.Large amounts of experiments and simulations show that reliabilities of improved life table and improved product limit method are closer to the true value and more conservative; moreover, weighted least square estimate(WLSE), with conversion frequency of censoring sample and variances of order statistics as the weights, can still estimate accurately with high proportion of censored data in samples.Algorithm in this paper has good effect and can accurately estimate the reliability of aileron actuator even with small sample and high censoring rate.This research has certain significance in theory and engineering practice.     

飞机整体驱动发电机可靠性与维修策略探究

针对飞机整体驱动发电机可靠性分析手段缺乏、故障样本小且维修策略相对保守的问题,提出了以历史故障数据为驱动的贝叶斯和马尔可夫链融合的可靠性分析方法。首先,利用蒙特卡洛方法对故障数据预处理以增大样本空间,并通过最大信息熵法求解飞机整体驱动发电机的先验分布;其次,利用马尔可夫链方法对复杂后验分布进行解算;最后,以可靠性为中心给出飞机IDG的维修建议。经过数值仿真软件计算后得IDG的累计失效函数参数估计误差分别为0.121 3和0.001 3,误差较小。仿真结果表明,提出的可靠性分析方法适用于小样本空间的飞机IDG可靠性分析,并根据结果给出了维修建议。     

基于EKF的小型涵道式无人机航姿系统算法研究

针对小型涵道式无人机,设计了一种基于扩展Kalman滤波的航姿估计算法。采用四元数作为状态变量,利用陀螺仪的输出构成状态方程,通过加速度计与磁阻传感器构造观测方程来进行扩展Kalman滤波解算。相对于通常的航姿估计算法,这种算法减少了运算量,更适合于基于嵌入式微处理器的航姿估计。实验结果表明这种算法有效的抑制了航姿系统的各种噪声与干扰,同时保证了姿态输出的精度与实时性,可以为小型无人机提供准确的航姿信息。