Failure-Informed Adaptive Sampling for PINNs,Part II:Combining with Re-sampling and Subset Simulation

This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks(PINNs).In our previous work(SIAM J.Sci.Comput.45:A1971–A1994),we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator,where the truncated Gaussian model has been adopted for estimating the indicator.Here,we present two extensions of that work.The first extension consists in combining with a re-sampling technique,so that the new algorithm can maintain a constant training size.This is achieved through a cosine-annealing,which gradually transforms the sampling of collocation points from uniform to adaptive via the training progress.The second extension is to present the subset simulation(SS)algorithm as the posterior model(instead of the truncated Gaussian model)for estimating the error indicator,which can more effectively estimate the failure probability and generate new effective training points in the failure region.We investigate the performance of the new approach using several challenging problems,and numerical experiments demonstrate a significant improvement over the original algorithm.

Multiple model PHD filter for tracking sharply maneuvering targets using recursive RANSAC based adaptive birth estimation

An algorithm to track multiple sharply maneuvering targets without prior knowledge about new target birth is proposed. These targets are capable of achieving sharp maneuvers within a short period of time, such as drones and agile missiles.The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems. However, the standard PHD filter operates on the single dynamic model and requires prior information about target birth distribution, which leads to many limitations in terms of practical applications. In this paper,we introduce a nonzero mean, white noise turn rate dynamic model and generalize jump Markov systems to multitarget case to accommodate sharply maneuvering dynamics. Moreover, to adaptively estimate newborn targets’information, a measurement-driven method based on the recursive random sampling consensus (RANSAC) algorithm is proposed. Simulation results demonstrate that the proposed method achieves significant improvement in tracking multiple sharply maneuvering targets with adaptive birth estimation.

Adaptive Linear Filtering Design with Minimum Symbol Error Probability Criterion

Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate （MSER） criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.

Variable step-size affine projection algorithm based on global speech absence probability for adaptive feedback cancellation

A novel approach is proposed for improving adaptive feedback cancellation using a variable step-size affine projection algorithm(VSS-APA) based on global speech absence probability(GSAP).The variable step-size of the proposed VSS-APA is adjusted according to the GSAP of the current frame.The weight vector of the adaptive filter is updated by the probability of the speech absence.The performance measure of acoustic feedback cancellation is evaluated using normalized misalignment.Experimental results demonstrate that the proposed approach has better performance than the normalized least mean square(NLMS) and the constant step-size affine projection algorithms.

Fuzzy adaptive genetic algorithm based on auto-regulating fuzzy rules

There are defects such as the low convergence rate and premature phenomenon on the performance of simple genetic algorithms （SGA） as the values of crossover probability （Pc） and mutation probability （Pro） are fixed. To solve the problems, the fuzzy control method and the genetic algorithms were systematically integrated to create a kind of improved fuzzy adaptive genetic algorithm （FAGA） based on the auto-regulating fuzzy rules （ARFR-FAGA）. By using the fuzzy control method, the values of Pc and Pm were adjusted according to the evolutional process, and the fuzzy rules were optimized by another genetic algorithm. Experimental results in solving the function optimization problems demonstrate that the convergence rate and solution quality of ARFR-FAGA exceed those of SGA, AGA and fuzzy adaptive genetic algorithm based on expertise （EFAGA） obviously in the global search.

Adaptive Object Tracking Discriminate Model for Multi-Camera Panorama Surveillance in Airport Apron

Autonomous intelligence plays a significant role in aviation security.Since most aviation accidents occur in the take-off and landing stage,accurate tracking of moving object in airport apron will be a vital approach to ensure the operation of the aircraft safely.In this study,an adaptive object tracking method based on a discriminant is proposed in multi-camera panorama surveillance of large-scale airport apron.Firstly,based on channels of color histogram,the pre-estimated object probability map is employed to reduce searching computation,and the optimization of the disturbance suppression options can make good resistance to similar areas around the object.Then the object score of probability map is obtained by the sliding window,and the candidate window with the highest probability map score is selected as the new object center.Thirdly,according to the new object location,the probability map is updated,the scale estimation function is adjusted to the size of real object.From qualitative and quantitative analysis,the comparison experiments are verified in representative video sequences,and our approach outperforms typical methods,such as distraction-aware online tracking,mean shift,variance ratio,and adaptive colour attributes.

An adaptive genetic algorithm for solving bilevel linear programming problem

Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.

Pre-stack seismic waveform inversion based on adaptive genetic algorithm

Pre-stack waveform inversion, by inverting seismic information, can estimate subsurface elastic properties for reservoir characterization, thus effectively guiding exploration. In recent years, nonlinear inversion methods, such as standard genetic algorithm, have been extensively adopted in seismic inversion due to its simplicity, versatility, and robustness. However, standard genetic algorithms have some shortcomings, such as slow convergence rate and easiness to fall into local optimum. In order to overcome these problems, the authors present a new adaptive genetic algorithm for seismic inversion, in which the selection adopts regional equilibrium and elite retention strategies are adopted, and adaptive operators are used in the crossover and mutation to implement local search. After applying this method to pre-stack seismic data, it is found that higher quality inversion results can be achieved within reasonable running time.

Fuzzy stochastic damage mechanics(FSDM) based on fuzzy auto-adaptive control theory

In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

一种基于模型概率单调性变化的自适应IMM-UKF改进算法

针对现有交互式多模型(IMM)算法模型间切换迟滞和转换速率慢的缺点,提出一种基于模型概率单调性变化的自适应交互式多模型无迹卡尔曼滤波改进算法(mIMM-UKF)。该算法利用后验信息模型概率的单调性,对马尔可夫转移概率矩阵及模型估计概率进行二次修正,加快了匹配模型的切换速度及转换速率。仿真结果表明,与现有算法相比,该算法通过快速切换匹配模型,有效提高了水下目标跟踪精度。

基于改进自适应IMM算法的高速列车组合定位

针对列车高精度定位问题,该文提出基于改进自适应交互多模型(IMM)的高速列车高精度组合定位方法。首先,根据列车定位需求和各传感器特点,设计了卫星接收器、轮轴测速传感器、测速雷达以及单轴陀螺仪4种传感器的组合定位方案。然后,针对IMM融合滤波算法因先验信息不准导致固定参数设置不当的问题,引入Sage-Husa自适应滤波和转移概率矩阵(TPM)自适应更新集成为自适应IMM算法。针对多模型切换的滞后问题,利用子模型似然函数值能快速反映模型变化趋势的特点,将似然函数值设为判定标志,并引入判定窗对TPM矩阵元素进行修正,有效提升了模型的切换速度。最后,基于改进自适应IMM算法对4种传感器定位信息进行融合滤波,实现高速列车的高精度组合定位。仿真结果表明:改进后的算法相比其他自适应IMM算法提升定位精度1.6%~14.7%,并且能通过提高模型间切换速度来有效降低位置误差峰值,同时具备较好的抗噪性能。

基于Beta分布的目标搜索概率自适应更新策略及其应用

针对不确定先验信息条件下的目标搜索问题,考虑传感器探测概率和虚警概率,设计了基于Beta分布的目标搜索概率自适应更新策略。首先,通过Beta分布建立了不确定先验环境的概率地图,并提出自适应目标搜索概率更新策略,使得无人机能够根据概率信息图动态更新检测次数;其次,在概率更新策略中引入了拒绝概率修正因子,根据地图概率差动态调整概率变化量,避免了搜索任务中可能存在的误检漏检问题;最后,通过数值仿真实验,验证了提出的目标搜索自适应更新策略可在不影响搜索效率的前提下,有效减小无人机的错误检测概率。

基于自适应无迹卡尔曼的目标跟踪算法研究

基于提高装甲车主动防护系统目标跟踪精度和收敛速度、提升目标拦截概率的目的,该文引入了噪声自适应系数对SUKFR(比例对称采样的UKFR)算法进行优化。通过Matlab软件使用Monte Carlo(蒙特卡罗)方法对UKFR(径向速度的无迹卡尔曼)、SUKFR和ASUKFR(自适应系数的SUKFR)算法的滤波性能进行仿真试验,结果表明,采用ASUKFR算法的主动防护系统不仅目标跟踪精度更高、收敛速度更快,而且拦截概率达到了90%以上,为装甲车主动防护目标跟踪领域提供了一种新思路。

多项式变异和自适应权重优化的阿奎拉鹰算法

针对基本阿奎拉鹰算法存在收敛精度低、易陷入局部最优的问题,通过在全局搜索阶段引入多项式变异扰动策略,在局部开发阶段引入自适应权重优化策略,改进了阿奎拉鹰算法的局部探索能力,并且引入了Tent混沌映射初始化种群,增加种群多样性,引入动态转换概率策略来平衡全局探索和局部开发的比重,故提出多项式变异和自适应权重优化的阿奎拉鹰算法。采用基本阿奎拉鹰算法、哈里斯鹰算法、灰狼算法、鲸鱼算法、海鸥算法做对比,9个基准测试函数和2个工程优化问题对改进后的算法进行寻优性能验证,结果表明:改进后的算法在多数测试函数上取得较好的寻优效果,在工程优化问题中,效果优于多数对比算法。证明了改进后的算法具有更快的收敛速度和精度,并在工程应用中取得较好效果。

一种基于AK-MCS-K的失效概率函数估计方法

针对可靠性优化设计中失效概率函数求解复杂、计算量大等问题,提出一种求解失效概率函数的高效方法。所提方法的基本思路是利用自主学习Kriging方法构造输入变量全空间在失效边界处的局部代理模型,进而通过该局部代理模型结合Monte Carlo模拟法计算在指定分布参数样本下结构的失效概率,然后基于Kriging方法拟合分布参数样本点与对应结构失效概率之间的函数关系,最终建立用Kriging模型表达的失效概率函数的隐式函数。为了检验所提方法的精度和效率,给出了两个算例,对比了所提方法与已有的求解失效概率函数方法的计算结果。算例结果表明,所提方法适用于求解复杂的功能函数问题,并在满足精度要求的基础上显著降低了计算量。

基于防水失效概率的混凝土屋面工程适应性技术

我国混凝土屋面工程防水领域具备丰富的经验,目前在分类、量化领域不断拓展,已开始探索概率分析法。采用基于蒙特卡罗方法的混凝土屋面防水失效概率计算程式,可对应用场景、构成、构造进行组合,基于统一的计算基准,对量化结果进行对比、分析,可对屋面构造、防水层道数、材料的气候适应性、材料类型等进行定量分析,得出相对客观的结论。

时变可靠性分析的高效近似最大可能轨迹法

现有的时变可靠性分析方法在处理飞行器复杂时变可靠性分析问题时,具有求解效率过低的缺点。在基于近似最大可能轨迹的时变可靠性分析方法的基础上,根据时间离散所得串联系统瞬时可靠度最小的组件决定整个系统可靠度的特点,在最大可能轨迹自适应建模过程中同时考虑轨迹模型的预测误差和预估值增加样本,提出时变可靠性分析的高效近似最大可能轨迹法;采用解析算例验证最大可能轨迹法的有效性,并将该可靠性分析方法应用于水动力涡轮叶片和航天飞机机翼的时变可靠性分析。结果表明:在精度相近的情况下,所提方法对极限状态函数调用次数不高于基于时间离散的可靠性分析方法的3%。

基于改进ATPM-IMM算法的外辐射源雷达机动目标跟踪

针对外辐射源雷达进行机动目标跟踪时,现有的自适应交互式多模型(AIMM)算法难以达到高精确度跟踪的问题,提出一种基于改进的自适应转移概率交互式多模型(ATPM-IMM)的机动目标跟踪算法。该算法在ATPM-IMM算法的基础上增加了自适应控制窗,对转移概率矩阵进行再次修正,从而可根据目标的机动情况自适应切换机动模型,提高真实模型的匹配概率。仿真和实测数据结果表明,所提算法可有效提高外辐射源雷达进行机动目标跟踪的精确度。

基于平衡分布自适应迁移学习的多风电机组运行状态监测方法

风电机组状态的准确监测对风电机组安全稳定运行和经济效益提升至关重要。但是,受不同风电机组运行数据分布差异的影响,现有状态监测方法在多风电机组应用场景下存在精度和效率难以兼顾的问题,而平衡分布自适应迁移学习(BDA)可以拉近数据距离,同化数据分布。因此,文章提出了一种基于BDA的多风电机组状态监测方法。首先,基于Copula熵的互信息法挖掘风电机组运行状态关键影响参量;然后,构建基于门控循环单元模型(GRU)和序贯概率比检验(SPRT)方法的单风电机组状态监测模型;最后,构建基于BDA的多风电机组运行数据分布同化模型,并用于多风电机组运行状态监测。算例结果表明,所提方法可以有效节省建模成本和计算成本,能够在保障多风电机组运行状态监测精度的前提下,显著提升监测效率。

采用统计线性回归的改进ATBI-GMPHD滤波

提出一种改进的自适应新生目标GM-PHD算法。该算法以存活目标的量测更新权值构建“似然函数”,通过该函数确定量测来源并对新生目标权值做重分配,有效解决了归一化失衡问题。在量测方程高度非线性情况下,引入统计线性回归方法对量测方程进行线性化近似,求解新生目标预测均值和协方差。仿真结果表明,在新生目标信息先验缺失时,改进后的算法具有良好的跟踪精度和较低的计算量。