An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Importance measure system of fuzzy and random input variables and its solution by point estimates

For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect from two aspects, i.e. its effect on the central distribution position and that on the fuzzy degree of the membership function of the output response. Taking the effects of the two kinds of input variables on the first moment and second one of the output response into account, the definitions of the importance measures of the input variables are given and their engineering significations are demonstrated. Combining with the advantages of the point estimates of Zhao and Ono, a solution of the proposed importance measures is provided. Several examples show that the proposed measure system is comprehensive and reasonable, and the proposed solution can improve computational efficiency considerably with acceptable precision.

Application of adaptive Kalman filter in rocket impact point estimation

In order to measure the parameters of flight rocket by using radar,rocket impact point was estimated accurately for rocket trajectory correction.The Kalman filter with adaptive filter gain matrix was adopted.According to the particle trajectory model,the adaptive Kalman filter trajectory model was constructed for removing and filtering the outliers of the parameters during a section of flight detected by three-dimensional data radar and the rocket impact point was extrapolated.The results of numerical simulation show that the outliers and noise in trajectory measurement signal can be removed effectively by using the adaptive Kalman filter and the filter variance can converge in a short period of time.Based on the relation of filtering time and impact point estimation error,choosing the filtering time of 8-10 scan get the minimum estimation error of impact point.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

Non-cooperative Space Target Estimation Algorithm Without Prior Information Dependence Based on Temporal Line of Sight Constraint

Under single-satellite observation,the parameter estimation of the boost phase of high-precision space noncooperative targets requires prior information.To improve the accuracy without prior information,we propose a parameter estimation model of the boost phase based on trajectory plane parametric cutting.The use of the plane passing through the geo-center and the cutting sequence line of sight(LOS)generates the trajectory-cutting plane.With the coefficient of the trajectory cutting plane directly used as the parameter to be estimated,a motion parameter estimation model in space non-cooperative targets is established,and the Gauss-Newton iteration method is used to solve the flight parameters.The experimental results show that the estimation algorithm proposed in this paper weakly relies on prior information and has higher estimation accuracy,providing a practical new idea and method for the parameter estimation of space non-cooperative targets under single-satellite warning.

Staring-imaging satellite pointing estimation based on sequential ISAR images

Pointing estimation for spacecraft using Inverse Synthetic Aperture Radar(ISAR)images plays a significant role in space situational awareness and surveillance.However,feature extraction and cross-range scaling of ISAR images create bottlenecks that limit performances of current estimation methods.Especially,the emergence of staring imaging satellites,characterized by complex kinematic behaviors,presents a novel challenge to this task.To address these issues,this article proposes a pointing estimation method based on Convolutional Neural Networks(CNNs)and a numerical optimization algorithm.A satellite’s main axis,which is extracted from ISAR images by a proposed Semantic Axis Region Regression Net(SARRN),is chosen for investigation in this article due to its unique structure.Specifically,considering the kinematic characteristic of the staring satellite,an ISAR imaging model is established to bridge the target pointing and the extracted axes.Based on the imaging model,pointing estimation and cross-range scaling can be described as a maximum likelihood estimation problem,and an iterative optimization algorithm modified by using the strategy of random sampling-consistency check and weighted least squares is proposed to solve this problem.Finally,the pointing of targets and the cross-range scaling factors of ISAR images are obtained.Simulation experiments based on actual satellite orbital parameters verify the effectiveness of the proposed method.This work can improve the performance of satellite reconnaissance warning,while accurate cross-range scaling can provide a basis for subsequent data processes such as 3D reconstruction and attitude estimation.

A New Statistical Tool： Scalar Score Function

The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.

Method to reconnoiter pulse amplitude train for phased array radar based on Hausdorff distance

This paper presents a method to estimate beam pointing of phased array radar by the pulse amplitude train, which is significant in radar electronic reconnaissance and electronic support measure. Firstly, the antenna patterns modeling of the phased array system is exploited to build the radar sweeping model and the signal propagation model. Secondly, the relationship between the variation of the radiated power and the antenna beam pointing angles in the given airspace is analyzed. Based on the above two points, the sample with obvious amplitude characteristics of the pulse amplitude train can be screened out after detecting the train peaks. Finally, the sample is matched to the subsequent pulse amplitude train based on the Hausdorff distance. The proposed methods have less prior knowledge and higher efficiency and are easier to process. By cross correlating the sample of the pulse amplitude train with the sample data of the antenna follow-up radiation, the probability of detection of the beam pointing direction becomes larger in case that the subsequent antenna beam returns to the specific position.

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

THE GLOBALIZATION OF DURAND-KERNER ALGORITHM

Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory

An improved probabilistic load flow in distribution networks based on clustering and Point estimate methods

Clustering approaches are one of the probabilistic load flow(PLF)methods in distribution networks that can be used to obtain output random variables,with much less computation burden and time than the Monte Carlo simulation(MCS)method.However,a challenge of the clustering methods is that the statistical characteristics of the output random variables are obtained with low accuracy.This paper presents a hybrid approach based on clustering and Point estimate methods.In the proposed approach,first,the sample points are clustered based on the𝑙-means method and the optimal agent of each cluster is determined.Then,for each member of the population of agents,the deterministic load flow calculations are performed,and the output variables are calculated.Afterward,a Point estimate-based PLF is performed and the mean and the standard deviation of the output variables are obtained.Finally,the statistical data of each output random variable are modified using the Point estimate method.The use of the proposed method makes it possible to obtain the statistical properties of output random variables such as mean,standard deviation and probabilistic functions,with high accuracy and without significantly increasing the burden of calculations.In order to confirm the consistency and efficiency of the proposed method,the 10-,33-,69-,85-,and 118-bus standard distribution networks have been simulated using coding in Python®programming language.In simulation studies,the results of the proposed method have been compared with the results obtained from the clustering method as well as the MCS method,as a criterion.

Suction-based Grasp Point Estimation in Cluttered Environment for Robotic Manipulator Using Deep Learning-based Affordance Map

Perception and manipulation tasks for robotic manipulators involving highly-cluttered objects have become increasingly indemand for achieving a more efficient problem solving method in modern industrial environments.But,most of the available methods for performing such cluttered tasks failed in terms of performance,mainly due to inability to adapt to the change of the environment and the handled objects.Here,we propose a new,near real-time approach to suction-based grasp point estimation in a highly cluttered environment by employing an affordance-based approach.Compared to the state-of-the-art,our proposed method offers two distinctive contributions.First,we use a modified deep neural network backbone for the input of the semantic segmentation,to classify pixel elements of the input red,green,blue and depth(RGBD)channel image which is then used to produce an affordance map,a pixel-wise probability map representing the probability of a successful grasping action in those particular pixel regions.Later,we incorporate a high speed semantic segmentation to the system,which makes our solution have a lower computational time.This approach does not need to have any prior knowledge or models of the objects since it removes the step of pose estimation and object recognition entirely compared to most of the current approaches and uses an assumption to grasp first then recognize later,which makes it possible to have an object-agnostic property.The system was designed to be used for household objects,but it can be easily extended to any kind of objects provided that the right dataset is used for training the models.Experimental results show the benefit of our approach which achieves a precision of 88.83%,compared to the 83.4%precision of the current state-of-the-art.

On nonparametric change point estimator based on empirical characteristic functions

We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Huˇskov′a and Meintanis(2006) plus the weight function used by Matteson and James(2014),where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by a_s which is also justified. Our simulation study shows that the change point estimate obtained by using a_s has a satisfactory performance. We also apply our method to a real dataset.

A sharp estimate of positive integral points in6-dimensional polyhedra and a sharp estimate of smooth numbers

Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y < 17, compared with the result obtained by Ennola.

ON CONVERGENCE OF NOUREIN ITERATIONS FOR SIMULTANEOUS FINDING ALL ZEROS OF A POLYNOMIAL

Presents the first estimation conditions for Nourein iterations for simultaneous finding all zeros of a polynomial under which the iteration processes are guaranteed to converge. Computational formulas; Theorems and proofs.

Estimation in Discrete Reliability Growth,a Growth Model with Coefficient Condition

This paper considers the well known problem of estimating reliability in discrete reliability growth context with sequence of dichotomous success-failure outcomes. More precisely, the authors generalize the simple order relationship constraint with some coefficients. The authors prove that under some mild conditions, the generalized constraint MLE problem can be transformed to a traditional isotonic problem. The authors also study the lower confidence limit estimation of reliability with sample space ranking method. A simulation is conducted to illustrate the superiority of the proposed method.