Welding Deviation Detection Algorithm Based on Extremum of Molten Pool Image Contour

The welding deviation detection is the basis of robotic tracking welding, but the on-line real-time measurement of welding deviation is still not well solved by the existing methods. There is plenty of information in the gas metal arc welding（GMAW） molten pool images that is very important for the control of welding seam tracking. The physical meaning for the curvature extremum of molten pool contour is revealed by researching the molten pool images, that is, the deviation information points of welding wire center and the molten tip center are the maxima and the local maxima of the contour curvature, and the horizontal welding deviation is the position difference of these two extremum points. A new method of weld deviation detection is presented, including the process of preprocessing molten pool images, extracting and segmenting the contours, obtaining the contour extremum points, and calculating the welding deviation, etc. Extracting the contours is the premise, segmenting the contour lines is the foundation, and obtaining the contour extremum points is the key. The contour images can be extracted with the method of discrete dyadic wavelet transform, which is divided into two sub contours including welding wire and molten tip separately. The curvature value of each point of the two sub contour lines is calculated based on the approximate curvature formula of multi-points for plane curve, and the two points of the curvature extremum are the characteristics needed for the welding deviation calculation. The results of the tests and analyses show that the maximum error of the obtained on-line welding deviation is 2 pixels（0.16 ram）, and the algorithm is stable enough to meet the requirements of the pipeline in real-time control at a speed of less than 500 mm/min. The method can be applied to the on-line automatic welding deviation detection.

Extremum of second-order directional derivatives

In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.

Analysis on membrane wrinkling using stress extremum method

A stress extremum method is developed based on Von Karman equations for analysis of membrane wrinkles in this paper. A mechanical model is also established for analyzing shear membrane wrinkles. Expressions of wrinkling wavelength,amplitude and angle are obtained in terms of the stress extremum method. A numerical analysis approach-directly disturbing method is proposed to analyze the configuration parameters of shear membrane wrinkles by introducing out-of-plane disturbing forces to trigger wrinkle formation,while it timely removes the applied forces in order to eliminate the effect of disturbing forces on analytical results. The simulation results agree well with analytical results,which demonstrate that the proposed approach is capable for analyzing the membrane wrinkles with good accuracy.

DYNAMIC HUNTING EXTREMUM CONTROL METHOD BASED ON MEASURE AND ESTIMATION

Objective To propose a dynamic hunting extremum control method based on comparison of the estimated value and measured value. Methods The output linear group of the system is approximately expressed as an nth order system with large time constant or with time delay. Moreover, the relation between input drive reversal of the logic circuit and dynamic output of the system is analyzed in detail. The calculating formulae for the drive reversal are given for different extremum control systems. Based on principles above, a controller using a micrprocessor and a testing laboratory plant were designed and implemented. Results With this new method, the controller achieves fast optimum point hunting process, good performance in extremum control systems for high order processes, and robust result under sudden change or drift of the extremum characteristics. Conclusion The new control owns the merits of rapid optimizing dynamics, robusticity, and wide applicability.

On the Negative Extremums of Fundamental Functions of Lagrange Interpolation Based on Chebyshev Nodes

In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.

OUTPUT MAXIMIZATION CONTROL FOR VSCF WIND ENERGY CONVERSION SYSTEM USING EXTREMUM CONTROL STRATEGY

The energy conversion optimization control strategy is presented for a family of horizontal-axis variablespeed fixed-pitch wind energy conversion systems,working in the partial load region.The system uses a variablespeed wind turbine(VSWT)driving a squirrel-cage induction generator(SCIG)connected to a grid.A new maximum power point tracking(MPPT)approach is proposed based on the extremum seeking control principles under the assumption that the wind turbine model and its parameters are poorly known.The aim is to drive the average position of the operation point close to optimality.Here the wind turbulence is used as search disturbance instead of inducing new sinusoidal search signals.The discrete Fourier transform(DFT)process of some available measures estimates the distance of operation point to optimality.The effectiveness of the proposed MPPT approach is validated under different operation conditions by numerical simulations in MATLAB/SIMULINK.The simulation results prove that the new approach can effectively suppress the vibration of system and enhance the dynamic performance of system.

A NEW SYSTEM DYNAMIC EXTREMUM SELF-SEARCHING METHOD BASED ON CORRELATION ANALYSIS

Objective To propose a new dynamic extremum self searching method, which can be used in industrial processes extremum optimum control systems, to overcome the disadvantages of traditional method. Methods This algorithm is based on correlation analysis. A pseudo random binary signal m sequence u(t) is added as probe signal in system input, construct cross correlation function between system input and output, the next step hunting direction is judged by the differential sign. Results Compared with traditional algorithm such as step forward hunting method, the iterative efficient, hunting precision and anti interference ability of the correlation analysis method is obvious over the traditional algorithm. The computer simulation experimental given illustrate these viewpoints. Conclusion The correlation analysis method can settle the optimum state point of device operating process. It has the advantage of easy condition , simple calculate process.

Extremum Principle for Very Weak Solutions of A-Harmonic Equation with Weight

Extremum principle for very weak solutions of A-harmonic equation div A(x,▽u)=0 is obtained, where the operator A:Ω × Rn→Rnsatisfies some coercivity and controllable growth conditions with Mucken-houpt weight.

RATE VARIATIONAL EXTREMUM PRINCIPLES FOR FINITE ELASTOPLASTICITY

Dual variational extremum principles for rate problems of classical elastoplasticitv at finite deformation are studied in Updated Lagrangian rate forms. It is proved that the convexity of the variational functionals are closely related to a so-called gap function, which plavs an important role in nonlinear variational problems.

Power Maximization and Control of Variable-Speed Wind Turbine System Using Extremum Seeking

Maximizing the power capture is an important issue to the turbines that are installed in low wind speed area. In this paper, we focused on the modeling and control of variable speed wind turbine that is composed of two-mass drive train, a Squirrel Cage Induction Generator (SCIG), and voltage source converter control by Space Vector Pulse Width Modulation (SPVWM). To achieve Maximum Power Point Tracking (MPPT), the reference speed to the generator is searched via Extremum Seeking Control (ESC). ESC was designed for wind turbine region II operation based on dither-modulation scheme. ESC is a model-free method that has the ability to increase the captured power in real time under turbulent wind without any requirement for wind measurements. The controller is designed in two loops. In the outer loop, ESC is used to set a desired reference speed to PI controller to regulate the speed of the generator and extract the maximum electrical power. The inner control loop is based on Indirect Field Orientation Control (IFOC) to decouple the currents. Finally, Particle Swarm Optimization (PSO) is used to obtain the optimal PI parameters. Simulation and control of the system have been accomplished using MATLAB/Simulink 2014.

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.

Distributed collaborative extremum response surface method for mechanical dynamic assembly reliability analysis

To make the dynamic assembly reliability analysis more effective for complex machinery of multi-object multi-discipline(MOMD),distributed collaborative extremum response surface method(DCERSM)was proposed based on extremum response surface method(ERSM).Firstly,the basic theories of the ERSM and DCERSM were investigated,and the strengths of DCERSM were proved theoretically.Secondly,the mathematical model of the DCERSM was established based upon extremum response surface function(ERSF).Finally,this model was applied to the reliability analysis of blade-tip radial running clearance(BTRRC)of an aeroengine high pressure turbine(HPT)to verify its advantages.The results show that the DCERSM can not only reshape the possibility of the reliability analysis for the complex turbo machinery,but also greatly improve the computational speed,save the computational time and improve the computational efficiency while keeping the accuracy.Thus,the DCERSM is verified to be feasible and effective in the dynamic assembly reliability(DAR)analysis of complex machinery.Moreover,this method offers an useful insight for designing and optimizing the dynamic reliability of complex machinery.

Reliability-based design optimization for flexible mechanism with particle swarm optimization and advanced extremum response surface method

To improve the computational efficiency of the reliability-based design optimization(RBDO) of flexible mechanism, particle swarm optimization-advanced extremum response surface method(PSO-AERSM) was proposed by integrating particle swarm optimization(PSO) algorithm and advanced extremum response surface method(AERSM). Firstly, the AERSM was developed and its mathematical model was established based on artificial neural network, and the PSO algorithm was investigated. And then the RBDO model of flexible mechanism was presented based on AERSM and PSO. Finally, regarding cross-sectional area as design variable, the reliability optimization of flexible mechanism was implemented subject to reliability degree and uncertainties based on the proposed approach. The optimization results show that the cross-section sizes obviously reduce by 22.96 mm^2 while keeping reliability degree. Through the comparison of methods, it is demonstrated that the AERSM holds high computational efficiency while keeping computational precision for the RBDO of flexible mechanism, and PSO algorithm minimizes the response of the objective function. The efforts of this work provide a useful sight for the reliability optimization of flexible mechanism, and enrich and develop the reliability theory as well.

A Novel Extremum Seeking Control to Enhance Convergence and Robustness in the Presence of Nonlinear Dynamic Sensors

This paper focuses on optimizing an unknown cost function through extremum seeking(ES)control in the presence of a slow nonlinear dynamic sensor responsible for measuring the cost.In contrast to traditional perturbation-based ES control,which often suffers from sluggish convergence,the proposed method eliminates the time-scale separation between sensor dynamics and ES control by using the relative degree of the nonlinear sensor system.To improve the convergence rate,the authors incorporate high-frequency dither signals and a differentiator.To enhance the robustness with the existence of rapid disturbances,an off-the-shelf linear high-gain differentiator is applied.The first result demonstrates that,for any desired convergence rate,with properly tuned parameters for the proposed ES algorithm,the input of the cost function can converge to an arbitrarily small neighborhood of the optimal solution,starting from any initial condition within any given compact set.Furthermore,the second result shows the robustness of the proposed ES control in the presence of sufficiently fast,zero-mean periodic disturbances.Simulation results substantiate these theoretical findings.

Extremum seeking control for UAV close formation flight via improved pigeon-inspired optimization

This paper proposes a comprehensive design scheme for the extremum seeking control(ESC)of the unmanned aerial vehicle(UAV)close formation flight.The proposed design scheme combines a Newton-Raphson method with an extended Kalman filter(EKF)to dynamically estimate the optimal position of the following UAV relative to the leading UAV.To reflect the wake vortex effects reliably,the drag coefficient induced by the wake vortex is considered as a performance function.Then,the performance function is parameterized by the first-order and second-order terms of its Taylor series expansion.Given the excellent performance of nonlinear estimation,the EKF is used to estimate the gradient and the Hessian matrix of the parameterized performance function.The output feedback of the proposed scheme is determined by iterative calculation of the Newton-Raphson method.Compared with the traditional ESC and the classic ESC,the proposed design scheme avoids the slow continuous time integration of the gradient.This allows a faster convergence of relative position extremum.Furthermore,the proposed method can provide a smoother command during the seeking process as the second-order term of the performance function is taken into account.The convergence analysis of the proposed design scheme is accomplished by showing that the output feedback is a supermartingale sequence.To improve estimation performance of the EKF,a improved pigeon-inspired optimization(IPIO)is proposed to automatically tune the noise covariance matrix.Monte Carlo simulations for a three-UAV close formation show that the proposed design scheme is robust to the initial position of the following UAV.

一种单信标测距辅助INS的导航方法

传统基于地球物理场的匹配辅助惯性导航方法在基础数据变化特征不明显或数据缺乏等苛刻条件下,难以实现有效匹配定位。为解决这一问题,提出了一种单信标测距辅助惯性导航系统(INS)的方法。首先,在单信标测距解析基准图上引入相关极值匹配辅助导航算法并进行重新建模。然后,采用差分进化寻优算法对该模型进行解算,并设计了一种固定匹配序列长度的建模方法以解决相关极值匹配算法实时性差的缺点。所提方法在缺乏地球物理基础数据条件下,仅需在海底布放单只声信标即可实现局部海域水下高精度实时定位。同时,由于采用的测距基准图为解析形式,所提方法也能较好地解决离散匹配算法定位精度受限于基准图分辨率等问题。最后,设计了相关实测实验,实验结果表明当惯导定位误差累积为1529.4 m时,采用所提方法与单信标匹配,定位误差减小为111.8 m,算法的有效性得到了验证。

Application of entransy dissipation extremum principle in radiative heat transfer optimization

The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during the radiative heat transfer processes due to the irreversibility. The extremum principle of entransy dissipation was developed for optimizing radiative heat transfer processes. This principle states that for a fixed boundary temperature the radiative heat transfer is optimized when the entransy dissipation is maximized, while for a fixed boundary heat flux the radiative heat transfer process is optimized when the entransy dissipation is minimized. Finally, examples for the application of the entransy dissipation extre- mum principle are presented.

板壳结构在声振联合试验下的振动响应耦合分析

目的研究具有工程实践意义的板壳组合结构在声振联合作用下的响应预测方法。方法在噪声试验、振动试验和声振联合试验响应曲线的基础上,分析板壳组合结构在噪声和振动同时激励下的响应耦合规律,并根据噪声试验和振动试验的响应极值包络法,来预测在声振联合试验作用下板壳结构的响应分布。结果声振联合试验响应曲线近似于噪声试验和振动试验的最大值包络线,噪声的面激励和随机振动的基础激励在不同的频率范围内对结构响应起着主要影响。试验件的噪声试验和振动试验响应曲线在给定的频率点出现相交,小于交越频率的声振联合试验响应与振动试验高度吻合,高于交越频率的响应则以噪声试验为主。结论在工程实际中,可以直接利用振动试验和噪声试验的响应数据对声振联合试验的响应进行预测。由于交越频率难以事先获得,因此响应叠加法在实践中更易于实现。

Extremum Problems of Laplacian Eigenvalues and Generalized Polya Conjecture(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.

基于扰动补偿的高速列车自适应滑模黏着控制

列车安全和平稳运行依赖于牵引力的有效发挥,而牵引力的有效发挥受限于轮轨间的黏着状态。为了解决高速列车行驶在低黏着轨面时牵引力不足的问题,考虑到车重、阻力、坡度等参数不易精确获取,设计一种基于扰动补偿的自适应滑模黏着控制算法。根据黏着计算模型和简化列车模型,建立高速列车轮轨动力学模型。通过设计动态观测精度更高的鲁棒黏着观测器,以精确获取当前轨面提供的黏着力。在此基础上,针对列车工作在最优黏着点附近时能够获得较大牵引力这一特性,采用梯度观测极值搜索算法获取该点附近的蠕滑速度。同时,设计基于扰动补偿的自适应滑模控制器控制电机输出转矩,使高速列车能够在部分系统参数未知的情况下跟踪极值搜索算法输出的蠕滑速度,从而提高列车牵引力。基于扰动补偿的自适应滑模控制,通过观测补偿系统不确定部分和自适应调节开关增益,减少滑模控制律抖振对黏着控制性能的影响。研究结果表明,基于扰动补偿的自适应滑模黏着控制算法在系统中存在未知参数时,能够控制列车在10 s内到达冰雪轨面最优黏着工作点附近,在1 s内到达潮湿轨面最优黏着工作点附近。此外,相比于传统滑模黏着控制和自适应滑模黏着控制,所提算法控制律抖振更低,并且能够更精确地搜寻和跟踪最优黏着工作点。所提算法可以为实际列车黏着控制算法设计提供参考。