Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method

In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP un-certainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20%are added to these original factors for con-structing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron(MLP),support vector machine(SVM)and random forest(RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2)With the proportions of random errors increasing from 5%to 20%,the LSP uncertainty increases continuously.(3)The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4)The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5)The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide sus-ceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors.

Uncertainties in landslide susceptibility prediction:Influence rule of different levels of errors in landslide spatial position

The accuracy of landslide susceptibility prediction(LSP)mainly depends on the precision of the landslide spatial position.However,the spatial position error of landslide survey is inevitable,resulting in considerable uncertainties in LSP modeling.To overcome this drawback,this study explores the influence of positional errors of landslide spatial position on LSP uncertainties,and then innovatively proposes a semi-supervised machine learning model to reduce the landslide spatial position error.This paper collected 16 environmental factors and 337 landslides with accurate spatial positions taking Shangyou County of China as an example.The 30e110 m error-based multilayer perceptron(MLP)and random forest(RF)models for LSP are established by randomly offsetting the original landslide by 30,50,70,90 and 110 m.The LSP uncertainties are analyzed by the LSP accuracy and distribution characteristics.Finally,a semi-supervised model is proposed to relieve the LSP uncertainties.Results show that:(1)The LSP accuracies of error-based RF/MLP models decrease with the increase of landslide position errors,and are lower than those of original data-based models;(2)70 m error-based models can still reflect the overall distribution characteristics of landslide susceptibility indices,thus original landslides with certain position errors are acceptable for LSP;(3)Semi-supervised machine learning model can efficiently reduce the landslide position errors and thus improve the LSP accuracies.

Topology Data Analysis-Based Error Detection for Semantic Image Transmission with Incremental Knowledge-Based HARQ

Semantic communication(SemCom)aims to achieve high-fidelity information delivery under low communication consumption by only guaranteeing semantic accuracy.Nevertheless,semantic communication still suffers from unexpected channel volatility and thus developing a re-transmission mechanism(e.g.,hybrid automatic repeat request[HARQ])becomes indispensable.In that regard,instead of discarding previously transmitted information,the incremental knowledge-based HARQ(IK-HARQ)is deemed as a more effective mechanism that could sufficiently utilize the information semantics.However,considering the possible existence of semantic ambiguity in image transmission,a simple bit-level cyclic redundancy check(CRC)might compromise the performance of IK-HARQ.Therefore,there emerges a strong incentive to revolutionize the CRC mechanism,thus more effectively reaping the benefits of both SemCom and HARQ.In this paper,built on top of swin transformer-based joint source-channel coding(JSCC)and IK-HARQ,we propose a semantic image transmission framework SC-TDA-HARQ.In particular,different from the conventional CRC,we introduce a topological data analysis(TDA)-based error detection method,which capably digs out the inner topological and geometric information of images,to capture semantic information and determine the necessity for re-transmission.Extensive numerical results validate the effectiveness and efficiency of the proposed SC-TDA-HARQ framework,especially under the limited bandwidth condition,and manifest the superiority of TDA-based error detection method in image transmission.

Relationships between Terrain Features and Forecasting Errors of Surface Wind Speeds in a Mesoscale Numerical Weather Prediction Model

Numerical weather prediction(NWP)models have always presented large forecasting errors of surface wind speeds over regions with complex terrain.In this study,surface wind forecasts from an operational NWP model,the SMS-WARR(Shanghai Meteorological Service-WRF ADAS Rapid Refresh System),are analyzed to quantitatively reveal the relationships between the forecasted surface wind speed errors and terrain features,with the intent of providing clues to better apply the NWP model to complex terrain regions.The terrain features are described by three parameters:the standard deviation of the model grid-scale orography,terrain height error of the model,and slope angle.The results show that the forecast bias has a unimodal distribution with a change in the standard deviation of orography.The minimum ME(the mean value of bias)is 1.2 m s^(-1) when the standard deviation is between 60 and 70 m.A positive correlation exists between bias and terrain height error,with the ME increasing by 10%−30%for every 200 m increase in terrain height error.The ME decreases by 65.6%when slope angle increases from(0.5°−1.5°)to larger than 3.5°for uphill winds but increases by 35.4%when the absolute value of slope angle increases from(0.5°−1.5°)to(2.5°−3.5°)for downhill winds.Several sensitivity experiments are carried out with a model output statistical(MOS)calibration model for surface wind speeds and ME(RMSE)has been reduced by 90%(30%)by introducing terrain parameters,demonstrating the value of this study.

Gross errors identification and correction of in-vehicle MEMS gyroscope based on time series analysis

This paper presents a novel approach to identify and correct the gross errors in the microelectromechanical system （MEMS） gyroscope used in ground vehicles by means of time series analysis. According to the characteristics of autocorrelation function （ACF） and partial autocorrelation function （PACF）, an autoregressive integrated moving average （ARIMA） model is roughly constructed. The rough model is optimized by combining with Akaike＇s information criterion （A/C）, and the parameters are estimated based on the least squares algorithm. After validation testing, the model is utilized to forecast the next output on the basis of the previous measurement. When the difference between the measurement and its prediction exceeds the defined threshold, the measurement is identified as a gross error and remedied by its prediction. A case study on the yaw rate is performed to illustrate the developed algorithm. Experimental results demonstrate that the proposed approach can effectively distinguish gross errors and make some reasonable remedies.

R-Factor Analysis of Data Based on Population Models Comprising R- and Q-Factors Leads to Biased Loading Estimates

Effects of performing an R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. Although R-factor analysis of data based on a population model comprising R- and Q-factors is possible, this may lead to model error. Accordingly, loading estimates resulting from R-factor analysis of sample data drawn from a population based on a combination of R- and Q-factors will be biased. It was shown in a simulation study that a large amount of Q-factor variance induces an increase in the variation of R-factor loading estimates beyond the chance level. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.

Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Error Analysis and Accuracy Assessment of GPS Absolute Velocity Determination without SA

Error sources which decrease the accuracy of GPS in absolute velocity determination have been changed since SA was turned off. Firstly, quantities of all kinds of error sources that influence velocity deter-mination are analyzed. The potential accuracy of GPS absolute velocity determination is derived from both theory and field GPS data simulation. After that, two tests were carried out to evaluate the performance of GPS absolute velocity determination in the case of a static and an airborne GPS receiver and INS (Inertial Navigation System) instrument in kinematic mode. In static mode, the receiver velocity has been estimated to be several mm/s with the carrier-phase derived Doppler measurements, and several cm/s with the receiver generated Doppler measurements. In kinematic mode, GPS absolute velocity estimates are compared with the synchronized measurements from the high accuracy INS. The root mean square statistics of the velocity discrepancies between GPS and INS come up to dm/s. Moreover, it has a strong correlation with the accel-eration or jerk of the aircraft.

In-situ strain measurement and error analysis of arc welding with 2D digital image correlation

The deformation and residual stress generated by the welding process can seriously affect the use of components.As a result,it is very important to understand the evolution of stress and strain during the welding process.The strain measurement method based on digital image correlation(DIC)is an excellent method to detect welding strain and residual stress.The out-of-plane translation and out-of-plane rotation introduce errors to the two-dimensional DIC.In this paper,the causes of errors are analyzed theoretically,and the formulas of errors caused by the out-of-plane displacement and the out-of-plane rotation are derived.The out-of-plane translation experiment and the out-of-plane rotation experiment were carried out to verify the theory,and the experimental results are consistent with the theoretical analysis results.The error caused by the out-of-plane translation can be reduced by increasing the object distance;the error caused by the out-of-plane rotation is greatly affected by the rotation angle.

Micro-Analysis of Errors : Categories and Causes

This research collects 3896 errors made by 965 Chinese students in 5 junior middle schools in Xining and then a detailed analysis is made to discover the possible causes behind these errors.This research comes to the following conclusions:first,during the course of English learning in junior middle school,the students make errors mainly in six specific areas:spelling,tenses,pronouns,verb“be”,articles,and numbers;second,the learners at an elementary level produce more interlingual errors than the learners at an advanced level.Third,error fossilization is serious.

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.

Complex geometric modeling and tooth contact analysis of a helical face gear pair with arc-tooth

A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.

Contact analysis and load distribution of double-envelop hourglass worm gearing affected by errors and load

An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.

Introduction of New Method on Engineering Risk Assessment:Engineering Errors and Effects Analysis(3EA)

Construction and commissioning accidents investigation shows that engineer’s errors in basic and detailed phases are the main causes.It will be gained more efficiency of investment when a relevant method is applied for error identification and risk assessment in basic and detailed phases.Most of risk assessment methods are related to construction phase,meanwhile hidden risks that were happen in previous phases cannot be found by these methods.Although HAZOP study can be applied in detail phase but it can help to find process defections.Importance of identifying risks in basic and detailed phases is to apply preventive actions against birth and grows risks.This risk assessment method can reduce costs and improve environmental protection,safety,and reliability of designs.The main purpose of this study is to identify engineer’s errors and analyse their HSE effects.The method is applied in seven oil and gas engineering projects in Iran,raising the level of engineer’s attention to safety precautions and environmentally-friendly design,reducing the cost of improving the level of safety and environmental protection,improving environmental protection,safety,and design reliability,and improving procedures related to design process and control have been achieved.

Analysis of students＇ problems in writing with reference to theory of cohesion and Error Analysis

This paper is to advocate the necessity of Error Analysis （EA） and cohesion in college English writing teaching. By analyzing the causes of the cohesive errors, the paper wishes to catch the attention of readers to the benefits EA brings to writing teaching and the seriousness of the problems concerning cohesion in writing, and hopes that these implications for college English writing teaching would be of great significance.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

DEVELOPMENT AND ERROR ANALYSIS OF AN INSPECTING SYSTEM FOR MEASURING THE ROTATIONAL INERTIA OF BULLETS

介绍了一种用于测量弹丸转动惯量的高精度测量仪器，该仪器利用双悬丝扭摆机构、光电计时系统提取摆动周期信息，由MCS-51系列单片机组成的测量系统进行数据处理，并由LED显示器测量结果。文中阐述了仪器的工作原理， 推导了所需的计算公式，分析了产生测量误差的因素，进行了定量精度分析，给出了实验结果与测量精度。