Digital twin-based analysis of volumetric error mapping procedures

The evaluation of the volumetric accuracy of a machine tool is an open challenge in the industry, and a wide variety of technical solutions are available in the market and at research level. All solutions have advantages and disadvantages concerning which errors can be measured, the achievable uncertainty, the ease of implementation, possibility of machine integration and automation, the equipment cost and the machine occupation time, and it is not always straightforward which option to choose for each application. The need to ensure accuracy during the whole lifetime of the machine and the availability of monitoring systems developed following the Industry 4.0 trend are pushing the development of measurement systems that can be integrated in the machine to perform semi-automatic verification procedures that can be performed frequently by the machine user to monitor the condition of the machine. Calibrated artefact based calibration and verification solutions have an advantage in this field over laser based solutions in terms of cost and feasibility of machine integration, but they need to be optimized for each machine and customer requirements to achieve the required calibration uncertainty and minimize machine occupation time.This paper introduces a digital twin-based methodology to simulate all relevant effects in an artefact-based machine tool calibration procedure, from the machine itself with its expected error ranges, to the artefact geometry and uncertainty, artefact positions in the workspace, probe uncertainty, compensation model, etc. By parameterizing all relevant variables in the design of the calibration procedure, this simulation methodology can be used to analyse the effect of each design variable on the error mapping uncertainty, which is of great help in adapting the procedure to each specific machine and user requirements. The simulation methodology and the analysis possibilities are illustrated by applying it on a 3-axis milling machine tool.     

广义正交码索引调制系统的性能分析

摘 要：为了提高码索引调制（code index modulation，CIM）系统的传输效率，提出了一种具有更低复杂度的单输入单输出（single input single output，SISO）的广义正交码索引调制（generalized orthogonal code index modulation，GQCIM）系统。CIM 系统使用扩频码和星座符号传输信息，但只能激活两个扩频码索引和一个调制符号。而 GQCIM 系统以一种新颖的方式克服了只激活一个调制符号的限制，同时充分利用了调制符号的正交性，增加扩频码索引以传输更多的额外信息位，提高了系统的传输效率。此外，分析了GQCIM系统的理论性能，推导了误码率性能的上界。通过蒙特卡罗仿真验证了GQCIM系统的性能，对比发现GQCIM系统的理论和仿真性能一致。而且在相同的传输效率下，结果显示GQCIM系统的性能优于同样具有正交性的调制系统，如广义码索引调制（generalized code index modulation，GCIM）系统、CIM系统、码索引调制-正交空间调制（code index modulation aided quadrature spatial modulation，CIM-QSM）系统、码索引调制-正交空间调制（code index modulation aided spatial modulation，CIM-SM）系统、脉冲索引调制（pulse index modulation，PIM）系统。     

Context-free grammars to detect straight segments and a novel polygonal approximation method

A new method for the polygonal approximation is presented. The method is based on the search for break points through a context-free grammar, that accepts digital straight segments with loss of information, as well as the decrease in the error committed employing the comparison of a tolerable error. We present an application of our method to different sets of objects widely used, as well as a comparison of our results with the best results reported in the literature, proving that our method achieves better values of error criteria. Besides, a new way to find polygonal approximations, with context-free grammars to recognize digital straight segments without loss of pixels, it is also addressed.     

An improved feedrate scheduling method for NURBS interpolation in five-axis machining

Five-axis machining plays an important role in manufacturing by dint of its high efficiency and accuracy. While two rotation axes benefit the flexibility of machining, it also brings limitations and challenges. In order to further balance machining precision and efficiency, an improved feedrate scheduling method is presented considering geometric error and kinematic constraints for the Non Uniform Rational B-Spline (NURBS) interpolation in five-axis machining. A simplification method is proposed to calculate the geometric error which describes the deviation between the ideal tool path and the real tool path induced by the non-linear movement. A linear relation between geometric error and feedrate is built to limit the feedrate. The constraints determined by single axis kinematic performance and tangential kinematic performance are also considered. Under these constraints, a constrained feedrate profile is determined. Aiming to get more constant feedrate in the difficult-to-machine areas, this work proposes a scheduling method which combines morphological filtering and S-shape acceleration/deceleration (acc/dec) mode. Simulations and experiments are performed to compare the proposed feedrate scheduling method with two previous feedrate scheduling method and the results prove that the proposed feedrate scheduling method is reliable and effective.     

Unreliable numbers: error and harm induced by bad design can be reduced by better design

Number entry is a ubiquitous activity and is often performed in safety- and mission-critical procedures, such as healthcare, science, finance, aviation and in many other areas. We show that Monte Carlo methods can quickly and easily compare the reliability of different number entry systems. A surprising finding is that many common, widely used systems are defective, and induce unnecessary human error. We show that Monte Carlo methods enable designers to explore the implications of normal and unexpected operator behaviour, and to design systems to be more resilient to use error. We demonstrate novel designs with improved resilience, implying that the common problems identified and the errors they induce are avoidable.     

On the performance of improved quadrature spatial modulation

Quadrature spatial modulation (QSM) utilizes the in‐phase and quadrature spatial dimensions to transmit the real and imaginary parts of a single signal symbol, respectively. The improved QSM (IQSM) transmits two signal symbols per channel use through a combination of two antennas for each of the real and imaginary parts. The main contributions of this study can be summarized as follows. First, we derive an upper bound for the error performance of the IQSM. We then design constellation sets that minimize the error performance of the IQSM for several system configurations. Second, we propose a double QSM (DQSM) that transmits the real and imaginary parts of two signal symbols through any available transmit antennas. Finally, we propose a parallel IQSM (PIQSM) that splits the antenna set into equal subsets and performs IQSM within each subset using the same two signal symbols. Simulation results demonstrate that the proposed constellations significantly outperform conventional constellations. Additionally, DQSM and PIQSM provide a performance similar to that of IQSM while requiring a smaller number of transmit antennas and outperform IQSM with the same number of transmit antennas.     

A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

We explore a truncation error criterion to steer adaptive step length refinement and coarsening in incremental-iterative path following procedures, applied to problems in large-deformation structural mechanics. Elaborating on ideas proposed by Bergan and collaborators in the 1970s, we first describe an easily computable scalar stiffness parameter whose sign and rate of change provide reliable information on the local behavior and complexity of the equilibrium path. We then derive a simple scaling law that adaptively adjusts the length of the next step based on the rate of change of the stiffness parameter at previous points on the path. We show that this scaling is equivalent to keeping a local truncation error constant in each step. We demonstrate with numerical examples that our adaptive method follows a path with a significantly reduced number of points compared to an analysis with uniform step length of the same fidelity level. A comparison with Abaqus illustrates that the truncation error criterion effectively concentrates points around the smallest-scale features of the path, which is generally not possible with automatic incrementation solely based on local convergence properties.     

A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

Anti‐Sway Crane Control Considering Wind Disturbance and Container Mass

A method for estimating the sway angle using an observer has already been proposed. The state observer estimates the sway angle accurately and must use the detected sway angle value. However, the estimated sway angle has an error owing to rope length error, friction force, and wind. Moreover, the container mass cannot be determined, and therefore the observer parameter is not suitable. We already proposed robust antisway control for overcoming rope length error without adding a new sensor. Further, we designed a friction disturbance observer to cancel out the influence of the friction force. In this paper, we first propose a container mass estimation method when a crane system performs rolling up control. The observer parameter can be selected using the estimated mass value. Second, in crane parallel shift control, we propose a robust antisway control even when there is a wind disturbance. We design a wind disturbance observer and propose a wind disturbance estimator to separate the friction observer output from the wind disturbance observer output. We confirm through experiments that the proposed method can reduce vibration.     

M-estimator based Chinese Remainder Theorem with few remainders using a Kroenecker product based mapping vector

The Chinese Remainder Theorem (CRT) explains how to estimate an integer-valued number from the knowledge of the remainders obtained by dividing such unknown integer by co-prime integers. As an algebraic theorem, CRT is the basis for several techniques concerning data processing. For instance, considering a single-tone signal whose frequency value is above the sampling rate, the respective peak in the DFT informs the impinging frequency value modulo the sampling rate. CRT is nevertheless sensitive to errors in the remainders, and many efforts have been developed in order to improve its robustness. In this paper, we propose a technique to estimate real-valued numbers by means of CRT, employing for this goal a Kroenecker based M-Estimation (ME), specially suitable for CRT systems with low number of remainders. Since ME schemes are in general computationally expensive, we propose a mapping vector obtained via Kroenecker products which considerably reduces the computational complexity. Furthermore, our proposed technique enhances the probability of estimating an unknown number accurately even when the errors in the remainders surpass 1/4 of the greatest common divisor of all moduli. We also provide a version of the mapping vectors based on tensorial n-mode products, delivering in the end the same information of the original method. Our approach outperforms the state-of-the-art CRT methods not only in terms of percentage of successful estimations but also in terms of smaller average error.