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.     

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.     

A review of the existing performance verification infrastructure for micro-CMMs

The performance verification of micro-CMMs is now of intense interest because of their capability to perform length measurements in three dimensions to high accuracy with low uncertainties. Currently, verification of micro-CMMs is completed in the spirit of existing specification standards, because strict adherence to these standards is often difficult. This review aims to present and discuss verification techniques available for micro-CMMs: specification standards, existing calibrated test lengths and traceability routes that can be associated with micro-CMMs. Three specification standards used in the testing of CMMs will be considered. In addition, a wide range of calibrated test lengths are reported, and any advantages and disadvantages associated with their use are discussed. It is concluded that micro-CMMs cannot yet be verified in accordance with existing specification standards. Suggestions are made for future standardisation work required to rectify these issues.     

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.     

嵌入式实时操作系统内核混合代码的自动化验证框架

"如何构造高可信的软件系统"已成为学术界和工业界的研究热点.操作系统内核作为软件系统的基础组件，它的安全可靠是构造高可信软件系统的重要环节.为了确保操作系统内核的安全可靠，将形式化方法引入到操作系统内核验证中，提出了一个自动化验证操作系统内核的框架.该验证框架包括：（1）分别对C语言程序和混合语言程序（C语言和汇编语言）进行验证；（2）在混合语言程序验证中，为汇编程序建立抽象模型，并将C语言程序和抽象模型粘合形成基于C语言验证工具可接收的验证模型；（3）从规范中提取性质，基于该自动验证工具，对性质完成自动验证；（4）该框架不限于特定的硬件架构.成功地运用该验证框架对两种不同硬件平台的嵌入式实时操作系统内核μC/OS-II进行了验证.结果显示：利用该框架在对两个不同的硬件平台上内核验证时，框架的可重复利用率很高，高达到88%，虽然其抽象模型需要根据不同的硬件平台进行重构.在对基于这两种平台的操作系统内核验证中，分别发现了10~12处缺陷.其中，在ARM平台上两处与硬件相关的问题被发现.实验表明，该方法对不同硬件平台的同一个操作系统分析验证具有一定的通用性.     

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.     

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis, the stress-strength model is often used to describe the life of a component which has a random strength (X) and is subjected to a random stress (Y). In this paper, we considered the problem of estimating the reliability R=P [Y<X] when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution. The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample, ranked set sampling and median ranked set sampling methods. Four different reliability estimators under median ranked set sampling are derived. Two estimators are obtained when both strength and stress have an odd or an even set size. The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa. The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study. The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample. In general, the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.