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.     

Flight control of a hexa-rotor airship: Uncertainty quantification for a range of temperature and pressure conditions

The present paper is concerned with the dynamic modeling and design of control laws for a small non-rigid multi-rotor airship constituted of an oblate-spheroid helium balloon coupled with an electric-powered hexa-rotor airframe. The vehicle is assumed to operate in windless and low-speed conditions. A six-degree-of-freedom nonlinear dynamic model is derived for it using the Newton–Euler approach and considering, among other efforts, a restoring torque due to the displacement of the balloon’s center of buoyancy above the vehicle’s center of mass and the added-mass effect resulting from the air–structure interaction. Using the derived model and assuming a time-scale separation between the translational and rotational dynamics, the attitude and position control laws are designed separately from each other. Both laws are formulated using feedback linearization combined with control input saturation within appropriate parallelepipedal sets, which are carefully chosen to respect pre-defined bounds on the control torque, control force and maximum inclination angle. The effect of temperature and pressure fluctuations is taken into account through a parametric probabilistic approach, where Maximum Entropy Principle is used to construct a physically consistent stochastic model and Monte Carlo method is used as the stochastic solver to propagate the uncertainties through the system. Extensive simulation results show the effectiveness of the proposed control system and quantify the uncertainty of its performance over a wide range of local temperature and pressure.     

An enhanced data-driven polynomial chaos method for uncertainty propagation

As a novel type of polynomial chaos expansion (PCE), the data-driven PCE (DD-PCE) approach has been developed to have a wide range of potential applications for uncertainty propagation. While the research on DD-PCE is still ongoing, its merits compared with the existing PCE approaches have yet to be understood and explored, and its limitations also need to be addressed. In this article, the Galerkin projection technique in conjunction with the moment-matching equations is employed in DD-PCE for higher-dimensional uncertainty propagation. The enhanced DD-PCE method is then compared with current PCE methods to fully investigate its relative merits through four numerical examples considering different cases of information for random inputs. It is found that the proposed method could improve the accuracy, or in some cases leads to comparable results, demonstrating its effectiveness and advantages. Its application in dealing with a Mars entry trajectory optimization problem further verifies its effectiveness.     

Kalman filter based production control of a failure-prone single-machine single-product manufacturing system with imprecise demand and inventory information

An adaptive production control structure for failure-prone manufacturing systems under inventory and demand uncertainty is proposed. It contains estimation and forecasting modules incorporated into a control loop. The customer demand is unknown and its rate is composed of ramp-type, seasonal and random components. Information available to decision maker consists of imprecise inventory records, and the Kalman filter technique is used for estimating the inventory level and demand rate online from noisy inventory measurements. Estimates obtained are shown to converge to the actual values in stochastic sense. They are subsequently used for demand component forecasting, once the estimation errors become sufficiently small. A forecasting algorithm allows estimating ramp-type and seasonal demand components, together with their potential errors. Obtained estimates are incorporated into production control procedures, recently developed for manufacturing systems under variable and uncertain demand. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained. A constructive numerical method for computing sub-optimal production policies is proposed and validated through numerical simulations.     

高效液相色谱法测定保健品益生菌粉中三氯蔗糖的不确定度评估

目的 按照食品安全国家标准GB 22255-2014规定的高效液相色谱法对保健品益生菌粉中三氯蔗糖含量进行测定。根据CNAS-GL006：2019要求以及JJF1059.1-2012对测定过程中影响检验结果的各个分量进行评估。方法 通过对测量重复性、标准品溶液配制、样品溶液的配制、高效液相色谱仪以及标准曲线拟合测量偏差这5个方面引入的不确定度进行分析,并确定各个不确定度分量,得到扩展不确定度。结果 经测定,保健品益生菌粉中三氯蔗糖含量为(0.78±0.046)g/kg,P=95%,(k=2)结论 高效液相色谱法因素对测量不确定度影响显著,由检验方法重复测量和标准品溶液配制体现。     

Multi carrier energy systems and energy hubs: Comprehensive review,survey and recommendations

In this paper, the multi carrier energy (MCE) systems are reviewed from different point of views including mathematical models, integrated components and technologies, uncertainty management, planning objectives, environmental pollution, resilience, and robustness. The basic of MCE systems is formed by combination of cooling, heating and power (CCHP). The natural gas and electricity are the main inputs to MCE systems and the cooling, heating, and electricity are the common outputs. The regular energy converters in the MCE systems are combined heat and power (CHP), gas boiler, absorption-electrical chillers, power to gas (P2G) and fuel-cell. The generic energy storages are electrical, heating, cooling, hydrogen, carbon dioxide (CO₂) and hydro systems.     

液相色谱质谱联用法测定牛奶中氯霉素的不确定度

目的 评定液质联用法测定牛奶中氯霉素的不确定度。方法 根据GB/T 20756-2006《可食动物肌肉、肝脏和水产品中氯霉素、甲砜霉素和氟苯尼考残留量的测定》，采用液相色谱-串联质谱法测定牛奶中氯霉素残留量，分析不确定度的来源并对其进行量化。结果 样品中氯霉素含量为5.1837 μg/kg ，取k=2,得到扩展不确定度为0.67938 μg/kg。其结果可表示为(5.1837+0.67938) μg/kg，真实反映测量的置信度和准确性。结论 影响检测结果不确定度的主要因素是标准储备液以及标准曲线各点的配制。     

Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos

This paper presents a new methodology to identify and diagnose intermittent stochastic faults occurring in a process. A generalized polynomial chaos (gPC) expansion representing the stochastic inputs is employed in combination with the nonlinear mechanistic model of the process to calculate the resulting statistical distribution of measured variables that are used for fault detection and classification. A Galerkin projection based stochastic finite difference analysis is utilized to transform the stochastic mechanistic equation into a coupled deterministic system of equations which is solved numerically to obtain the gPC expansion coefficients. To detect and recognize faults, the probability density functions (PDFs) and joint confidence regions (JCRs) of the measured variables to be used for fault detection are obtained by substituting samples from a random space into the gPC expansions. The method is applied to a two dimensional heat transfer problem with faults consisting of stochastic changes combined with step change variations in the thermal diffusivity and in a boundary condition. The proposed methodology is compared with a Monte Carlo (MC) simulations based approach to illustrate its advantages in terms of computational efficiency as well as accuracy.     

An integrated systematic analysis of uncertainties in UK energy transition pathways

Policy goals to transition national energy systems to meet decarbonisation and security goals must contend with multiple overlapping uncertainties. These uncertainties are pervasive through the complex nature of the system, the long term consequences of decisions, and in the models and analytical approaches used. These greatly increase the challenges of informing robust decision making. Energy system studies have tended not to address uncertainty in a systematic manner, relying on simple scenario or sensitivity analysis. This paper utilises an innovative UK energy system model, ESME, which characterises multiple uncertainties via probability distributions and propagates these uncertainties to explore trade-offs in cost effective energy transition scenarios. A linked global sensitivity analysis is used to explore the uncertainties that have most impact on the transition. The analysis highlights the strong impact of uncertainty on delivering the required emission reductions, and the need for an appropriate carbon price. Biomass availability, gas prices and nuclear capital costs emerge as critical uncertainties in delivering emission reductions. Further developing this approach for policy requires an iterative process to ensure a complete understanding and representation of different uncertainties in meeting mitigation policy objectives.     

Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach

This paper presents the Kriging model approach for stochastic free vibration analysis of composite shallow doubly curved shells. The finite element formulation is carried out considering rotary inertia and transverse shear deformation based on Mindlin’s theory. The stochastic natural frequencies are expressed in terms of Kriging surrogate models. The influence of random variation of different input parameters on the output natural frequencies is addressed. The sampling size and computational cost is reduced by employing the present method compared to direct Monte Carlo simulation. The convergence studies and error analysis are carried out to ensure the accuracy of present approach. The stochastic mode shapes and frequency response function are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results using Kriging model and its performance.