Employing statistical model emulation as a surrogate for CFD

This work focuses on substituting a computationally expensive simulator by a cheap emulator to enable studying applications where running the simulator is prohibitively expensive. The procedure consists of two steps. In a first step, the emulator is calibrated to closely mimic the simulator response for a number of pre-defined cases. In a second step the calibrated emulator is used as surrogate for the simulator in the otherwise prohibitively expensive application. An appealing feature of the proposed framework contrary to other approaches is that the uncertainty on the emulator prediction can be determined. While the proposed framework is applicable in virtually all areas of natural sciences, we discuss the approach and evaluate its performance based on a typical example in the realm of computational wind engineering, namely the determination of the wind field in an urban area.     

An optimization decision support approach for risk analysis of carbon emission trading in electric power systems

Concerns over dramatic increasing electricity demand, exacerbating power shortage and changing climatic condition are emerging associated with municipal electric power systems (EPS). In this study, a risk-explicit mixed-integer full-infinite programming (RMFP) approach is developed for planning carbon emission trading (CET) in EPS. RMFP-CET has advantages in risk reflection and policy analysis, particularly when the input parameters are provided as crisp and functional intervals as well as probabilistic distributions. The developed method is applied to a real case study of CET planning of EPS in Beijing. Various electricity policies are incorporated within the modeling formulation for enhancing the RMFP-CET's capability. The results indicate that reasonable solutions have been generated, which are useful for making decisions of electricity production and supply as well as gaining insight into the tradeoffs among electricity supply risk, system cost, and CO₂ mitigation strategy.     

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.     

Adaptive fuzzy neuro-observer applied to low cost INS/GPS

A combined MEMS Inertial Navigation System (INS) with GPS is used to provide position and velocity data of land vehicles. Data fusion of INS and GPS measurements are commonly achieved through a conventional Extended Kalman filter (EKF). Considering the required accurate model of system together with perfect knowledge of predefined error models, the performance of the EKF is decreased due to unmodeled nonlinearities and unknown bias uncertainties of MEMS inertial sensors. Universal knowledge based approximators comprising of neural networks and fuzzy logic methods are capable of approximating the nonlinearities and the uncertainties of practical systems. First, in this paper, a new fuzzy neural network (FNN) function approximator is used to model unknown nonlinear systems. Second, the process of design and real-time implementation of an adaptive fuzzy neuro-observer (AFNO) in integrated low-cost INS/GPS positioning systems is proposed. To assess the long time performance of the proposed AFNO method, wide range tests of a real INS/GPS with a car vehicle have been performed. The unbiased estimation results of the AFNO show the superiority of the proposed method compared with the classic EKF and the adaptive neuro-observer (ANO) including a pure artificial neural network (ANN) function approximator.     

Water density formulations and their effect on gravimetric water meter calibration and measurement uncertainties

In the gravimetric calibration method of water meters, the volume of water that has passed through the equipment under test (EUT) is generally collected into a tank and the quantity (mass) determined by weighing. The mass of water collected is then converted into a volume. This conversion of mass into volume requires knowledge of the water density, which can be estimated, measured directly or determined by other means. The error of measurement of the EUT is determined by comparing the volume recorded by the EUT and the volume collected in the tank. The density of water is, therefore, one of the major causes of measurement uncertainty in laboratory calibration of water meters using the gravimetric method. Water meter calibration facilities commonly use density formulations proposed by the International Standards Organisation (ISO) and the Organisation for International Legal Metrology (OIML). In Australia, additional guidance in water density determination is provided by the National Measurement Institute (NMI). In this study, testing was undertaken using ten positive displacement water meters arranged in series in the test rig to evaluate some of the common water density formulations used in Australia. The effect of these different formulations on the water meter error measurement was determined, as well as the effect on the measurement uncertainties. The results shows that the use of these different density formulations evaluated do not significantly affect the water meter error of measurement or the uncertainty of measurement. There was no apparent correlation between the water meter error and the meter position in the test rig. It was also determined that if the water density was adjusted only for temperature effects, a maximum of 0.05 and 0.15% drift in meter error and measurement uncertainty respectively, can be expected.     

Extended state observer for uncertain lower triangular nonlinear systems

The extended state observer (ESO) is a key part of the active disturbance rejection control approach, a new control strategy in dealing with large uncertainty. In this paper, a nonlinear ESO is designed for a kind of lower triangular nonlinear systems with large uncertainty. The uncertainty may come from unmodeled system dynamics and external disturbance. We first investigate a nonlinear ESO with high constant gain and present a practical convergence. Two types of ESO are constructed with explicit error estimations. Secondly, a time varying gain ESO is proposed for reducing peaking value near the initial time caused by constant high gain approach. The numerical simulations are presented to show visually the peaking value reduction. The mechanism of peaking value reduction by time varying gain approach is analyzed.     

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 integrated knowledge-based and optimization tool for the sustainable selection of wastewater treatment process concepts

The increasing demand on wastewater treatment plants (WWTPs) has involved an interest in improving the alternative treatment selection process. In this study, an integrated framework including an intelligent knowledge-based system and superstructure-based optimization has been developed and applied to a real case study. Hence, a multi-criteria analysis together with mathematical models is applied to generate a ranked short-list of feasible treatments for three different scenarios. Finally, the uncertainty analysis performed allows for increasing the quality and robustness of the decisions considering variation in influent concentrations. For the case study application, the expert system identifies 5 potential process technologies and, using this input, the superstructure identifies membrane bioreactors as the optimal and robust solution under influent uncertainties and tighter effluent limits. A mutual benefit and synergy is achieved when both tools are integrated because expert knowledge and expertise are considered together with mathematical models to select the most appropriate treatment alternative.     

Laboratory evaluation of dripper performance

The catch can method is traditionally used for evaluating performance of drip systems. Two variations of this method are commonly applied in laboratory testing of drippers: the sequential and the simultaneous method. This study compared uniformity and measurement uncertainty of the two methods, with the overall aim of improving irrigation water management. The simultaneous method was found to have a lower coefficient of variation (C_v) and measurement uncertainty, indicating that it is more accurate than the sequential method. In all the tests, however, the C_v was determined to be <5%, which is acceptable as per the current reference standard.