Dependent Weighting Functions Research Articles

Enhanced AOCS verification techniques for Euclid's high-pointing performance*

This paper presents an enhanced Verification and Validation (V&V) framework accompanied by dedicated tools that allows to analytically evaluate pointing error performance of high-pointing accuracy missions in the presence of disturbances and uncertainties. The proposed analysis approach poses the V&V problem in the robust control framework using linear fractional transformation modelling theory (to include model uncertainties) and frequency dependent weighting functions (to capture the spectral properties of the disturbances and the pointing error performance metrics), and is based on the structured singular value approach as well as the integral quadratic constraint (IQC) framework. The validity of this formal approach is exemplified through the verification of the stringent pointing performance of the Euclid mission during the science observation phase. The results show that the proposed enhanced V&V approach is capable of providing certificates for robust stability and performance for all modelled uncertainties.

Fixed gain multichannel active noise control with disturbance dependent objectives and iterative solution.

This paper presents a solution method for a fixed multichannel frequency domain feedforward controller, which is optimized for different sound field disturbances, each corresponding to a different control objective. A controller determined on the basis of identical control objectives for different disturbances can be solved efficiently by using the inverse of two relatively small matrices, the Hermitian square of the secondary path and the cross-spectral density matrix of all combinations between the reference signals. In contrast, the dependence between the disturbance and the control objective results in a large matrix, which may not fit in the memory of a computer. To design the controller for systems with relatively large numbers of sensors and sources, an iterative method based on the conjugate gradient technique is used. A preconditioner based on a disturbance-independent control objective is proposed. This preconditioner improves the convergence rate for some applications. A numerical example of the iterative method is given for active control of the acoustic field inside a room in which a disturbance dependent weighting function is applied to the cost function. It is shown that the iterative method efficiently finds the solution for the disturbance dependent active noise control problem.

H∞/LPV controller design for an active anti-roll bar system of heavy vehicles using parameter dependent weighting functions

Vehicle rollover is a very serious problem when considering the safety of heavy vehicles, which can result in large financial and environmental consequences. This paper investigates the interest of a Linear Parameter Varying (LPV) controller for an active anti-roll bar system of single unit heavy vehicles, in order to enhance roll stability. We propose a parameter dependent H∞/LPV controller with weighting functions, scheduled by the forward velocity (the varying parameter of the vehicle LPV model) and by the normalized load transfers at the two axles (part of the parameter dependent weighting functions) providing an on-line performance adaptation to the vehicle rollover risk. The effectiveness of the proposed controller is validated by using the TruckSim® simulation software with two different types of heavy vehicle: a fully loaded bus and a truck. The simulation results, in the frequency and time domains, show that the proposed strategy drastically improves the vehicle roll stability when compared with a H∞/LTI controller, a fixed weighting functions H∞/LPV controller and a passive anti-roll bar system.

How to cope with unmeasurable premise variables in Takagi–Sugeno observer design: Dynamic extension approach

In this paper, a new strategy to cope with unmeasurable premise variables in observer design for Takagi–Sugeno (TS) models is proposed. The guiding principles are the immersion techniques and auxiliary dynamics generation, allowing to immerge a given TS system with unmeasured state dependent weighting functions into a larger TS system with weighting functions depending only on measured variables. This result relaxes the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. An example is provided to illustrate the performances of the proposed approach.

The second Sandia Fracture Challenge: blind prediction of dynamic shear localization and full fracture characterization

In the context of the second Sandia Fracture Challenge, dynamic tensile experiments performed on a Ti–6Al–4V alloy with a complex fracture specimen geometry are modeled numerically. Sandia National Laboratories provided the participants with limited experimental data, comprising of uniaxial tensile test and V-notched rail shear test results. To model the material behavior up to large plastic strains, the flow stress is described with a linear combination of Swift and Voce strain hardening laws in conjunction with the inverse method. The effect of the strain rate and temperature is incorporated through the Johnson–Cook strain rate hardening and temperature softening functions. A strain rate dependent weighting function is used to compute the fraction of incremental plastic work converted to heat. The Hill’48 anisotropic yield function is adopted to capture weak deformation resistance under in-plane pure shear stress. Fracture initiation is predicted by the recently developed strain rate dependent Hosford–Coulomb fracture criterion. The calibration procedure is described in detail, and a good agreement between the blind prediction and the experiments at two different speeds is obtained for both the crack path and the force–crack opening displacement (COD) curve. A comprehensive experimental and numerical follow-up study on leftover material is conducted, and plasticity and fracture parameters are carefully re-calibrated. A more elaborate modeling approach using a non-associated flow rule is pursued, and the fracture locus of the Ti–6Al–4V is clearly identified by means of four different fracture specimens covering a wide range of stress states and strain rates. With the full characterization, a noticeable improvement in the force–COD curve is obtained. In addition, the effect of friction is studied numerically.

Auxiliary dynamics for observer design of nonlinear TS systems with unmeasurable premise variables

In this paper, the problem of observers for Takagi-Sugeno (TS) models with unmeasurable premise variables is investigated and a new design approach is proposed. The idea, is motivated by the immersion techniques and auxiliary dynamics generation, and consists in the transformation of the TS system with state dependent weighting functions in a new TS system with weighting functions depending only on the measured variables. This result aims to relax the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. Illustrative example is provided to discuss the performances of the proposed approach.

Influences of the day‐night differences of ionospheric variability on the estimation of GPS differential code bias

AbstractThe estimation of differential code bias (DCB) of GPS system is one of the necessary steps for total electron content (TEC) derivation from GPS measurements. Usually, the method for estimating the GPS DCBs follows the assumption of the gentle temporal and spatial variation of the ionosphere, but this assumption is just an approximation because of the ionosphere's inherent variability. It has been indicated that the estimated GPS satellite DCBs are sometimes influenced by the ionospheric conditions. In this paper, we demonstrate a possible influence of ionospheric variability that differs between day and night on the estimated DCBs from measurements of a single GPS station. It is found that the average standard deviations (STDs) of the satellite DCBs estimated with daytime data are higher than that with the nighttime data. To reduce this day‐night difference effect on GPS DCB determination, we use an improved estimation method based on the primary features of the ionospheric variability with local time. A local time dependent weighting function was introduced into the original least squares DCBs estimation algorithm. A test with data for BJFS station (39.60°N, 115.89°E) in 2001 indicates that the STD of the DCBs decreases from 2.533 TECU (total electron content unit, 1 TECU = 1016 el m−2) to 2.308 TECU, or by 8.9%, after the improved method was applied. For comparison, another test for the same station in 2009 indicates that the STD decreases from 1.344 TECU to 1.295 TECU. The amplitude of the 2009 improvement is very limited, only about 3.6%. The difference of the percentage improvements can probably be attributed to the different ionospheric conditions between 2001 and 2009.

Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling

Low, intermediate and high strain rate tensile experiments are carried out on flat smooth, notched and central-hole tensile specimens extracted from advanced high strength steel sheets. A split Hopkinson pressure bar testing system is used in conjunction with a load inversion device to perform the high strain rate tension experiments. Selected surface strains, as well as local displacements, are measured using high speed photography in conjunction with planar digital image correlation (video extensometer). Through thickness necking precedes fracture in all experiments. A hybrid experimental–numerical approach is therefore employed to determine the strain to fracture inside the neck. To obtain an accurate description of the local strain fields at very large deformations, a plasticity model with a Johnson–Cook type of rate and temperature-dependency and a combined Swift–Voce strain hardening law is used in conjunction with a non-associated anisotropic flow rule. The incremental change in temperature is computed using a strain rate dependent weighting function instead of solving the thermal field equations. The comparison of the computed and measured force–displacement curves and surface strain histories shows good agreement before and after the onset of necking. From each experiment, the loading path to fracture is determined describing the evolution of the equivalent plastic strain in terms of the stress triaxiality, Lode angle parameter, strain rate and temperature. An empirical extension of the stress-state dependent Hosford–Coulomb fracture initiation model is proposed to account for the effect of strain rate on the onset of ductile fracture. The model is subsequently calibrated and successfully validated using the results from fracture experiments on DP590 and TRIP780 steels.

Coordination of storage and generation in power system frequency control using an H ∞ approach

This study proposes a novel H∞ -based approach called advanced frequency control (AFC) to integrate storage into frequency control. The objective is to split the task of balancing frequency deviations introduced by renewable energy source (RES) and load variations according to the capabilities of storage and generators. Hence, via frequency dependent weighting functions, a so-called frequency separation objective is achieved: the conventional generators mainly balance the low-frequency components of the RES and load variations while the energy storage devices compensate the high-frequency components. First, a state-space structure-preserving model of the power system is derived, which is needed for the design of the controller. In order to enable the controller design for storage devices located at buses with no generators, a model for the frequency at such a bus is developed. Then, AFC controllers are synthesised through decentralised static output feedback to reduce the complexity in the practical implementation of such controllers. An existing linear matrix inequality algorithm is improved and employed to solve the involved H∞ problem. Finally, the WECC 9-bus test system is used to verify the performance of the AFC design.

3자유도 차량모델을 이용한 차선추종 µ 제어기 설계

Many articles have been published about a 2-degree of freedom model that includes the lateral and yaw motions for controller synthesis in intelligent transport system applications. In this paper, a 3-degree of freedom linear model that includes the roll motion is developed to design a robust steering controller for lane following maneuvers using <TEX>${\mu}$</TEX>-synthesis. This linear perturbed system includes a set of parametric uncertainties in cornering stiffness and unmodelled dynamics in steering actuators. The state-space model with parametric uncertainties is represented in linear fractional transformation form. Design purpose can be obtained by properly choosing the frequency dependent weighting functions. The objective of this study is to keep the tracking error and steering input energy small in the presence of variations of the cornering stiffness coefficients. Furthermore, good ride quality has to be achieved against these uncertainties. Frequency-domain analyses and time-domain numerical simulations are carried out in order to evaluate these performance specifications of a given vehicle system. Finally, the simulation results indicate that the proposed robust controller achieves good performance over a wide range of uncertainty for the given maneuvers.

Optimization of high speed EMU suspension parameters for vibration reduction

Various designs of high speed EMU (electric multiple units) operating at maximum speed of 400 km/h or above are under active development in many countries. Driving at such extreme high speed, the EMUs that are equipped with multiple power units and non articulated bogies normally experience severe level of vibration. Noting one of the primary design issues of the vertical EMU vibration, the present work tries an optimization of vehicle suspension system using ten degree of freedom analytical EMU model. The objective function for the work is consisted of the rail power spectral density (PSD), transfer function of car body, and frequency dependent weighting function which may represent human riding comfort. The transfer function is formulated using an autocorrelation of the model in frequency domain. For the enhanced reliability of the optimization work, both the US FRA (Federal Railway Administration) rail PSD and the actual rail PSD acquired from Kyeong-bu high speed rail in Korea on which the particular EMU will be driven are used. The well proven BFGS (Broyden-Fletcher-Goldfarb-Shanno) method is adopted for the optimization. The optimized design is verified using a commercial dynamic system simulation code at various operating conditions.

Predicting ductile fracture of low carbon steel sheets: Stress-based versus mixed stress/strain-based Mohr–Coulomb model

Two distinct implementations of the Mohr–Coulomb failure model are used in conjunction with a non-associated quadratic plasticity model to describe the onset of fracture in low carbon steel sheets. The stress-based version corresponds to the original Mohr–Coulomb model in stress space. For the mixed stress/strain-based version, the Mohr–Coulomb failure criterion is first transformed into the space of stress triaxiality, Lode angle parameter and equivalent plastic strain and then used as stress-state dependent weighting function in a damage indicator model. Basic fracture experiments including tensile specimens of different notch radii and a punch test are performed to calibrate the material parameters of the respective models. Subsequently, the models are used to predict the crack initiation in a Hasek test and during the stamping of an anticlastic structure. Unlike for the calibration experiments, the loading history during stamping is highly non-linear. Both models can be calibrated with similar accuracy, but the strain-based model predicts the instant of onset of fracture with greater accuracy in the stamping experiment which is an advantage of the empirical damage accumulation rule.

Finite elasto-viscoplastic modeling of polymers including asymmetric effects

Asymmetric effects between compression and tension are a pronounced behavior for glassy polymers such as polycarbonate. For its simulation an elasto-viscoplastic framework is formulated within a geometrically nonlinear theory. Here a new approach within the concept of stress mode dependent weighting functions is used, where each material parameter is additively decomposed into a sum of weighted stress mode-related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The constitutive equations are formulated for large strains in terms of logarithmic Hencky strains and its work conjugated Hill stresses. The resulting evolution equations are updated using a semi-implicit Euler scheme, and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation is also used to identify the material parameters thus resulting into a good agreement with experimental data. Furthermore, the model is used to simulate the cold drawing processes for a dumbbell-shaped specimen in tension and a perforated strip in compression and tension.

Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part II: Ductile fracture

The anisotropic ductile fracture of a 6260-T6 anisotropic aluminum alloy extrusion is investigated using a hybrid experimental–numerical approach. A basic fracture testing program covering a wide range of stress states and different material orientations is carried out. It comprises experiments on notched tensile specimens, tensile specimens with a central hole and butterfly shear specimens. The surface strain fields are obtained using two-dimensional Digital Image Correlation (DIC), while detailed finite element simulations are performed of all experiments to determine the local stress and strain histories inside the specimens. The analysis shows that the use of the newly-proposed extension of the Yld2000 yield function for three-dimensional stress states (see companion paper) together with an isotropic hardening law is able to predict the elasto-plastic behaviors of the present anisotropic aluminum alloy in all experiments. The experimental results show a strong dependency of the strain to fracture on the material orientation with respect to the loading direction. An uncoupled non-associated anisotropic fracture model is proposed which makes use of a stress state dependent weighting function and an anisotropic plastic strain measure. The latter is obtained from applying the von Mises equivalent plastic strain definition after the linear transformation of the plastic strain tensor. It is shown that the use of the isotropic Modified Mohr–Coulomb (MMC) stress state weighting function in this anisotropic fracture modeling framework provides accurate predictions of the onset of fracture for all thirteen fracture experiments.

Microdosimetry study of THOR BNCT beam using tissue equivalent proportional counter

Boron neutron capture therapy (BNCT) is a cancer treatment modality using a nuclear reactor and a boron compound drug. In Taiwan, Tsing Hua open-pool reactor (THOR) has been modulated for the basic research of BNCT for years. A new BNCT beam port was built in 2004 and used to prepare the first clinical trial in the near future. This work reports the microdosimetry study of the THOR BNCT beam by means of the tissue equivalent proportional counter (TEPC). Two self-fabricated TEPCs (the boron-doped versus the boron-free counter wall) were introduced. These dual TEPCs were applied to measure the lineal energy distributions in air and water phantom irradiated by the THOR BNCT mixed radiation field. Dose contributions from component radiations of different linear energy transfers (LETs) were analyzed. Applying a lineal energy dependent biological weighting function, r( y), to the total and individual lineal energy distributions, the effective relative biological effectiveness (RBE), neutron RBE, photon RBE, and boron capture RBE (BNC RBE) were all determined at various depths of the water phantom. Minimum and maximum values of the effective RBE were 1.68 and 2.93, respectively. The maximum effective RBE occurred at 2 cm depth in the phantom. The average neutron RBE, photon RBE, and BNC RBE values were 3.160±0.020, 1.018±0.001, and 1.570±0.270, respectively, for the THOR BNCT beam.

Asymmetric effects of polymers in finite thermoviscoplasticity

AbstractGlassy polymers such as polycarbonate exhibit different behaviours in different loading scenarios, such as tension and compression. For the simulation of these asymmetric effects we present a framework for thermoviscoplastic modelling of polymers at large strains. To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation which is decomposed into a sum of weighted stress mode related quantities. The different stress modes are chosen such that they are accessible to individual examination in the laboratory, where tension and compression are typical examples. The characterisation of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the Lode angle, such that stress mode dependent scalar weighting functions can be constructed. Furthermore the numerical implementation of the resulting set of constitutive equations is used in the finite element program ABAQUS to simulate the laser transmission welding process. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Thermoviscoplastic modelling of asymmetric effects for polymers at large strains

Glassy polymers such as polycarbonate exhibit different behaviours in different loading scenarios, such as tension and compression. To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation and decomposed into a sum of weighted stress mode related quantities. The different stress modes are chosen such that they are accessible to individual examination in the laboratory, where tension and compression are typical examples. The characterisation of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the Lode angle, such that stress mode dependent scalar weighting functions can be constructed. Furthermore the numerical implementation of the constitutive equations into a finite element program is briefly described. In a numerical example, the model is used to simulate the laser transmission welding process.

Simulation of asymmetric effects for shape memory alloys

AbstractExperimental results of shape memory alloys show a pronounced asymmetric behaviour between tension, compression and shear. For simulation of these effects in the constitutive equations different transformation strain tensors are introduced. These are related to the different variants for the multi‐variant‐ and detwinned‐martensite as a consequence of different stress states. In the framework of plasticity the concept of stress mode dependent weighting functions is applied in order to characterize the different stress states. Verification of the proposed methodology is succeeded for simulation of the pseudoelastic behaviour of shape memory alloys with different hardening characteristics in tension, compression and shear. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Simulation of asymmetric effects for shape memory alloys using the concept of stress mode dependent weighting functions

Experimental results of shape memory alloys show a pronounced asymmetric behaviour between tension, compression and shear. For simulation of these effects in the constitutive equations different transformation strain tensors are introduced. These are related to the different variants for the multi-variant- and detwinned-martensite as a consequence of different stress states. In the framework of plasticity the concept of stress mode dependent weighting functions is applied in order to characterize the different stress states. Verification of the proposed methodology is succeeded for simulation of the pseudoelastic behaviour of shape memory alloys with different hardening characteristics in tension and shear.

Simulation of rate dependent plasticity for polymers with asymmetric effects

Polycarbonate is an amorphous polymer which exhibits a pronounced strength-differential effect between compression and tension. Also strain rate and temperature influence the mechanical response of the polycarbonate. The concept of stress mode dependent weighting functions is used in the proposed model to simulate the asymmetric effects for different loading speeds. In this concept, an additive decomposition of the flow rule is assumed into a sum of weighted stress mode related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The resulting evolution equations are updated using a backward Euler scheme and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation of the resulting set of constitutive equations is used in a finite element program for parameter identification. The proposed model is verified by showing a good agreement with the experimental data. After that the model is used to simulate the laser transmission welding process.