Linear Rule Research Articles

Perfect tracking control of discrete-time quadratic TS fuzzy systems via feedback linearisation

ABSTRACTPerfect tracking control is an important and frequently encountered requirement in various industries (e.g. robotic control). We developed a novel systematic framework for designing a fuzzy controller via feedback linearisation to control a class of discrete-time Takagi–Sugeno (TS) fuzzy systems with quadratic rule consequents to achieve such tracking. We established a necessary condition for its local stability and a necessary and sufficient condition for the boundedness of the controller. The feedback linearisation is known to fail to work in certain systems due to the unboundedness of the tracking controller output. To address this issue, we developed a method to check whether any given quadratic TS fuzzy system will cause such a failure. We developed a scheme to ensure that the output of the controller designed for any failure-causing system will be bounded and the resulting controller will attain nearly perfect tracking performance. Applying feedback linearisation to the quadratic fuzzy systems is innovative relative to the literature exclusively dealing with the TS fuzzy systems with linear rule consequents (including our previous results), which are now generalised by the new findings. Two numerical examples are provided to illustrate the effectiveness and utility of our new theoretical results.

Multistage adaptive optimization using hybrid scenario and decision rule formulation

AbstractScenario‐based stochastic programming and linear decision rule (LDR)‐based robust optimization are prevalent methods for solving multistage adaptive optimization (MSAP) problems. In practical applications such as capacity expansion planning of chemical processes, often multiple sources of uncertainty affect the problem which introduces challenges to traditional stochastic optimization methods. While a large number of uncertain parameters exist in the problem, using scenario‐based method results in very large problem size and the solution becomes computationally expensive. In addition, when the constraints include multiplication of uncertain parameters and adaptive variables, the constraints are not linear with respect to uncertain parameters when the LDR method is used. In order to address these challenges, we propose two different hybrid methods where scenario and decision rule methods are combined to solve the MSAP problem. The article demonstrates the computational performance of the proposed hybrid methods using two chemical process planning examples.

Limited Sampling Strategy for the Estimation of Mycophenolic Acid and its Acyl Glucuronide Metabolite Area under the Concentration-Time Curve in Japanese Lung Transplant Recipients.

The dose of mycophenolate mofetil (MMF) used to prevent rejection after lung transplantation is often adjusted based on the 12-hour area under the concentration-time curve (AUC0-12) of mycophenolic acid (MPA). A limited sampling strategy (LSS) is useful to define the pharmacokinetic (PK) profiles of MPA and mycophenolic acid acyl glucuronide (AcMPAG). Therefore, this study aimed to design a LSS based on multiple linear regression for estimating the AUC0-12 of MPA and AcMPAG at the minimum blood sampling points in Japanese lung transplant patients with concomitant tacrolimus. Forty-five lung transplantation recipients were enrolled in a PK study of MPA, mycophenolic acid glucuronide (MPAG), and AcMPAG. The plasma MPA, MPAG, and AcMPAG concentrations were determined just before and at 0.5, 1, 2, 4, 8, and 12 hours after dosing. The AUC0-12 of MPA and AcMPAG was calculated using a linear trapezoidal rule from the plasma concentration of each blood sampling time. LSS was used to develop models for estimated AUC in the model group (n = 23) and was evaluated in the validation group (n = 22). The best three time-point equation was 4.04 + 1.64·C1 + 3.08·C4 + 5.17·C8 for MPA, and -0.13 + 3.01·C1 + 3.51·C4 + 5.74·C8 for AcMPAG. The prediction errors (PE) and the absolute prediction errors (APE) were within the clinically acceptable ± 5% and 15% range, respectively (MPA: PE = 2.00%, APE = 11.66%, AcMPAG: PE = 0.98%, APE = 14.69%). The percentage of estimated AUC0-12 within ± 15% of the observed AUC0-12 was 77.27% for MPA and 81.82% for AcMPAG. LSS using three time-point (C1, C4, and C8) provides the most reliable and accurate simultaneous estimation of the AUC0-12 of MPA and AcMPAG in Japanese lung transplant patients.

Fatigue Assessment on Suspenders under Stochastic Wind and Traffic Loads Based on In-Situ Monitoring Data

As a critical component of a suspension bridge, the integrity of the suspenders plays a critical role in the serviceability and reliability of the bridge during its life time. Despite the wide recognition of the importance of the suspenders, very few studies have been devoted to the condition evaluation of suspenders in operation. The present study performs the fatigue assessment on the suspenders accounting for the stochastic wind and traffic loads using the in-situ monitoring data. To this end, a probabilistic numerical framework is proposed to predict the time-dependent fatigue reliability of the suspenders under stochastic wind and traffic loads during the bridge’s life time, based on the linear fatigue damage rule. As a demonstration, the proposed numerical framework is applied to a long-span suspension bridge located in a mountainous canyon. The results indicate that it is of paramount importance to consider both the wind and traffic load effects in the fatigue reliability evaluation of the suspenders. In addition, it was also found that among the suspenders under investigation, the short suspender at the bridge mid-span (S36) is more prone to the fatigue damage, while the long suspender at the end of the bridge girder (S2) is less prone to the fatigue damage. Finally, provided with a target reliability index of 3.0, the fatigue life of the suspenders S36 and S2, considering the life time wind and traffic load, is estimated as 53 years and 167 years, respectively. The present research could provide essential guidelines for the optimization of inspection and replacement in maintenance practices for suspenders.

Application of the graph cellular automaton in generating languages

The purpose of this research is to strengthen the core of Cellular Automaton using the concept of Graph theory and Automata theory. In this paper we introduce a new approach of defining the Graph Cellular Automaton GCA, V,I,δ consisting of set of vertices and input symbols along with the time evolution function δ. Using the Basic Linear Rules, we define the kth generation GCA. This method enables us to capture the complete characterization of the future generations. When the defined GCA is taken as a graph corresponding to a given finite automaton, then the language generated by the kth generation GCA is predicted corresponding to the fundamental basic linear rules. This enables us to predict the language of the kth generation automaton using all the 512 rules. All explained concepts are illustrated with suitable examples.

Isospin dependence of electromagnetic transition strengths among an isobaric triplet

Electric quadrupole matrix elements, Mp, for the Jπ=2+→0+, ΔT=0, T=1 transitions across the A=46 isobaric multiplet 46Cr-46V-46Ti have been measured at GSI with the FRS-LYCCA-AGATA setup. This allows direct insight into the isospin purity of the states of interest by testing the linearity of Mp with respect to Tz. Pairs of nuclei in the T=1 triplet were studied using identical reaction mechanisms in order to control systematic errors. The Mp values were obtained with two different methodologies: (i) a relativistic Coulomb excitation experiment was performed for 46Cr and 46Ti; (ii) a “stretched target” technique was adopted here, for the first time, for lifetime measurements in 46V and 46Ti. A constant value of Mp across the triplet has been observed. Shell-model calculations performed within the fp shell fail to reproduce this unexpected trend, pointing towards the need of a wider valence space. This result is confirmed by the good agreement with experimental data achieved with an interaction which allows excitations from the underlying sd shell. A test of the linearity rule for all published data on complete T=1 isospin triplets is presented.

Multi-view correlation tracking with adaptive memory-improved update model

Recently, some researchers concentrate on applying multi-view learning to the correlation filter tracking to achieve both the efficiency and accuracy. However, most of them fail to effectively collaborate multiple views to deal with more complex environment. Moreover, their methods are prone to drift in case of long-term occlusion due to the memory loss. In this paper, we propose a novel multi-view correlation filters-based tracker for robust visual tracking. First, we present an adaptive multi-view collaboration strategy to highlight different contributions of different views by jointly considering the reliability and discrimination. Second, an effective memory-improved model update rule is introduced to avoid falling into a contaminated target model. Compared with the conventional linear interpolation update rule, it can effectively deal with long-term occlusion by improving the memory of historical models. Furthermore, instead of assigning a unified learning rate for all views in each frame, we design varying learning rates for different views according to their respective evaluations on the current tracking result, which can prevent the target models of all views from being contaminated at the same time. Finally, a failure-aware scale update scheme is developed to avoid noisy scale estimation in case of temporal tracking failure. Extensive experimental results on the recent benchmark demonstrate that our tracker performs favorably against other state-of-the-art trackers with a real-time performance.

Proposal for peruvian standard considering the effect of bidirectionality and the angle of incidence of an earthquake

Currently, it is considered that seismic actions act independently in two or three main directions orthogonal to each other, applying them to the building, without this necessarily being valid. It is for such, that seismic analysis of buildings should consider the bidirectional effects that seismic actions have, being possible if an angle of real incidence of each seismic action was considered, to estimate the maximum effects of the structural elements.
 These effects will be analyzed by using the linear time-history analysis of 11 structures with different rigidities and eccentricities in both directions, using angles of incidence every 10° and 20 Peruvian seismic records between very rigid, intermediate and soft soils obtained from data base of CISMID and IGP. Afterwards, a non-linear time-history analysis will be carried out, which will be applied to one of the 11 structures and use angles of incidence every 10° and a seismic record. Likewise, 2 models will be made to scale so that they are tested on a platform of six degrees of freedom, entering the records of the accelerations in their three directions. The maximum responses of all the verifications will be compared with the maximum response of the spectral modal analysis obtaining linear rules for amplification factors.
 Finally, it will be obtained a relation between the spectral modal analysis and the time-history analysis that consider the effects of the bidirectionality and the angle of incidence in reinforced concrete structures.

Poincaré constraints on the gravitational form factors for massive states with arbitrary spin

In this work we analyse the constraints imposed by Poincar\'e symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distributional approach, we prove for the first time non-perturbatively that the zero momentum transfer limit of the leading two form factors in the decomposition are completely independent of the spin of the states. It turns out that these constraints arise due to the general Poincar\'e transformation and on-shell properties of the states, as opposed to the specific characteristics of the individual Poincar\'e generators themselves. By expressing these leading form factors in terms of generalised parton distributions, we subsequently derive the linear and angular momentum sum rules for states with arbitrary spin.

An adjustable robust optimization approach for periodic timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing a periodic timetable that can easily be adjusted in case of small periodic disturbances. We develop a solution method for a parametrized class of uncertainty regions. This class relates closely to uncertainty regions known in the robust optimization literature, and naturally defines a metric for the robustness of the timetable. The proposed solution method combines a linear decision rule with well-known reformulation techniques and cutting-plane methods. We show that the RPTP can be solved for practical-sized instances by applying the solution method to practical cases of Netherlands Railways (NS). In particular, we show that the trade-off between the efficiency and robustness of a timetable can be analyzed using our solution method.

Fatigue Calculation of Offshore Jacket Structural For Monitoring

Based on the IEC 61400-3 offshore wind turbine(OWT) design guidelines. The NREL 5MW wind turbine with Taiwan domestic jacket support structure in 18 meters water depth was selected to perform the fatigue strength calculation for the support structure. Commercial software Bladed and SACS are used to perform the required structural responses and fatigue strength calculations. The stress concentration factors(SCF) and S-N curves for the stress calculations of tubular joints are adopted based on the recommendation of DNV GL guidelines. The magnitude of the stress variation range and the corresponding number of counts are obtained by the rainflow counting algorithm. Finally under the assumption of Palmgren-Miner linear cumulative damage rule, the cumulative damage of the structure component can be calculated and then the fatigue life can be estimated. The numerical evaluation results can also be available for the further reference on the determination of sensor locations for the structural monitor system.

Using the Hybrid Simulated Annealing-M5 Tree Algorithms to Extract the If-Then Operation Rules in a Single Reservoir

The environmental water demand of the Mahabad River in the Urmia Lake basin in Iran was first estimated, using the flow duration curve shifting method (FDC Shifting) in this study. Secondly, the optimal operating model of the reservoir was developed with the goals of decreasing the deficiencies and considering the downstream demands of the reservoir, especially the environmental water demands by employing the simulated annealing (SA) and non-linear programming (NLP) methods. The results of the SA algorithm were compared with those of the NLP model with the indices of reliability, resiliency velocity, vulnerability, and sustainability. Then, the optimum released water values in the current month, the optimum water storage values in the reservoir, reservoir inflows and monthly demands were considered as inputs of the M5 tree model, and the optimum values of released water in the next month were considered as outputs of the M5 model. Finally, the optimum operation rules from the reservoir were developed in the form of if-then linear rules for future uses. One of the main advantages of the M5 tree model is to present two operation rules as if-then rules for all the operating periods with relatively acceptable accuracy. The results showed that the SA-M5 tree model, as a method of data mining, can extract the operation rules with relatively high accuracy.

Modeling the Strain-Range Dependent Cyclic Hardening of SS304 and 08Ch18N10T Stainless Steel with a Memory Surface

This paper deals with the development of a cyclic plasticity model suitable for predicting the strain range-dependent behavior of austenitic steels. The proposed cyclic plasticity model uses the virtual back-stress variable corresponding to a cyclically-stable material under strain control. This new internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. First, the proposed model was validated on experimental data published for the SS304 material (Kang et al., Constitutive modeling of strain range dependent cyclic hardening. Int J Plast 19 (2003) 1801–1819). Subsequently, the proposed cyclic plasticity model was applied to our own experimental data from uniaxial tests realized on 08Ch18N10T at room temperature. The new cyclic plasticity model can be calibrated by the relatively simple fitting procedure that is described in the paper. A comparison between the results of a numerical simulation and the results of real experiments demonstrates the robustness of the proposed approach.

Strength Evaluation of a Bogie Frame by Different Methods

Some crucial loads that current strength design specifications have not taken into account are also considered when assessing the strength of a bogie frame. Calculation methods of these loads come from load analysis. Finite element simulation and fatigue test rig have been used to assess static strength and fatigue strength of a bogie frame. In addition to the two methods, actual running test is also used to assess bogie frame fatigue strength. In finite element simulation method, endurance limit and modified Goodman fatigue limit diagram are two important tools to judge whether fatigue strength of a bogie frame meets requirement. In actual running test method, Miner linear cumulative damage rule is used to assess bogie frame fatigue strength.

Evolution of water column pulled by partially submerged spheres with different velocities and submergence depths

Abstract The evolution of a water column pulled by a partially submerged sphere, known as the water exit problem, is evaluated by numerical simulation. The lattice Boltzmann method was combined with a mass-tracking algorithm. The accuracy of the numerical method was demonstrated by comparisons with previous experimental results. Moreover, the evolution processes of the water column with different Froude and Weber numbers (0.4134 ≤ Fr ≤ 8.2479, 5.15 × 102 ≤ We ≤ 2.06 × 105), as well as different initial submergence depths (Hs/D = 1/2, 1/4, 1/8), were discussed. Spontaneous breakup of water column was observed for higher Weber numbers. Moreover, vertical stretching of the water column approximately followed a power law in which the power exponent depended on the initial setup of the sphere and its time scales. However, the horizontal evolution of the water column followed an approximately linear rule. Variation in the water column diameter appeared to be irregular at different physical times or in non-dimensional time. Furthermore, the initial submergence depth of the sphere was also a significant factor in the pinch-off dynamics and water column evolution. This study of water exit is of a great importance in designing marine vehicles that take off from a free water surface.

Experimental investigation of natural gas reactivity using a fuel substitution method

Fuel substitution tests using reference fuels of methane/hydrogen and methane/propane were performed for the pure test fuels hydrogen, ethane, ethylene, propane, n-butane, n-heptane, and isooctane using HCCI combustion. The reactivity of each test fuel relative to the reference fuels was quantified with a newly defined hydrogen index (HI) and propane index (PI). It was observed that the common hydrocarbon fuels tested show a strong sensitivity of HI and PI to temperature and pressure, and that the reactivity relative to the reference fuels can change substantially at different operating conditions. The fuels that have similar low temperature chemistry (n-butane, n-heptane, and isocotane) exhibited PI that were independent of operating condition. Ethane, ethylene, and hydrogen exhibited PI that were strongly dependent on operating condition, with the relative reactivities increasing with increasing temperature. Fuel substitution tests performed with two multi-component methane number (MN) gas mixtures followed trends similar to those observed for the pure hydrocarbon fuel testing, exhibiting similar relative reactivity trends as for propane relative to the reference fuels for the different operating conditions. A linear energy-based blending rule was used to predict the HI of each fuel mixture from the individual fuel components and seen to match experimental trends; however, predicted HI were lower than experimental HI across all operating conditions. The MN was also used to predict the HI of each fuel mixture and was seen to match experimental results only at low pressure/high temperature conditions but not at high pressure/low temperature conditions.

Leibniz complexity of Nash functions on differentiations

The derivatives of Nash functions are Nash functions which are derived algebraically from their minimal polynomial equations. In this paper we show that, for any non-Nash analytic function, it is impossible to derive its derivatives algebraically, i.e., by using linearity and Leibniz rule finite times. In fact we prove the impossibility of such kind of algebraic computations, algebraically by using Kähler differentials. Then the notion of Leibniz complexity of a Nash function is introduced in this paper, as a computational complexity on its derivative, by the minimal number of usages of Leibniz rules to compute the total differential algebraically. We provide general observations and upper estimates on Leibniz complexity of Nash functions, related to the binary expansions, the addition chain complexity, the non-scalar complexity and the complexity of Nash functions in the sense of Ramanakoraisina.

Effects of Al and Mo on high temperature oxidation behavior of refractory high entropy alloys

Refractory high entropy alloys have superior mechanical properties at high temperatures, and the oxidation behavior of these alloys is very important. The present work investigated the high temperature oxidation behavior of three alloys with compositions of TiNbTa0.5Zr, TiNbTa0.5ZrAl and TiNbTa0.5ZrAlMo0.5, and the effects of alloying elements were discussed. Results indicated that the oxidation rates of the TiNbTa0.5Zr and TiNbTa0.5ZrAl alloys are controlled by diffusion, and obey the exponential rule. However, the oxidation rate of the TiNbTa0.5ZrAlMo0.5 alloy is controlled by interface reaction, and obeys the linear rule. The addition of Al leads to a better oxidation resistance by forming a protective oxide scale. However, the protection of Al-rich scale is weakened by the addition of Mo. Extensive pores and cracks occur in the oxide scale of the TiNbTa0.5ZrAlMo0.5 alloy, resulting in a significant decrease in oxidation resistance.

Parametric probabilistic approach for cumulative fatigue damage using double linear damage rule considering limited data

This work proposes a parametric probabilistic approach to model damage accumulation using the double linear damage rule (DLDR) considering the existence of limited experimental fatigue data. A probabilistic version of DLDR is developed in which the joint distribution of the knee-point coordinates is obtained as a function of the joint distribution of the DLDR model input parameters. Considering information extracted from experiments containing a limited number of data points, an uncertainty quantification framework based on the Maximum Entropy Principle and Monte Carlo simulations is proposed to determine the distribution of fatigue life. The proposed approach is validated using fatigue life experiments available in the literature.

Maxwell–Stefan diffusion coefficient model derived from entropy generation minimization principle for binary liquid mixtures

A new model for the Maxwell–Stefan (MS) diffusion coefficient was developed in this study. The entropy generation minimization principle was used to derive the expression of the MS diffusion coefficient, which has a similar form as Eyring’s model. Molar excess internal energy based on two-liquid theory was derived to correct the error induced by the linear mixing rule. The local surface area fraction was used to replace the bulk fraction by considering the intermolecular friction force exerting on the molecular surfaces. The new model was applied to calculate the Fick diffusion coefficients for four binary systems, which were measured experimentally by digital holographic interferometry. Comparison of the experimental and calculation results indicated that the proposed model has a good performance for calculating the diffusion coefficients for the mentioned binary systems.