Optimal Weight Function Research Articles

Alternative weighting schemes for fine‐tuned extended similarity indices

AbstractExtended similarity indices (i.e., generalization of pairwise similarity) have recently gained importance because of their simplicity, fast computation, and superiority in tasks like diversity picking. However, they operate with several meta parameters that should be optimized. Earlier, we extended the binary similarity indices to “discrete non‐binary” and “continuous” data; now we continue with introducing and comparing multiple weighting functions. As a case study, the similarity of CYP enzyme inhibitors (4016 molecules after curation) was characterized by their extended similarities, based on 2D descriptors, MACCS and Morgan fingerprints. A statistical workflow based on sum of ranking differences (SRD) and analysis of variance (ANOVA) was used for finding the optimal weight function(s). Overall, the best weighting function is the fraction (“frac”), which corresponds to the principle of parsimony. Optimal extended similarity indices were also found, and their differences are revealed across different data sets. We intend this work to be a guideline for users of extended similarity indices regarding the various weighting options available. Source code for the calculations is available at https://github.com/mqcomplab/MultipleComparisons.

Geographically Weighted Panel Regression Modelling of Dengue Hemorrhagic Fever Data Using Exponential Kernel Function

Geographically Weighted Panel Regression (GWPR) model is a panel regression model applied to spatial data. This research takes the Fixed Effect Model (FEM) panel regression as the global model and GWPR as the local model for dengue hemorrhagic fever (DHF) in East Kalimantan Province data over the years 2018-2020. DHF is a disease that has the potential to become an extraordinary event which is accompanied by death. In comparison to Indonesia, East Kalimantan Province's DHF Incident Rate (IR) was high in 2020. East Kalimantan's IR is 60.6 per 100,000 population, compared to Indonesia's IR of 40.0 per 100,000 population. This research aims to obtain the GWPR model, as well as to acquire factors that affect DHF in East Kalimantan Province over the years 2018-2020 based GWPR model. The parameter of the GWPR model was estimated on each observation location using the Weighted Least Square (WLS) method, which is an Ordinary Least Square (OLS) with the addition of spatial weighting. The spatial weighting on the GWPR model was determined by the best weighting function between fixed exponential and adaptive exponential. The optimum weighting function with a minimum cross-validation (CV) value of 1.7317×106 is adaptive exponential. Based on GWPR parameter testing, factors that affect DHF are local and diverse in each 10 regencies/municipalities in East Kalimantan Province. These factors are population density, number of health facilities, percentage of proper sanitation use in the household, percentage of household with qualified drinking water sources, and percentage of health services. The coefficient of determination of the GWPR model obtains a higher value than the FEM, which is 95.33%. Based on the measurement of goodness using the coefficient of determination value, it can be concluded that GWPR is the best method to model the DHF data rather than the FEM.

Fuzzy variable gain robust control of active magnetic bearings rigid rotor system

AbstractA high speed rigid rotor system supported by active magnetic bearings (AMBs) puts forward higher requirements on the performance of controllers. The fuzzy variable gain H‐infinity robust control (FVGRC) method is proposed to simplify controller design while suppressing system uncertainty. First, the T‐S fuzzy model of four‐degree‐of‐freedom (4‐DOF) AMBs was established based on the 4‐DOF AMBs rigid rotor equivalent coupling model optimised by the μ‐gap metric. Then, based on the fuzzy models of AMBs systems under different operating conditions, the relative optimal weight function value of H‐infinity robust controller was calculated when AMBs system was at value of the speed endpoint, and the fuzzy variable gain H‐infinity robust (FVGR) controller was designed on this basis. Finally, the simulation and experimental results showed that the FVGRC can simplify the model of controller and ensure the stable operation of AMBs rigid rotor system in the full speed range under high‐speed conditions.

Geographically Weighted Panel Regression Modelling of Human Development Index Data in East Kalimantan Province in 2017-2020

Geographically Weighted Panel Regression (GWPR) model is a panel regression model applied on spatial data. This research applied Fixed Effect Model (FEM) on panel regression as the global model and GWPR as the local model for Human Development Index (HDI) regencies/municipalities in East Kalimantan Province data over the years 2017-2020. The aim of this research is to obtain the GWPR model of HDI data, as well as to acquire factors that influence it. The parameter of GWPR model was estimated on each observation location using the Weighted Least Square (WLS) method, namely Ordinary Least Square (OLS) with addition of spatial weighting. The spatial weighting on GWPR model was calculated using fixed bisquare, fixed tricube, adaptive bisquare and adaptive tricube. After the selection process, the optimum weighting function is adaptive tricube which provides a minimum Cross Validation (CV) value of 5.1419. Based on GWPR parameter testing, factors that affect HDI are local and diverse in each 10 regencies/municipalities in East Kalimantan Province. These factors are the labor force participation rate, number of health facilities, Gini ratio, population growth rate, open unemployment rate, poverty gap index and percentage of food expenditure. The coefficient of determination of the GWPR model obtains a value of 94.36% with the RMSE value of 0.1221.

Improved semiparametric estimation of the proportional rate model with recurrent event data.

Owing to its robustness properties, marginal interpretations, and ease of implementation, the pseudo-partial likelihood method proposed in the seminal papers of Pepe and Cai and Lin etal. has become the default approach for analyzing recurrent event data with Cox-type proportional rate models. However, the construction of the pseudo-partial score function ignores the dependency among recurrent events and thus can be inefficient. An attempt to investigate the asymptotic efficiency of weighted pseudo-partial likelihood estimation found that the optimal weight function involves the unknown variance-covariance process of the recurrent event process and may not have closed-form expression. Thus, instead of deriving the optimal weights, we propose to combine a system of pre-specified weighted pseudo-partial score equationsvia the generalized method of moments and empirical likelihood estimation. We show that a substantial efficiency gain can be easily achieved without imposing additional model assumptions. More importantly, the proposed estimation procedures can be implemented with existing software. Theoretical and numerical analyses show that the empirical likelihood estimator is more appealing than the generalized method of moments estimator when the sample size is sufficiently large. An analysis of readmission risk in colorectal cancer patients is presented to illustrate the proposedmethodology.

Instrumented Roadway Characterized through an Optimized Indicators Method

In recent years, pavement instrumentation became a common practice for structural monitoring. Instrumented roadway includes different type of sensors such as strain gauges, accelerometers or geophones. Data processing consists often in extracting different values such as extremum, number of positives or negatives peaks, calculate threshold, on so on. These values are generally representative of variations in the whole structure, but make it more difficult to follow a specific characteristic of the structure. To overcome this limitation, an original method has been defined. It consists in finding a weighting function of the signal that is particularly sensitive to a specific characteristic of the structure without being sensitive to the other characteristics. This weighting function is calculated using a model of the structure. The sensitivity of the response of the simulated sensor to different variations in the characteristics of the structure is studied. From these sensitivities, it is possible to define specific weighting functions. The application of these weighting functions to the measured signals makes it possible to deduce indicators specific to different characteristics of the structure. This method has been applied during an experiment on the Nantes fatigue carousel. Stain gauges equipped the roadways and lot of signals has been recorded during the loading phase. A viscoelastic pavement model has been defined and the response under a running load was calculated. Optimal weighting functions have been estimated and specific indicators constructed. Stain gauge measurements have been processed to calculate the indicator; The paper presents a comparison between constructed indicators and conventionally used indicators.

An Efficient Orthogonal Polynomial Method for Auxetic Structure Analysis with Epistemic Uncertainties

Traditional approaches used for analyzing the mechanical properties of auxetic structures are commonly based on deterministic techniques, where the effects of uncertainties are neglected. However, uncertainty is widely presented in auxetic structures, which may affect their mechanical properties greatly. The evidence theory has a strong ability to deal with uncertainties; thus, it is introduced for the modelling of epistemic uncertainties in auxetic structures. For the response analysis of a typical double-V negative Poisson’s ratio (NPR) structure with epistemic uncertainty, a new sequence-sampling-based arbitrary orthogonal polynomial (SS-AOP) expansion is proposed by introducing arbitrary orthogonal polynomial theory and the sequential sampling strategy. In SS-AOP, a sampling technique is developed to calculate the coefficient of AOP expansion. In particular, the candidate points for sampling are generated using the Gauss points associated with the optimal Gauss weight function for each evidence variable, and the sequential-sampling technique is introduced to select the sampling points from candidate points. By using the SS-AOP, the number of sampling points needed for establishing AOP expansion can be effectively reduced; thus, the efficiency of the AOP expansion method can be improved without sacrificing accuracy. The proposed SS-AOP is thoroughly investigated through comparison to the Gaussian quadrature-based AOP method, the Latin-hypercube-sampling-based AOP (LHS-AOP) method and the optimal Latin-hypercube-sampling-based AOP (OLHS-AOP) method.

A weighted range‐free localization algorithm for irregular multihop networks

SummaryRange‐free localization is a widely concerned technique that supports many essential network applications like coverage and clustering. Most existing localization technologies assume that nodes are uniformly distributed in a regular network with no obstacles and that propagation paths between pairwise nodes are close to straight lines. However, in real‐world scenarios, network topology is usually irregular, resulting in estimated distances that differ significantly from the corresponding physical distances and poor anchor deployment. These will lead to erroneous distance measurement and inaccurate localization results. This paper proposes a new algorithm, called the weighted range‐free localization algorithm (WRL for short), to improve the localization performance in irregular networks. Specifically, we first present a feasible scheme that can fulfill the information exchange and relative distance estimation for each node simultaneously. We then employ an optimal weight function to suppress the effect of cumulative errors and introduce the weighted bounding‐box algorithm to mitigate outlier location estimation induced by probably collinear anchor nodes. Simulation results show that, compared to state‐of‐the‐art methods, WRL improves localization accuracy while incurring lower computation and communication overheads in various irregular network topologies.

Competing risks regression models with covariates-adjusted censoring weight under the generalized case-cohort design.

A generalized case-cohort design has been used when measuring exposures is expensive and events are not rare in the full cohort. This design collects expensive exposure information from a (stratified) randomly selected subset from the full cohort, called the subcohort, and a fraction of cases outside the subcohort. For the full cohort study with competing risks, He et al. (Scand J Stat 43:103-122, 2016) studied the non-stratified proportional subdistribution hazards model with covariate-dependent censoring to directly evaluate covariate effects on the cumulative incidence function. In this paper, we propose a stratified proportional subdistribution hazards model with covariate-adjusted censoring weights for competing risks data under the generalized case-cohort design. We consider a general class of weight functions to account for the generalized case-cohort design. Then, we derive the optimal weight function which minimizes the asymptotic variance of parameter estimates within the general class of weight functions. The proposed estimator is shown to be consistent and asymptotically normally distributed. The simulation studies show (i) the proposed estimator with covariate-adjusted weight is unbiased when the censoring distribution depends on covariates; and (ii) the proposed estimator with the optimal weight function gains parameter estimation efficiency. We apply the proposed method to stem cell transplantation and diabetes data sets.

State of Health Prediction of Lithium-Ion Batteries Based on the Discharge Voltage and Temperature

Accurate state of health (SOH) prediction of lithium-ion batteries is essential for battery health management. In this paper, a novel method of predicting the SOH of lithium-ion batteries based on the voltage and temperature in the discharging process is proposed to achieve the accurate prediction. Both the equal voltage discharge time and the temperature change during the discharge process are regarded as health indicators (HIs), and then, the Pearson and Spearman relational analysis methods are applied to evaluate the relevance between HIs and SOH. On this basis, we modify the relevance vector machine (RVM) to a multiple kernel relevance vector machine (MKRVM) by combining Gaussian with sigmoid function to improve the accuracy of SOH prediction. The particle swarm optimization (PSO) is used to find the optimal weight and kernel function parameters of MKRVM. The aging data from NASA Ames Prognostics Center of Excellence are used to verify the effectiveness and accuracy of the proposed method in numerical simulations, whose results show that the MKRVM method has higher SOH prediction accuracy of lithium-ion batteries than the relevant methods.

3D Snow Sculpture Reconstruction Based on Structured-Light 3D Vision Measurement

Structured-light technique is an effective method for indoor 3D measurement, but it is hard to obtain ideal results outdoors because of complex illumination interference on sensors. This paper presents a 3D vision measurement method based on digital image processing to improve resistance to noise of measuring systems, which ensuresnormal operation of a structured-light sensor in the wild without changing its components, and the method is applied in 3D reconstruction of snow sculpture. During image preprocessing, an optimal weight function is designed based on noise classification and minimum entropy, and the color images are transformed into monochromatic value images to eliminate most environmental noise. Then a Decision Tree Model (DTM) in a spatial-temporal context of video sequence is used to extract and track stripe. The model is insensitive to stubborn noise and reflection in the images, and the result of the model after coordinate transformation is a 3D point cloud of the corresponding snow sculpture. In experimental results, the root mean square (RMS) error and mean error are less than 0.722 mm and 0.574 mm respectively, showing that the method can realize real-time, robust and accurate measurement under a complex illumination environment, and can therefore provide technical support for snow sculpture 3D measurement.

An efficient range-free multi-hop localisation algorithm for irregular wireless sensor networks

In the range-free multi-hop localisation algorithm, the physical distance between nodes is estimated based on hops, and complex ranging equipment is not required during this process. This could help realise simpler system configuration, while lowering the node cost and consumption of energy in wireless sensor networks. During the actual deployment of nodes, the deviation of the final estimated location from the actual location is generally caused by factors such as shielding or barriers during the hop distance conversion. In this paper, an improved method for range-free multi-hop localisation is proposed which could improve the precision without increasing the cost and reducing the performance of the algorithm. First, we obtain the optimal weighting function for location estimation according to the error between the estimated locations of non-beacon nodes and their actual locations. Then, we correct the inaccurate estimated locations of non-beacon nodes through geometric constraints. Lastly, we demonstrate via simulation that our proposed localisation method outperforms the basic range-free multi-hop algorithms as well as their improved methods in irregular wireless sensor networks.

Robust LFT-LPV H∞ Control of an Underactuated Inverted Pendulum on a Cart with Optimal Weighting Functions Selection by GA and ES

Abstract This article investigates the robust stabilization and control of the inverted pendulum on a cart against disturbances, measurement noises, and parametric uncertainties by the LFT-based LPV technique (Linear-Fractional-Transformation based Linear-Parameter-Varying). To make the applying of the LPV technique possible, the LPV representation of the inverted pendulum on a cart model is developed. Besides, the underactuated constraint of this vehicle is overcome by considering both degrees of freedom (the rotational one and the translational one) in the structure. Moreover, the selection of the weighting functions that represent the desired performance is solved by two approaches of evolutionary algorithms; Genetic Algorithms (GA) and Evolutionary Strategies (ES) to find the weighting functions’ optimal parameters. To validate the proposed approach, simulations are performed and they show the effectiveness of the proposed approach to obtain robust controllers against external signals, as well as the parametric uncertainties.

A Unified Control Framework for Traction Machine Drive Using Linear Parameters Varying-Based Field-Oriented Control

Abstract The performance of an electrified powertrain in extreme operating conditions is greatly compromised. This is due to the fact that meeting the road loads, ensuring efficient powertrain operation, and minimizing the loss of lifetime (aging) of an electric machine are three essential but conflicting targets. In this paper, a unified multi-objective linear parameters varying (LPV)-based field-oriented control (FOC) framework is proposed to solve the problem of conflicting objectives mentioned above. The outer loop in a unified control framework generates the reference currents using linear matrix inequality (LMI)-based torque and flux controllers. Moreover, optimal flux is estimated using LPV observer to ensure efficient machine operations. In the inner loop of a unified control framework, the multi-objective controller (MOC) is synthesized by selecting optimal weighting functions using LMI-based convex optimization approach. The stability of the proposed unified control framework is also analyzed. The effectiveness of the proposed unified control framework is tested for a direct drive electrified powertrain of a three-wheeled vehicle commonly found in urban transportation for Asian countries. The urban driving schedule-based simulation results confirm that the lifetime of traction machine can be enhanced by appropriate control framework design without compromising its performance.

A New Perspective in Functional EIV Linear Models: Part II

In Error-in-Variables (EIV) models, all variables are subject to error and their estimators are heavily biased especially in the case of small sample sizes. This paper extends the results of Al-Sharadqah and proposes a new estimator for the problem of fitting 3D planes to data. Instead of minimizing an objective function obtained by the likelihood principles or others, a family of objective functions depending on an unknown smooth weight is considered. Then, the optimal weight function is derived so that the minimizer of the corresponding objective function has a zero second-order bias. To derive such a weight, a general form of the second-order bias is derived by applying our perturbation theory. This leads to a system of two first-order linear partial differential equations that admits a unique solution. The explicit formula of the weight is derived yielding the objective function. This turns to be a standard nonlinear least squares problem. Accordingly, the Levenberg-Marquardt (LM) algorithm is implemented. Finally, the effectiveness and superiority of our method are assessed by a series of numerical experiments.

Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier–Stokes equations

To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes equations. The explicit particle method is based on a penalty problem, which converges theoretically to the incompressible Navier--Stokes equations, and is discretized in space by generalized approximate operators defined as a wider class of approximate operators than those of the smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods. By considering an analytical derivation of the explicit particle method and truncation error estimates of the generalized approximate operators, sufficient conditions of convergence are conjectured.Under these conditions, the convergence of the explicit particle method is confirmed by numerically comparing errors between exact and approximate solutions. Moreover, by focusing on the truncation errors of the generalized approximate operators, an optimal weight function is derived by reducing the truncation errors over general particle distributions. The effectiveness of the generalized approximate operators with the optimal weight functions is confirmed using numerical results of truncation errors and driven cavity flow. As an application for flow problems with free surface effects, the explicit particle method is applied to a dam break flow.

Stochastic Quasi-Likelihood for Case-Control Point Pattern Data

ABSTRACT We propose a novel stochastic quasi-likelihood estimation procedure for case-control point processes. Quasi-likelihood for point processes depends on a certain optimal weight function and for the new method the weight function is stochastic since it depends on the control point pattern. The new procedure also provides a computationally efficient implementation of quasi-likelihood for univariate point processes in which case a synthetic control point process is simulated by the user. Under mild conditions, the proposed approach yields consistent and asymptotically normal parameter estimators. We further show that the estimators are optimal in the sense that the associated Godambe information is maximal within a wide class of estimating functions for case-control point processes. The effectiveness of the proposed method is further illustrated using extensive simulation studies and two data examples.

General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED

We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to quantify different noise contributions in the readout amplification chain.

Privacy Preserving Over Big Data Through VSSFA and MapReduce Framework in Cloud Environment

The main intention of this paper is develop a technique for privacy preserving-aware over big data in clouds using variation step size firefly algorithm and MapReduce framework. This paper consists of two phases such as MapReduce phase and evaluation phase. In MapReduce phase, at first we split the big data into a number of maps. After that, we apply the convolution process to the dataset and create a new kernel matrix. Once the convolution process is over, the privacy-persevering framework over big data in cloud systems is performed based on the evaluation phase. In evaluation module, the neural network is trained based on the optimal weight and radial basis function neural network algorithm, which is improving the utility of the privacy data. After that, a MapReduce framework is to protect the private information. Finally, the reduced privacy data are stored in the computer service provider. In this big data experiment, we used census income KDD dataset to evaluate the result.

Second-order quasi-likelihood for spatial point processes.

Applications of spatial point processes for large and complex data sets with inhomogeneities as encountered, example, in tropical rain forest ecology call for estimation methods that are both statistically and computationally efficient. We propose a novel second-order quasi-likelihood procedure to estimate the parameters for a second-order intensity reweighted stationary spatial point process. Our approach is to derive first- and second-order estimating functions and then combine them linearly using appropriate weight functions. In the stationary case, we argue that the asymptotically optimal weight functions are respectively a constant and a function of lags between distinct locations in the observation window. This leads to a considerable gain in computational efficiency. We further exploit this simplification in the nonstationary case. Simulations show that, when compared with several existing approaches, our method can achieve significant gains in statistical efficiency. An application to a tropical rain forest data set further illustrates the advantages of our procedure.