Time-varying Weights Research Articles

Estimating Time-Varying Networks With a State-Space Model

We propose the use of state-space models (SSMs) to estimate dynamic spatial relationships from time series data. At each time step, the weight matrix, capturing the latent state, is updated by a spatial autoregressive model. Specifically, we consider two types of SSM: the first one calibrates the spatial model to a multivariate regression, while the second one updates the spatial matrix by leveraging the maximum likelihood (ML) estimation. Different filtering algorithms are proposed to estimate the state. The simulation results show that the first model performs robustly for all cases, while the performance of the second model is sensitive to the state dimension. In a real-world case study, we estimate the time-varying weight matrices with weekly credit default swap (CDS) data for 16 banks, and show that the methods can identify communities which are coherent with the country-driven partitions.

Predictive management approach for the coordination of wind and water-based power supplies

This paper addresses the coordinated operation between wind farms and reservoir hydropower plants in networks with weak transmission capacity. The joint operation of the energy sources is captured by a Virtual Power Plant (VPP) representation. With the aim of maximising renewable energy penetration while ensuring a suitable VPP integration, a supervisory controller for the energy dispatch layer is proposed. To deal with the variable nature of both resources, the controller has been designed into a model predictive control framework including mixed-integer quadratic programming (given the hybrid considered model) for solving the related optimisation problem, and complementary techniques as constraints softening and time-varying weighting. The results indicate that the predictive control approach achieves a better Independent System Operator (ISO) reference tracking that, together with reservoir management, are the most important factors to ensure a suitable VPP incorporation to the main grid. As a case study, a sub-network of the Argentinian power system is tackled. The controller performance is quantitatively and qualitatively assessed under uncertain conditions and compared with other approaches over a nine-year period. By means of the proposed power management policy, the ISO’s effort to balance the sub-network is reduced 56% with regard to other approaches without any water spillage.

Nonlinear MPC with time-varying terminal cost for tracking unreachable periodic references

In this paper, nonlinear model predictive control is investigated for a nonlinear system using a time-varying terminal cost function. An artificial reference and a control input are added as decision variables for tracking an unreachable periodic reference. Some constraints are given in an optimization problem to guarantee feasibility if the periodic references change suddenly for the reason of that the constraints are independent on the periodic references. A time-varying periodic polytopic linear difference inclusion is proposed to guarantee behavior locally around the artificial reference of the nonlinear system. A time-varying weight matrix is designed for the time-varying terminal cost function to ensure stability of the nonlinear system. Effectiveness of the developed tracking control scheme is shown by a simulation example on a mobile robot system.

The Contribution of Jump Activity and Sign to Forecasting Stock Price Volatility

This paper proposes a novel approach to decompose realized jump measures by type of activity (finite/infinite) and by sign. We also provide noise-robust versions of the ABD jump test (Andersen et al. 2007) and realized semivariance measures for use at high frequency sampling intervals. The volatility forecasting exercise involves the use of different types of jumps, forecast horizons, sampling frequencies, calendar and transaction time-based sampling schemes, as well as standard and noise-robust volatility measures. We find that infinite (finite) jumps improve the forecasts at shorter (longer) horizons; but the contribution of signed jumps is limited. Noise-robust estimators, that identify jumps in the presence of microstructure noise, deliver substantial forecast improvements at higher sampling frequencies. However, standard volatility measures at the 300-second frequency generate the smallest MSPEs. Since no single model dominates across sampling frequency and forecast horizon, we show that model averaged volatility forecasts - using time-varying weights and models from the model confidence set - generally outperform forecasts from both the benchmark and single best extended HAR model.

Adaptive Bipartite Event-Triggered Output Consensus of Heterogeneous Linear Multiagent Systems Under Fixed and Switching Topologies.

This article addresses the adaptive bipartite event-triggered output consensus issue for heterogeneous linear multiagent systems. We consider both cooperative interaction and antagonistic interaction between neighbor agents in both fixed and switching topologies. An adaptive bipartite compensator consisting of time-varying coupling weights and dynamic event-triggered mechanism is first proposed to estimate the leader's state in a fully distributed manner. Different from the existing methods, the proposed compensator has three advantages: 1) it does not depend on any global information of the network graph; 2) it avoids the continuous communication between neighbor agents; and 3) it is applicable for the signed communication topology. Assume that the system states are unmeasurable, and we thus design the state observer. Based on the devised compensator and observer, the distributed control law is developed such that the bipartite event-triggered output consensus problem can be achieved. Moreover, we extend the results in fixed topology to switching topology, which is more challenging in that state estimation is updated in two cases: 1) the interaction graph is switched or 2) the event-triggered mechanism is satisfied. It is proven that no agent exhibits Zeno behavior in both fixed and switching interaction topologies. Finally, two examples are provided to illustrate the feasibility of the theoretical results.

Multiple imputation methods for handling missing values in longitudinal studies with sampling weights: Comparison of methods implemented in Stata.

Many analyses of longitudinal cohorts require incorporating sampling weights to account for unequal sampling probabilities of participants, as well as the use of multiple imputation (MI) for dealing with missing data. However, there is no guidance on how MI and sampling weights should be implemented together. We simulated a target population based on the Australian Bureau of Statistics Estimated Resident Population and drew 1000 random samples dependent on three design variables to mimic the Longitudinal Study of Australian Children. The target analysis was the weighted prevalence of overweight/obesity over childhood. We evaluated the performance of several MI approaches available in Stata, based on multivariate normal imputation (MVNI), fully conditional specification (FCS) and twofold FCS: a weighted imputation model, imputing missing data separately for each quintile sampling weight grouping, including the design stratum indicator in the imputation model, and using sampling weights as a covariate in the imputation model. Approaches based on available cases and inverse probability weighting (IPW), with time-varying weights, were also compared. We observed severe issues of convergence with FCS and twofold FCS. All MVNI-based approaches performed similarly, producing minimal bias and nominal coverage, except for when imputation was conducted separately for each quintile sampling weight group. IPW performed equally as well as MVNI-based approaches in terms of bias, however, was less precise. In similar longitudinal studies, we recommend using MVNI with the design stratum as a covariate in the imputation model. If this is unknown, including the sampling weight as a covariate is an appropriate alternative.

A Framework for Autonomous Impedance Regulation of Robots Based on Imitation Learning and Optimal Control

In this work, we propose a framework to address the autonomous impedance regulation problem of robots in a class of constrained manipulation tasks. In this framework, a human arm endpoint stiffness model is used to extract the task stiffness geometry along the constrained trajectory, which is then encoded offline and reproduced online by a Gaussian Mixture Model (GMM) and the Gaussian Mixture Regression (GMR), respectively. Furthermore, the full Cartesian impedance of the robot is formulated through an optimal control problem, i.e., the Linear-Quadratic Regulator (LQR), in which the task stiffness geometry (extracted from human demonstrations) is considered as the time-varying weighting matrix Q. The optimal impedance is eventually realised by the robot through a task geometry consistent Cartesian impedance controller. A tank-based passivity observer is implemented to give evidence on the stability of the system during online impedance variations. To evaluate the performance of the framework, a comparative experiment with three different impedance settings (i.e., the proposed framework, the framework without LQR and the framework without GMM/GMR) for Franka Emika Panda to perform a door opening task was conducted. The results reveal that our framework outperforms the other two, in terms of tracking error and the interaction forces.

Bipartite output synchronization of heterogeneous time-varying multi-agent systems via edge-based adaptive protocols

This paper considers a bipartite output synchronization problem for heterogeneous linear multi-agent systems with time-varying communication networks using an adaptive distributed observer-based control strategy. Based on the relative output information from neighboring agents, a reduced-dimensional distributed observer is proposed to estimate the unavailable state information of each agent. Meanwhile, an edge-based adaptive law is designed for each agent to assign the time-varying interaction weight such that the connectivity of the communication network is preserved. Theoretical analysis is presented for the convergence of the output tracking errors under the proposed output feedback control strategy. Some numerical results are also presented to validate the proposed control strategy.

Time-varying model averaging

Structural changes often occur in economics and finance due to changes in preferences, technologies, institutional arrangements, policies, crises, etc. Improving forecast accuracy of economic time series with structural changes is a long-standing problem. Model averaging aims at providing an insurance against selecting a poor forecast model. All existing model averaging approaches in the literature are designed with constant (non-time-varying) combination weights. Little attention has been paid to time-varying model averaging, which is more realistic in economics under structural changes. This paper proposes a novel model averaging estimator which selects optimal time-varying combination weights by minimizing a local jackknife criterion. It is shown that the proposed time-varying jackknife model averaging (TVJMA) estimator is asymptotically optimal in the sense of achieving the lowest possible local squared error loss in a class of time-varying model averaging estimators. Under a set of regularity assumptions, the TVJMA estimator is Th-consistent. A simulation study and an empirical application highlight the merits of the proposed TVJMA estimator relative to a variety of popular estimators with constant model averaging weights and model selection.

Leader-following consensus of second-order multi-agent systems with time-varying delays and arbitrary weights

Using Lyapunov first method instead of traditional Lyapunov second method, this paper focuses on studying the consensus tracking control problem of multi-agent systems (MASs) with time-varying delays and arbitrary adjacent weights under fixed topology and switching topology, respectively. We first give four equivalent criteria for MASs with fixed communication topology, where the positive stability of matrix [Formula: see text] ( L is the Laplacian matrix of [Formula: see text], B is the leader’s adjacency matrix) not only plays a key role as usual but also becomes an urgent and more complicated problem due to the introduction of negative weights in MASs. Second, for MASs with switching communication topology if the average dwell time of switching topology, the total activation time of stable subsystems and the upper bound of time delay satisfy some conditions, then MASs with all stable subsystems (partially stable subsystems) can achieve consensus tracking. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.

Developing an online air quality warning system based on streaming data for dynamic environmental management

Obtaining valuable information from streaming data of air pollutants concentration is of considerable significance to facilitate dynamic environmental management. However, the complex nonlinear characteristics, especially concept drift, in the streaming data renders the study to be considerably challenging, which increases the necessity of developing an online air quality warning system (AQWS). Aiming to accurately forecast future trends and uncertainty of the streaming data and provide a scientific evaluation of air quality, a novel online AQWS, including the modules of data preprocessing, forecasting, performance assessment, and air quality evaluation, is established in this study, which can be considered a contribution to the field. In the proposed online AQWS, an advanced denoising algorithm is developed in the module of data preprocessing to purify the studied streaming data, which is conducive to ensuring the generalization of the forecasting module; further, a probabilistic and nonparametric Bayesian method, i.e., the sparse spectrum Gaussian process regression, is developed in the module of forecasting to perform the deterministic forecasting and uncertainty quantification of the streaming data; finally, this study also constructs an online air quality evaluation model based on a cloud model in the module of air quality evaluation, which can model the fuzziness and randomness involved in the evaluation process simultaneously. In particular, an improved super scale weight method based on the theory of entropy is proposed in the cloud model to determine the time-varying weight of air pollutants dynamically, which can constitute an important contribution of the study. To validate the effectiveness and feasibility of the proposed online AQWS, two case studies based on the streaming data from Zhengzhou city and Changchun city in China are carried out, and corresponding results in the modules of performance assessment and air quality evaluation demonstrate that the online AQWS can yield more accurate prediction results compared to the benchmarks considered and has great potential for application to dynamic environmental management.

Moving Horizon Estimation for Uncertain Networked Control Systems with Packet Loss

This paper studies a moving horizon estimation approach to solve the constrained state estimation problem for uncertain networked systems with random packet loss. The system model error range is known, and the packet loss phenomena are modeled by a binary switching random sequence. Taking the model error, the packet loss, the system constraints, and the network transmission noise into account, a time-varying weight matrix is obtained by solving a least-square problem. Then, a robust moving horizon estimator is designed to estimate the system state by minimizing an optimization problem with an arrival cost function. The proposed estimator ensures that the optimal estimated state can be obtained in the worst case. Furthermore, the asymptotic convergence of the estimator is analyzed and some sufficient conditions for convergence are given. Finally, the validity of the proposed approach can be demonstrated by numerical simulations.

The response of Zimbabwe tobacco exports to real exchange rates volatility: 1980–2019

The focus of this study was on investigating the response of tobacco exports to real exchange rates and real exchange rate volatility and other factors in Zimbabwe using secondary data spanning from 1980 to 2019. Bilateral nominal exchange rates and time-variant weights of Zimbabwe’s 10 major trading partners were calculated and used to compute the real exchange rate index. The time-dependent weighting system was used to better represent the evolution of trade patterns in the index. The arithmetic method was employed for computing the index. Generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional heteroscedasticity (ARCH) models were used to generate the real exchange rate volatility index. The export response function was adopted as the tobacco exports response model. The variables in the tobacco exports response model were the realworld Gross Domestic Product (GDP), real exchange rate, terms of trade, real exchange rate volatility and dollarization. A vector error correction model (VECM) was used to estimate the response of tobacco exports to real exchange rate, real exchange rate volatility and other factors. The VECM results indicated that real world GDP was insignificant in both the short and long run. In the long run, the real exchange rate appreciation had a negative impact on tobacco exports. Conversely, in the short run, the depreciation of real exchange rate had a positive impact on tobacco exports. Hence, the government has to adopt other mechanisms that reduce uncertain movements of exchange rates.

Family-based treatment program contributors to child weight loss.

BackgroundMulti-component family-based behavioral treatment program for pediatric obesity (FBT) includes nutrition and physical activity education, as well as behavior therapy techniques. Studies suggest that parent weight loss is the best predictor of child weight loss in FBT. However, given the important role that parents play in the implementation of FBT for their child, isolating the effects of specific FBT treatment component requires consideration of parent influences over time.MethodsThe following treatment components were assessed: stimulus control (high/low-fat food items in home), nutrition knowledge, energy intake, physical activity, and parental monitoring, as well as weekly anthropometric measures. Adjusted models of interest using inverse probability weights (IPW) were used to evaluate the effect of specific FBT components on time-varying child weight loss rate, adjusting for time-varying influence of parent weight loss.Results137 parent-child dyads (CHILD: mean BMI = 26.4 (3.7) and BMIz=2.0 (0.3); mean age =10.4 (1.3); 64.1% female; ADULT: mean BMI = 31.9 (6.3); mean age= 42.9 (6.5); 30.1% Hispanic parents; 87.1% female) participated in an FBT program. In traditional model, adult BMI change (b=0.08; p<0.01) was the most significant predictor of child weight loss rates and no other treatment components were significant (p’s>0.1). In models that accounted for potential influences from parental weight loss and differential attendance during treatment period, lower availability of high-fat items (b=1.10, p<0.02), higher availability of low-fat items (b=3.73; p<0.01), and higher scores on parental monitoring practices (b=1.10, p<0.01) were associated with greater rates of weight-loss, respectively.ConclusionResults suggest that outside of parent weight change, changes in stimulus control strategies at home and improved parental-monitoring practices are important FBT components for child weight loss.

Bounded Integral Controller With Limited Control Power for Nonlinear Multiple-Input Multiple-Output Systems

In this brief, a bounded integral controller (BIC) with limited control power is proposed for a class of nonlinear multiple-input multiple-output (MIMO) systems. The sum-of-squares constraint on the control inputs with time-varying weights is studied and handled through the BIC design, which guarantees that both the control inputs and an auxiliary time-varying variable are dynamically constrained on a designed control circle. The BIC inherits the properties of the traditional integral controller to eliminate tracking errors and achieve disturbance rejections. Even under time-varying input weights, the BIC guarantees limited control power independently of both plant information and system states. The input-to-state (practical) stability of the closed-loop system is established. To demonstrate the effectiveness of the proposed method, experimental validations are conducted for two systems: a system with multiple dc motors subject to a power limit with time-varying input weights and a permanent magnet synchronous motor system subject to a voltage limit with time-invariant input weights.

Globally optimal distributed time-varying weight information filter of mobile sensor network

The networked state estimation for a linear dynamic system is studied in this paper. Firstly, a time-varying distributed communication protocol governed by the network topology is introduced for delivering information among the neighboring sensors. Secondly, based on this protocol, a two stage distributed state estimation algorithm is presented to achieve the global optimal results in a least square sense. In the first stage of the proposed algorithm, distributed computation on the sum of global information vector contributions is conducted, and the second stage is to derive the state estimations via utilizing the interaction results offered by the first stage. Thirdly, it is shown that the proposed algorithm only demands finite neighbor interaction times to obtain global optimal estimations. The optimality and stability properties of the proposed algorithm are also proved by using the Riccati equation. Finally, through numerical simulations, it is further illustrated that the proposed algorithm could outperform the previous distributed estimators.

A novel dynamic ensemble air quality index forecasting system

The air quality index (AQI) can reflect the change of air quality in real time. It has linear characteristics, nonlinear and fuzzy features. However, a single model cannot fit the dynamic changes of AQI scientifically and reasonably. Therefore, this paper proposes a new dynamic ensemble forecasting system based on multi-objective intelligent optimization algorithm to forecast AQI, which has time-varying parameter weights and mainly contains three module: data preprocessing module, dynamic integration forecasting module and system evaluation module. In the data preprocessing module, the off-line frequency domain filtering approach is applied to identify and correct the outliers in the series. To better extract the series information and remove the random noise, the time series is decomposed into multi-level utilizing decomposition strategy and reconstructed. In the dynamic integration forecasting module, three hybrid models based on ARIMA, optimized extreme learning machine and fuzzy time series model, named as HCA, HCME and HCFL respectively, are used to forecast the reconstructed series and time varying parameters are employed to dynamically combine the forecasting results. In the system evaluation module, the accuracy of the system was tested by parameter test method and non-parametric test method respectively. The results demonstrate that the proposed dynamic integrated model is not only superior to other comparison models in forecasting accuracy, but also provides strong technical support for air quality forecasting and treatment.

An optimal early warning system for currency crises under model uncertainty

This paper assesses several early warning (EWS) models of financial crises to propose a model that can predict the incidence of a currency crisis in developing countries. For this purpose, we employ the equal weighting (EW) and dynamic model averaging (DMA) approaches to combine forecast from individual models allowing for time-varying weights. Taking Egypt as a case study and focusing only on currency crises, our findings show that combined forecast (EW- and DMA-based EWS), to account for uncertainty, perform better than other competing models in both in-sample and out-of-sample forecasts.

Complexity to Forecast Flood: Problem Definition and Spatiotemporal Attention LSTM Solution

With significant development of sensors and Internet of things, researchers nowadays can easily know what happens in physical space by acquiring time-varying values of various factors. Essentially, growing data category and size greatly contribute to solve problems happened in physical space. In this paper, we aim to solve a complex problem that affects both cities and villages, i.e., flood. To reduce impacts induced by floods, hydrological factors acquired from physical space and data-driven models in cyber space have been adopted to accurately forecast floods. Considering the significance of modeling attention capability among hydrology factors, we believe extraction of discriminative hydrology factors not only reflect natural rules in physical space, but also optimally model iterations of factors to forecast run-off values in cyber space. Therefore, we propose a novel data-driven model named as STA-LSTM by integrating Long Short-Term Memory (LSTM) structure and spatiotemporal attention module, which is capable of forecasting floods for small- and medium-sized rivers. The proposed spatiotemporal attention module firstly explores spatial relationship between input hydrological factors from different locations and run-off outputs, which assigns time-varying weights to various factors. Afterwards, the proposed attention module allocates temporal-dependent weights to hidden output of each LSTM cell, which describes significance of state output for final forecasting results. Taking Lech and Changhua river basins as cases of physical space, several groups of comparative experiments show that STA-LSTM is capable to optimize complexity of mathematically modeling floods in cyber space.

An ensemble prognostic method for lithium-ion battery capacity estimation based on time-varying weight allocation

Capacity estimation is of great significance to help assess the performance degradation of lithium-ion batteries, so as to take actions to extend their lifetime. Traditional capacity estimation methods for Lithium-ion batteries are usually based on individual model-based or data-driven prognostic approaches. However, no single prognostic method performs appropriately for all possible situations as each individual method presents particular assumptions and application limitations. Therefore, this paper presents an ensemble prognostic framework that combines multiple individual prognostic algorithms to improve the accuracy and robustness of battery capacity estimation. In the proposed ensemble prognostic framework, the degraded capacity data of the full battery life cycles are divided into three parts: a training dataset, a validation dataset, and a test dataset, among which the training and validation datasets are employed for member prognostic model training, the validation dataset is utilized for weight calculation, and the test dataset is used for prognostic performance assessment. A validation-data based induced ordered weighted averaging (IOWA) operator, i.e. V-IOWA operator, is proposed to realize time-varying weight assignment. By summing the weighted prognostic results of each member prognostic algorithm, the ensemble prognostic results are finally obtained. Effectiveness of the proposed approach was validated based on datasets provided by NASA Ames Prognostics Center of Excellence. The experiment results indicated that the proposed ensemble prognostic approach outperforms individual prognostic algorithms with a higher accuracy.