Estimation Of Unknown Parameters Research Articles

Frontiers in Operations: Equitable Data-Driven Facility Location and Resource Allocation to Fight the Opioid Epidemic

Problem definition: The opioid epidemic is a crisis that has plagued the United States for decades. One central issue of the epidemic is inequitable access to treatment for opioid use disorder (OUD), which puts certain populations at a higher risk of opioid overdose. Methodology/results: We integrate a predictive dynamical model and a prescriptive optimization problem to compute high-quality opioid treatment facility and treatment budget allocations for each U.S. state. Our predictive model is a differential equation-based epidemiological model that captures the dynamics of the opioid epidemic. We use a process inspired by neural ordinary differential equations to fit this model to opioid epidemic data for each state and obtain estimates for unknown parameters in the model. We then incorporate this epidemiological model into a corresponding mixed-integer optimization problem (MIP) that aims to minimize the number of opioid overdose deaths and the number of people with OUD. We develop strong relaxations based on McCormick envelopes to efficiently compute approximate solutions to our MIPs that have a mean optimality gap of 3.99%. Our method provides socioeconomically equitable solutions, as it incentivizes investments in areas with higher social vulnerability (from the U.S. Centers for Disease Control’s Social Vulnerability Index) and opioid prescribing rates. On average, when allowing for overbudget solutions, our approach decreases the number of people with OUD by [Formula: see text], increases the number of people in treatment by [Formula: see text], and decreases the number of opioid-related deaths by [Formula: see text] after 2 years compared with the baseline epidemiological model’s predictions. Managerial implications: Our solutions show that policymakers should target adding treatment facilities to counties that have significantly fewer facilities than their population share and are more socially vulnerable. Furthermore, we demonstrate that our optimization approach, guided by epidemiological and socioeconomic factors, should help inform these strategic decisions, as it yields population health benefits in comparison with benchmarks based solely on population and social vulnerability. History: This paper has been accepted in the Manufacturing & Service Operations Management Frontiers in Operations Initiative. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0042 .

Sobolev Calibration of Imperfect Computer Models

Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer models, Sobolev calibration, which can rule out calibration parameters that generate overfitting calibrated functions. We prove that the Sobolev calibration enjoys desired theoretical properties including fast convergence rate, asymptotic normality and semiparametric efficiency. We also demonstrate an interesting property that the Sobolev calibration can bridge the gap between two influential methods: L 2 calibration and Kennedy and O’Hagan’s calibration. In addition to exploring the deterministic physical experiments, we theoretically justify that our method can transfer to the case when the physical process is indeed a Gaussian process, which follows the original idea of Kennedy and O’Hagan’s. Numerical simulations as well as a real-world example illustrate the competitive performance of the proposed method.

Adaptive suboptimal control of some discrete-time plants with nonstochastic bounded disturbances

This paper deals with the adaptive suboptimal control of linear, discrete-time, time-invariant, minimum phase, scalar plants in the presence of nonstochastic bounded unmeasurable disturbances whose upper and lower bounds, which may be asymmetric, are assumed to be unknown a priori. Additional assumption is that an order of the difference equation describing the plant is known a priori. The distinguishing feature of the problem stated in this paper is that neither bounds on the unmeasured disturbances, nor bounds on an allowable region to which the unknown plant parameters belong are assumed to be known a priori. To solve this problem, adaptation procedures for the point and membership set estimation are utilized. The standard recursive procedure with adjustable dead zone is employed in order to derive the point estimates of unknown plant parameters together with the point estimate of time-invariant disturbance component. The size of this dead zone depends on the previous point estimate of the bounds on the time-varying disturbance component and also on a fixed suboptimality index chosen by the designer. The estimates generated by the point estimation procedure are directly exploited to derive the adaptive control law. The main idea advanced in this paper is that, instead of unknown a priori membership set of these parameters, their peculiar hypothetical a posteriori membership sets are designed via the use of the measured system’s signals together with the current point estimate of bounds on the time-varying disturbance component. Contrary to the usual membership set estimation approach, this set is updated if only it is discovered that the unknown parameter vector does not belong in reality to this set. To this end, a remarkable property of the point estimation procedure is utilized. Such an approach makes it possible to reconstruct this set and to update the previous estimate of the bounds on the time-varying disturbance component. The finite convergence of the adaptation procedures and also the ultimate boundedness of system’s signals are established. To demonstrate an efficiency of the adaptive controller and support the theoretical study, simulation results are presented.

Statistical inference for a two-parameter Rayleigh distribution under generalized progressive hybrid censoring scheme

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose.

Evaluating the lifetime performance index of omega distribution based on progressive type-II censored samples

Besides achieving high quality products, statistical techniques are applied in many fields associated with health such as medicine, biology and etc. Adhering to the quality performance of an item to the desired level is a very important issue in various fields. Process capability indices play a vital role in evaluating the performance of an item. In this paper, the larger-the-better process capability index for the three-parameter Omega model based on progressive type-II censoring sample is calculated. On the basis of progressive type-II censoring the statistical inference about process capability index is carried out through the maximum likelihood. Also, the confidence interval is proposed and the hypothesis test for estimating the lifetime performance of products. Gibbs within Metropolis–Hasting samplers procedure is used for performing Markov Chain Monte Carlo (MCMC) technique to achieve Bayes estimation for unknown parameters. Simulation study is calculated to show that Omega distribution's performance is more effective. At the end of this paper, there are two real-life applications, one of them is about high-performance liquid chromatography (HPLC) data of blood samples from organ transplant recipients. The other application is about real-life data of ball bearing data. These applications are used to illustrate the importance of Omega distribution in lifetime data analysis.

Efficiency improvement strategy of fuel cell system based on oxygen excess ratio and cathode pressure two-dimensional optimization

Improving the commercial fuel cell system efficiency is critical to reducing hydrogen consumption and improving the operational economy. This paper studies the power consumption pattern of the air supply subsystem, the most power-consuming auxiliary components, aiming to improve the system’s efficiency. A method was proposed to get the extremum of the system net power by optimizing the oxygen excess ratio and cathode pressure. Mathematical models describing the fuel cell stack and air supply subsystem power characteristics were developed based on the mechanism analysis and estimation of unknown parameters. Then, a system net power model for energy efficiency optimization was developed. The operating conditions for optimal efficiency at a specific current density can be obtained by numerical calculation. To verify the method’s effectiveness, a series of experiments were conducted, and the results show that the proposed method can maximize system net power output at various current density conditions. Compared with the conventional oxygen excess rate based one-dimensional optimization, the two-dimensional method can improve system efficiency by 2.06%, offering a good application prospect.

Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix

Banding the inverse of a covariance matrix has become a popular technique for estimating a covariance matrix from a limited number of samples. It is of interest to provide criteria to determine if a matrix is bandable, as well as to test the bandedness of a matrix. In this paper, we pose the bandedness testing problem as a hypothesis testing task in statistical signal processing. We then derive two detectors, namely the complex Rao test and the complex Wald test, to test the bandedness of a Cholesky-factor matrix of a covariance matrix’s inverse. Furthermore, in many signal processing fields, such as radar and communications, the covariance matrix and its parameters are often complex-valued; thus, it is of interest to focus on complex-valued cases. The first detector is based on the complex parameter Rao test theorem. It does not require the maximum likelihood estimates of unknown parameters under the alternative hypothesis. We also develop the complex parameter Wald test theorem for general cases and derive the complex Wald test statistic for the bandedness testing problem. Numerical examples and computer simulations are given to evaluate and compare the two detectors’ performance. In addition, we show that the two detectors and the generalized likelihood ratio test are equivalent for the important complex Gaussian linear models and provide an analysis of the root cause of the equivalence.

Adaptive optimal ℓ∞‐induced robust stabilization of minimum phase SISO plant under bounded disturbance and coprime factor perturbations

AbstractThis paper addresses the problem of optimal robust stabilization of a discrete‐time minimum‐phase plant in the framework of robust control theory in the setup and under poor a priori information. Coefficients of the transfer function of the plant nominal model with stable zeros are unknown and belong to a known bounded polyhedron in the space of coefficients. The gains of coprime factor perturbations of the plant and the upper bound of external disturbance are also unknown. The problem under consideration is to design adaptive controller that minimizes, with the prescribed accuracy, the worst‐case asymptotic upper bound of the output. Solution of the problem is based on set‐membership estimation of unknown parameters and treating the control criterion as the identification criterion. A hard nonconvex problem of on‐line computation of optimal estimates is reduced, under additional nonrestrictive assumption, to a linear‐fractional programming via a nonlinear transformation of estimated parameters. Despite the non‐identifiability of the unknown parameters, the proposed adaptive controller guarantees, with the prescribed accuracy, the same optimal asymptotic upper bound of the output of adaptive system as the optimal controller for the plant with known parameters. In addition to the optimality of adaptive control, the proposed solution provides on‐line verification/validation of current estimates and a priori assumptions.

Distributed Control for Uncertain Multiagent Systems With the Powers of Positive-Odd Numbers: A Low-Complexity Design Approach

This work shows that low-complexity prescribed performance control (PPC) can be used to realize leader-following consensus for uncertain second-order multi-agent systems (MASs) with the powers of positive odd numbers, i.e., agents whose dynamics are a chain of integrators with positive odd powers. Low-complexity PPC is a control methodology whose strongest feature is its adaptation-free structural simplicity: uncertainty can be handled without estimation of unknown parameters nor approximation structures (neural networks, fuzzy logic systems, etc.) being involved in the control design. While the state of the art has focused on strict- and pure-feedback MASs, i.e., dynamics including a chain of integrators with powers equal to one: in this note, we show that the same low-complexity can be retained for more general integrator dynamics (with positive-odd-integer powers). To this purpose, several new technical tools are proposed to handle the challenges caused by the presence of high powers in the integrators both in leader and follower agents. A dynamical boiler-turbine units system is used to validate the effectiveness of the theoretical findings.

Event-Triggered Adaptive Neural Control for MIMO Nonlinear Systems With Rate-Dependent Hysteresis and Full-State Constraints via Command Filter.

This article presents an event-triggered adaptive NN command-filtered control for a class of multi-input and multi-output (MIMO) nonlinear systems with unknown rate-dependent hysteresis in the actuator and the constraints on full states. The ETM is used to reduce the communication frequency between controller and actuator. The command filter technique is first employed to solve the dilemma between the nondifferentiable control signal at triggering instants and rate-dependent hysteresis input premise while avoiding the "explosion of complexity" problem. During the backstepping design, the barrier Lyapunov functions are utilized to guarantee that system states will stay in certain regions and the unknown nonlinear items are approximated by adaptive neural networks. The compensating signals are constructed to eliminate filtering errors. The estimates of unknown hysteresis parameters are updated by adaptive laws. The stability analysis is given and the effectiveness of the proposed method is verified by simulation.

Reliability estimation stress–strength dependent model based on copula function using ranked set sampling

In the stress-strength reliability analysis, it is usually assumed that both stress and strength are independent variables. In most cases, stress and strength depend on each other. In this paper, Clayton copula function is selected when stress and strength variables follow Kumaraswamy distribution and Weibull distribution respectively, and the maximum likelihood estimate and least squares estimate of unknown parameters of stress-strength dependent model are derived by two-step method under ranked set sample. At the same time, the approximate confidence intervals are constructed by using the asymptotic distribution of maximum likelihood and the parametric bootstrap percentile method. In addition, the simulation results of simple random sample and ranked set sample are compared by Monte Carlo simulation method. Finally, a real case is selected to illustrate the feasibility of the proposed model.

Multiagent-Based Control for Plug-and-Play Batteries in DC Microgrids with Infrastructure Compensation

The influence of the DC infrastructure on the control of power-storage flow in micro- and smart grids has gained attention recently, particularly in dynamic vehicle-to-grid charging applications. Principal effects include the potential loss of the charge–discharge synchronization and the subsequent impact on the control stabilization, the increased degradation in batteries’ health/life, and resultant power- and energy-efficiency losses. This paper proposes and tests a candidate solution to compensate for the infrastructure effects in a DC microgrid with a varying number of heterogeneous battery storage systems in the context of a multiagent neighbor-to-neighbor control scheme. Specifically, the scheme regulates the balance of the batteries’ load-demand participation, with adaptive compensation for unknown and/or time-varying DC infrastructure influences. Simulation and hardware-in-the-loop studies in realistic conditions demonstrate the improved precision of the charge–discharge synchronization and the enhanced balance of the output voltage under 24 h excessively continuous variations in the load demand. In addition, immediate real-time compensation for the DC infrastructure influence can be attained with no need for initial estimates of key unknown parameters. The results provide both the validation and verification of the proposals under real operational conditions and expectations, including the dynamic switching of the heterogeneous batteries’ connection (plug-and-play) and the variable infrastructure influences of different dynamically switched branches. Key observed metrics include an average reduced convergence time (0.66–13.366%), enhanced output-voltage balance (2.637–3.24%), power-consumption reduction (3.569–4.93%), and power-flow-balance enhancement (2.755–6.468%), which can be achieved for the proposed scheme over a baseline for the experiments in question.

Huber-Dutter estimation of linear models with dependent errors

In this article, we investigate a linear model that incorporates stationary causal processes, with a focus on utilizing Huber-Dutter methods to investigate the estimators of unknown parameters and a scale for the errors. Our results indicate that the Huber-Dutter methods can effectively be utilized for linear models that feature errors, which are short-range dependent linear processes, heavy-tailed linear processes, as well as some commonly used non linear time series.

Parameter estimation for fractional mixed fractional Brownian motion based on discrete observations

The object of investigation is the mixed fractional Brownian motion of the form ${X_{t}}=\kappa {B_{t}^{{H_{1}}}}+\sigma {B_{t}^{{H_{2}}}}$, driven by two independent fractional Brownian motions ${B_{1}^{H}}$ and ${B_{2}^{H}}$ with Hurst parameters ${H_{1}}\lt {H_{2}}$. Strongly consistent estimators of unknown model parameters ${({H_{1}},{H_{2}},{\kappa ^{2}},{\sigma ^{2}})^{\top }}$ are constructed based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for $0\lt {H_{1}}\lt {H_{2}}\lt \frac{3}{4}$.

Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses

This paper studies the estimation problem for semi-varying coefficient heteroscedastic instrumental variable models with missing responses. First, we propose the adjusted estimators for unknown parameters and smooth functional coefficients utilizing the ordinary profile least square method and instrumental variable adjustment technique with complete data. Second, we present an adjusted estimator of the stochastic error variance by employing the Nadaraya–Watson kernel estimation technique. Third, we apply the inverse probability-weighted method and instrumental variable adjustment technique to construct the adaptive-weighted adjusted estimators for unknown parameters and smooth functional coefficients. The asymptotic properties of our proposed estimators are established under some regularity conditions. Finally, numerous simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed estimators.

Integrated L1 adaptive cartesian PD control for robotic loco-manipulation

This paper presents an integrated framework of L1 adaptive control and Cartesian PD control that overcomes the inherent limitations of the latter controller in tracking end effector position for loco-manipulation tasks. In a simplified system, this work represented the loco-manipulation problem with the Cartesian space dynamics of the end effector object, capturing the dominating parts of the dynamics in linear terms. The unmodeled nonlinear dynamics, along with other model uncertainties and external disturbances, are accounted for by the L1 adaptive controller, taking the Cartesian PD input as a component of the control law to resemble its behavior for the desired system dynamics modeled in the state predictor of the L1 adaptive controller. Through simulation results of various combinations of model perturbations and external disturbances, we show that this integrated framework can achieve similar tracking performances of the end effector and object without the need to re-tune controller parameters. This work demonstrated the mitigation of effects from system uncertainties with model perturbation of up to 100% higher than expected mass and up to 15N of sinusoidal external disturbances, with higher disturbance rejection possible through designing for more conservative estimates of unknown model parameters. Combined with the low computational cost of this framework, the improvement in state command tracking gives rise to potential implementation on robotic systems controlled with linear optimization formulations.

The E-Bayesian and hierarchical Bayesian estimations for the reliability analysis of Kumaraswamy generalized distribution based on upper record values

This paper investigates the E-Bayesian and hierarchical Bayesian estimations of shape parameter and reliability function of Kumaraswamy generalized distribution based on upper record values. The classical estimation method is utilized to deduce the maximum likelihood estimation of unknown parameter and reliability function. Bayesian estimates are derived by using conjugate Gamma prior distributions under quadratic and general entropy loss functions. Furthermore, assuming that hyper-hyperparameters obey three prior distributions, the E-Bayesian estimates of unknown parameters and reliability functions are obtained. The hierarchical Bayesian estimates are obtained by using hierarchical prior distributions. We also explore some characteristics and size relationships of E-Bayesian and hierarchical Bayesian estimations. The performance of E-Bayesian, Hierarchical Bayesian, Bayesian, and maximum likelihood estimations is compared based on the minimum mean square error criterion. Finally, the proposed estimation methods are applied to evaluate the reliability of the specimen under ultrasonic fatigue testing, and the results align with their structures and profiles.

A Comparative Study on Accurate Parameter Estimation of Solar Photovoltaic Models Using Metaheuristic Optimization Algorithms

Fossil fuel prices are increasing day by day due to growing demand and resource limitations. This situation shifts conventional electricity generation to renewable power generation. Among renewables, solar photovoltaic (PV) energy is very promising as the third fastest growing one. However, PV system modeling requires the estimation of unknown parameters of PV cells and modules. This problem remains a compelling task due to its multi-dimensional, multi-model and non-linear characteristics. In order to contribute to the solution of this optimization problem, this work makes a detailed comparison of artificial hummingbird algorithm, artificial rabbits optimization, enhanced Jaya algorithm, flow direction algorithm and artificial gorilla troops optimizer for determining the unknown parameters of PV models. Experimental results demonstrate that artificial hummingbird algorithm in single diode modeling of PV cell, flow direction algorithm in double diode modeling of PV cell and artificial rabbits optimization in single diode modeling of PV module are found to be capable of estimating accurate and efficient design coefficients for PV systems. In addition, the mentioned metaheuristic algorithms show reasonable convergence characteristics for the corresponding PV models.

Network-based uncertainty quantification for mathematical models in epidemiology

After the new Coronavirus disease (COVID-19) emerged in the end of January 2020 in Germany, a large number of individuals suffered from severe symptoms and eventually needed intensive care in hospitals. Due to the rapid spread of the disease, the number of deceased individuals increased as well, which is a motivation to prevent as many new infections as possible. Therefore, the knowledge about the current evolution of the virus spread is crucial to predict its future behavior and to react with suitable interventions. In this paper, the evolution of the COVID-19 pandemic in Germany is forecasted by a network-based inference method, in which the interactions of individuals are taken into account using a contact matrix. Then the results are compared to the predictions without considering a contact matrix as well as to the logistic regression, which shows the advantage of incorporating the contact matrix. Furthermore, the basic reproduction number of the pandemic in Germany using a neural network approach is estimated and used for further predictions of the evolution of COVID-19 in Germany. In order to mathematically model the different compartments of the population in the considered regions, the classical SIR model is employed. In this work, we deploy the LASSO (Least Absolute Shrinkage and Selection Operator) for the unknown parameter estimation. Furthermore, we calculate and illustrate the MAPE (Mean Absolute Percentage Error) of the estimations to show the accuracy of the predictions. The results include model parameter estimation and model validation, as well as the outbreak forecasting using network-informed algorithms. Our findings show that the network-inference based approach outperforms the logistic regression as well as the neural network approach and the SIR model calibration without a contact network. Furthermore according to the results, the network-inference based approach is particularly suitable for short- to mid-term predictions, even when there is not much information about the new disease. Moreover, the predictions based on the estimation of the reproduction number in Germany can yield more reliable results with increasing the availability of data, but could not outperform the network-inference based algorithm.

The Data Assimilation Approach in a Multilayered Uncertainty Space

The simultaneous consideration of a numerical model and of different observations can be achieved using data-assimilation methods. In this contribution, the ensemble Kalman filter (EnKF) is applied to obtain the system-state development and also an estimation of unknown model parameters. An extension of the Kalman filter used is presented for the case of uncertain model parameters, which should not or cannot be estimated due to a lack of necessary measurements. It is shown that incorrectly assumed probability density functions for present uncertainties adversely affect the model parameter to be estimated. Therefore, the problem is embedded in a multilayered uncertainty space consisting of the stochastic space, the interval space, and the fuzzy space. Then, we propose classifying all present uncertainties into aleatory and epistemic ones. Aleatorically uncertain parameters can be used directly within the EnKF without an increase in computational costs and without the necessity of additional methods for the output evaluation. Epistemically uncertain parameters cannot be integrated into the classical EnKF procedure, so a multilayered uncertainty space is defined, leading to inevitable higher computational costs. Various possibilities for uncertainty quantification based on probability and possibility theory are shown, and the influence on the results is analyzed in an academic example. Here, uncertainties in the initial conditions are of less importance compared to uncertainties in system parameters that continuously influence the system state and the model parameter estimation. Finally, the proposed extension using a multilayered uncertainty space is applied on a multi-degree-of-freedom (MDOF) laboratory structure: a beam made of stainless steel with synthetic data or real measured data of vertical accelerations. Young’s modulus as a model parameter can be estimated in a reasonable range, independently of the measurement data generation.