Estimation Of Uncertain Parameters Research Articles

A Least Squares Fitting Method for Uncertain Parameter Estimation in Solidification Model

This study proposes an automated method for estimating the uncertain parameters of the solidification model in response to the inefficient and time-consuming problem of manually estimating multiple uncertain parameters of the solidification model. The method establishes an uncertain parameter estimation model based on the relationship between the simulated images equiaxed crystal ratio and the uncertain parameters of the solidification model, fits the parameters of the model by the least squares method, and finally estimates the uncertain parameters in the solidification model using the parameters of the fitted model. In comparison with the traditional method of calculating uncertain parameters manually through empirical formulas, this method reduces the difficulty of tuning parameters and solves the problem of tuning multiple parameters simultaneously in the nonlinear solidification model. The experimental results show that the proposed method can accurately estimate the uncertain parameters of the solidification model, improve the efficiency and accuracy of the solidification model estimation parameters, and play a guiding role in simulating the solidification process of continuously casting billet to control the solidification structure.

Propagating input uncertainties into parameter uncertainties and model prediction uncertainties—A review

AbstractA review of uncertainty quantification techniques is provided for a variety of situations involving uncertainties in model inputs (independent variables). The situations of interest are divided into three categories: (i) when model prediction uncertainties are quantified based on uncertainties in uncertain inputs, (ii) when parameter estimate uncertainties are calculated by propagation of uncertainties from measured inputs and outputs, and (iii) when model prediction uncertainties are quantified based on corresponding uncertainties in measured inputs and uncertain parameter estimates. For all three situations, linearization‐based and Monte Carlo‐based techniques are reviewed and details for their corresponding algorithms are presented. Recommendations are provided on which uncertainty quantification techniques are best for different types of chemical engineering models based on the amount of input uncertainty and nonlinearity over the range of plausible input and parameter values.

An Extended Super-Twisting Algorithm for simultaneous estimation of reaction rates and input disturbance in bioprocess

The present contribution deals with the simultaneous estimation of the reaction rates and input disturbances in a bioprocess. Online estimation of just the reaction rates is possible by sliding mode observer techniques or high-gain observers, in finite-time or with exponential convergence, respectively. However, these techniques are not robust against unpredictable input bioreactor disturbances and are not readily adaptable to treat external disturbances. Motivated by these facts, we propose a novel extended super-twisting algorithm for a class of nonlinear systems, such that the estimation of uncertain parameters, unknown internal dynamics, and external disturbances converge in a finite time or a neighborhood near its nominal values. The effectiveness of the developed algorithm is tested through simulations in an anaerobic digestion process using a batch and a continuous bioreactor. Simulation results show good robustness performance of the extended super-twisting algorithm.

Uncertain random enhanced index tracking for portfolio selection with parameter estimation and hypothesis test

The enhanced index tracking is an effective method for portfolio optimization that focuses on imitating the behavior of a special benchmark and achieving an excess return. In addition, uncertainty and randomness are two intrinsic attributes of real world systems. In this paper, we study an uncertain random enhanced index tracking for portfolio optimization with parameter estimation and hypothesis test based on chance theory, which combines uncertainty theory and probability theory. First, we formulate an uncertain random mean–variance enhanced index tracking model including both random risky securities and uncertain risky securities. Then the presented model is transformed into a quadratic programming problem and the analytical solutions are derived for some special cases. Furthermore, the uncertain hypothesis test is applied to examine the correctness of the unknown parameters solved by uncertain parameter estimation. Finally, three numerical simulations are presented for showing the applicability of the formulated models and the effectiveness of the enhanced index tracking strategies.

A method for estimating fish density through the catches of gillnets

AbstractWe propose a new method for estimating fish density using catches obtained by gillnets of given mesh size. This method builds on work for estimating the number of fish approaching a gillnet by modelling the fish movement that leads to a gillnet encounter. The theoretical framework is developed, and the method is tested on catch data for cod Gadus morhua and Dolly Varden Salvelinus malma to demonstrate how the method can be applied. The method relies on knowledge of geometric properties of the net, and morphological and behavioural properties of the fish, so we explore the sensitivity of the estimates to some of these parameters. Estimates are most sensitive to the morphological parameter of the angle the mouth is open while swimming and largely invariant to estimates of uncertain parameters like maximum number of fish that can be caught by the particular net.

Robust Optimization of an Imperfect Process when the Mean and Variance are Jointly Monitored under Dependent Multiple Assignable Causes

Abstract Imperfect processes experience fault productions over time due to specific causes. Integrating the statistical process control, maintenance policy, and economic production quantity has led to more favorable results for the imperfect processes in literature. When monitoring a process, multiple assignable causes (ACs) may shift it to an out-of-control state. As indicated recently, if the interdependency of ACs is neglected, the total cost will be underestimated. Moreover, the mean and variance can simultaneously be affected by the occurrence of ACs. A non-central chi-square (NCS) chart was suggested for its decent performance against X-R chart in detecting the process disturbances and lowering quality loss cost. Besides, the increased occurrence rate of ACs over time leads to higher quality and maintenance costs. Employing a non-uniform sampling (NUS) scheme can significantly reduce costs. In the literature of modeling for imperfect processes under multiple ACs, all input parameters have always been fixed. The effectiveness of the models depends somewhat on the accurate estimates of these parameters. In reality, the estimation of parameters may be associated with uncertainty. For the first time, a robust design approach is proposed for designing NCS chart by considering the interval estimation of uncertain parameters. A particle swarm optimization (PSO) algorithm is used to present solutions. The proposed model is investigated through a real numerical example.

Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network

This study suggests a novel method for estimation of uncertain stock model parameters driven by Liu process. The proposed method decomposes the parameter estimation problem into two sub-problems: the first sub-problem implements an optimized artificial neural network based on the observed data, and the next sub-problem estimates the uncertain model parameters according to the optimized artificial neural network. We apply Nelder–Mead algorithm to optimize the artificial neural network and parameter estimation problem. The main supremacy of the presented method is that the estimation problem is independent of time intervals among observations and can be used to model future data. Providing a comparative method shows that the proposed approach can be effective for non-linear problems in which the artificial neural network structures perform well.

Adaptive robot climbing with magnetic feet in unknown slippery structure.

Firm foot contact is the top priority of climbing robots to avoid catastrophic events, especially when working at height. This study proposes a robust planning and control framework for climbing robots that provides robustness to slippage in unknown environments. The framework includes 1) a center of mass (CoM) trajectory optimization under the estimated contact condition, 2) Kalman filter–like approach for uncertain environment parameter estimation and subsequent CoM trajectory re-planing, and 3) an online weight adaptation approach for whole-body control (WBC) framework that can adjust the ground reaction force (GRF) distribution in real time. Though the friction and adhesion characteristics are often assumed to be known, the presence of several factors that lead to a reduction in adhesion may cause critical problems for climbing robots. To address this issue safely and effectively, this study suggests estimating unknown contact parameters in real time and using the evaluated contact information to optimize climbing motion. Since slippage is a crucial behavior and requires instant recovery, the computation time for motion re-planning is also critical. The proposed CoM trajectory optimization algorithm achieved state-of-art fast computation via trajectory parameterization with several reasonable assumptions and linear algebra tricks. Last, an online weight adaptation approach is presented in the study to stabilize slippery motions within the WBC framework. This can help a robot to manage the slippage at the very last control step by redistributing the desired GRF. In order to verify the effectiveness of our method, we have tested our algorithm and provided benchmarks in simulation using a magnetic-legged climbing robot Manegto.

Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems

Task-space cooperative tracking control of the networked multiple Euler–Lagrange systems is studied in this paper. On the basis of establishing kinematic and dynamic modeling of a Euler–Lagrange system, an innovative task-space coordination controller is designed to deal with the time-varying communicating delays and uncertainties. First, in order to weaken the influence of the uncertainty of kinematic and dynamic parameters on the control error of the system, the product of the Jacobian matrix and the generalized spatial velocity are linearly parameterized; thus, the unknown parameters are separated from known parameters. The online estimation of uncertain parameters is realized by designing parameters and by proposing new adaptive laws for the dynamic and kinematic parameters. Furthermore, to describe the transmission of time-varying delay errors among networked agents, a new error term is introduced, obtained by adding the observation error and tracking error, and the coefficient of the network mutual coupling term related to the time-varying delay rate is added with reference to the generalized space velocity and task-space velocity of the Lagrange systems. In the end, the influence of the time-varying delay on the cooperative tracking control error of the networked multiple Euler–Lagrange systems is eliminated. With the help of Lyapunov stability theory, the tracking errors and synchronization errors of this system are calculated by introducing the Lyapunov–Krasovskii functional; the asymptotic convergence results rigorously prove the stability of the adaptive cooperative control systems. The simulation results verify the excellent performance of the controller.

A Mean-Variance robust model to minimize operational risk and supply chain cost under aleatory uncertainty: A real-life case application in petroleum supply chain

The purpose of the research work is to consider a multi-echelon, multi-product, and multi-modal petroleum supply chain network design problem along with its various sources of uncertainties (demand, supply, production, etc.), and to minimize both total supply chain cost and risk simultaneously. The problem is articulated as a robust optimization problem and the results are derived under various risk attitudes (viz. risk-seeking, risk-neutral and risk-averse behaviors). The non-linear problem is proposed as a Mean-Variance robust optimization problem. Two-stage stochastic programming is extended to incorporate the robustness and capture the risk aversion behavior. The scenario-based planning method is used for the estimation of uncertain parameters. A real-life case study of petroleum supply chain is conducted in the Indian scenario, considering the requisite challenges and constraints. The results show that total supply chain cost and risk demonstrate conflicting behavior with each other. Total supply chain cost increases with an increase in risk aversion level. Significant amount of operational risks can be reduced with slight increase in total supply chain cost. Penalty cost contributes the maximum to the increase in total supply chain cost along with risk aversion level.

Adaptive Contraction-based Control of Uncertain Nonlinear Processes using Neural Networks

Driven by the flexible manufacturing trend in the process control industry and the uncertain nature of chemical process models, this article aims to achieve offset-free tracking for a family of uncertain nonlinear systems (e.g., using process models with parametric uncertainties) with adaptable performance. The proposed adaptive control approach incorporates into the control loop an adaptive neural network embedded contraction-based controller (to ensure convergence to time-varying references) and an online parameter identification module coupled with reference generation (to ensure modelled parameters converge those of the physical system). The integrated learning and control approach involves training a state and parameter dependent neural network to learn a contraction metric parameterized by the uncertain parameter and a differential feedback gain. This neural network is then embedded in an adaptive contraction-based control law which is updated by parameter estimates online. As uncertain parameter estimates converge to the corresponding physical values, offset-free tracking, simultaneously with improved convergence rates, can be achieved, resulting in a flexible, efficient and less conservative approach to the reference tracking control of uncertain nonlinear processes. An illustrative example is included to demonstrate the overall approach.

Cluster Gauss-Newton and CellNOpt Parameter Estimation in a Small Protein Signaling Network of Vorinostat and Bortezomib Pharmacodynamics.

Ordinary differential equation (ODE)-based models of signal transduction pathways often contain parameters that are unidentifiable or unmeasurable by experimental data, and calibrating such models to data remains challenging. Here, two efficient parameter estimation methods, cluster Gauss-Newton (CGN) and CellNOpt (CNO), were applied to fit a signaling network model of U266 multiple myeloma cells to the activity dynamics of key proteins in response to vorinostat and/or bortezomib. A logic-based network model was constructed and transformed to 17 ODEs with 79 parameters estimated within broad ranges of biologically plausible values. The top 10% best-fit parameters by both methods had high uncertainties with CV > 50% for the majority of parameters. The root mean square and prediction errors were comparable without statistically significant differences between the two methods. Despite uncertain parameter estimation, protein dynamics after the sequential combination of bortezomib and vorinostat was predicted with reasonable accuracy and precision. Global sensitivity analyses of partial rank correlation coefficients and Sobol sensitivity demonstrated that apoptosis induction was most sensitive to parameters governing the activity of the proteasome-JNK-caspase-8 axis. Simulations revealed that the greatest magnitude of pharmacodynamic drug interactions between bortezomib and vorinostat occurred at caspase-9, AKT, and Bcl-2. Two sequential combinations were explored in silico, and the outcome matched qualitatively with an empirical evaluation of the pharmacodynamic interaction based on cell viability. Overall, the CGN and CNO algorithms performed similarly for this ODE-based network model calibration, and the calibrated model provided meaningful insights into cellular signaling mechanisms in response to pharmacological perturbations.

Sensitivity and Interdependency Analysis of the HBV Conceptual Model Parameters in a Semi-Arid Mountainous Watershed

Hydrological models, with different levels of complexity, have become inherent tools in water resource management. Conceptual models with low input data requirements are preferred for streamflow modeling, particularly in poorly gauged watersheds. However, the inadequacy of model structures in the hydrologic regime of a given watershed can lead to uncertain parameter estimation. Therefore, an understanding of the model parameters’ behavior with respect to the dominant hydrologic responses is of high necessity. In this study, we aim to investigate the parameterization of the HBV (Hydrologiska Byråns Vattenbalansavedelning) conceptual model and its influence on the model response in a semi-arid context. To this end, the capability of the model to simulate the daily streamflow was evaluated. Then, sensitivity and interdependency analyses were carried out to identify the most influential model parameters and emphasize how these parameters interact to fit the observed streamflow under contrasted hydroclimatic conditions. The results show that the HBV model can fairly reproduce the observed daily streamflow in the watershed of interest. However, the reliability of the model simulations varies from one year to another. The sensitivity analysis showed that each of the model parameters has a certain degree of influence on model behavior. The temperature correction factor (ETF) showed the lowest effect on the model response, while the sensitivity to the degree-day factor (DDF) highly depends on the availability of snow cover. Overall, the changes in hydroclimatic conditions were found to be mostly responsible for the annual variability of the optimal parameter values. Additionally, these changes seem to actuate the interdependency between the parameters of the soil moisture and the response routines, particularly Field Capacity (FC), the recession coefficient K0, the percolation coefficient (KPERC), and the upper reservoir threshold (UZL). The latter combines either to shrink the storage capacity of the model’s reservoirs under extremely high peak flows or to enlarge them under overestimated water supply, mainly provoked by abundant snow cover.

Urban pluvial flood risk assessment – data resolution and spatial scale when developing screening approaches on the microscale

Abstract. Urban development models typically provide simulated building areas in an aggregated form. When using such outputs to parametrize pluvial flood risk simulations in an urban setting, we need to identify ways to characterize imperviousness and flood exposure. We develop data-driven approaches for establishing this link, and we focus on the data resolutions and spatial scales that should be considered. We use regression models linking aggregated building areas to total imperviousness and models that link aggregated building areas and simulated flood areas to flood damage. The data resolutions used for training regression models are demonstrated to have a strong impact on identifiability, with too fine data resolutions preventing the identification of the link between building areas and hydrology and too coarse resolutions leading to uncertain parameter estimates. The optimal data resolution for modeling imperviousness was identified to be 400 m in our case study, while an aggregation of the data to at least 1000 m resolution is required when modeling flood damage. In addition, regression models for flood damage are more robust when considering building data with coarser resolutions of 200 m than with finer resolutions. The results suggest that aggregated building data can be used to derive realistic estimations of flood risk in screening simulations.

Global Sensitivity Analysis of the Rodgers and Rowland Model for Prediction of Tissue: Plasma Partitioning Coefficients: Assessment of the Key Physiological and Physicochemical Factors That Determine Small-Molecule Tissue Distribution.

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fup) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation.

Adaptive Dynamic Surface Control for Active Suspension With Electro-Hydraulic Actuator Parameter Uncertainty and External Disturbance

In this paper, a new adaptive dynamic surface control strategy is proposed to deal with the uncertainty parameters of electro-hydraulic actuator and unknown external disturbances of vehicle active suspension system. A dynamic model of nonlinear vehicle active suspension is established. The adaptive parameter estimation laws are designed to estimate the uncertain parameters caused by the change of the physical characteristics of the electro-hydraulic actuator. In other words, the estimation of uncertain parameters in hydraulic system is beneficial to improve the control precision of vehicle. Nonlinear robust feedback signal is introduced to suppress unknown external disturbances. Then, this paper proposes an idea of dynamic surface in order to avoid explosion of complexity that caused by virtual control signal. The dynamic surface function replaces the derivative of virtual control signal in backstepping control, which reduces the computational complexity and improves the riding comfort. The simulation comparison shows that the presented method is effective in improving riding comfort and driving safety.

Estimation-Based Quadratic Iterative Learning Control for Trajectory Tracking of Robotic Manipulator With Uncertain Parameters

In this paper, we consider iterative learning control for trajectory tracking of robotic manipulator with uncertainty. An improved quadratic-criterion-based iterative learning control approach (Q-ILC) is proposed to obtain better trajectory tracking performance for the robotic manipulator. Besides of the position error information, which has been used in existing Q-ILC methods for robotic control, the velocity error information is also taken into consideration such that a new norm-optimal objective function is constructed. Convergence and error sensitivity properties for the proposed method are also analyzed. To deal with uncertainty, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are incorporated for estimation of uncertain parameters by constructing extended system states. The performances between the two filters are also compared. Simulations on a 2DOF Robot manipulator demonstrate that the improved Q-ILC with parameter estimators can achieve faster convergence and better transient performance compared to the original Q-ILC, in the presence of measurement noise and model uncertainty.

Nonlinear adaptive output feedback robust control of hydraulic actuators with largely unknown modeling uncertainties

In this paper, a nonlinear adaptive output feedback robust controller is proposed for motion control of hydraulic servo systems in the presence of largely unknown matched and mismatched modeling uncertainties. Different from the existing control technologies, the presented hydraulic closed-loop controller which can deal with strong matched and mismatched parametric uncertainties is synthesized via the backstepping technique. Specially, a nonlinear disturbance observer which can estimate the largely mismatched disturbance is integrated into the design of the linear extended state observer to obtain estimation of unmeasurable system states, uncertain parameters and strong disturbances simultaneously. In addition, the projection-type adaptive law is synthesized into the design of the resulting controller. More importantly, the global stability of the whole closed-loop system is strictly guaranteed by the Lyapunov analysis. Furthermore, the effectiveness and practicability of the presented control strategy have been demonstrated by comparative experiments under different working conditions.

Reliability growth planning based on information gap decision theory

Abstract Resources allocation is one of the key issues in the planning of reliability growth testing. Sparse information and testing prototypes are available for program managers in the research and development phases, especially at the early development stage. However, program managers or engineers are often needed to make decisions with incomplete information or even severe uncertainty. Optimizing strategy has been used to allocate resources for reliability growth testing, which sets up optimization models and maximizes the reliability within the resource constraints. A novel robust decision method for the planning of reliability growth testing based on the information gap decision theory is proposed, which aims to satisfy the system reliability requirements and keeps the decision insensitive to the initial estimation of relevant uncertain parameters. The information gap robustness function provides an alternative approach to address the planning of reliability growth testing. The case study demonstrates the applicability of the proposed method in practical problems. The main advantage of this method is that only a few information of the uncertain parameters is required. The results indicate that this method is useful for program managers and reliability practitioners who are engaged in reliability growth planning.

An adaptive robust model predictive control for indoor climate optimization and uncertainties handling in buildings

Model predictive control (MPC) in building automation and control (BAC) applications is challenged by difficulties in constructing accurate building models and handling uncertain disturbances. An adaptive robust model predictive control (ARMPC) is proposed to refine building models and handle uncertainty of disturbances. A model adaptation function is incorporated to perform online estimation of uncertain parameters of the building model using online measured building operation data, as the MPC controller is in operation. An additive uncertainty model to represent uncertainties of disturbances is integrated with the building model for robust optimization. The control performance of the ARMPC is compared with MPC controllers without adaptive modelling and robust optimization, as well as a conventional thermostat through simulation constructed based on a test building. When an energy-saving-biased setting is applied, ARMPC achieves the best thermal comfort performance among the tested controllers. The energy savings achieved by the ARMPC vary from ≈20% to ≈15%, compared to the thermostat, as uncertainty level of internal load increases from 0% to 60%. MPC controllers without adaptive modelling and robust optimization maintain ≈20% energy savings as the uncertainty level increases but at the expense of compromising thermal comfort. When a thermal-comfort-biased setting is applied, the MPC controllers maintain the indoor predicted mean vote (PMV) within a narrow range around thermal neutrality while achieving energy savings of around 10%, compared to the thermostat. The adaptive modelling and robust optimization of the ARMPC prevent the indoor condition from violating the constrains due to model inaccuracy and uncertainties in measured disturbances.