Multiple-Response Surface Approach: Modeling and Optimization

2011 ◽  
Vol 339 ◽  
pp. 321-325
Author(s):  
Bin Nie ◽  
Dan Liao ◽  
Jing Ding ◽  
Yao Dong He
Keyword(s):  
Operating Conditions ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Multiple Response ◽  
Response Models ◽  
Modeling And Optimization ◽  
Response Data ◽  
Model Average ◽  
Response Optimization ◽  
Single Response

Many products and processes have multidimensional characteristics and criteria. As these responses involve common parameters and processes, the response data are correlated. The quality and reliability improvement of such products and processes will typically involve multiple-response optimizations to find optimal operating conditions. Many of the current multiple-response optimization approaches assume a single-response uncertainty in the response models, and the uncertainty in the parameter estimates of the models. In this paper, we consider a Bayesian Model Average (BMA) approach to the modeling and optimization of variability of the predictions and the uncertainty of the model parameters. We further propose a Mahalanobis distance (MD) approach to account for the correlations among the response and the variation in the estimation of the response model.

Multi-objective performance investigation of orthopaedic bone drilling using Taguchi membership function

2017 ◽  
Vol 231 (12) ◽  
pp. 1133-1139 ◽  
Author(s):  
Gurmeet Singh ◽  
Vivek Jain ◽  
Dheeraj Gupta
Keyword(s):  
Membership Function ◽  
Bone Cells ◽  
Optimization Technique ◽  
Real Life ◽  
Multiple Response ◽  
Bone Drilling ◽  
Taguchi Optimization ◽  
Response Characteristics ◽  
Response Optimization ◽  
Single Response

Orthopaedic bone drilling attacks the surrounded bone cells and tissues in terms of thermal and mechanical in such a way that these cells can get damaged permanently. This damage to the surrounding of drill point upsurges the rehabilitation time of injury and in some cases leads to the failure of the bone screw joint. This study is based on the optimization of multiple response characteristics to minimize the damage during the bone drilling. All real-life problems, including bone drilling, require the multiple response optimization for getting a combined optimization result for all countable response characteristics. The Taguchi optimization technique is observed as a highly recommended tool for single response optimization. This article uses the Taguchi technique with little modification of membership function that will help to convert the multiple response characteristics into single response and further optimize it as a single function of performance. Rotational speed, feed rate of tool at three different levels with three different kinds of drilling tools are the drilling parameters selected for the study. The objective of this study is to minimize the surface roughness and thrust force simultaneously. Analysis of variance helps to find the percentage contribution and significance of each parameter on the performance.

Symptom Presence and Symptom Severity as Unique Indicators of Psychopathology: An Application of Multidimensional Zero-Inflated and Hurdle Graded Response Models

2021 ◽  
pp. 001316442110618
Author(s):  
Brooke E. Magnus ◽  
Yang Liu
Keyword(s):  
Symptom Severity ◽  
Latent Variables ◽  
Latent Variable ◽  
Suicide Attempts ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Response Models ◽  
Explanatory Variables ◽  
Graded Response ◽  
Scale Scores

Questionnaires inquiring about psychopathology symptoms often produce data with excess zeros or the equivalent (e.g., none, never, and not at all). This type of zero inflation is especially common in nonclinical samples in which many people do not exhibit psychopathology, and if unaccounted for, can result in biased parameter estimates when fitting latent variable models. In the present research, we adopt a maximum likelihood approach in fitting multidimensional zero-inflated and hurdle graded response models to data from a psychological distress measure. These models include two latent variables: susceptibility, which relates to the probability of endorsing the symptom at all, and severity, which relates to the frequency of the symptom, given its presence. After estimating model parameters, we compute susceptibility and severity scale scores and include them as explanatory variables in modeling health-related criterion measures (e.g., suicide attempts, diagnosis of major depressive disorder). Results indicate that susceptibility and severity uniquely and differentially predict other health outcomes, which suggests that symptom presence and symptom severity are unique indicators of psychopathology and both may be clinically useful. Psychometric and clinical implications are discussed, including scale score reliability.

scholarly journals Modeling Bacterial Regrowth and Trihalomethane Formation in Water Distribution Systems

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 463
Author(s):  
Gopinathan R. Abhijith ◽  
Leonid Kadinski ◽  
Avi Ostfeld
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Mechanistic Model ◽  
Water Distribution Systems ◽  
Sensitivity Study ◽  
Operating Conditions ◽  
Growth Rate Constant ◽  
Model Parameters ◽  
Bacterial Regrowth ◽  
The Impact

The formation of bacterial regrowth and disinfection by-products is ubiquitous in chlorinated water distribution systems (WDSs) operated with organic loads. A generic, easy-to-use mechanistic model describing the fundamental processes governing the interrelationship between chlorine, total organic carbon (TOC), and bacteria to analyze the spatiotemporal water quality variations in WDSs was developed using EPANET-MSX. The representation of multispecies reactions was simplified to minimize the interdependent model parameters. The physicochemical/biological processes that cannot be experimentally determined were neglected. The effects of source water characteristics and water residence time on controlling bacterial regrowth and Trihalomethane (THM) formation in two well-tested systems under chlorinated and non-chlorinated conditions were analyzed by applying the model. The results established that a 100% increase in the free chlorine concentration and a 50% reduction in the TOC at the source effectuated a 5.87 log scale decrement in the bacteriological activity at the expense of a 60% increase in THM formation. The sensitivity study showed the impact of the operating conditions and the network characteristics in determining parameter sensitivities to model outputs. The maximum specific growth rate constant for bulk phase bacteria was found to be the most sensitive parameter to the predicted bacterial regrowth.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals Weighted mixed-effects dose–response models for tables of correlated contrasts

2021 ◽  
Vol 21 (2) ◽  
pp. 320-347
Author(s):  
Nicola Orsini
Keyword(s):  
Dose Response ◽  
Response Pattern ◽  
Mixed Effects ◽  
Data Generation ◽  
Measures Of Association ◽  
Response Models ◽  
Response Data ◽  
Hazard Ratios ◽  
Health Related ◽  
Generation Mechanisms

Recognizing a dose–response pattern based on heterogeneous tables of contrasts is hard. Specification of a statistical model that can consider the possible dose–response data-generating mechanism, including its variation across studies, is crucial for statistical inference. The aim of this article is to increase the understanding of mixed-effects dose–response models suitable for tables of correlated estimates. One can use the command drmeta with additive (mean difference) and multiplicative (odds ratios, hazard ratios) measures of association. The postestimation command drmeta_graph greatly facilitates the visualization of predicted average and study-specific dose–response relationships. I illustrate applications of the drmeta command with regression splines in experimental and observational data based on nonlinear and random-effects data-generation mechanisms that can be encountered in health-related sciences.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

Multi-day flow forecasting using the Kalman filter

1991 ◽  
Vol 18 (2) ◽  
pp. 320-327 ◽  
Author(s):  
Murray A. Fitch ◽  
Edward A. McBean
Keyword(s):  
Kalman Filter ◽  
Prediction Model ◽  
Linear Prediction ◽  
Measured Data ◽  
System Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Forecasting Performance ◽  
Optimal Forecasting ◽  
Linear Prediction Model

A model is developed for the prediction of river flows resulting from combined snowmelt and precipitation. The model employs a Kalman filter to reflect uncertainty both in the measured data and in the system model parameters. The forecasting algorithm is used to develop multi-day forecasts for the Sturgeon River, Ontario. The algorithm is shown to develop good 1-day and 2-day ahead forecasts, but the linear prediction model is found inadequate for longer-term forecasts. Good initial parameter estimates are shown to be essential for optimal forecasting performance. Key words: Kalman filter, streamflow forecast, multi-day, streamflow, Sturgeon River, MISP algorithm.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

Conditioning Model Ensembles to Various Observed Data (Field and Regional Level) by Applying Machine-Learning-Augmented Workflows to a Mature Field with 70 Years of Production History

2021 ◽  
pp. 1-18
Author(s):  
Gisela Vanegas ◽  
John Nejedlik ◽  
Pascale Neff ◽  
Torsten Clemens
Keyword(s):  
Machine Learning ◽  
Oil Recovery ◽  
Numerical Models ◽  
Operating Conditions ◽  
Model Parameters ◽  
Large Set ◽  
Model Parameter ◽  
Production History ◽  
Hydrocarbon Fields ◽  
Parameter Distributions

Summary Forecasting production from hydrocarbon fields is challenging because of the large number of uncertain model parameters and the multitude of observed data that are measured. The large number of model parameters leads to uncertainty in the production forecast from hydrocarbon fields. Changing operating conditions [e.g., implementation of improved oil recovery or enhanced oil recovery (EOR)] results in model parameters becoming sensitive in the forecast that were not sensitive during the production history. Hence, simulation approaches need to be able to address uncertainty in model parameters as well as conditioning numerical models to a multitude of different observed data. Sampling from distributions of various geological and dynamic parameters allows for the generation of an ensemble of numerical models that could be falsified using principal-component analysis (PCA) for different observed data. If the numerical models are not falsified, machine-learning (ML) approaches can be used to generate a large set of parameter combinations that can be conditioned to the different observed data. The data conditioning is followed by a final step ensuring that parameter interactions are covered. The methodology was applied to a sandstone oil reservoir with more than 70 years of production history containing dozens of wells. The resulting ensemble of numerical models is conditioned to all observed data. Furthermore, the resulting posterior-model parameter distributions are only modified from the prior-model parameter distributions if the observed data are informative for the model parameters. Hence, changes in operating conditions can be forecast under uncertainty, which is essential if nonsensitive parameters in the history are sensitive in the forecast.

Sign in / Sign up

Export Citation Format

Share Document