Reliable Estimation Of Model Parameters Research Articles

Analysis of Relatively Short Variable Rate “Noisy” Well Test Data Using Non-Linear Deconvolution

Short well test data are pressure-rate-time data that are not long enough to be used to infer the reservoir boundary model and are very common in the oil and gas industry. Short rate well test data may occur when companies try to cut costs of well test jobs or mostly due to improper well test design. Nevertheless, one may wish to extract the most amount of information from this limited data because the de-convolve response can allow the reservoir engineer to make the best use of the available data in selecting a suitable interpretation model by narrowing down the possible boundary models and also providing a reliable estimates of model parameters. The aim of this study is to demonstrate the usefulness and significance of pressure-rate deconvolution in analyzing relatively short variable rate data using a hypothetical case study. The simulation was carried out using Sapphire’s test design module by assuming the presence of an exploratory well in an oil reservoir above bubble point pressure. Further assumption is that the reservoir is homogenous, therefore the possibility of a changing wellbore model was neglected from the analysis. The computer codes for the simulation were inputted using python programming language. We observed from the study that although pressure and flow rate relationship can be nonlinear, the problem can be formulated as a linear problem and the nonlinearity is expressed in the features of the reservoir. The simulation results were satisfactory using the test case and deviations between model parameters and actual reservoir parameters used in simulation was shown to have an absolute value less than 8% which is within acceptable engineering limits.

Implementing planned missingness in stimulus sampling designs: Strategies for optimizing statistical power and precision while limiting participant burden

The stimulus sampling design (SSD) is a widely applied research paradigm in which participants evaluate a series of visual or auditory stimuli. Researchers are often interested in phenomena reflected by differences across stimuli, and recent simulation work suggests that more than 100 stimuli may be necessary to detect smaller effects. Unfortunately, administering a large number of stimuli to each participant may compromise the validity of responses due to individual differences in susceptibility to fatigue and distraction. The present work describes the application of planned missingness design strategies to maximize statistical power, while minimizing participant burden in SSD studies. A Monte Carlo simulation study was conducted to determine the number of stimuli per rater (SPR) and average raters per stimuli (RPS) needed to ensure unbiased estimates of model parameters, as well as the desired statistical power and interval coverage. Findings suggest that two commonly used statistical estimation techniques, restricted maximum likelihood and the Markov Chain Monte Carlo algorithm, provide reliable estimates of model parameters and maintain adequate statistical power under substantial levels of planned missingness. Incorporating these methods will allow researchers to design more efficient and powerful experiments by reducing redundancies and minimizing sources of methodological error. Recommendations for incorporating planned missingness strategies in SSDs are provided.

Bifurcated Topological Optimization for IVIM.

In this work, we shed light on the issue of estimating Intravoxel Incoherent Motion (IVIM) for diffusion and perfusion estimation by characterizing the objective function using simplicial homology tools. We provide a robust solution via topological optimization of this model so that the estimates are more reliable and accurate. Estimating the tissue microstructure from diffusion MRI is in itself an ill-posed and a non-linear inverse problem. Using variable projection functional (VarPro) to fit the standard bi-exponential IVIM model we perform the optimization using simplicial homology based global optimization to better understand the topology of objective function surface. We theoretically show how the proposed methodology can recover the model parameters more accurately and consistently by casting it in a reduced subspace given by VarPro. Additionally we demonstrate that the IVIM model parameters cannot be accurately reconstructed using conventional numerical optimization methods due to the presence of infinite solutions in subspaces. The proposed method helps uncover multiple global minima by analyzing the local geometry of the model enabling the generation of reliable estimates of model parameters.

Solar Bayesian Analysis Toolkit—A New Markov Chain Monte Carlo IDL Code for Bayesian Parameter Inference

We present the Solar Bayesian Analysis Toolkit (SoBAT) which is a new easy to use tool for Bayesian analysis of observational data, including parameter inference and model comparison. SoBAT is aimed (but not limited) to be used for the analysis of solar observational data. We describe a new Interactive Data Language (IDL) code designed to facilitate the comparison of user-supplied model with data. Bayesian inference allows prior information to be taken into account. The use of Markov chain Monte Carlo (MCMC) sampling allows efficient exploration of large parameter spaces and provides reliable estimation of model parameters and their uncertainties. The Bayesian evidence for different models can be used for quantitative comparison. The code is tested to demonstrate its ability to accurately recover a variety of parameter probability distributions. Its application to practical problems is demonstrated using studies of the structure and oscillation of coronal loops.

ГЕОЭЛЕКТРИЧЕСКИЕ МОДЕЛИ МЕЛОВЫХ КОЛЛЕКТОРОВ ЗАПАДНОЙ СИБИРИ И СИГНАЛЫ ЭЛЕКТРОКАРОТАЖА

Geoelectric models describe the main types of the Cretaceous sediments of Western Siberia. Permeable layers in thin-layered model may be isotropic or anisotropic and include invaded and annulus zones formed during drilling. Galvanic and electromagnetic logs do not provide an accurate resistivity evaluation for thin electrically contrasting layers. The use of special signal transformations partially solves this problem, but 2D inversion provides a more reliable estimation of model parameters.

Reliability Modeling on Time between Failures of NC Machine Tools

A reliability modeling method is proposed based on the time between failures of NC machine tools. According to the field data of the time between failures of a certain type of NC machine tools, parameter estimation of reliability model is made by use of particle swarm optimization (PSO)-based correlation coefficient optimization method, and it is proved that time between failure of CNC machine tool obeyed mathematical model of 3-parameter Weibull distribution via hypothesis testing. This provides the basis for reliability assessment of NC machine tool as well as the development of maintenance strategy in the future. Meanwhile, it also provides a theoretical reference for the reliability prediction of the whole NC machine tool.

Analysis on Mean Time between Failures Based on Artificial Neural Network

Aimed at the reparable characteristic of the mechanical product, a method of the reliability model recognition of mean time between failure s based on the BP neural network was developed, and a method of parameter estimation of reliability model based on adaptive linear network was proposed by means of theory of artificial neural network with M ATLAB and reliability engineering theory. By network test and numerical simulation, reliability model recognition system and reliability parameters estimation system are verified. The results obtained from the simulation is better than those from the reliability paper for the common reliability model in engineering reliability and indicate the method is feasible. According to the method, the distribution model and function of reliability for mean time between failure s of mechanical product were gained by this means.

A parameter identifiability and estimation study in Yesilirmak River

Water quality models have relatively large number of parameters, which need to be estimated against observed data through a non-trivial task that is associated with substantial difficulties. This work involves a systematic model calibration and validation study for river water quality. The model considered was composed of dynamic mass balances for eleven pollution constituents, stemming from QUAL2E water quality model by considering a river segment as a series of continuous stirred-tank reactors (CSTRs). Parameter identifiability was analyzed from the perspective of sensitivity measure and collinearity index, which indicated that 8 parameters would fall within the identifiability range. The model parameters were then estimated by an integration based optimization algorithm coupled with sequential quadratic programming. Dynamic field data consisting of major pollutant concentrations were collected from sampling stations along Yesilirmak River around the city of Amasya in Turkey, and compared with model predictions. The calibrated model responses were in good agreement with the observed river water quality data, and this indicated that the suggested procedure provided an effective means for reliable estimation of model parameters and dynamic simulation for river streams.

Contribution of roots and hyphae to phosphorus uptake of mycorrhizal onion (Allium cepa L.)—A mechanistic modeling approach

AbstractPhosphorus uptake by plant roots and arbuscular mycorrhizae (AM) hyphae can be described based on morphological and physiological uptake characteristics and parameters affecting P transport in the soil to the uptake surface. The current study aimed to quantify the relative contribution of hyphae and roots to P uptake of onion and to investigate the associated mechanisms using a mechanistic simulation model. Onion was grown in a growth chamber under controlled conditions at five levels of P supply with (M) or without (NM) AM. Uptake by onion roots and AM hyphae was simulated separately using a nutrient‐uptake model, which was developed for roots. Model parameters describing P transport in the soil, as well as morphological and physiological uptake characteristics of roots and hyphae were derived from soil and nutrient‐solution experiments. The model fairly described P uptake of M and NM plants at the highest level of P supply (28 µM P in soil solution) where roots and hyphae contributed nearly equally to P uptake of M plants. However, at lower P levels (≤0.41 µM P), hyphae accounted for nearly the whole P uptake whereas roots hardly explained any uptake. The effectiveness of AM hyphae at low P supply was well explained by their favorable morphological and physiological uptake properties. Hyphae were characterized by a diameter of 3 × 10–4 cm, a Km of 0.25 µM, and a Cmin of 0.04 µM, values that are about 200, 40, and 10 times lower, respectively, compared to those of roots. Not more than 60% of the uptake at lower levels of P supply could be explained by the sum of predicted uptake of roots and hyphae suggesting that hyphae and roots may have used mechanisms additional to those described by the model to mobilize P. This work demonstrated that mechanistic models can be useful tools to study the role of AM in P uptake of plants, although reliable estimation of model parameters, especially physiological uptake properties of AM, is still limiting this approach.

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

An essential part of mathematical modelling is the accurate and reliable estimation of model parameters. In biology, the required parameters are particularly difficult to measure due to either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, resulting from generalised mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using suitable nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables. An important advantage of the proposed method is that it allows to identify suitable measurements and/or model structures for which the parameters can be estimated. Furthermore, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation.

Dynamic Simulation and Parameter Estimation in River Streams

Predictions and quality management issues for environmental protection in river basins rely on water-quality models. The key step in model calibration and verification is obtaining the right values of the model parameters. Current practice in model calibration is such that the reaction coefficients are adjusted by trial-and-error until the predicted values and measured data are within a pre-selected margin of error, and this may be a very time consuming task. This study is directed towards developing a parameter estimation strategy coupled with the simulation of water quality models so that the heavy burden of finding reaction rate coefficients is overcome. Dynamic mass balances for different forms of nitrogen and phosphorus, biological oxygen demand, dissolved oxygen, coliforms, nonconservative constituent and algae were written for a single computational element. The model parameters conforming to those in QUAL2E water quality model were estimated by a nonlinear multi-response parameter estimation strategy coupled with a stiff integrator. Yesilırmak river basin around the city of Amasya in Turkey served as the prototype system for the model development. Samples were collected simultaneously from two stations, and concentrations of many water-quality constituents were determined either on-site or in laboratory. This dynamic data was then used for numerical parameter estimation during computer simulation. When the model was simulated with the estimated parameters, it was seen that the model was quite able to predict the dynamics of major water quality constituents. It is concluded that the proposed method shows promise for automatically generating reliable estimates of model parameters.

Global nonlinear inversion of transient EM data from conducting surroundings using a free‐space plate model

A platelike conducting body in free space is used as a model to invert transient electromagnetic data using the very fast simulated annealing procedure as a global optimization tool. When the host rock conductivity is non‐zero, acceptable fits between the observed and computed responses are difficult to obtain. In general, the conducting body is assigned a lower conductance, larger dimensions (strike length and depth extent) and a smaller depth than the true values. We approximate the response of a conducting host to yield reliable estimates of model parameters as well as a good fit between the observed and computed responses. Our procedure is based on the assumption that the observed electromagnetic response is the sum of the response due to the conductive target and the response due to conducting surroundings (host and overburden). It is also assumed that the host response is laterally invariant, implying a layered earth and fixed source‐receiver geometry. The validity of the superposition assumption is tested against the full solution for a conductive plate in a finite conducting host. The efficacy of our approach is demonstrated using noise‐free and noisy synthetic data and two field examples measured in different geological conditions.

Introducing optimal experimental design in predictive modeling: A motivating example

Predictive microbiology emerges more and more as a rational quantitative framework for predicting and understanding microbial evolution in food products. During the mathematical modeling of microbial growth and/or inactivation, great, but not always efficient, effort is spent on the determination of the model parameters from experimental data. In order to optimize experimental conditions with respect to parameter estimation, experimental design has been extensively studied since the 1980s in the field of bioreactor engineering. The so-called methodology of optimal experimental design established in this research area enabled the reliable estimation of model parameters from data collected in well-designed fed-batch reactor experiments. In this paper, we introduce the optimal experimental design methodology for parameter estimation in the field of predictive microbiology. This study points out that optimal design of dynamic input signals is necessary to maximize the information content contained within the resulting experimental data. It is shown that from few dynamic experiments, more pertinent information can be extracted than from the classical static experiments. By introducing optimal experimental design into the field of predictive microbiology, a new promising frame for maximization of the information content of experimental data with respect to parameter estimation is provided. As a case study, the design of an optimal temperature profile for estimation of the parameters D ref and z of an Arrhenius-type model for the maximum inactivation rate k max as a function of the temperature, T, was considered. Microbial inactivation by heating is described using the model of Geeraerd et al. (1999). The need for dynamic temperature profiles in experiments aimed at the simultaneous estimation of the model parameters from measurements of the microbial population density is clearly illustrated by analytical elaboration of the mathematical expressions involved on the one hand, and by numerical simulations on the other.