Parameter estimation in fluid flow models from aliased velocity measurements

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

A methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

When model-based controllers are used for carrying out precise tasks, the estimation of model parameters is key for a better trajectory tracking performance. We consider the scenario of a free-flying space robot with limited actuation that has grasped an object of unknown properties. The inertial parameters - mass, centre of mass and the inertia tensor - of the robot-object system are to be determined. In our previous works, we used a parameter estimation algorithm where truncated Fourier series were used to represent both the reference excitation trajectory and the executed one. That algorithm is the focus of this paper, along with a study of the factors that could contribute to a loss of accuracy in the obtained estimates. Simulation results with the Space CoBot free-flyer robot are used to find the causes of the latter: first, a modified version of the minimum condition number criterion is used to generate feasible excitatory trajectories. The results are compared with those given by the maximum information criterion to check for better excitation. Next, an appropriate number of harmonics has to be found for the Fourier series, which will be used to fit the measured data. This is done autonomously, based on the least squares residual. Finally, the relation between input saturation while executing the excitation trajectory and the errors in the resulting parameter estimates is studied.

A hybrid approach for efficient and robust parameter estimation in biochemical pathways

BackgroundThe development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times.Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies.ResultsThe performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network.The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used.ConclusionsThe new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

This paper presents a new methodology for parameter estimation of models with limit cycle and Hopf bifurcation. By calculating average cycle values for the process signal, a convex objective function can be produced using a maximum likelihood approach. This methodology allows for the proper statistical analysis of the results and the usage of local optimization algorithms for fast and efficient estimation. A case study is presented for a simplified well model of slugging oil systems, for which parameter estimation is crucial to correctly represent any system of interest. Two other objective functions from the literature are compared through Particle Swarm Optimization. The proposed method outperformed those of previous works as determined by a rigorous statistical assessment.

Functional relationship model is used to study the data that are subjected to errors. In this paper, we consider the linear functional relationship model with bivariate circular data where the pair of errors is with unequal concentration parameters. The parameter estimation of the model for circular data is different from linear data due to its wrapped around nature. We propose some improvements on the parameter estimation where some iterative procedures are considered. The concentration parameters are estimated based on the Bessel function. Also, we derive the corresponding covariance matrix of the model based on the Fisher Information matrix. Monte Carlo simulation studies were performed to study the suitability of the estimation method. It is found that the biasness of the estimates is small. Practical application of the method is illustrated by using real data set. Keywords: circular data; covariance matrix; Von Mises distribution; simulation study

Parameter estimation in complicated rational functions

Gaussian process regression and conditional Karhunen-Loève models for data assimilation in inverse problems

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

Modeling and Identification of a Nuclear Reactor

The primary challenge of software reliability growth model is to find the unknown model parameters that are used to validate on software failure dataset. Though, numerical estimation technique plays a vital role in parameter estimation of software reliability growth models, they are not optimal as they suffer from constraints sucha as sample size, biasing, and initialisation of parameters. In this study, a parameter estimation of software reliability growth model that utilises a variant of harmony search is proposed. Extensive experiments are conducted on seven different software datasets of varying complexity. A robust experimental setup is developed employing an orthogonal array and Taguchi method. Two‐fold performance comparisons are performed. First, the authors tested their proposed approach against Cuckoo search and numerical method (least square estimation) considering mean square error and Theil's statistics as a quality measure. Second, the authors applied statistical tests are performed that demonstrate the superiority of their approach over the others. The underlying motivation to conduct this study is to motivate researchers to utilise their approach for a better estimation of model parameters.

Parameter Estimation by Picard-Iteration for Biochemical Networks with Noisy Data