Practical Identifiability Analysis and Optimal Experimental Design for the Parameter Estimation of the ASM2d-Based EBPR Anaerobic Submodel

The problem of optimal experimental design (OED) for parameter estimation of nonlinear dynamic systems is considered. It is shown how this problem can be formulated as a dynamic optimization (optimal control) problem where the performance index is usually a scalar function of the Fisher information matrix. Numerical solutions can be obtained using direct methods, which transform the original problem into a nonlinear programming (NLP) problem via parametrizations. However, because of the frequent nonsmoothness of the cost functions, the use of gradient-based methods to solve this NLP might lead to local solutions. Stochastic methods of global optimization are suggested as robust alternatives. A case study considering the OED for parameter estimation in a fed-batch bioreactor is used to illustrate the performance and advantages of two selected stochastic algorithms.

Numerical strategies for optimal experimental design for parameter identification of non-linear dynamic (Bio-)chemical processes

AMIGO: A model identification toolbox based on global optimization and its applications in biosystems

We consider the problem of A-optimal design of experiment under a Bayesian probabilistic model with both categorical and continuous response variables. The utility function of the local design problem is derived by applying Bayesian experimental design framework. We also develop an efficient optimization algorithm to obtain the local optimal design by combining the particle swarm optimization and the blocked coordinate descent methods. In addition, we discuss two different ways of constructing the global optimal design based on the algorithm for local optimal design. Simulation studies are presented to illustrate the efficiency of our approach.

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

Summary When Shannon entropy is used as a criterion in the optimal design of experiments, advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters. Following previous work in which this idea was used in spatial sampling, the method is applied to standard parameterized Bayesian optimal experimental design. Under suitable conditions, which include non-linear as well as linear regression models, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions. It is shown using this marginal formulation that under normality assumptions every standard model which has a two-point prior distribution on the parameters gives an optimal design supported on a single point. Other results include a new asymptotic formula which applies as the error variance is large and bounds on support size.

In this paper, optimal experimental design for parameter estimation of unstructured microbial growth models during growth of biomass on a single limiting substrate in a fed-batch bioreactor is considered. The ratio Λ(F) of the largest to the smallest eigenvalue of the Fisher information matrix F (i.e. the modified E-criterion for optimal experimental design) is used to evaluate the information content of several simulation experiments, each with a different volumetric feed rate profile. The optimal value for this criterion (namely. Λ(F) = 1) is obtained for several feed rate profiles with different structures, after optimization of their corresponding degrees of freedom with respect to the information content of the experiment. Therefore. the solution to the problem of optimal experimental design is not unique, which means that additional specifications can be taken into account.

Multiple Input Multiple Output (MIMO) vibration testing provides the capability to expose a system to a field environment in a laboratory setting, saving both time and money by mitigating the need to perform multiple and costly large-scale field tests. However, MIMO vibration test design is not straightforward oftentimes relying on engineering judgment and multiple test iterations to determine the proper selection of response Degree of Freedom (DOF) and input locations that yield a successful test. This work investigates two DOF selection techniques for MIMO vibration testing to assist with test design, an iterative algorithm introduced in previous work and an Optimal Experiment Design (OED) approach. The iterative-based approach downselects the control set by removing DOF that have the smallest impact on overall error given a target Cross Power Spectral Density matrix and laboratory Frequency Response Function (FRF) matrix. The Optimal Experiment Design (OED) approach is formulated with the laboratory FRF matrix as a convex optimization problem and solved with a gradient-based optimization algorithm that seeks a set of weighted measurement DOF that minimize a measure of model prediction uncertainty. The DOF selection approaches are used to design MIMO vibration tests using candidate finite element models and simulated target environments. The results are generalized and compared to exemplify the quality of the MIMO test using the selected DOF.

This article focuses on analyzing the process of jam formation during the discharge by gravity of granular material stored in a two-dimensional silo. The aim of the article is two-fold. First, optimal experimental designs are computed, in which four approaches are considered: D-optimality, a combination of D-optimality and a cost/gain function, Bayesian D-optimality, and sequential designing. These results reveal that the efficiency of the design used by the experimenters can be improved dramatically. A sensitivity analysis with respect to the most important parameter is also performed. Second, estimation of the unknown parameters is done using least squares, that is, assuming normality, and also via maximum likelihood assuming the exponential distribution. Simulations for the designs considered in this article show that the variance, the mean squared error, and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares. Supplementary materials for this article are available online.

Optimal experimental designs for (possibly) censored data

In environmental and water resource (EWR) engineering, different types of design problems exist, such as operation design, monitoring design, detection design, and remediation design. This chapter is devoted to the subject of experimental design for model calibration and parameter estimation. Experimental design plays a critical role in model construction because the reliability of a model is mainly dependent on the quantity and quality of data used for its calibration. In other words, the experimental design dictates how data should be collected in field campaigns and how many observations are needed. An optimal experimental design (OED), when it is executed, should provide the maximum amount of information with the minimum cost. Basic concepts, theories, and methods of OED are well established in statistics and have been applied to various scientific and engineering disciplines.

Express thermo-gravimetric method for the vaporization enthalpies appraisal for very low volatile molecular and ionic compounds

Microfluidic diffusion measurements: The optimal H-cell

Optimal measurement design for parameter identification in mechanized tunneling

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the large size of the search space containing the candidates and the substantial computational cost of high-fidelity property prediction models makes screening practically challenging. In this work, we propose a general framework for constructing and optimizing a virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return-on-computational-investment (ROCI). Based on both simulated as well as real data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate screening virtually without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.