Optimal Experimental Design Research Articles

Surface Mechanical Property Prediction and Process Optimization of 18CrNiMo7-6 Carburized Steel Stator Guide Based on Radial Basis Function Neural Network and NSGA-II Algorithm

The carburizing process is a key technology that affects the mechanical properties of the surface of the hydraulic motor stator guide rail, and the related process parameters have an important influence on surface hardness, the thickness of the carburized layer, and the deformation of the guide rail. However, at present, the relationship between the carburizing process parameters and the surface mechanical properties of the target is not clear. This paper proposes a “hardness prediction and process parameter optimization” method. Firstly, a finite element model is established, with carburizing time, temperature, and carbon potential as the three input factors; the optimal Latin hypercubic experimental design and sensitivity analysis are applied. Secondly, surface hardness, carburized layer thickness, and deformation are taken as the output values, and an RBF neural network is used to construct the prediction model. The results show that the RBF neural network can be accurately used for the prediction of surface hardness, the thickness of the carburized layer, and deformation, and for the optimization of process parameters. The optimized parameters of surface hardness and the thickness of the carburized layer were increased by 4.2% and 5.1%, respectively, and the deformation amount was reduced to 0.31 mm, achieving the goal of optimal design.

Deep optimal experimental design for parameter estimation problems

Abstract Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter estimation techniques are changing rapidly with the introduction of deep learning techniques to replace traditional estimation methods. This in turn requires the adaptation of optimal experimental design that is associated with these new techniques. In this paper we investigate a new experimental design methodology that uses deep learning. We show that the training of a network as a Likelihood Free Estimator can be used to significantly simplify the design process and circumvent the need for the computationally expensive bi-level optimization problem that is inherent in optimal experimental design for non-linear systems. Furthermore, deep design improves the quality of the recovery process for parameter estimation problems. As proof of concept we apply our methodology to two different systems of Ordinary Differential Equations.

Tractable optimal experimental design using transport maps*

Abstract We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality criteria, prior distributions and noise models. The key to our approach is the construction of a transport-map-based surrogate to the joint probability law of the design, observational and inference random variables. This order-preserving transport map is constructed using tensor trains and can be used to efficiently sample from (and evaluate approximate densities of) conditional distributions that are required in the evaluation of many commonly-used optimality criteria. The algorithm is also extended to sequential data acquisition problems, where experiments can be performed in sequence to update the state of knowledge about the unknown parameters. The sequential BOED problem is made computationally feasible by preconditioning the approximation of the joint density at the current stage using transport maps constructed at previous stages. The flexibility of our approach in finding optimal designs is illustrated with some numerical examples inspired by disease modeling and the reconstruction of subsurface structures in aquifers.

Optimal experiment design for inverse problems via selective normalization and zero-shift times

Optimal experiment design for inverse problems via selective normalization and zero-shift times

Determination of a small elliptical anomaly in electrical impedance tomography using minimal measurements

Abstract We consider the problem of determining a small elliptical conductivity anomaly in a unit disc from boundary measurements. The conductivity of the anomaly is assumed to be a small perturbation from the constant background. A measurement of voltage across two point-electrodes on the boundary through which a constant current is passed. We further assume the limiting case when the distance between two electrodes go to zero, creating a dipole field. We show that three such measurements suffice to locate the anomaly size and location inside the disc. Two further measurements are needed to obtain the aspect ratio and the orientation of the ellipse. The investigation includes the studies of the stability of the inverse problem and optimal experiment design.

Acceleration of ferromagnetic resonance measurements by Bayesian experimental design.

Ferromagnetic resonance (FMR) is a broadly used dynamical measurement used to characterize a wide range of magnetic materials. Applied research and development on magnetic thin film materials is growing rapidly alongside a growing commercial appetite for magnetic memory and computing technologies. The ability to execute high-quality, fast FMR surveys of magnetic thin films is needed to meet the demanding throughput associated with rapid materials exploration and quality control. Here, we implement optimal Bayesian experimental design software developed by [McMichael etal. J. Res. Natl. Inst. Stand. Technol. 126, 126002 (2021)] in a vector network analyzer-FMR setup to demonstrate an unexplored opportunity to accelerate FMR measurements. A systematic comparison is made between the optimal Bayesian measurement and the conventional measurement. Reduced uncertainties in the linewidth and resonance frequency ranging from 40% to 60% are achieved with the Bayesian implementation for the same measurement duration. In practical terms, this approach reaches a target uncertainty of ±5MHz for the linewidth and ±1MHz for the resonance frequency in 2.5× less time than the conventional approach. As the optimal Bayesian approach only decreases random errors, we evaluate how large systematic errors may limit the full advantage of the optimal Bayesian approach. This approach can be used to deliver gains in measurement speed by a factor of 3 or more and as a software add-on has the flexibility to be added on to any FMR measurement system to accelerate materials discovery and quality control measurements, alike.

Failure analysis and optimization design of CFRP automotive seat back under multiple conditions

This study explores the adoption of carbon fiber reinforced plastic (CFRP) in automotive seat backrests, aiming to improve compliance with regulatory standards and enhance performance. By replacing conventional materials with CFRP, and employing mechanical performance tests alongside the principle of equal stiffness, the study tackles material failure issues. A novel multi-criteria decision-making method, coupled with an optimal Latin hypercube experimental design, is used to optimize the layup sequence. The optimized design not only meets regulatory requirements but also significantly enhances driver and passenger safety and comfort during collisions.

Enhanced feature matching in single-cell proteomics characterizes IFN-γ response and co-existence of cell states

Proteome analysis by data-independent acquisition (DIA) has become a powerful approach to obtain deep proteome coverage, and has gained recent traction for label-free analysis of single cells. However, optimal experimental design for DIA-based single-cell proteomics has not been fully explored, and performance metrics of subsequent data analysis tools remain to be evaluated. Therefore, we here formalize and comprehensively evaluate a DIA data analysis strategy that exploits the co-analysis of low-input samples with a so-called matching enhancer (ME) of higher input, to increase sensitivity, proteome coverage, and data completeness. We assess the matching specificity of DIA-ME by a two-proteome model, and demonstrate that false discovery and false transfer are maintained at low levels when using DIA-NN software, while preserving quantification accuracy. We apply DIA-ME to investigate the proteome response of U-2 OS cells to interferon gamma (IFN-γ) in single cells, and recapitulate the time-resolved induction of IFN-γ response proteins as observed in bulk material. Moreover, we uncover co- and anti-correlating patterns of protein expression within the same cell, indicating mutually exclusive protein modules and the co-existence of different cell states. Collectively our data show that DIA-ME is a powerful, scalable, and easy-to-implement strategy for single-cell proteomics.

A cutting edge potentiometric determination of baricitinib in synthetic wastewater and in tablet dosage form using modified carbon paste ion-selective membrane

After the recent hit of COVID-19, many drugs were successively administered to save patients’ lives and those drugs reached aquatic sources, one of those drugs was Baricitinib. Driven by the current situation, a potentiometric technique using an ion-selective membrane (ISM) recipe drop cast on a modified carbon paste electrode was optimized for the superior determination of Baricitinib (BAR). The molecular docking was customized to optimize the proper ionophores incorporated in the ISM, revealing that beta-cyclodextrin (β-CD) is the most compatible ionophore with the studied drug. A multivariate optimization experimental design was employed to optimize the best experimental condition for the analytical method. To this end; dual nanoparticles (multi-walled carbon nanotubes and copper oxide nanoparticles) were incorporated in the carbon paste electrode, and the ISM recipe was enriched with β-CD and cation-exchanger (phosphotungstic acid) in a polyvinylchloride matrix plasticized with dibutyl phthalate. A Nernstian slope equal to 19.97 mV/decade with a linearity range of 7.99 × 10−7–1.00 × 10−3 M was obtained. The validated sensor exhibited good recovery when used to determine the studied drug in synthetic wastewater and tablet dosage form. The greenness of the method was evaluated using the Complementary Green Analytical Procedure Index and Blue Applicability Grade Index.

A multi-stage lithium-ion battery aging dataset using various experimental design methodologies

This dataset encompasses a comprehensive investigation of combined calendar and cycle aging in commercially available lithium-ion battery cells (Samsung INR21700-50E). A total of 279 cells were subjected to 71 distinct aging conditions across two stages. Stage 1 is based on a non-model-based design of experiments (DoE), including full-factorial and Latin hypercube experimental designs, to determine the degradation behavior. Stage 2 employed model-based parameter individual optimal experimental design (pi-OED) to refine specific dependencies, along with a second non-model-based approach for fair comparison of DoE methodologies. While the primary aim was to validate the benefits of optimal experimental design in lithium-ion battery aging studies, this dataset offers extensive utility for various applications. They include training of machine learning models for battery life prediction, calibrating of physics-based or (semi-)empirical models for battery performance and degradation, and numerous other investigations in battery research. Additionally, the dataset has the potential to uncover hidden dependencies and correlations in battery aging mechanisms that were not evident in previous studies, which often relied on pre-existing assumptions and limited experimental designs.

Statistical estimation theory detection limits for label-free imaging.

The emergence of label-free microscopy techniques has significantly improved our ability to precisely characterize biochemical targets, enabling non-invasive visualization of cellular organelles and tissue organization. However, understanding each label-free method with respect to the specific benefits, drawbacks, and varied sensitivities under measurement conditions across different types of specimens remains a challenge. We link all of these disparate label-free optical interactions together and compare the detection sensitivity within the framework of statistical estimation theory. To achieve this goal, we introduce a comprehensive unified framework for evaluating the bounds for signal detection with label-free microscopy methods, including second-harmonic generation, third-harmonic generation, coherent anti-Stokes Raman scattering, coherent Stokes Raman scattering, stimulated Raman loss, stimulated Raman gain, stimulated emission, impulsive stimulated Raman scattering, transient absorption, and photothermal effect. A general model for signal generation induced by optical scattering is developed. Based on this model, the information obtained is quantitatively analyzed using Fisher information, and the fundamental constraints on estimation precision are evaluated through the Cramér-Rao lower bound, offering guidance for optimal experimental design and interpretation. We provide valuable insights for researchers seeking to leverage label-free techniques for non-invasive imaging applications for biomedical research and clinical practice.

Probiotic Encapsulation: Bead Design Improves Bacterial Performance during In Vitro Digestion (Part 2: Operational Conditions of Vibrational Technology).

The development of functional foods is a viable alternative for the prevention of numerous diseases. However, the food industry faces significant challenges in producing functional foods based on probiotics due to their high sensitivity to various processing and gastrointestinal tract conditions. This study aimed to evaluate the effect of the operational conditions during the extrusion encapsulation process using vibrating technology on the viability of Lactobacillus fermentum K73, a lactic acid bacterium with hypocholesterolemia probiotic potential. An optimal experimental design approach was employed to produce sweet whey-sodium alginate (SW-SA) beads with high bacterial content and good morphological characteristics. In this study, the effects of frequency, voltage, and pumping rate were optimized for a 300 μm nozzle. The microspheres were characterized using RAMAN spectroscopy, scanning electron microscopy, and confocal laser scanning microscopy. The optimal conditions for bead production were found: 70 Hz, 250 V, and 20 mL/min with a final cell count of 8.43 Log10 (CFU/mL). The mean particle diameter was 620 ± 5.3 µm, and the experimental encapsulation yield was 94.3 ± 0.8%. The INFOGEST model was used to evaluate the survival of probiotic beads under gastrointestinal tract conditions. Upon exposure to in vitro conditions of oral, gastric, and intestinal phases, the encapsulated viability of L. fermentum was 7.6 Log10 (CFU/mL) using the optimal encapsulation parameters, which significantly improved the survival of probiotic bacteria during both the encapsulation process and under gastrointestinal conditions compared to free cells.

A Non‐Linear Model for Multiple Alcohol Intakes and Optimal Designs Strategies

ABSTRACTThis study addresses the complex dynamics of alcohol elimination in the human body, very important in forensic and healthcare areas. Existing models often oversimplify with the assumption of linear elimination kinetics, limiting practical application. This study presents a novel non‐linear model for estimating blood alcohol concentration after multiple intakes. Initially developed for two different alcohol incorporations, it can be straightforwardly extended to the case of more intakes. Emphasising the significance of accurate parameter estimation, the research underscores the importance of precise experimental design, utilising optimal experimental design (OED) methodologies. Sensitivity analysis of model coefficients and the determination of D‐optimal designs, considering correlation structures among observations, reveal a strong linear relationship between support points. This relationship can be used to obtain nearly optimal designs that are highly efficient and much easier to compute.

Sequential optimal experimental design for vapor-liquid equilibrium modeling

We propose a general methodology of sequential locally optimal design of experiments for explicit or implicit nonlinear models, as they abound in chemical engineering and, in particular, in vapor-liquid equilibrium modeling. As a sequential design method, our method iteratively alternates between performing experiments, updating parameter estimates, and computing new experiments. Specifically, our sequential design method computes a whole batch of new experiments in each iteration and this batch of new experiments is designed in a two-stage locally optimal manner. In essence, this means that in every iteration the combined information content of the newly proposed experiments and of the already performed experiments is maximized. In order to solve these two-stage locally optimal design problems, a recent and efficient adaptive discretization algorithm is used. We demonstrate the benefits of the proposed methodology on the example of the parameter estimation for the non-random two-liquid model for narrow azeotropic vapor-liquid equilibria. As it turns out, our sequential optimal design method requires substantially fewer experiments than traditional factorial design to achieve the same model precision and prediction quality. Consequently, our method can contribute to a substantially reduced experimental effort in vapor-liquid equilibrium modeling and beyond.

Optimal experimental designs for characterising ion channel gating by filling the phase-voltage space of model dynamics

Optimal experimental designs for characterising ion channel gating by filling the phase-voltage space of model dynamics

Optimal design of large-scale nonlinear Bayesian inverse problems under model uncertainty

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the inversion parameters, the governing PDEs include secondary uncertain parameters. We focus on problems with infinite-dimensional inversion and secondary parameters and present a scalable computational framework for optimal design of such problems. The proposed approach enables Bayesian inversion and OED under uncertainty within a unified framework. We build on the Bayesian approximation error (BAE) approach, to incorporate modeling uncertainties in the Bayesian inverse problem, and methods for A-optimal design of infinite-dimensional Bayesian nonlinear inverse problems. Specifically, a Gaussian approximation to the posterior at the maximum a posteriori probability point is used to define an uncertainty aware OED objective that is tractable to evaluate and optimize. In particular, the OED objective can be computed at a cost, in the number of PDE solves, that does not grow with the dimension of the discretized inversion and secondary parameters. The OED problem is formulated as a binary bilevel PDE constrained optimization problem and a greedy algorithm, which provides a pragmatic approach, is used to find optimal designs. We demonstrate the effectiveness of the proposed approach for a model inverse problem governed by an elliptic PDE on a three-dimensional domain. Our computational results also highlight the pitfalls of ignoring modeling uncertainties in the OED and/or inference stages.

Identifying Bayesian optimal experiments for uncertain biochemical pathway models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.

Improving breathing effort estimation in mechanical ventilation via optimal experiment design

Estimation of the breathing effort and relevant lung parameters of a ventilated patient is essential to keep track of a patient’s clinical condition. The aim of this paper is to increase estimation accuracy through experiment design. The main method is an experiment design approach across multiple breaths within a linear regression framework to accurately identify the patient’s condition. Identifiability and persistence of excitation are used to formulate an estimation problem with a unique solution. Furthermore, Fisher information is used for assessing the parameters sensitivity to slight changes of the ventilator settings to improve the variance of the estimation. The estimation method is applied to simulated patients who breathe regularly but also to patients who have variable breathing patterns. A virtual experiment is conducted for both situations to generate estimation results. The results are analyzed using mathematical tools and show that uniquely estimating the lung parameters and breathing effort over multiple breaths for both regularly and variably breathing patients is possible in the presented framework. The proposed estimation method obtains clinically relevant estimates for a large set of breathing disturbances from the simulation case-study.

A comprehensive approach to sparse identification of linear parameter-varying models for lithium-ion batteries using improved experimental design

This paper proposes a comprehensive approach to the identification of battery models in the linear parameter-varying (LPV) framework inspired by the equivalent-circuit model structures. The proposed LPV model structure is formulated using the input–output representation, wherein the model parameters are considered to depend on the state-of-charge, the current magnitude, and the current direction. The aforementioned dependence is explained using a suitable set of basis functions motivated with appropriate physical insight. Furthermore, the optimal experimental design problem is discussed to propose an improved input design for the model identification procedure. Subsequently, the Least Absolute Shrinkage and Selection Operator (LASSO) along with the ridge regression are employed for the selection of significant model terms and parameter estimation to yield a sparse model with adequate simulation capabilities. Finally, several battery models with varying model order and basis-function complexity are identified, which are subsequently validated and compared using a real drive-cycle dataset. The corresponding voltage simulation results yield the root-mean-squared error (RMSE) value for the best-performing model to be around 24.5 mV when a 1 A h NMC battery gets discharged with the lower voltage cutoff as low as 2.5 V.

An experimental platform for semi-autonomous kinetic model refinement combining optimal experimental design, computer-controlled experiments, and optimization leads to new understanding of N[formula omitted]O + O

Automated platforms could enable the unprecedented pace required for modeling the countless proposed alternative fuels relevant to future technologies, but existing platforms rely exclusively on automatically generated computational data and lack experimental validation. Here, we introduce an experimental platform for rapid kinetic model refinement that combines optimal experimental design, computer-controlled experiments, and optimization—each of which are tailored in novel ways to form a cohesive platform together. The optimal experimental design considers (1) realistic uncertainties in both experimental conditions and measurements and (2) diverse reactant mixtures that can include “chemical sensitizers,” which are not necessarily reactants in a specified Quantity of Interest (QoI) but sensitize kinetic information relevant to a QoI. Similarly, our High-Throughput Jet-Stirred Reactor (HT-JSR) features (1) rapid multi-species diagnostics that can measure dozens of species within minutes, (2) a flow delivery system that can prepare up to ∼10-component reactant mixtures, and (3) computer-controlled operation of all components. Finally, a post-processing code automatically retrieves data from the instruments, quantifies uncertainties in both experimental conditions and measurements, and produces self-contained files usable for optimization in our MultiScale Informatics software. This platform is demonstrated for the rate constant for N2O + O ⇌ N2 + O2 as the QoI where, unlike for N2O + O ⇌ NO + NO, proposed values at ∼1000 K span ∼5 orders of magnitude yet give equally good agreement with previous experimental data—suggesting that previous experiments fail to constrain the branching ratio of N2O + O. The results show that optimal conditions with more species as both reactants and analytes—particularly NO2 as both a reactant and analyte—enable unambiguous discrimination of the main products of N2O + O. Specifically, the data preclude N2 + O2 as the main products at ∼1000 K—contrary to most recently proposed values.Novelty and significance statementWe introduce a novel experimental platform for rapid kinetic model refinement that combines optimal design, computer-controlled experiments, and optimization—each uniquely tailored to form a cohesive platform. It notably employs high levels of automation, high-throughput multi-species diagnostics, and uniquely diverse reactant mixtures to accelerate scientific discovery. This platform is shown to achieve a goal that no previous experiment has: decipher the main products of N2O + O. This success—attributable to the platform’s unique design principles—demonstrates the effectiveness of this experimental platform as a tool for accelerating scientific discovery and kinetic model development.