Experiment design for control‐relevant identification of partially known stable multivariable systems

Ensuring integral controllability for robust multivariable control

Optimal experimental design for materials discovery

This study presents a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by increasing input standard deviations for efficient computation in sampling-based RBDO. First, for linear performance functions with independent normal random inputs, an exact probability of failure is derived in terms of the ratio of the input standard deviation, which is denoted by δ. Then, the probability of failure estimation is generalized for any random input and performance functions. For the generalization of the probability of failure estimation, two coefficients need to be determined by equating the probability of failure and its sensitivity with respect to the standard deviation at the current design point. The sensitivity of the probability of failure with respect to the standard deviation is obtained using the first-order score function for the standard deviation. To apply the proposed method to an RBDO problem, a concept of an equivalent standard deviation, which is an increased standard deviation corresponding to the low reliability model, is also introduced. Numerical results indicate that the proposed method can estimate the probability of failure accurately as a function of the input standard deviation compared to the Monte Carlo simulation results. As anticipated, the sampling-based RBDO using the surrogate models and the equivalent standard deviation helps find the optimum design very efficiently while yielding relatively accurate optimum design which is close to the one obtained using the original standard deviation.

The evolutionary approach of Genetic Programming (GP) has been applied extensively to model various non-linear systems. The distinct advantage of using GP is that prior assumptions for the selection of a model structure are not required. The GP automatically evolves the optimal model structure and its parameters that best describe the system characteristics. However, the evolution of an optimal model structure is highly dependent on the experimental designs used to sample the problem (system) domain and capture its characteristics. The literature reveals that very few researchers have studied the effect of various experimental designs on the performance of GP models and therefore the optimum choice of an experimental design is still unknown. This paper studies the effect of various experimental designs on the performance of GP models on two non-linear test functions. The objective of the paper is to identify the most robust (best) experimental design for effective modeling of non-linear test functions using GP. The analysis reveals that for the test function 1, the experimental design that gives best performance of GP models is response surface faced design and for test function 2, the best experimental design is 5-level full factorial design. Thus, the result concludes that the selection of the robust experimental design is a crucial preprocessing step for the effective modeling of non-linear systems using GP.

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

A robust experimental design for conceptual model discrimination based on information theory

The development of mathematical models to describe reaction kinetics is crucial in process design, control, and optimisation. However, distinguishing between different candidate kinetic models presents a non-trivial challenge. Recent works on this topic introduced an approach that employs artificial neural networks (ANNs) to identify kinetic models. In this paper, the ANNs-based model identification approach is expanded by introducing an optimal experimental design procedure. The performance of the method is evaluated through a case study related to the identification of kinetics in a batch reaction system, where different combinations of experimental design variables and noise level on the measurements are compared to assess their impact on kinetic model identification. The proposed experimental design methodology effectively reduces the number of required experiments while enhancing the artificial neural network's ability to accurately identify the appropriate set of equations defining the kinetic model structure.

The recently completed volume of Quality and Reliability Engineering International is its 25th anniversary. The mission of the journal is to provide information on new developments in many aspects of the discipline to professionals with research articles, review papers, and applications and case study papers. It is appropriate to look back over this anniversary volume and identify some important themes, highlight some of the significant papers that contribute to those themes, and discuss what we hope to see in the future. Statistical Process Control (SPC) and related topics continue to be an important area of research and applications. The journal published many noteworthy papers in this area, including the papers on adaptive procedures by Li et al.1 and Kooli and Liman2, run-to-run control3, integration of SPC with other techniques4, 5, design of control charts6, 7, and methods for identifying the change point in high-yield processes8. Reliability engineering and the associated statistical methods continue to be a key focus area for the journal. Koka et al.9 present an interdisciplinary approach to reliability in design and Samet10 discusses fault-tolerant computing. Accelerated life testing techniques are discussed by Liu and Tang11 and Pan12. Remenyte-Prescott and Andrews13 present a new real-time method for the efficient analysis of non-coherent fault trees. Anderson-Cook et al.14 investigate resource allocation for a complex system with aging components. Designed experiments and robust design are an integral part of both product design and process improvement. Methodology for robust product or process design is considered by Shaibu et al.15, Steenackers et al.16 and Rodriguez et al.17. Hazelrigg18 discusses many interesting aspects of engineering design. Other extremely useful papers include Gaudard et al.19 on the interaction between data mining and designed experiments, Guo et al.20 on the general balanced metric for mixed-level fractional factorial designs, Wesley et al.21 on prediction variance in split-plot designs, Guo et al.22 on optimal fold-over designs for mixed-level fractional factorial designs, and Jones and Johnson23 on designs for computer experiments. The journal also presented several interesting case studies, including Monroe and Pan24, Carmignani25, Magniez et al.26, Johnson et al.27 and Aksoy and Orbak28. Case studies are an important part of this journal. We have a high standard for these papers. They must represent the best of contemporary practice either through the application of new methodology or the application of existing methods in unique environments. Quality and reliability engineers are knowledge workers. They accumulate, generate and deploy knowledge with the express objective of improving products, processes, services and society. Case studies facilitate the generation and widespread adoption of new methods or provide insight about how existing methods can be used in novel situations. These types of papers can perform a valuable service to our profession. We encourage potential authors of case studies to contribute to our journal.

Solution formulations involving polymers are the basis for a wide range of products spanning consumer care, therapeutics, lubricants, adhesives, and coatings. These multicomponent systems typically show rich self-assembly and phase behavior that are sensitive to even small changes in chemistry and composition. Longstanding computational efforts have sought techniques for predictive modeling of formulation structure and thermodynamics without experimental guidance, but the challenges of addressing the long time scales and large length scales of self-assembly while maintaining chemical specificity have thwarted the emergence of general approaches. As a consequence, current formulation design remains largely Edisonian. Here, we present a multiscale modeling approach that accurately predicts, without any experimental input, the complete temperature-concentration phase diagram of model diblock polymers in solution, as established postprediction through small-angle X-ray scattering. The methodology employs a strategy whereby atomistic molecular dynamics simulations is used to parametrize coarse-grained field-theoretic models; simulations of the latter then easily surmount long equilibration time scales and enable rigorous determination of solution structures and phase behavior. This systematic and predictive approach, accelerated by access to well-defined block copolymers, has the potential to expedite in silico screening of novel formulations to significantly reduce trial-and-error experimental design and to guide selection of components and compositions across a vast range of applications.

Purpose: For more than 30 years, robust parameter design (RPD), which attempts to minimize the process bias (i.e., deviation between the mean and the target) and its variability simultaneously, has received consistent attention from researchers in academia and industry. Based on Taguchi’s philosophy, a number of RPD methodologies have been developed to improve the quality of products and processes. The primary purpose of this paper is to review and discuss existing RPD methodologies in terms of the three sequential RPD procedures of experimental design, parameter estimation, and optimization.Methods: This literature study composes three review aspects including experimental design, estimation modeling, and optimization methods.Results: To analyze the benefits and weaknesses of conventional RPD methods and investigate the requirements of future research, we first analyze a variety of experimental formats associated with input control and noise factors, output responses and replication, and estimation approaches. Secondly, existing estimation methods are categorized according to their implementation of least-squares, maximum likelihood estimation, generalized linear models, Bayesian techniques, or the response surface methodology. Thirdly, optimization models for single and multiple responses problems are analyzed within their historical and functional framework.Conclusion: This study identifies the current RPD foundations and unresolved problems, including ample discussion of further directions of study.

Despite more than a decade of research, the magnitude of wastewater leakage from defective sewer systems into groundwater supplies is still largely unknown, partly because reliable measurement methods are lacking. Although recently suggested in‐sewer tracer studies present a promising solution, it is unclear how to optimally design such studies in network settings. In this study we present a formal experimental design procedure, which uses Bayesian data analysis to improve the diagnosis of sewer leakage by combining tracer test data with prior knowledge on network topology and condition. From a simulation study, we show that (1) if a single sewer section is expected to have high leakage, that section should be distinguished in measurement layouts through isolated tests or appropriate overlapping of multiple tests; (2) if multiple sections are expected to have high leakage, layouts with tests that cover more than one high‐leakage section should be avoided; and (3) if a robust experimental design is desired, a balanced layout of tests that overlap multiple sections of high leakage, yet minimizes stretch length, should be chosen. This design will have the additional benefit of inducing covariance in the posterior distribution of exfiltration estimates, which can be used to advantage in subsequent studies. We apply these guidelines to a case study of a catchment in Zurich, Switzerland, and find that optimal layout design can improve the anticipated gain of information substantially relative to designs based on practical considerations alone. Remaining concerns regarding the procedure include (1) the generally poor understanding of the mechanisms governing sewer leakage, which can hamper reliable prior information on exfiltration; (2) the currently low measurement precision of sewer tracer studies, which might only allow for the detection of large leaks; and (3) the need for numerical implementation of the Bayesian inference procedure, which requires careful tuning and long computation times. In general, we were able to demonstrate that the incorporation of prior information through a Bayesian procedure adds significant value to experimental design, especially in situations with few “hard” data but good site‐specific knowledge, which is common in water resources research.

Reading is an essential skill for learners, yet numerous individuals face challenges in understanding text, particularly in digital learning. This study aims to introduce an experimental design plan to improve reading performance in online learning environments. The experimental design incorporates various visual components, including images and colored text, alongside audio elements that may influence reading comprehension. This experimental design utilizes an eye-tracking study methodology. The result of this study can be used for robust experimental designs. The result of the experiment can be used to optimize online learning materials, thereby enhancing students’ reading skills in an online context.

Taguchi Method is a powerful technique to optimize performance of the products or process. Taguchi’s main purpose is to reduce the variability around the target value of product properties via a systematic application of statistical experimental design which called robust design. Robust Design is an important technique for product manufacturability and product life. Taguchi simplified the usage of orthogonal arrays to setup experimental design. Thanks to this development, researchers and engineers saved both time and money. Furthermore, Taguchi proposed the usage of S/N ratio in order to measure the effects of factors on the performance characteristics. In this study a brief knowledge about the Taguchi Method is given. Orthogonal Arrays and S/N ratios are described. Summary of a case study is given.

An optimal experiment design for system identification is studied. The main contribution is the development of an adaptive method for the direct design of FIR filters for the input spectrum design problem. The accuracy of the identified model is measured in terms of the closed-loop performance of the system using the controller designed from the model. Under the assumption that the identified parameters are sufficiently close to their true values, we show that this problem may be formulated as a convex optimization problem with linear matrix inequality constraints. Thus, a global solution (if feasible) is guaranteed and the solution may further achieve any demanded accuracy. The problem formulation is particularly suited for a practical implementation, thus the extension of the experiment design problem into an iterative/adaptive identification-experiment design framework is straight forward. The adaptive approach is further studied in a simulation example, where the rapid convergence of the method is noted, and the superior result compared to an arbitrary experiment design is clear. The example support the use of the approximations taken in the theoretical approach.

Analyses of effective connectivity provide neuropsychiatric studies with new endophenotypes that are expressed in psychiatric disorders. Dynamic causal modelling (DCM) is a framework for the identification of neural networks in the brain that treats the networks as nonlinear input-state-output systems. In setting up a DCM, one can estimate (1) parameters that mediate the driving influence of exogenous or experimental inputs on brain states, (2) parameters that mediate endogenous coupling among neuronal states and (3) parameters that allow the inputs to modulate that coupling. Issues concerning selection among alternative models naturally arise in DCM analyses. Bayesian model selection (BMS) is a statistical procedure for computing how probable one model is in relation to another. This chapter presents the motivation and procedures for DCM of evoked brain responses – as well as the theoretical and operational details on which BMS rests. We describe procedures for parameter-, model- and family-level inference in the context of analysis of data from a group of subjects, and close with examples of how these procedures have been used in psychiatric neuroimaging.