Optimal Design Theory Research Articles

Penalized Bayesian D-Optimal Designs for Regression Models of Continuous Response

We propose extending the use of desirability functions in Bayesian optimal designs for regression models. This technique generates experimental designs with good statistical inference properties according to Bayesian optimal design theory and practical features, as defined by an investigator. These practical features are defined by a penalty function, using an overall desirability function, which is added to a Bayesian $D$-optimal design criterion to penalize impractical experimental designs. This methodology is illustrated by two examples of regression models: quadratic and exponential. Then, we compare designs obtained for different prior distributions of unknown parameters by efficiency calculations and simulation study. Results show that the $D$-efficiencies of the penalized designs relative to the non-penalized Bayesian D-optimal designs are competitive.

Efficient Study Design and Analysis of Longitudinal Dose-Response Data Using Fractional Polynomials.

Correctly characterising the dose-response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous-time dose-response model can substantially increase the efficiency of estimation of the dose-response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose-response in a population with a between/within-patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose-response models using two fractional polynomial terms are robust to mis-specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose-response at interim or final analyses.

Trilateral Evolutionary Game Strategy for the Design Optimization of Engineering General Contracting Projects in the Chinese Context

The engineering general contracting mode is an advanced engineering transaction mode, and design optimization is one of the important driving forces for vigorously promoting the general contracting mode. The application proportion of the general contracting mode in infrastructure projects is not high, the number of successful projects is not large, and the implementation effect is not ideal. One of the main reasons is that the design optimization theory and practice of international standard general contracting projects cannot adapt to the general contracting projects in the Chinese context, making local general contracting projects face huge challenges such as low enthusiasm for design optimization from all parties and unsatisfactory design optimization effects. Therefore, under the premise of bounded rationality, when the owner adopts control methods of different intensities, an evolutionary game study on the selection of design optimization strategies between the design and construction parties is carried out, and stability control strategies are proposed through case experiments and simulations. The research results indicate the following: firstly, the design optimization of general contracting projects in the Chinese context is feasible, but it depends on the distribution ratio of benefits obtained from the design optimization. Compared with general civil construction general contracting projects, the design optimization allocation ratio of industrial construction general contracting projects is more significant; secondly, the mixed control method of strong control and weak control is the optimal choice for the owner of the general contracting project; and thirdly, there are multiple evolutionary stable points, and mechanism design or incentive measures should be used to guide owners to choose weak control strategies, while design and construction parties should choose their design optimization strategies. The research results provide a reference for owners to determine the proportion and scheme of design optimization allocation, and for construction parties to determine design optimization strategies.

Loss-Optimized Design of Magnetic Devices.

Maximizing efficiency, power density, and reliability stands as paramount objectives in the advancement of power electronic systems. Notably, the dimensions and losses of magnetic components emerge as primary constraints hindering the miniaturization of such systems. Researchers have increasingly focused on the design of loss minimization and size optimization of magnetic devices. In this paper, with the objective of minimizing the loss of magnetic devices, an optimal design method for the winding structure of devices is proposed based on the coupling relationship between the loss prediction model and the design variables. The method examines the decoupling conditions between the design variables and the loss model, deriving optimized design closure equations for the design variables. This approach furnishes a technical foundation for the miniaturized design of miniature apparatuses incorporating magnetic components, offering a straightforward and adaptable design methodology. The finite element method simulation results and experimental measurement data verify the accuracy of the prediction of the proposed method and the validity of the optimal design theory of device loss.

R-optimal designs for Becker’s models for mixture experiments

This paper investigates the R-optimal designs for Becker’s models H 2 and H 3. We derive the R-optimal allocations for Becker’s models H 2 and H 3 using optimal design theory. Moreover, we verify that the saturated R-optimal allocations cannot satisfy the R-optimality equivalence theorem, and the non-saturated R-optimal designs are discussed by increasing the number of support points. In addition, we prove the equivalence of the R-optimal designs for the two models H 2 and H 3 for the {q, q} weighted simplex-centroid design. Numerical results have verified the necessary and sufficient conditions of R-optimality of the non-saturated weighted simplex-centroid design.

Optimizing large-scale hydrogen storage: A novel hybrid genetic algorithm approach for efficient pipeline network design

As hydrogen production technologies continue to advance, efficient and high-capacity hydrogen storage solutions become increasingly crucial. To address the complex optimization challenges in the design of large-scale hydrogen storage pipeline networks, the study introduces a mixed integer nonlinear optimization model inspired by hydrogen pipeline design optimization theory. The model not only focuses on optimizing network design parameters but also aims to minimize investment costs. To achieve this, the study proposes an innovative hybrid genetic algorithm that combines the Modified Feasible Directions Method (MFDM) and Genetic Algorithm Theory (GAT), specifically targeting the optimization of pipeline diameter's discrete distribution challenges. Comparative analyses with SUMT and GA algorithms demonstrate the superiority of the approach. In continuous space, the algorithm achieves a lower convergence cost of 232.4437 × 104 Yuan, while in discrete space, the cost further decreases to 212.1636 × 104 Yuan. Additionally, the study delves into the sensitivity of the HGA-MFDM algorithm to ambient temperature and wellhead temperature in hydrogen storage facilities. The analysis reveals that wellhead temperature has a more significant impact on pipeline network investment, whereas ambient temperature exhibits a more pronounced effect on iteration curves. The findings provide valuable insights for the precise adjustment and optimization of hydrogen storage pipeline networks in practical applications.

Optimal Calibration of Items for Multidimensional Achievement Tests

AbstractMultidimensional achievement tests are recently gaining more importance in educational and psychological measurements. For example, multidimensional diagnostic tests can help students to determine which particular domain of knowledge they need to improve for better performance. To estimate the characteristics of candidate items (calibration) for future multidimensional achievement tests, we use optimal design theory. We generalize a previously developed exchange algorithm for optimal design computation to the multidimensional setting. We also develop an asymptotic theorem saying which item should be calibrated by examinees with extreme abilities. For several examples, we compute the optimal design numerically with the exchange algorithm. We see clear structures in these results and explain them using the asymptotic theorem. Moreover, we investigate the performance of the optimal design in a simulation study.

Active Data Selection and Information Seeking

Bayesian inference typically focuses upon two issues. The first is estimating the parameters of some model from data, and the second is quantifying the evidence for alternative hypotheses—formulated as alternative models. This paper focuses upon a third issue. Our interest is in the selection of data—either through sampling subsets of data from a large dataset or through optimising experimental design—based upon the models we have of how those data are generated. Optimising data-selection ensures we can achieve good inference with fewer data, saving on computational and experimental costs. This paper aims to unpack the principles of active sampling of data by drawing from neurobiological research on animal exploration and from the theory of optimal experimental design. We offer an overview of the salient points from these fields and illustrate their application in simple toy examples, ranging from function approximation with basis sets to inference about processes that evolve over time. Finally, we consider how this approach to data selection could be applied to the design of (Bayes-adaptive) clinical trials.

Experimental optimization design synthesis for up-conversion luminescence performance in SrBi4Ti4O15: Er3+/Yb3+ red-green phosphors

Er3+/Yb3+ co-doped SrBi4Ti4O15 crystalline powders were synthesized using the high-temperature solid-phase method. The crystal structure of the obtained phosphors was analyzed through x-ray diffraction (XRD), confirming the purity of all products such as SrBi4Ti4O15. Employing experimental design optimization theory, regression equations were established to correlate the Er3+/Yb3+ doping concentrations with the luminescent intensities. The genetic algorithm was utilized to compute the optimal solutions of the equations, resulting in Er3+ and Yb3+ doping concentrations of 3 mol% (molar fraction) and 20 mol% under 980 nm laser excitation and 3 mol% and 29.79 mol% under 1550 nm laser excitation. The up-conversion fluorescence emission spectra of the samples were measured under 980 nm excitation, revealing intense green emissions at 525 nm, 550 nm, and 662 nm, corresponding to the 2H11/2→4I15/2, 4S3/2→4I15/2, and 4F9/2→4I15/2 energy levels, respectively. Under 1550 nm excitation, peaks corresponding to the same energy levels were observed at 523 nm, 548 nm, and 661 nm. The relationship between the up-conversion fluorescence and the laser operating current for the optimal samples under 980 nm and 1550 nm excitations was explored, indicating two-photon and three-photon processes, respectively. Detailed analysis and discussion of the up-conversion fluorescence mechanisms were conducted. Additionally, the relationship between the up-conversion fluorescence and the temperature for the optimal samples was investigated, revealing excellent temperature sensing characteristics under 980 and 1550 nm laser excitations. The CIE coordinates for the optimal samples were calculated as (0.3111, 0.6747) and (0.5254, 0.4671) under 980 nm and 1550 nm excitations, respectively.

Subregional Differentiated Safety Factors Design Based on Nonprobabilistic Structural Reliability

The structural safety factor is an essential parameter in aircraft design, representing the ratio of the design load to the operating load. Traditional design methods rely on subjective determination of safety factor values based on experience, lacking objectivity in quantifying uncertainty. However, with advancements in aircraft design technology and increasing competition in the commercial space market, new-generation hypersonic aircraft with complex load environments require a more optimal approach. Applying a uniform safety factor to each component within subregions of the aircraft leads to overly conservative results and impacts flight performance. To address this limitation, a design scheme that incorporates subregional, differentiated safety factors is necessary. This approach allows for better material utilization and ensures compliance with safety requirements. This paper utilizes reliability-based design optimization theory to consider uncertainty in structural systems. It establishes a mapping relationship between structural reliability and differentiated safety factors, providing safety under uncertainty while guaranteeing weight reduction. Additionally, this paper develops a subregional, differentiated safety factors distribution program to determine the safety factors of different subregions of the structure. Consequently, a refined subregional differentiated safety factors scheme that balances safety and economy is derived.

An interactive tool for designing efficient toxicology experiments.

The design of dose-response experiments is an important part of toxicology research. Efficient design of these experiments requires choosing optimal doses and assigning the correct number of subjects to those doses under a given criterion. Optimal design theory provides the tools to find the most efficient experimental designs in terms of cost and statistical efficiency. However, the mathematical details can be distracting and make these designs inaccessible to many toxicologists. To facilitate use of these designs, we present an easy to use web-app for finding two types of optimal designs for models commonly used in toxicology. We include tools for checking the optimality of a given design and for assessing efficiency of any user-supplied design. Using state-of-the-art nature-inspired metaheuristic algorithms, the web-app allows the user to quickly find optimal designs for estimating model parameters or the benchmark dose.

Optimal design for a perforated panel absorber combined with Helmholtz-resonance and plate vibration

This study proposes a perforated panel sound absorber combined with Helmholtz-resonance and plate vibration and its optimal design method to broaden the sound absorption characteristics. The proposed perforated absorber has a simple structure consisting of a flexible panel with a hole and an air cavity. The conventional optimal design theory of the dynamic vibration absorber is applied to the perforated absorber. The proposed absorber is designed so that the acoustic impedance density will be equalized and almost minimized at two points independently of the damping of the panel. Optimal parameters are related to the Helmholtz-resonance frequency, the natural frequency of the panel, and the loss factor of the panel. The absorber with the optimal parameters was fabricated, and the sound absorption coefficient was measured using an acoustic impedance tube. The experimental results shows that the proposed method can effectively design the perforated panel absorber with the broadband sound absorption characteristics.

Research on Fracturing Technology for Low Production and Low Efficiency Casing Damaged Wells

With the further development of Daqing Oilfield, the proportion of casing damaged wells is increasing day by day, because the casing damage location is mostly located in the upper part of the reservoir, the conventional technology can not carry out targeted fracturing construction,the low-yield and low-efficiency wells which limits the efficient development of the oil field. In order to satisfy the needs of subdivision and large-scale fracturing construction of low-yield and low-efficiency wells with casing damage, this paper studied the fracturing design principles, determined the optimal design theory of different types of wells, and can make effective fracturing schemes for different reservoirs and well conditions. At the same time, a kind of small diameter segmented fracturing tools have been developed, which can meet the fracturing operation of wells with diameter above 104mm, so that the number of fracturing segments and the scale of reconstruction are greatly higher than those of conventional technology. 30 wells have been tested in the field, and the effect of increasing oil and injection is obvious. The results show that this process can effectively improve the production status of casing damage, low production and low efficiency wells and increase the productivity of single wells.

Active SLAM: A Review on Last Decade.

This article presents a comprehensive review of the Active Simultaneous Localization and Mapping (A-SLAM) research conducted over the past decade. It explores the formulation, applications, and methodologies employed in A-SLAM, particularly in trajectory generation and control-action selection, drawing on concepts from Information Theory (IT) and the Theory of Optimal Experimental Design (TOED). This review includes both qualitative and quantitative analyses of various approaches, deployment scenarios, configurations, path-planning methods, and utility functions within A-SLAM research. Furthermore, this article introduces a novel analysis of Active Collaborative SLAM (AC-SLAM), focusing on collaborative aspects within SLAM systems. It includes a thorough examination of collaborative parameters and approaches, supported by both qualitative and statistical assessments. This study also identifies limitations in the existing literature and suggests potential avenues for future research. This survey serves as a valuable resource for researchers seeking insights into A-SLAM methods and techniques, offering a current overview of A-SLAM formulation.

An Optimized Design Method and Experimental Study of Belt-Type Ultra-High-Pressure Dies

In this study, various structures are designed to improve the bearing capacity of belt-type ultra-high-pressure dies. Via theoretical analysis, numerical simulation, and destructive experiments, the stress distribution, bearing capacity, and failure principle of various dies are analyzed. The results demonstrate that the positive and negative values of the third invariant of the deviatoric stress tensor J3′ determine the deformation mode of the cylinder; when J3′ > 0, the cylinder is in the tensile deformation state, and when J3′ < 0, the cylinder is in the compressive deformation state. The third invariant of the deviatoric stress tensor of the belt-type cylinder is J3′ > 0, which causes tensile failure and rupture due to excessive circumferential stress. The use of a split cylinder can significantly reduce the circumferential stress, thus effectively reducing the maximum shear stress and von Mises stress and improving the pressure capacity of the cavity. However, when J3′ > 0 for the split cylinder, the pressure capacity is affected and the cylinder experiences tensile failure. A tangential split cylinder has a compressive deformation of J3′ < 0, which can fully utilize the properties of hard alloy materials and significantly improve the pressure-bearing capacity of the cylinder. This article provides an effective optimization design theory for belt-type dies, and the effectiveness of this method is proven through experiments.

Optimal structures for focusing and energy accumulation: mathematical models and intuition

Metamaterials and composite structures are able to manipulate waves and focus fields and currents in desirable directions. Designs based on spatial and temporal variation of material properties create structures forcing fluxes into specified parts of the domain or concentrating energy into arrays of progressively sharpening pulses. The paper discusses examples of focusing structures, mathematical and intuitive considerations that influence optimal design theory. The optimality requirement introduces zones of optimal composites with variable microgeometry. The observed absence of classical solutions motivates the extension of the class of optimal partitions to composites. Such materials also provide a solution to the problem of optimal design of a thermal lens focusing thermal fluxes when the incoming fluxes are not completely known in advance. An extension of designs to dynamical materials such as space–time checkerboard composites introduces metamaterials with additional capabilities that control the accumulation of energy in the propagating waves. The discussed mathematical methods of focusing and suitable properties alternation targeted on optimality are illustrated by physical examples.

Toward more numerically stable computations of optimal experimental designs

The optimal experimental design theory is based on working with the so-called information matrix which measures the amount of information provided by a design. As a consequence, the crucial expressions that are evaluated in algorithms for finding optimal designs generally involve the information matrix. However, we show that these expressions can be based on a matrix of a simpler form, which we denote as half-information matrix. In particular, we show that by using suitable matrix decompositions, many algorithms can be formulated just in the terms of with no need to compute the information matrix. Crucially, working with the half-information matrix is more stable: its condition number is the square root of that of the information matrix. As a consequence, stabilized versions of algorithms (i.e. those based on working with ) can be applied to much more ill-conditioned models. We show on examples for both exact and approximate designs that the stabilized algorithms work on models that are unfeasible for the standard versions. We also show that the use of suitable rank-one updates of the utilized matrix decompositions can lead to a significant speed-up of the exchange-type algorithms.

Uncertain optimization for composite base plate of mortar under impact load

Information warfare places higher requirements on the remoteness, precision and mobility of artillery weapon systems. As an indispensable and important category of artillery, mortar plays an important role. As an important component of mortar, the base plate bears tremendous impact load. Its design level has an important influence on the shooting stability, shooting accuracy and maneuverability of the mortar. Composite base plate helps improve the maneuverability of the mortar, but it will also make the force and movement rule of mortar launching more complex and lead to a more acute contradiction between artillery power and maneuverability, which propose a huge challenge to modern artillery optimization design theory. Under this background, this manuscript conducts research on the structural uncertain optimization of composite material base plate for the mortar. In order to obtain the optimal solution and reasonable interval of uncertain parameters with main dimension parameters, this manuscript uses interval model to carry out deterministic transformation for uncertain objective function and uncertain constraints, combines multi-objective genetic algorithm to solve the problem, and carries out numerical simulation to verify the optimal value. The result shows that the design idea and method are feasible for uncertain optimization of composite base sheet of mortar under impact load, and the optimization objectives and strategies are effective, which can provide reference for the uncertain optimization research of composite base plate.

Practical implementation of optimal experimental design using the fractional-order Fricke–Morse bioimpedance model

This paper provides, for the first time, the application of the Optimal Experimental Design (OED) theory. Two algorithms for computing exact and approximate optimal designs have been adapted for the fractional-order Fricke–Morse circuit model (which is widely used to describe experimental bioimpedance data). Frequencies at which the impedance is measured are optimized, while reducing the measurement acquisition time and maximizing the information about the fractional-order electrical behaviour of the biological tissue. As a practical implementation of this methodology, for a sample of apple tissue, D-optimal approximate and exact designs are computed to obtain the best estimates of the parameters values according to a criteria. These designs were compared with the classical design commonly used by practitioners showing the efficiencies of the optimal designs. The application of OED theory to this type of problems opens up many possibilities for future research.

Robust optimal designs using a model misspecification term

Much of classical optimal design theory relies on specifying a model with only a small number of parameters. In many applications, such models will give reasonable approximations. However, they will often be found not to be entirely correct when enough data are at hand. A property of classical optimal design methodology is that the amount of data does not influence the design when a fixed model is used. However, it is reasonable that a low dimensional model is satisfactory only if limited data is available. With more data available, more aspects of the underlying relationship can be assessed. We consider a simple model that is not thought to be fully correct. The model misspecification, that is, the difference between the true mean and the simple model, is explicitly modeled with a stochastic process. This gives a unified approach to handle situations with both limited and rich data. Our objective is to estimate the combined model, which is the sum of the simple model and the assumed misspecification process. In our situation, the low-dimensional model can be viewed as a fixed effect and the misspecification term as a random effect in a mixed-effects model. Our aim is to predict within this model. We describe how we minimize the prediction error using an optimal design. We compute optimal designs for the full model in different cases. The results confirm that the optimal design depends strongly on the sample size. In low-information situations, traditional optimal designs for models with a small number of parameters are sufficient, while the inclusion of the misspecification term lead to very different designs in data-rich cases.