Various different item response theory (IRT) models can be used in educational and psychological measurement to analyze test data. One of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets. Therefore, it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates. The results from the statistical theory on optimal design can be applied for efficient estimation of the parameters.

A major problem in finding an optimal design for IRT models is that the designs are only optimal for a given set of parameters, that is, they are locally optimal. Locally optimal designs can be constructed with a sequential design procedure. In this paper minimax designs are proposed for IRT models to overcome the problem of local optimality. Minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs.

When large achievement tests are conducted regularly, items need to be calibrated before being used as operational items in a test. Methods have been developed to optimally assign pretest items to examinees based on their abilities. Most of these methods, however, are intended for situations where examinees arrive sequentially to be assigned to calibration items. In several calibration tests, examinees take the test simultaneously or in parallel. In this article, we develop an optimal calibration design tailored for such parallel test setups. Our objective is both to investigate the efficiency gain of the method as well as to demonstrate that this method can be implemented in real calibration scenarios. For the latter, we have employed this method to calibrate items for the Swedish national tests in Mathematics. In this case study, like in many real test situations, items are of mixed format and the optimal design method needs to handle that. The method we propose works for mixed-format tests and accounts for varying expected response times. Our investigations show that the proposed method considerably enhances calibration efficiency.

In this paper, optimal designs will be derived for estimating the ability parameters of the Rasch model when difficulty parameters are known. It is well established that a design is locally D-optimal if the ability and difficulty coincide. But locally optimal designs require that the ability parameters to be estimated are known. To attenuate this very restrictive assumption, prior knowledge on the ability parameter may be incorporated within a Bayesian approach. Several symmetric weight distributions, e.g., uniform, normal and logistic distributions, will be considered. Furthermore, maximin efficient designs are developed where the minimal efficiency is maximized over a specified range of ability parameters.

Electromagnetic source analysis yields estimates of the sources of the Electro- and/or MagnetoEncephaloGram (EEG/MEG) and thus generates a functional description of the human brain. The standard errors of the source estimates are influenced by the number and position of EEG/MEG sensors, by the number of time samples, and by the number of trials in which EEG/MEG is measured. Therefore, optimal design theory is applied to determine the required number and position of sensors, the required number of samples, and the required number of trials. To that end, the Fedorov exchange algorithm is extended to incorporate multi-response models. A simulation study and an empirical study on visual evoked potentials indicate that the proposed method is fast and reliable, and improves source precision considerably.

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the abilities. Both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of A-optimality and D-optimality lead to the most accurate estimates when all abilities are intentional, with the former slightly outperforming the latter. The criterion of E-optimality showed occasional erratic behavior for this case of adaptive testing, and its use is not recommended. If some of the abilities are nuisances, application of the criterion of As-optimality (or Ds-optimality), which focuses on the subset of intentional abilities is recommended. For the measurement of a linear combination of abilities, the criterion of c-optimality yielded the best results. The preferences of each of these criteria for items with specific patterns of parameter values was also assessed. It was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters.

An optimal adaptive design for test-item calibration based on Bayesian optimality criteria is presented. The design adapts the choice of field-test items to the examinees taking an operational adaptive test using both the information in the posterior distributions of their ability parameters and the current posterior distributions of the field-test parameters. Different criteria of optimality based on the two types of posterior distributions are possible. The design can be implemented using an MCMC scheme with alternating stages of sampling from the posterior distributions of the test takers’ ability parameters and the parameters of the field-test items while reusing samples from earlier posterior distributions of the other parameters. Results from a simulation study demonstrated the feasibility of the proposed MCMC implementation for operational item calibration. A comparison of performances for different optimality criteria showed faster calibration of substantial numbers of items for the criterion of D-optimality relative to A-optimality, a special case of c-optimality, and random assignment of items to the test takers.

Blocked designs in functional magnetic resonance imaging (fMRI) are useful to localize functional brain areas. A blocked design consists of different blocks of trials of the same stimulus type and is characterized by three factors: the length of blocks, i.e., number of trials per blocks, the ordering of task and rest blocks, and the time between trials within one block. Optimal design theory was applied to find the optimal combination of these three design factors. Furthermore, different error structures were used within a general linear model for the analysis of fMRI data, and the maximin criterion was applied to find designs which are robust against misspecification of model parameters.

The second smallest eigenvalue of the Laplacian matrix, known as algebraic connectivity, determines many network properties. This paper investigates the optimal design of interconnections that maximizes algebraic connectivity in multilayer networks. We identify an upper bound for maximum algebraic connectivity for total weight below a threshold, independent of interconnections pattern, and only attainable with a particular regularity condition. For efficient numerical approaches in regions of no analytical solution, we cast the problem into a convex framework and an equivalent graph embedding problem associated with the optimum diffusion phases in the multilayer. Allowing more general settings for interconnections entails regions of multiple transitions, giving more diverse diffusion phases than the more studied one-toone interconnection case. When there is no restriction on the interconnection pattern, we derive several analytical results characterizing the optimal weights using individual Fiedler vectors. We use the ratio of algebraic connectivity and layer sizes to explain the results. Finally, we study the placement of a limited number of interlinks heuristically, guided by each layer’s Fiedler vector components.

This study presents a novel 4-DOF two-limb gripper mechanism with a simple design that offers high adaptability for different objects. The mechanism integrates a three-finger end effector and employs a 2-DOF driving system in both serial kinematic chains mounted on the base, addressing performance problems caused by moving actuators. First, the architecture of the gripper mechanism is described, and its mobility is verified. Next, the inverse and forward kinematic problems are solved, and the Jacobian matrix is derived to analyze the singularity conditions. The inverse and forward singularity surfaces are plotted. The workspace is investigated using a search method, and two indices, manipulability and dexterity, are studied. The proposed manipulator’s parameters are optimized for improved dexterity. The novel gripper mechanism has high potential for grasping different types of parts within a large workspace, making it a valuable addition to the field of robotics.

The performance of hypersonic vehicles in the take-off stage considerably influences their capability of accomplishing the flight tasks. This study is aimed at enhancing the take-off performance of a cruise aircraft using the improved chimp optimisation algorithm. The proposed algorithm, which uses the Sobol sequence for initial population generation and a function of the weight factors, can effectively overcome the problems of premature convergence and low accuracy of the original algorithm. In particular, the Sobol sequence aims to obtain a better fitness value in the first iteration, and the weight factor aims to accelerate the convergence speed and avoid the local optimal solution. The take-off mass model of the hypersonic vehicle is constructed considering the flight data obtained using the pseudo-spectral method in the climb phase. Simulations are performed to evaluate the algorithm performance, and the results show that the algorithm can rapidly and stably optimise the benchmark function. Compared to the original algorithm, the proposed algorithm requires 28.89% less optimisation time and yields an optimised take-off mass that is 1.72kg smaller.

We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the relaxation with respect to a pair $(\chi,u)$, where $\chi$ is the characteristic function of a set of finite perimeter and $u$ is a function of bounded deformation, of an energy with a bulk term depending on the symmetrized gradient as well as a perimeter term.

A mobile manipulator is treated as a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator mounted on the platform. The kinematics of the mobile manipulator can be represented as a driftless control system with outputs. By adopting the endogenous configuration space approach we propose two kinematic dexterity measures, called local and global dexterity. The local dexterity, modeled upon the manipulability of stationary manipulators, indicates how infinitesimal motions in the configuration space propagate to the taskspace of the mobile manipulator. The global dexterity corresponds to L2-norm of the local dexterity over a prescribed region of the configuration space. Advantages of the endogenous dexterity measures over traditional performance measures of mobile manipulators known from the literature are described. Both the dexterities are employed for determining optimal configurations and optimal geometries of an exemplary mobile manipulator.

This work presents a systematic design selection methodology that utilizes a co-design strategy for system-level optimization of compliantly actuated robots that are known for their advantages over robotic systems driven by rigid actuators. The introduced methodology facilitates a decision-making strategy that is instrumental in making selections among system-optimal robot designs actuated by various degrees of variable or fixed compliance. While the simultaneous co-design method that is utilized throughout guarantees systems performing at their full potential, a homotopy technique is used to maintain integrity via generation of a continuum of robot designs actuated with varying degrees of variable and fixed compliance. Fairness of the selection methodology is ensured via utilization of common underlying (variable) compliant actuation principle and dynamical task requirements throughout the generated system designs. The direct consequence of the developed methodology is that it allows robot designers make informed selections among a variety of systems which are guaranteed to perform at their best. Applicability of the introduced methodology has been validated using a case study for system-optimal design of an active knee prosthesis that is driven by a mechanically adjustable compliance and controllable equilibrium position actuator (MACCEPA) under a periodic/real-life dynamical task.

PMs with two rotations and one translation (2R1T) have been used as skeletons in various advanced manufacturing equipment where high accuracy and stiffness are basic requirements. Considering the advantages of redundant actuation and overconstrained structure, such as reduced singularities and improved stiffness, a new 2R1T overconstrained PM with actuation redundancy, called Hex4, is proposed in this paper. This is a 2-PUR/2-RPU PM (where P denotes an actuated prismatic joint, U a universal joint, and R a revolute joint) that is actuated by four prismatic joints. Compared with some existing 2R1T overconstrained PMs with actuation redundancy, the main advantage of the proposed PM is that the heavy motors of two limbs are mounted on the base to reduce the movable mass and improve dynamic response. First, mobility analysis, inverse kinematics, and velocity analysis are presented. Then, the local transmission index and good transmission workspace are used to evaluate the motion/force transmissibility of the Hex4 PM. The variation tendencies of the two indices with different link parameters are investigated. The singularity is then discussed by considering the motion/force transmissibility. Finally, link parameters are optimized to obtain an improved good transmission workspace. It is shown that the proposed PM has a good potential for high precision applications.

This paper considers simple step-stress accelerated life tests (SSALTs) for one-shot devices. The one-shot device is an item that cannot be used again after the test, for instance, munitions, rockets, and automobile air-bags. Either left-or right-censored data are collected instead of actual lifetimes of the devices under test. An expectation-maximization algorithm is developed here to find the maximum likelihood estimates of the model parameters based on one-shot device testing data collected from simple SSALTs. Furthermore, the asymptotic variance of the mean lifetime under normal operating conditions is determined under the expectation-maximization framework. On the other hand, the optimal design that minimizes the asymptotic variance of the estimate of the mean lifetime under normal operating conditions in terms of three decision variables, including stress levels, inspection times, and sample allocation is discussed. A procedure then is presented to determine the decision variables when a range of stress levels and the termination time of the test as well as normal operating conditions of the devices are given. The properties of the optimal design and the effects of errors in pre-specified planning values of the model parameters are also investigated. Comprehensive simulation studies show that the procedure is quite reliable for the design of simple SSALTs.

This paper addresses the dimensional-synthesis-based kineto-elastostatic performance optimization of the delta parallel mechanism. For the manipulator studied here, the main consideration for the optimization criteria is to find the maximum regular workspace where the robot delta must posses high stiffness and dexterity. The dexterity is a kinetostatic quality measure that is related to joint's stiffness and control accuracy. In this study, we use the Castigliano's energetic theorem for modeling the elastostatic behavior of the delta parallel robot, which can be evaluated by the mechanism's response to external applied wrench under static equilibrium. In the proposed formulation of the design problem, global structure's stiffness and global dexterity are considered together for the simultaneous optimization. Therefore, we formulate the design problem as a multi-objective optimization one and, we use evolutionary genetic algorithms to find all possible trade-offs among multiple cost functions that conflict with each other. The proposed design procedure is developed through the implementation of the delta robot and, numerical results show the effectiveness of the proposed design method to enhancing kineto-elastostatic performance of the studied manipulator's structure.

This paper investigates the reduction of backscatter radar cross section (RCS) for a rectangular cavity embedded in the ground plane. The bottom of the cavity is coated by a thin, multilayered radar absorbing material (RAM) with possibly different permittivities. The objective is to minimize the backscatter RCS by the incidence of a plane wave over a single or a set of incident angles. By formulating the scattering problem as a Helmholtz equation with artificial boundary condition, the gradient with respect to the material permittivities is determined efficiently by the adjoint state method, which is integrated into a nonlinear optimization scheme. Numerical example shows the RCS may be significantly reduced.