Simultaneous control of maintenance and production rates of a manufacturing system with defective products

In the past three decades, studies of simultaneous maintenance and production planning have been focusing on age-dependent machine failure and inventory. This paper presents the interaction between defective products and optimal control of production rate, lead time and inventory. Our aim is to minimize the expected discounted overall cost due to maintenance activities, inventory holding and backlogs. Through Condition-Based Maintenance, we monitor in a real time the manufacturing system’s health by describing N operational states. We consider two maintenance states of a machine controlled by two decision variables: production and maintenance rates. The optimal policy is characterized by the dynamic programming solution to a piecewise deterministic optimal control problem. A numerical illustration and a sensitive analysis are developed with a set of parameters calibrated on an existing manufacturing system.     

Optimal electrode shaping for precise modal electromechanical filtering

This paper addresses the optimal shape design of segmented spatial sensors and actuators that isolate selected mode shapes and perform modal filtering. Electromechanical filters have reappeared with the new manufacturing capabilities of micro-electro-mechanical structures (MEMS). In such small dimensions it proves essential to treat their elastic behaviour as continuous rather than discrete systems that require suitable design methods, some of which are developed here. In MEMS filters, the input signal is converted to external electrostatic forces and in order to perform the desired filtering, the electrodes need to be shaped such that they excite only a desired part of the dynamics. An optimization scheme that shapes these electrodes to achieve optimal filtering is developed. In order to enhance the filter’s performance and minimize energy lost to the supporting structure, a special support tuning method is proposed. Several simulated examples examine the effectiveness of the proposed optimization methods.     

The FEM optimization of active vibration control in structures by solving the corresponding two-point-boundary-value problem

An algorithm for solving optimal active vibration control problems by the finite element method (FEM) is presented. The optimality equations for the problem are derived from Pontryagin’s principle in the form of a set of the fourth order ordinary differential equations that, together with the initial and final boundary conditions, constitute the boundary value problem in the time domain, which in control is referred to as a two-point-boundary-value problem. These equations decouple in the modal space and can be solved by the FEM technique. An analogy between the optimality equations and the governing equations for a set of certain static beams permits obtaining numerical solutions to the optimal control problem with the help of standard ‘structural’ FEM software. The optimal action of actuators is automatically calculated by applying the independent modal space control concept. The structure’s response to actuation forces is also determined and can independently be verified for spillover effects. As an illustration, the algorithm is used for the analysis of optimal action of actuators to attenuate vibrations of an elastic fin.     

On the optimal shape of a compressed column subjected to restrictions on the cross-sectional area

By using Pontryagin’s principle we study the optimal shape of an elastic compressed column with clamped ends and restrictions on cross-sectional area. The restrictions are imposed on either maximum or both minimal and maximum value of the cross-sectional area. We analyzed a column on elastic foundation of Winkler type and a column without foundation. It is shown that the optimization can be both bimodal and unimodal. We determine the transition value between unimodal and bimodal optimization for specified values of parameters.     

Optimal design of 2D conducting graded materials by minimizing quadratic functionals in the field

We explore a typical optimal design problem in 2D conductivity: given fixed amounts of two isotropic dielectric materials, decide how we are to mix them in a 2D domain so as to minimize a certain cost functional depending on the underlying electric field. We rely on a reformulation of the optimal design problem as a vector variational problem and examine its relaxation, taking advantage of the explicit formulae for the relaxed integrands recently computed in Pedregal (2003). We provide numerical evidence, based on our relaxation, that Tartar’s result Tartar (1994) is verified when the target field is zero (also for divergence-free fields) and optimal solutions are given by first-order laminates. This same evidence also holds for a general quadratic functional in the field.     

Why Neighbor-Joining Works

We show that the neighbor-joining algorithm is a robust quartet method for constructing trees from distances. This leads to a new performance guarantee that contains Atteson’s optimal radius bound as a special case and explains many cases where neighbor-joining is successful even when Atteson’s criterion is not satisfied. We also provide a proof for Atteson’s conjecture on the optimal edge radius of the neighbor-joining algorithm. The strong performance guarantees we provide also hold for the quadratic time fast neighbor-joining algorithm, thus providing a theoretical basis for inferring very large phylogenies with neighbor-joining.     

On robust online scheduling algorithms

While standard parallel machine scheduling is concerned with good assignments of jobs to machines, we aim to understand how the quality of an assignment is affected if the jobs’ processing times are perturbed and therefore turn out to be longer (or shorter) than declared. We focus on online scheduling with perturbations occurring at any time, such as in railway systems when trains are late. For a variety of conditions on the severity of perturbations, we present bounds on the worst case ratio of two makespans. For the first makespan, we let the online algorithm assign jobs to machines, based on the non-perturbed processing times. We compute the makespan by replacing each job’s processing time with its perturbed version while still sticking to the computed assignment. The second is an optimal offline solution for the perturbed processing times. The deviation of this ratio from the competitive ratio of the online algorithm tells us about the “price of perturbations”. We analyze this setting for Graham’s algorithm, and among other bounds show a competitive ratio of 2 for perturbations decreasing the processing time of a job arbitrarily, and a competitive ratio of less than 2.5 for perturbations doubling the processing time of a job. We complement these results by providing lower bounds for any online algorithm in this setting. Finally, we propose a risk-aware online algorithm tailored for the possible bounded increase of the processing time of one job, and we show that this algorithm can be worse than Graham’s algorithm in some cases.     

Control improvement and approximately optimal synthesis in the neighborhood of a support trajectory

We consider problems of optimal control improvement and synthesis for continuous and discrete processes with a unified scheme that includes searching for an, at least, locally optimal process and implementing it via an approximately optimal positional control with Krotov’s estimate. For regular problems, this scheme is based on local approximation of the well-known Krotov-Bellman relations; for degenerate problems, on the corresponding generalized relations. We show how this scheme relates to the A.M. Letov’s ACOC theory and give specific examples.     

Modeling and deforming a virtual dense elastic object with the haptic device PHANToM

In recent years, there have been various problems in medical treatments, of which human error by the surgeon in an operation is one of the most serious. In order to minimize human error in an operation, we need a medical training system by which inexperienced surgeons can try operating again and again to improve their skill. In this research, we construct a system of modeling a virtual dense elastic object, and deforming that object using a haptic device called PHANToM. In the system which we construct, we use two PCs to distribute the process of calculation, and SCRAMNet+ is used to connect each PC. PHANToM is used to operate on the object and to express the force which is generated from the deformation of the object. We represent the dense object by using voxels and tetrahedrons, and the elastic object by using a spring-mass model. A virtual dense elastic object is obtained by computed tomography (CT) or magnetic resonance imaging (MRI) to express the patient’s organs.     

Reinforcement learning technique using agent state occurrence frequency with analysis of knowledge sharing on the agent’s learning process in multiagent environments

Reinforcement learning techniques like the Q-Learning one as well as the Multiple-Lookahead-Levels one that we introduced in our prior work require the agent to complete an initial exploratory path followed by as many hypothetical and physical paths as necessary to find the optimal path to the goal. This paper introduces a reinforcement learning technique that uses a distance measure to the goal as a primary gauge for an autonomous agent’s action selection. In this paper, we take advantage of the first random walk to acquire initial information about the goal. Once the agent’s goal is reached, the agent’s first perceived internal model of the environment is updated to reflect and include said goal. This is done by the agent tracing back its steps to its origin starting point. We show in this paper, no exploratory or hypothetical paths are required after the goal is initially reached or detected, and the agent requires a maximum of two physical paths to find the optimal path to the goal. The agent’s state occurrence frequency is introduced as well and used to support the proposed Distance-Only technique. A computation speed performance analysis is carried out, and the Distance-and-Frequency technique is shown to require less computation time than the Q-Learning one. Furthermore, we present and demonstrate how multiple agents using the Distance-and-Frequency technique can share knowledge of the environment and study the effect of that knowledge sharing on the agents’ learning process.     

Movement-based checkpointing and logging for failure recovery of database applications in mobile environments

In this paper, we present an efficient failure recovery scheme for mobile database applications based on movement-based checkpointing and logging. Current approaches take checkpoints periodically without regard to the mobility behavior of mobile users. Our movement-based checkpointing scheme takes a checkpoint only after a threshold of mobility handoffs has been exceeded. The optimal threshold is governed by the failure rate, log arrival rate, and the mobility rate of the mobile host. This allows the tuning of the checkpointing rate on a per-user basis. We identify the optimal movement threshold which will minimize the recovery cost per failure as a function of the mobile node’s mobility rate, failure rate and log arrival rate. We derive the mobile database application recoverability, i.e., the probability that the recovery can be done by a specified recovery time deadline. Numeric data are presented to demonstrate the feasibility of our approach with its applicability given.     

Minimization of sound radiation from vibrating bi-material structures using topology optimization

Up to now, work on topological design optimization of vibrating structures against noise radiation has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, and minimization of the dynamic compliance subject to harmonic loading on the structure. In this paper, we deal with topology optimization problems formulated directly with the design objective of minimizing the sound power radiated from the structural surface(s) into a surrounding acoustic medium. Bi-material elastic continuum structures without material damping are considered. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. It is assumed that air is the acoustic medium and that a feedback coupling to the structure can be neglected. Certain conditions are assumed that imply that the sound power emission from the structural surface can be obtained in a simpler way than by solving Helmholz’ integral equation. Hereby, the computational cost of the structural-acoustical analysis is substantially reduced. Several numerical results are presented and discussed for plate- and pipe-like structures with different sets of boundary and loading conditions.     

Assessing architectural evolution: a case study

This paper proposes to use a historical perspective on generic laws, principles, and guidelines, like Lehman’s software evolution laws and Martin’s design principles, in order to achieve a multi-faceted process and structural assessment of a system’s architectural evolution. We present a simple structural model with associated historical metrics and visualizations that could form part of an architect’s dashboard. We perform such an assessment for the Eclipse SDK, as a case study of a large, complex, and long-lived system for which sustained effective architectural evolution is paramount. The twofold aim of checking generic principles on a well-know system is, on the one hand, to see whether there are certain lessons that could be learned for best practice of architectural evolution, and on the other hand to get more insights about the applicability of such principles. We find that while the Eclipse SDK does follow several of the laws and principles, there are some deviations, and we discuss areas of architectural improvement and limitations of the assessment approach.     

Sulla programmazione lineare stocastica

A linear progranuming problem is said to be stochastic, when some of its data are random variables of known probability distribution. The aim of this paper is to give a simple algorithm, which enable us to determine at least an inferior bound of the probability distribution of the solution of the problem, when the coefficients of the linear function to minimize are random variables, while the other data are constant.

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Lavoro eseguito nell’ambito dell’attività del gruppo di ricerca matematica n. 38 (Ca’ Foscari, Venezia) del C.N.R. per l’anno accademico 1966–67.     

Exact solutions in the reinforcement of a circular plate under concentrated loads

A thin elastic plate, supported along the boundary, is loaded either by a single concentrated force at a given internal point, or by two equal and opposite concentrated forces at given internal diametrically opposite points. In each problem, the compliance, defined as the work done by the load, can be reduced on stiffening the plate by the addition to the boundary of an elastic strip whose cross-section is variable but whose total volume is prescribed. The cross-sectional area that minimises the compliance provides the optimal reinforcement for both problems. The respective compliances are compared with those obtained when the plate’s boundary is reinforced by a strip of uniform cross-section and of the given volume.     

Understanding user commands by evaluating fuzzy linguistic information based on visual attention

This article proposes a method for understanding user commands based on visual attention. Normally, fuzzy linguistic terms such as “very little” are commonly included in voice commands. Therefore, a robot’s capacity to understand such information is vital for effective human-robot interaction. However, the quantitative meaning of such information strongly depends on the spatial arrangement of the surrounding environment. Therefore, a visual attention system (VAS) is introduced to evaluate fuzzy linguistic information based on the environmental conditions. It is assumed that the corresponding distance value for a particular fuzzy linguistic command depends on the spatial arrangement of the surrounding objects. Therefore, a fuzzy-logic-based voice command evaluation system (VCES) is proposed to assess the uncertain information in user commands based on the average distance to the surrounding objects. A situation of object manipulation to rearrange the user’s working space is simulated to illustrate the system. This is demonstrated with a PA-10 robot manipulator.     

Effective on-line algorithms for reliable due date quotation and large-scale scheduling

We consider the sequencing of a series of jobs that arrive at a single processor over time. At each job’s arrival time, a due date must be quoted for the job, and the job must complete processing before its quoted due date. The objective is to minimize the sum (or average) of quoted due dates, or equivalently, the average quoted lead time. In this paper, we propose on-line heuristics for this problem and characterize the conditions under which these heuristics are asymptotically optimal. Computational testing further demonstrates the relative effectiveness of these heuristics under various conditions. Both authors made equal contributions to this paper and are listed in alphabetical order.     

Experimental determination of mechanical properties of Ni and Ni-Fe microbars

 In this study, nickel and nickel-iron alloy microsamples produced using the LIGA technique are investigated. With vibration tests and tensile tests, design parameters such as Young’s modulus, elastic limit, and failure stress are determined. A new microsample tensile test apparatus is presented, in which forces and elongation are separately measured with very high accuracy. The comparison between the Young’s modulus which is determined with vibration experiments and the Young’s modulus derived from tensile tests ensures the reliability of the measurements presented. The error sources are analysed with the help of finite element models and the uncertainty in determining the Young’s modulus is calculated. The strength values measured for LIGA specimens are about 3 times higher than for comparable macroscopic specimens. Received 27 February 1996 / Accepted: 11 March 1996     

Experimental determination of mechanical properties of Ni and Ni-Fe microbars

In this study, nickel and nickel-iron alloy microsamples produced using the LIGA technique are investigated. With vibration tests and tensile tests, design parameters such as Young’s modulus, elastic limit, and failure stress are determined. A new microsample tensile test apparatus is presented, in which forces and elongation are separately measured with very high accuracy. The comparison between the Young’s modulus which is determined with vibration experiments and the Young’s modulus derived from tensile tests ensures the reliability of the measurements presented. The error sources are analysed with the help of finite element models and the uncertainty in determining the Young’s modulus is calculated. The strength values measured for LIGA specimens are about 3 times higher than for comparable macroscopic specimens. This paper was not presented at the International Conference of High Aspect-Ratio Microstructure Technology HARMST ’95 in July 1995.