Piezoresistive Cantilever Performance—Part I: Analytical Model for Sensitivity

An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors. $hfill$[2009-0104]      

Modeling, Design, Fabrication, and Demonstration of a Digital Micromirror With Interdigitated Cantilevers

We present the modeling, design, fabrication, and measurement results of a novel digital micromirror based on a new actuator called interdigitated cantilevers. In contrast to conventional micromirrors that rotate through the twisting actuation of a hinge, this micromirror has a symmetric bidirectional rotation through a bending actuation of interdigitated cantilevers hidden under a mirror plate. For the static and dynamic characteristics of the proposed micromirror, analytical models were developed first on the basis of the Euler–Bernoulli beam equation, as well as both distributed- and lumped-parameter models. The results of the developed analytical models are in good agreement with those of a finite-element-method (FEM) simulation, having just a 10% deviation. On the basis of these analytical models, we successfully designed, fabricated, and evaluated a micromirror with a mirror size of $16 muhbox{m} times 16 muhbox{m}$. The fabricated micromirror has a mechanical rotation angle of $pm 10^{circ}$, a pull-in voltage of 54 V, a resonant frequency of 350 kHz, and a switching response time of 17 $muhbox{s}$. The measurement results compare favorably with those of analytical models and FEM simulations, with deviations of less than 15% and 10%, respectively. $hfill$[2009-0139]      

An interior-point sequential approximate optimization methodology

The use of optimization in a simulation-based design environment has become a common trend in industry today. Computer simulation tools are commonplace in many engineering disciplines, providing the designers with tools to evaluate a designs performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulations. One of these approaches is known as sequential approximate optimization. In sequential approximate minimization a sequence of optimizations are performed over local response surface approximations of the system. This paper details the development of an interior-point approach for trust-region-managed sequential approximate optimization. The interior-point approach will ensure that approximate feasibility is maintained throughout the optimization process. This facilitates the delivery of a usable design at each iteration when subject to reduced design cycle time constraints. In order to deal with infeasible starting points, homotopy methods are used to relax constraints and push designs toward feasibility. Results of application studies are presented, illustrating the applicability of the proposed algorithm.     

Reliability-based design optimization for elastoplastic mechanical structures

In this paper, two special formulations to carry out a reliability-based design optimization of elastoplastic mechanical structures are introduced. The first approach is based on a well-known two-level method where the first level involves the optimization for the design parameters whereas the evaluation of the probabilistic constraints is carried out in a sub-optimization level. Because the evaluation of the probabilistic constraints in a sub-optimization level causes non-convergence behavior for some problems as indicated in the literature, an alternative formulation based on one-level is developed considering the optimality conditions of the β-computation by which the probabilistic constraint appears in the first level reliability-based design optimization formulation. In both approaches, an explicit parameter optimization problem is proposed for the computation of a design point for elastoplastic structures.Three examples in this paper demonstrate that the one-level reliability-based design optimization formulation is superior in terms of convergence to an optimal design than the two-level reliability-based design optimization formulation.     

Optimizing discrete stochastic systems using simulated annealing and simulation

The objective of this paper is to present an integrated approach of two models: simulation and optimization. This approach is used to determine the design parameters of stochastically constrained systems where the measure of performance is available only via simulation. The optimization model is solved using simulated annealing (SA) for parameter selection followed by the use of Monte Carlo simulation to evaluate the measure of performance. Based on the expected simulation output, the parameter set is either accepted or rejected. A modified rejection/acceptance criterion is presented for the proposed SA algorithm taking into consideration the stochastic system constraints. Moreover, a control variate is employed as a variance reduction technique in order to obtain an efficient estimate of performance measure. The proposed approach is tested using three real cases of the multi-echelon repairable item inventory systems (MERIIS). The results show that the proposed method is efficient in determining an optimal choice of spares and repair channels in these systems.     

Ordinal optimization approach to rare event probability problems

In this paper we introduce a new approach to rare event simulation. Because of the extensive simulation required for precise estimation of performance criterion dependent on rare event occurrences, obstacles such as computing budget/time constraints and pseudo-random number generator limitations can become prohibitive, particularly if comparative study of different system designs is involved. Existing methods for rare events simulation have focused on simulation budget reduction while attempting to generate accurate performance estimates. In this paper we propose a new approach for rare events system analysis in which we relax the simulation goal to the isolation of a set of good enough designs with high probability. Given this relaxation, referred to as ordinal optimization and advanced by Ho et al. (1992), this paper's approach calls instead for the consideration of an appropriate surrogate design problem This surrogate problem is characterized by its approximate ordinal equivalence to the original problem and its performance criterion's dependence not on rare event occurrences, but on more frequent events. Evaluation of such a surrogate problem under the relaxed goals of ordinal optimization has experimentally resulted in orders of magnitude reduction in simulation burden.     

A performance index for topology and shape optimization of plate bending problems with displacement constraints

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending. Received November 27, 1998?Revised version received June 6, 1999     

6-MHz 2-N/m piezoresistive atomic-force microscope cantilevers withINCISIVE tips

Piezoresistive atomic force-microscope (AFM) cantilevers with lengths of 10 μm, displacement sensitivities of (ΔR/R)/A 1.1×10^-5, displacement resolutions of 2×10^-3 A/√Hz, mechanical response times of less than 90 ns, and stiffnesses of 2 N/m have been fabricated from a silicon-on-insulator (SOI) wafer using a novel frontside-only release process. To reduce mass, the cantilevers utilize novel inplane crystallographically defined silicon variable aspect-ratio (INCISIVE) tips with radius of curvature of 40 A. The cantilevers have been used in an experimental AFM data-storage system to read back data with an areal density of 10 Gb/cm ². Four-legged cantilevers with both imaging and thermomechanical surface modification capabilities have been used to write 2-Gb/cm² data at 50 kb/s on a spinning polycarbonate sample and to subsequently read the data. AFM imaging has been successfully demonstrated with the cantilevers. Some cantilever designs have sufficient displacement resolution to detect their own mechanical-thermal noise in air. The INCISIVE tips also have applications to other types of sensors     

A Novel Approach to $H_{bm infty}$ Decentralized Fuzzy-Observer-Based Fuzzy Control Design for Nonlinear Interconnected Systems

In general, due to the interactions among subsystems, it is difficult to design an $H_{infty }$-decentralized output-feedback controller for nonlinear interconnected systems. This study introduces $H_{infty }$-decentralized fuzzy-observer-based fuzzy control design, where the premise variables depend on the state variables estimated by a fuzzy observer, for nonlinear interconnected systems via T--S fuzzy models. The fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only. A novel decoupled method is proposed in this study to transform the non-linear matrix inequality (non-LMI) conditions into some LMI forms. By the proposed decoupled method, the problem of $H_{infty }$-decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP) with five prespecified scalars for each subsystem. In general, it is a difficult task to solve the EVP with five prespecified scalars. Fortunately, this special EVP can be easily solved by using a genetic algorithm and an LMI-based optimization method. Finally, a simulation example is given to illustrate the design procedure and robust performance of the proposed methods.      

A Framework for Optimal Correction of Inconsistent Linear Constraints

The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as model correction is the problem we address in this paper in the context of linear constraints over the reals. The correction of the right hand side alone, which is very close to a fuzzy constraints approach, was one of the first proposals to deal with inconsistency, as it may be mapped into a linear problem. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, that provide corrections with quite rigid patterns, the optimization of the important Frobenius norm was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer.     

丢包网络化控制系统非脆弱量化H∞控制

针对非线性网络化控制（NCS）系统中控制器参数存在摄动的问题,考虑传感器—控制器和控制器—执行器均存在随机丢包和量化误差,提出了一种加性非脆弱量化H_∞控制器的设计方法．利用李亚普诺夫稳定性理论和线性矩阵不等式（LMI）方法,将该问题转化为线性矩阵不等式约束和线性目标函数的凸优化问题进行求解,给出了丢包下的非脆弱量化H_∞控制器存在的充分条件．所设计的控制器在容许的参数摄动、丢包概率和量化密度条件下,不仅能保证闭环NCS的稳定性和性能要求,而且是非脆弱的．数值仿真验证了所提方法的有效性．     

Stochastic structural topology optimization: discretization and penalty function approach

We consider structural topology optimization problems, including unilateral constraints arising from, for example, non-penetration conditions in contact mechanics or non-compression conditions for elastic ropes. To construct more realistic models and to circumvent possible failures or inefficient behaviour of optimal structures, we allow parameters (for example, loads) defining the problem to be stochastic. The resulting non-smooth stochastic optimization problem is an instance of stochastic mathematical programs with equilibrium constraints (MPEC), or stochastic bilevel programs. We propose a solution scheme based first on the approximation of the given topology optimization problem by a sequence of simpler sizing optimization problems, and second on approximating the probability measure in the latter problems. For stress-constrained weight-minimization problems, an alternative to -perturbation based on a new penalty function is proposed.     

Control-structure integrated multiobjective design for flexible spacecraft using MOEA/D

This paper proposes a multiobjective optimization method for the control-structure integrated design of flexible spacecraft to reduce the total mass and optimize the control performance. The equations of motion for flexible spacecraft are derived from the Lagrange’s principle and the assumed modes method. The design variables are the structural dimensions of the flexible structure and controller parameters. The objectives and constraints are derived from structure and control performance indexes. The objectives include total mass, control cost, and vibrational energy, and the constraints include the stability of the closed-loop system, settling time, overshoot, maximum control, and maximum vibrational displacement of the tip. A modified version of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) with our proposed hybrid constraint handling method is proposed for optimization. As a case study, it has been applied to a spacecraft with symmetrically installed flexible appendages to find optimal tradeoffs in control-structure design. The simulation results show that the multiobjective optimization method for the control-structure integrated design of flexible spacecraft is feasible and effective, and could give an improvement of structural and control designs.     

Simulation based optimization of stochastic systems with integer design variables by sequential multipoint linear approximation

Optimization problems are considered for which objective function and constraints are defined as expected values of stochastic functions that can only be evaluated at integer design variable levels via a computationally expensive computer simulation. Design sensitivities are assumed not to be available. An optimization approach is proposed based on a sequence of linear approximate optimization subproblems. Within each search subregion a linear approximate optimization subproblem is built using response surface model building. To this end, N simulation experiments are carried out in the search subregion according to a D-optimal experimental design. The linear approximate optimization problem is solved by integer linear programming using corrected constraint bounds to account for any uncertainty due to the stochasticity. Each approximate optimum is evaluated on the basis of M simulation replications with respect to objective function change and feasibility of the design. The performance of the optimization approach and the influence of parameters N and M is illustrated via two analytical test problems. A third example shows the application to a production flow line simulation model. Received April 28, 2000     

Decentralized $H_{infty }$ Filter Design for Discrete-Time Interconnected Fuzzy Systems

This paper describes a decentralized $H_{infty }$ filter design for discrete-time interconnected fuzzy systems based on piecewise-quadratic Lyapunov functions. The systems consist of $J$discrete-time interconnected Takagi–Sugeno (T–S) fuzzy subsystems, and a decentralized $H_infty$ filter is designed for each subsystem. It is shown that the stability of the overall filtering-error system with $H_{infty }$ performance can be established if a piecewise-quadratic Lyapunov function can be constructed. Moreover, the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Two simulation examples are given to show the effectiveness of the proposed approach.      

Performance Analysis of Banyan-Type Multistage Interconnection Networks Under Nonuniform Traffic Pattern

Multistage Interconnection Networks(MINs) have a number of applications in the areas of computer and communications. The most widely researched structure among MINs is the (1)banyan type network. It has several variations such as buffered banyan, batcher-banyan, tandem banyan, recirculating banyan and banyan with contention resolution phase. Analytical performance evaluation is crucial for justifying the merit of the design in different operational conditions. While several analytical models have been proposed for the performance evaluation of MINs, they are mainly for uniform traffics. Even the models for nonuniform traffics have several shortcomings such as they only consider output buffered structure or do not consider blocking conditions.In this paper, the more accurate models than any other ones so far have been proposed for the performance evaluation of multibuffered banyan-type MINs under nonuniform traffic condition is obtained. The accuracy of proposed models are conformed by comparing with the results from simulation.Firstly, single buffer model is developed. Markov chain is used for the analysis. Multibuffer model is obtained from single buffer model. Simulation is performed using Discrete Evenet Simulaton(DES) method. As a results, proposed model proves to be very accurate.     

A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization

Predicting the transient response of structures by high-fidelity simulation models within design optimization and uncertainty quantification often leads to unacceptable computational cost. This paper presents a reduced-order modeling (ROM) framework for approximating the transient response of linear elastic structures over a range of design and random parameters. The full-order response is projected onto a lower-dimensional basis spanned by modes computed from a proper orthogonal decomposition (POD) of full-order model simulation results at multiple calibration points. The basis is further enriched by gradients of the POD modes with respect to the design/random parameters. A truncation strategy is proposed to compensate for the increase in basis vectors due to the proposed enrichment strategies. The accuracy, efficiency and robustness of the proposed framework are studied with a two-dimensional model problem. The numerical results suggest that the proposed ROM approach is well suited for large parameter changes and that the number of basis vectors needs to be increased only linearly with the number of design and random parameters to maintain a particular ROM performance. The application of the proposed ROM approach to robust shape optimization demonstrates significant savings in computational cost over using full-order models. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

Real-Time Models of Electrostatically Actuated Cantilever Probes With Integrated Thermal Sensor for Nanoscale Interrogation

Microcantilevers with integrated thermal sensor for topography measurement, which can be electrostatically actuated, are well suited for a highly parallel dynamic-mode operation where multiple cantilevers scan the media. Interpretation of data in dynamic-mode operation utilizing such cantilevers is complex because of diverse forces acting on the cantilever that include electrostatic, interatomic, structural, thermal, and, possibly, magnetic forces. In addition, the thermal sensor introduces new dynamics making interpretation of measured data challenging. In this paper, tractable models that are suited for real-time purposes, which can quantitatively predict the cantilever motion and the thermal-sensor measurement, are presented. Furthermore, it is demonstrated that all parameters of the model can be estimated solely from thermal-sensor data. This paper also provides a comprehensive understanding of the dynamics of the thermal sensor.$hfill$ [2009-0041]      

Simultaneous analysis and design optimization of nonlinear response

The optimal structural design requiring nonlinear analysis and design sensitivity analysis can be an enormous computational task. It is extremely important to explore ways to reduce the computational effort so that more realistic and larger-scale structures can be optimized. The optimal design process is iterative requiring response analysis of the structure for each design improvement. A recent study has shown that up to 90 percent of the total computational effort is spent in computing the nonlinear response of the structure during the optimal design process. Thus, efficiency of the optimization process for nonlinear structures can be substantially improved if numerical effort for analyzing the structure can be reduced. This paper explores the idea of using design sensitivity coefficients (computed at each iteration to improve design) to predict displacement response of the structure at a changed design. The iterative procedure for nonlinear analysis of the structure is then started from the predicted response. This optimization procedure is called mixed and the original procedure where sensitivity information is not used is called the conventional approach. The numerical procedures for the two approaches are developed and implemented. They are compared on some truss type structures by including both geometric and material nonlinearities. Stress, strain, displacement, and buckling load constraints are imposed. The study shows the mixed method to be numerically stable and efficient.