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.     

Global optimization methods for engineering applications: A review

A review of the methods for global optimization reveals that most methods have been developed for unconstrained problems. They need to be extended to general constrained problems because most of the engineering applications have constraints. Some of the methods can be easily extended while others need further work. It is also possible to transform a constrained problem to an unconstrained one by using penalty or augmented Lagrangian methods and solve the problem that way. Some of the global optimization methods find all the local minimum points while others find only a few of them. In any case, all the methods require a very large number of calculations. Therefore, the computational effort to obtain a global solution is generally substantial. The methods for global optimization can be divided into two broad categories: deterministic and stochastic. Some deterministic methods are based on certain assumptions on the cost function that are not easy to check. These methods are not very useful since they are not applicable to general problems. Other deterministic methods are based on certain heuristics which may not lead to the true global solution. Several stochastic methods have been developed as some variation of the pure random search. Some methods are useful for only discrete optimization problems while others can be used for both discrete and continuous problems. Main characteristics of each method are identified and discussed. The selection of a method for a particular application depends on several attributes, such as types of design variables, whether or not all local minima are desired, and availability of gradients of all the functions.Notation Number of equality constraints - () ^T A transpose of a vector - A A hypercubic cell in clustering methods - Distance between two adjacent mesh points - Probability that a uniform sample of sizeN contains at least one point in a subsetA ofS - A(v, x) Aspiration level function - A The set of points with cost function values less thanf(x _G ^* ) +. Same asA _f () - A _f () A set of points at which the cost function value is within off(x _G ^* ) - A () A set of points x with[f(x)] smaller than - A _N The set ofN random points - A _q The set of sample points with the cost function value f _q - _Q The contraction coefficient; –1 _Q 0 - _R The expansion coefficient; _E > 1 - _R The reflection coefficient; 0 < _R 1 - A _x () A set of points that are within the distance from x _G ^* - D Diagonal form of the Hessian matrix - det() Determinant of a matrix - d _j A monotonic function of the number of failed local minimizations - d _t Infinitesimal change in time - d _x Infinitesimal change in design - A small positive constant - (t) A real function called the noise coefficient - ₀ Initial value for(t) - exp() The exponential function - f ^(c) The record; smallest cost function value over X^(C) - [f(x)] Functional for calculating the volume fraction of a subset - Second-order approximation tof(x) - f(x) The cost function - An estimate of the upper bound of global minimum - f ^E The cost function value at x^E - f ^L The cost function value at x^L - f _opt The current best minimum function value - f ^P The cost function value at x ^P - f ^Q The cost function value at x ^Q - f _q A function value used to reduce the random sample - f ^R The cost function value at x ^R - f ^S The cost function value at x^S - f _{T F min} A common minimum cost function value for several trajectories - f _{TF opt} The best current minimum value found so far forf _{TF min} - f ^W The cost function value at x ^W - G Minimum number of points in a cell (A) to be considered full - The gamma function - A factor used to scale the global optimum cost in the zooming method - Minimum distance assumed to exist between two local minimum points - gi(x) Constraints of the optimization problem - H The size of the tabu list - H(x^*) The Hessian matrix of the cost function at x^* - h _j Half side length of a hypercube - h _m Minimum half side lengths of hypercubes in one row - I The unity matrix - ILIM A limit on the number of trials before the temperature is reduced - J The set of active constraints - K Estimate of total number of local minima - k Iteration counter - The number of times a clustering algorithm is executed - L Lipschitz constant, defined in Section 2 - L The number of local searches performed - _i The corresponding pole strengths - log () The natural logarithm - LS Local search procedure - M Number of local minimum points found inL searches - m Total number of constraints - m(t) Mass of a particle as a function of time - m() TheLebesgue measure of thea set - Average cost value for a number of random sample of points inS - N The number of sample points taken from a uniform random distribution - n Number of design variables - n(t) Nonconservative resistance forces - n _c Number of cells;S is divided inton _c cells - NT Number of trajectories - Pi (3.1415926) - P _i ^(j) Hypersphere approximating thej-th cluster at stagei - p(x ⁽ⁱ⁾⁾ Boltzmann-Gibbs distribution; the probability of finding the system in a particular configuration - pg A parameter corresponding to each reduced sample point, defined in (36) - Q An orthogonal matrix used to diagonalize the Hessian matrix - _i (i = 1, K) The relative size of thei-th region of attraction - r _i ^(j) Radius of thej-th hypersp here at stagei - R _x ^* Region of attraction of a local minimum x^* - r _j Radius of a hypersphere - r A critical distance; determines whether a point is linked to a cluster - R ⁿ A set ofn tuples of real numbers - A hyper rectangle set used to approximateS - S The constraint set - A user supplied parameter used to determiner - s The number of failed local minimizations - T The tabu list - t Time - T(x) The tunneling function - T _c (x) The constrained tunneling function - T _i The temperature of a system at a configurationi - TLIMIT A lower limit for the temperature - TR A factor between 0 and 1 used to reduce the temperature - u(x) A unimodal function - V(x) The set of all feasible moves at the current design - v(x) An oscillating small perturbation. - V(y⁽ⁱ⁾) Voronoi cell of the code point y⁽ⁱ⁾ - v^–1 An inverse move - v _k A move; the change from previous to current designs - w(t) Ann-dimensional standard. Wiener process - x Design variable vector of dimensionn - x^# A movable pole used in the tunneling method - x⁽⁰⁾ A starting point for a local search procedure - X^(c) A sequence of feasible points {x⁽¹⁾, x⁽²⁾,,x^(c)} - x(t) Design vector as a function of time - X^* The set of all local minimum points - x^* A local minimum point forf(x) - x^*(i) Poles used in the tunneling method - x _G ^* A global minimum point forf(x) - Transformed design space - The velocity vector of the particle as a function of time - Acceleration vector of the particle as a function of time - x ^C Centroid of the simplex excluding x ^L - x ^c A pole point used in the tunneling method - x ^E An expansion point of x ^R along the direction x ^C x ^R - x ^L The best point of a simplex - x ^P A new trial point - x ^Q A contraction point - x ^R A reflection point; reflection of x ^W on x ^C - x ^S The second worst point of a simplex - x ^W The worst point of a simplex - The reduced sample point with the smallest function value of a full cell - Y The set of code points - y ⁽ⁱ⁾ A code point; a point that represents all the points of thei-th cell - z A random number uniformly distributed in (0,1) - Z ^(c) The set of points x where [f ^(c) – ] is smaller thanf(x) - []₊ Max (0,) - | | Absolute value - The Euclidean norm - f[x(t)] The gradient of the cost function     

Barrier coverage with wireless sensors

When a sensor network is deployed to detect objects penetrating a protected region, it is not necessary to have every point in the deployment region covered by a sensor. It is enough if the penetrating objects are detected at some point in their trajectory. If a sensor network guarantees that every penetrating object will be detected by at least k distinct sensors before it crosses the barrier of wireless sensors, we say the network provides k-barrier coverage. In this paper, we develop theoretical foundations for k-barrier coverage. We propose efficient algorithms using which one can quickly determine, after deploying the sensors, whether the deployment region is k-barrier covered. Next, we establish the optimal deployment pattern to achieve k-barrier coverage when deploying sensors deterministically. Finally, we consider barrier coverage with high probability when sensors are deployed randomly. The major challenge, when dealing with probabilistic barrier coverage, is to derive critical conditions using which one can compute the minimum number of sensors needed to ensure barrier coverage with high probability. Deriving critical conditions for k-barrier coverage is, however, still an open problem. We derive critical conditions for a weaker notion of barrier coverage, called weak k-barrier coverage.     

Function Follows Form: Correlation between the Growth and Local Emission of Perovskite Structures and the Performance of Solar Cells

Understanding the relationship between the growth and local emission of hybrid perovskite structures and the performance of the devices based on them demands attention. This study investigates the local structural and emission features of CH₃NH₃PbI₃, CH₃NH₃PbBr₃, and CH(NH₂)₂PbBr₃ perovskite films deposited under different yet optimized conditions using X‐ray scattering and cathodoluminescence spectroscopy, respectively. X‐ray scattering shows that a CH₃NH₃PbI₃ film involving spin coating of CH₃NH₃I instead of dipping is composed of perovskite structures exhibiting a preferred orientation with [202] direction perpendicular to the surface plane. The device based on the CH₃NH₃PbI₃ film composed of oriented crystals yields a relatively higher photovoltage. In the case of CH₃NH₃PbBr₃, while the crystallinity decreases when the HBr solution is used in a single‐step method, the photovoltage enhancement from 1.1 to 1.46 V seems largely stemming from the morphological improvements, i.e., a better connection between the crystallites due to a higher nucleation density. Furthermore, a high photovoltage of 1.47 V obtained from CH(NH₂)₂PbBr₃ devices could be attributed to the formation of perovskite films displaying uniform cathodoluminescence emission. The comparative analysis of the local structural, morphological, and emission characteristics of the different perovskite films supports the higher photovoltage yielded by the relatively better performing devices.     

Stochastic analysis and maintenance planning of the ash handling system in the thermal power plant

This paper discusses stochastic analysis of the ash handling system in a thermal power plant. The system consists of four subsystems A_i, B_j, C and D_k in series, with three possible states: good, reduced and failed. Failure and repair rates for each subsystem are taken to be constants. Using a probabilistic approach, the differential equations are generated and the expression for steady state availability is computed. Taking data from the thermal power plant, situated in North India, the behaviour of each working unit is analysed. Problems and remedies with appropriate maintenance schedules have been discussed. The results are discussed with the plant personnel and are helpful to the management in predicting the behaviour of each operating unit, so that timely decisions can be taken for maintaining the system in upstate for a long duration.     

A student project for layered network protocol development

A student project to accompany a course on computer interfacing and local area networks is described. The audience at which the course is aimed consists of beginning graduate students and seniors. The course addresses fundamental concepts in computer networks in general, and local networks in particular. Students are given the specification of a simple sliding window protocol that provides sequence control and error recovery over an unreliable data link. The task is to implement this protocol on the Apple Macintosh computer as a Layer-3 protocol using the services of the link access protocol (Layer 2) already existent on the machine as part of the Appletalk network. Typical implementations and the cost of benefits of utilizing inexpensive microcomputers for projects in the field of computer networks are discussed     

Wavelength Conversion Placement in WDM Mesh Optical Networks*

Wavelength conversion helps improve the performance of wavelength division multiplexed (WDM) optical networks that employ wavelength routing. In this paper, we address the problem of optimally placing a limited number of wavelength converters in mesh topologies. Two objective functions, namely, minimizing the average blocking probability and minimizing the maximum blocking probability over all routes, are considered. In the first part of the paper, we extend an earlier analytical model to compute the blocking probability on an arbitrary route in a mesh topology, given the traffic and locations of converters. We then propose heuristic algorithms to place wavelength converters, and evaluate the performance of the proposed heuristics using the analytical model. Results suggest that simple heuristics are sufficient to give near-optimal performance.     

MOSFET substrate current model for circuit simulation

A simple, accurate MOSFET substrate current model suitable for a circuit simulator is presented. The effect of substrate bias on substrate current is modeled without introducing additional parameters. The accuracy of this model is demonstrated by its ability to fit the experimental data for both standard and LDD devices with average errors of less than 6%. The new model is compared with the substrate current models reported in the literature. In addition, the temperature dependence of the substrate current in the range of 0-120°C is also modeled. The new model has been implemented in a circuit-level hot-electron reliability simulator, and the results obtained from simulation of an inverter circuit are presented     

Numerical and experimental analysis of large passivation opening for solder joint reliability improvement of micro SMD packages

In this paper, using a recently developed solder fatigue model for wafer level-chip scale package (WL-CSP), we investigated the improvement on solder joint reliability for a 8-bump micro SMD package by enlarging the passivation layer opening at the solder–die interface. The motivation to enlarge the passivation opening is to reduce the severity of the stress concentration caused by the original design, and also to increase the contact area between the solder bump and aluminum bump pad. It was confirmed in the thermal shock test that with the new design, package fatigue life improved by more than 70%. To numerically predict this improvement represents a unique challenge to the modeling. This is because in order to capture the slightest geometrical difference on the order of a few microns between the two designs, the multiple-layer solder-die interface needs to be modeled using extremely fine mesh, while the overall dimensions of the package and the test board are on the order of millimeters. To bridge this tremendous gap in geometry, a single finite element model that incorporates all necessary geometrical details is deemed computationally prohibitive and impractical. In this paper, we applied a global–local modeling scheme that was also suggested by others [1, 2 and 3]. The global model contains the complete package with much simplified solder–die interface whereas the local model includes only one solder joint, but with detailed solder–die interface. Unlike most global–local models proposed by others, we included time-independent plasticity and temperature-dependent materials in the global model. This greatly improved model correlation accuracy with only moderate increase in run time. Energy-based solder fatigue model was used to correlate the inelastic strain energy with the package fatigue life. In an earlier study [4], we have found that Darveaux’s equations tended to be conservative when applied to the micro SMD, and hence new correlations based on curve-fitting the test data were derived. In this paper, we used the newly derived equation and achieved less than 20% error in N₅₀ life for both designs, which is on par with Darveaux’s equations when used for BGAs. The analysis also revealed two factors that may account for the life improvement. First, a slight decrease in inelastic energy dissipation after enlarging the passivation opening. Second, the shift of the crack initiation location which leads to longer crack growth length for the new design. The second factor was also independently confirmed by the failure analysis.