Linear Optimization Techniques Research Articles

Estimation of Gravity Parameters Related to Simple Geometrical Structures by Developing an Approach Based on Deconvolution and Linear Optimization Techniques

An easy and practical method for interpreting residual gravity anomalies due to simple geometrically shaped models such as cylinders and spheres has been proposed in this paper. This proposed method is based on both the deconvolution technique and the simplex algorithm for linear optimization to most effectively estimate the model parameters, e.g., the depth from the surface to the center of a buried structure (sphere or horizontal cylinder) or the depth from the surface to the top of a buried object (vertical cylinder), and the amplitude coefficient from the residual gravity anomaly profile. The method was tested on synthetic data sets corrupted by different white Gaussian random noise levels to demonstrate the capability and reliability of the method. The results acquired show that the estimated parameter values derived by this proposed method are close to the assumed true parameter values. The validity of this method is also demonstrated using real field residual gravity anomalies from Cuba and Sweden. Comparable and acceptable agreement is shown between the results derived by this method and those derived from real field data.

Discourse about Linear Programming and Lean Manufacturing: Two Different Approaches with a Similar, Converging Rational

In recent years, the Toyota Production System has also assumed in western manufacturing plants a predominant position. Lean Manufacturing, as it is usually called in the occidental world, aims at a “Single-piece-flow” job handling and has its advantages compared to the classic “Batch and Queue” job handling. On the other hand, mathematical Linear Programming optimization techniques have passed into oblivion, having obtained the feel to be inappropriate for production planning. Although the two approaches have different aims and application, they give particular attention to scarce resources. The concepts of “bottleneck” in Lean Manufacturing and “shadow price” in Linear Programming are complementary. The paper shows the different focus of the two approaches and crystallizes their synergic values.

Efficient optimization‐oriented design methodology of high‐order 3‐D filters using 2‐D and 3‐D electromagnetic simulators

SummaryThis paper proposes a computationally highly efficient interface between two‐dimensional (2‐D) and three‐dimensional (3‐D) electromagnetic (EM) simulators for the optimization‐oriented design of high‐order 3‐D filters. In a first step, the novel optimization‐oriented design methodology aligns the 3‐D EM simulator response with the 2‐D EM simulator response of a low‐order 3‐D filter by using an inverse linear space mapping optimization technique. Then, a second mapping performs a calibration with the optimal 2‐D and 3‐D design parameters obtained from the first mapping. The optimization of high‐order filters is carried out using only the efficient 2‐D EM simulator, and the calibration equations directly give the design parameters of the 3‐D filter. The potential and the effectiveness of the proposed optimization‐oriented design methodology are demonstrated through the design of C‐band 3‐D evanescent rectangular waveguide bandpass filters with increasing orders from three to eight. Copyright © 2014 John Wiley & Sons, Ltd.

Allocating Classes for Soft-Then-Hard Subpixel Mapping Algorithms in Units of Class

There is a type of algorithm for subpixel mapping (SPM), namely, the soft-then-hard SPM (STHSPM) algorithm that first estimates soft attribute values for land cover classes at the subpixel scale level and then allocates classes (i.e., hard attribute values) for subpixels according to the soft attribute values. This paper presents a novel class allocation approach for STHSPM algorithms, which allocates classes in units of class (UOC). First, a visiting order for all classes is predetermined, and the number of subpixels belonging to each class is calculated using coarse fraction data. Then, according to the visiting order, the subpixels belonging to the being visited class are determined by comparing the soft attribute values of this class, and the remaining subpixels are used for the allocation of the next class. The process is terminated when each subpixel is allocated to a class. UOC was tested on three remote sensing images with five STHSPM algorithms: back-propagation neural network, Hopfield neural network, subpixel/pixel spatial attraction model, kriging, and indicator cokriging. UOC was also compared with three existing allocation methods, i.e., linear optimization technique (LOT), sequential assignment in units of subpixel (UOS), and a method that assigns subpixels with highest soft attribute values first (HAVF). Results show that for all STHSPM algorithms, UOC is able to produce higher SPM accuracy than UOS and HAVF; compared with LOT, UOC is able to achieve at least comparable accuracy but needs much less computing time. Hence, UOC provides an effective and real-time class allocation method for STHSPM algorithms.

H ∞ filtering for impulsive networked control systems with random packet dropouts and randomly occurring nonlinearities

SummaryIn this paper, the problem of H ∞ filtering for impulsive networked control systems with random packet dropouts and randomly occurring nonlinearities is investigated. By utilizing an impulsive model, the network‐induced imperfections including packet dropout and delay are described by the Bernoulli distributed sequence. The delay in the model is assumed to be time varying. Moreover, nonlinearity in the model is assumed to satisfy sector‐like nonlinearities. The H ∞ filter is designed by using the linear matrix inequality (LMI) approach and convex optimization technique. The filter gain matrices for the nonlinear networked control systems can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd.

Algorithmic Aspects in Planning Fixed and Flexible Optical Networks With Emphasis on Linear Optimization and Heuristic Techniques

From an algorithmic perspective, planning and operating optical networks falls in the broad category of network optimization problems. We give a short introduction on algorithmic techniques that can be used to solve network optimization problems, emphasizing on linear optimization and heuristics. We present examples of applying these techniques to optimize resource allocation during the planning of optical networks. In particular, we focus on fixed-grid WDM networks, which is the current practice, and on flexible optical networks, considered as the most promising architecture for meeting next generation core and metro network requirements. In doing so, we describe a generic problem definition that can capture both types of networks in a unified manner.

Optimization of Stand-alone PV-FC Hybrid System under Thailand Climate

The linear programing optimization technique is used for system optimal design. The objective function was set to minimize the system cost. Cost of energy (COE) was also considered. The average solar irradiance and average ambient temperature of Thailand are 800 W/m2 and 30°C, respectively. The electrical load profile varies with time of the day that is dependent on the activity patterns and the type of appliances used. The optimization results shows that the optimal size of PV array, fuel cell (FC) and electrolyzer (ELE) capacity were 5.50 kW, 1.80 kW, and 2.44 kW, respectively. Whereas the minimum system cost was 516,800 Baht. The long-term performance analysis of a standalone PV-FC hybrid system under Thailand climate is showed with normalized yearly analysis as follows; the monthly final yield Yf is 3.55 h/d. The corresponding performance ratio PR ranges from 40 to 53%. The capture loss (LC) and system loss (LS) range from 0.46 h/d to 0.80 h/d and 1.73 h/d to 3.01 h/d, respectively.

Dynamic resource allocation in OFDM systems using DE and FRBS

Dynamic allocation of the resources for optimum utilization is one of the most important fields of study in engineering as well as other disciplines nowadays. In this process the available resources are allocated in such a way that these resources are maximally utilized to enhance the overall system throughput while satisfying certain constraints at the same time. In this paper a similar constrained optimization problem is focused for Orthogonal Frequency Division Multiplexing OFDM environment, in which the transmission parameters namely code rate, modulation scheme and power are adapted in such a way that overall system data rate is maximized with a constrained bit error rate and transmit power. This is a highly non-linear problem that cannot be solved by ordinary linear optimization techniques. A Fuzzy Rule Base System FRBS is proposed for adapting the code rate and modulation scheme while Differential Evolution is used for choosing the optimum power vector. The proposed scheme is compared with other schemes.

From Bayes to Tarantola: New insights to understand uncertainty in inverse problems

Anyone working on inverse problems is aware of their ill-posed character. In the case of inverse problems, this concept (ill-posed) proposed by J. Hadamard in 1902, admits revision since it is somehow related to their ill-conditioning and the use of local optimization methods to find their solution. A more general and interesting approach regarding risk analysis and epistemological decision making would consist in analyzing the existence of families of equivalent model parameters that are compatible with the prior information and predict the observed data within the same error bounds. Otherwise said, the ill-posed character of discrete inverse problems (ill-conditioning) originates that their solution is uncertain. Traditionally nonlinear inverse problems in discrete form have been solved via local optimization methods with regularization, but linear analysis techniques failed to account for the uncertainty in the solution that it is adopted. As a result of this fact uncertainty analysis in nonlinear inverse problems has been approached in a probabilistic framework (Bayesian approach), but these methods are hindered by the curse of dimensionality and by the high computational cost needed to solve the corresponding forward problems. Global optimization techniques are very attractive, but most of the times are heuristic and have the same limitations than Monte Carlo methods. New research is needed to provide uncertainty estimates, especially in the case of high dimensional nonlinear inverse problems with very costly forward problems. After the discredit of deterministic methods and some initial years of Bayesian fever, now the pendulum seems to return back, because practitioners are aware that the uncertainty analysis in high dimensional nonlinear inverse problems cannot (and should not be) solved via random sampling methodologies. The main reason is that the uncertainty “space” of nonlinear inverse problems has a mathematical structure that is embedded in the forward physics and also in the observed data. Thus, problems with structure should be approached via linear algebra and optimization techniques. This paper provides new insights to understand uncertainty from a deterministic point of view, which is a necessary step to design more efficient methods to sample the uncertainty region(s) of equivalent solutions.

An Optimal PID Control Algorithm for Training Feedforward Neural Networks

The training problem of feedforward neural networks (FNNs) is formulated into a proportional integral and derivative (PID) control problem of a linear discrete dynamic system in terms of the estimation error. The robust control approach greatly facilitates the analysis and design of robust learning algorithms for multiple-input-multiple-output (MIMO) FNNs using robust control methods. The drawbacks of some existing learning algorithms can therefore be revealed clearly, and an optimal robust PID-learning algorithm is developed. The optimal learning parameters can be found by utilizing linear matrix inequality optimization techniques. Theoretical analysis and examples including function approximation, system identification, exclusive-or (XOR) and encoder problems are provided to illustrate the results.

Output frequency response function based design of additional nonlinear viscous dampers for vibration control of multi-degree-of-freedom systems

This paper is concerned with the development of a new technique for the optimal placement and design of additional nonlinear viscous dampers for vibration control of Multi-Degree-Of-Freedom (MDOF) systems. The MDOF systems described by a multi-storey shear building model and subjected to harmonic loadings are first considered in the present study; then, the basic ideas of the design are extended to the cases of earthquake loadings. The studies are based on the concept of Output Frequency Response Function (OFRF) and associated methods proposed recently by the authors in control engineering and extend, for the first time, the well-established linear viscous damper optimal placement and design techniques for MDOF system vibration control to the nonlinear case. The design examples verify the effectiveness of the new technique, and demonstrate the beneficial effects of the designed additional nonlinear dampers on the MDOF system vibration control and the advantages of nonlinear viscous dampers over linear dampers in such applications.

Effect of Slow-Active Suspension Controller Design on the Performance of Anti-Lock Brake System

This paper presents an advanced integrated control system comprising the benefits of anti-lock brake system (ABS) and slow-active suspension system. A linear optimization technique is followed to improve the ride dynamics in terms of suspension working space, body vertical acceleration and tire dynamic normal load. The ABS controller regulates theapplied barking pressure to maintain the tire skid ratio within the desired range. The presented investigation is applied to a quarter car model embracing an idealized limited bandwidth actuator in series with a suspension spring. This combination is further integrated with hydraulic circuit to modulate the braking pressure. The mathematical derivation isnumerically solved using MATLAB package. Several simulation results are carried out considering typical performance measures such as stopping time, stopping distance and body vertical acceleration. The proposed design of the slow active suspension controller is suitable for both the ride vibration and brake performance which are widely applied in modernvehicles.

An optimized design of nonuniform filter bank using variable-combinational window function

This paper proposes an optimized tree structure technique for the design of near perfect reconstruction (NPR) non-uniform filterbank. Popular variable window functions like Kaiser, Dolph-Chebyshev (DC) and Parzen-cos6 (nπ/N) (PC6) are used in the design of prototype filter. The NPR condition, results the distortion at the output. Therefore a linear iterative optimization technique is used to minimize the distortion. The proposed algorithm provides lowest value of distortion parameter than earlier reported publications with minimum computation overhead.

Guaranteed cost distributed fuzzy observer‐based control for a class of nonlinear spatially distributed processes

The guaranteed cost distributed fuzzy (GCDF) observer‐based control design is proposed for a class of nonlinear spatially distributed processes described by first‐order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer‐based control design is developed in terms of a set of space‐dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed‐loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug‐flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013

Machine Tool Rotary Axis Compensation Trough Volumetric Verification Using Laser Tracker

This paper aims to present different methods of volumetric verification in long range machine toll with lineal and rotary axes using a commercial laser tracker as measurement system. This method allows characterizing machine tool geometric errors depending on the kinematic of the machine and the work space available during the measurement time. The kinematic of the machine toll is affected by their geometric errors, which are different depending on the number and type of movement axes. Obtaining the transformation matrix that defined the kinematic of the machine tool, the measurement system, the rotation nominal matrix of the rotational axis, the relation between laser tracker and machine tool coordinates is obtained. The verification procedure and the characterization technique to use are determined by the available space during the measurement. The best combination of parameters, techniques and methods were obtained through the realization of a large number of synthetic tests based on not linear optimization techniques.

Estimating Dynamic Workplace Capacities by Means of Public Transport Smart Card Data and Household Travel Survey in Singapore

The number and the temporal and spatial distribution of work locations are crucial information for any transport demand model. To generate the initial transport demand of MATSim, an activity-based multiagent simulation framework, it is necessary to determine dynamic workplace capacities with high spatial resolution, either on a parcel or even a building level. Commonly applied methods to derive work locations are based on census of enterprises information, unemployment insurance database, or combined information of a building's gross floor area and individual work space requirements. As an alternative, the authors present a methodology that combines public transport smart card transaction data, travel diary surveys, and building information data sources. Work activities are detected from smart card transactions based on observed activity duration and start time and therefore related to public transport stops. To link the observed work activities to individual buildings, a linear programming optimization technique is applied that minimizes the walking time between public transport stops and potential work locations. The method classifies work activities in representative work schedules obtained by clustering methods. Information on maximum allowed building gross floor area derived from land use regulation is combined with estimates on individual work space requirements to ensure that buildings are only assigned with work activities according to their maximal capacity. To account for private transport based work activities, mode shares as observed in a travel diary are taken into account. To demonstrate the applicability, the proposed approach is implemented in Singapore and the results critically reviewed.

Local adaptive H∞ consistency of delayed complex networks with noise

The local adaptive H∞ consistency is intensively investigated for delayed complex dynamical networks with noise. The network under consideration contains unknown but bounded nonlinear coupling functions and time-varying delays which appear in the coupling term and the node system simultaneously. Based on the Lyapunov stability theory, linear matrix inequality optimization technique and adaptive control, several local adaptive H∞ consistency schemes are established which guarantee robust asymptotically consistency for each node of noise-perturbed network as well as achieving a prescribed robust H∞ performance level. Finally, detailed and satisfactory numerical simulations validate the feasibility and the correctness of the proposed techniques.

An efficient iterative method for nearly perfect reconstruction non-uniform filter bank

In this paper, a computationally efficient iterative algorithm is presented for the design of multi-channel nearly perfect reconstruction nonuniform filter bank using the modified window functions such as Kaiser, Cosh and Exponential windows with exploiting a new perfect reconstruction condition of nonuniform filter banks instead of using complex objective functions. The cutoff frequency is optimized using linear optimization technique such that the magnitude response of a prototype filter at quadrature frequency is approximately equal to 0.707. The simulation results illustrate significant reduction in amplitude distortion, number of iteration and computation time as compared to earlier existing techniques. The proposed algorithm is simple, easy to implement, and linear in nature. When exploited for subband coding of electrocardiogram (ECG) signals, the proposed method yields good fidelity performance measuring parameters.

An optimization approach to nonlinear diagnostic filter synthesis

We consider the synthesis problem for diagnostic filters based on nonlinear models of the systems being diagnosed. To solve the problem, we propose a new approach that unites the methods of algebra of functions and differential geometry when performing a nonlinear trans- formation of the original mathematical model for the diagnosed system with linear optimization techniques. An advantage of the proposed approach is that it overcomes principled obstacles of existing diagnostic filter synthesis methods and gets a solution for systems with parametric uncertainties. DOI: 10.1134/S0005117912080127

Multivariable norm optimal and parameter optimal iterative learning control: a unified formulation

This article investigates the two paradigms of norm optimal iterative learning control (NOILC) and parameter optimal iterative learning control (POILC) for multivariable (MIMO) ℓ-input, m-output linear discrete-time systems. The main result is a proof that, despite their algebraic and conceptual differences, they can be unified using linear quadratic multi-parameter optimisation techniques. In particular, whilst POILC has been naturally regarded as an approximation to NOILC, it is shown that the NOILC control law can be generated from a suitable choice of control law parameterisation and objective function in a multi-parameter MIMO POILC problem. The form of this equivalence is used to propose a new general approach to the construction of POILC problems for MIMO systems that approximates the solution of a given NOILC problem. An infinite number of such approximations exist. This great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that extend previously published work.