Nonlinear Optimization Approach Research Articles

Modeling the creep of polymer-based nanocomposites by using an alternative nonlinear optimization approach

A method of nonlinear optimization based on the Laplace–Carson transform to determine the parameters of a model of the mechanical behavior of viscous materials is presented. The introduction of time-dependent functional relationships between stresses and strains leads to an analysis of the Volterra integral equation of the second kind. In practice, this equation is successfully used in modeling a wide class of structural materials. One of optimum kernels of the operator in the governing equation for describing the deformation of materials with “memory” is the Rabotnov fractional-exponential function. The search for the optimum values of model parameters is reduced to the problem of minimization of a functional. The results of analytic modeling are compared with experimental data obtained in the creep and quasi-static loading of polymer composites containing various carbon modifications in the form of nanotubes. The essential distinctions in the behavior of the nanocomposites are compared. These distinctions are found to correlate with the results of structural investigations by the atomic-force microscopy, scanning electron microscopy, and micro- and nanoindentation.

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (I) Problems Without Path Constraints

This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.

An Assessment of Nonlinear Optimization and Speeded up Robust Features (SURF) Algorithm for Estimating Object Space Transformation Parameters for UAV Pose Estimation

Localizing set of features (with known coordinates) on the ground and finding their matches in the image taken by imaging sensor on the aerial vehicle is the basic concept behind Vision Based Navigation (VBN). The number of matching points necessary for solving the collinearity equation is a critical factor to be investigated while using the VBN approach for navigation. Although a robust scale and rotation invariant image matching algorithm is important for VBN of aerial vehicles, the proper estimation of the collinearity equation object space transformation parameters improves the efficiency of the navigation process through the real-time estimation of transformation parameters. These parameters can then be used in aiding the inertial measurements data in the navigation estimation filter. The main objective of this paper is to investigate the estimation of the object space transformation parameters necessary for VBN of aerial vehicles with the assumption that the aerial vehicle experiences large values of the rotational angles, which will lead to non-linearity of the estimation model. In this case, traditional least squares approaches will fail or will take longer to estimate the object space transformation parameters, because of the expected non-linearity of the mathematical model. Five different nonlinear optimization methods are presented for estimating the transformation parameters – these include four gradient based nonlinear optimization methods; Trust region, Trust region dogleg algorithm, Levenberg-Marquardt, and Quasi-Newton line search method and one non-gradient method; Nelder-Mead simplex direct search is employed for the six transformation parameters estimation process. Assessments of the proposed nonlinear optimization approaches on the image matching algorithm necessary for the VBN approach are investigated.

A new model to predict multi-stage pyrolysis of flammable materials in standard fire tests

Test procedures to assess material flammability are focused on radiative heating of the examined material followed by ignition of volatiles produced by pyrolysis. In this work, a new model (Pyropolis) for predicting thermal degradation of polymer materials exposed to the external heat flux is presented. Composite materials of interest consist of a matrix polymer and a (glass or carbonized) fiber. If temperature is sufficiently high, the matrix polymer degrades thereby producing solid and/or gaseous components. Solid decomposition products may exhibit a considerable size change, which is a notable feature of intumescent materials also considered in this work. The model incorporates multi-step decomposition mechanism including two reactions in anaerobic conditions and four reactions in oxidative atmosphere. Kinetic data could be derived from TGA, DSC and PCFC/MCC measurements, which are processed by either simplified (peak value based) or comprehensive (non-linear optimization) approach suitable for both n-th order and autocatalytic reactions. The model is validated by comparing predictions of gasification rates for to two distinct types of non-charring (PS) and charring intumescent (PC) polymers. Reasonable agreement has been obtained with the measured mass loss rates, which are proportional to the heat release rates if volatiles are ignited.

Household No-Notice Evacuation Logistics: How Well Do Households Optimize?

In no-notice events, adults must decide whether and how to gather household dependents. This article examines how effectively households plan their evacuation logistics for a daytime event in a multimodal network and how these plans match the outcomes of a nonlinear integer optimization approach that simultaneously determines optimal meeting locations, final destinations, and family member pickup assignment and sequencing. The model outcomes are compared to information from 59 in-depth interviews. Households largely assign emergency-gathering activities to the parent normally responsible for child-related travel and prefer to meet at home; these decisions are optimal only in some cases. The authors also identify the sensitivity of the optimized logistics to the time adults spend at pickup locations gathering their dependents and “break-even” points where a combination of walking and trains become competitive with personal vehicles. For some households, the additional travel time to make these modes competitive is fewer than 2 h, which is not necessarily an unexpected delay during evacuations. Thus, emergency management agencies should continue to include transit agencies in their planning process and ensure that employees are available to provide services for cases where severe congestion is encountered, and not just for socioeconomically vulnerable populations.

A Nonlinear Optimal Control Approach Based on the Control-Lyapunov Function for an AC/DC Converter Used in Electric Vehicles

AC/DC converters used in electric vehicles generally consist of two stages: an input power factor correction (PFC) boost AC/DC stage that converts input AC voltage to an intermediate DC voltage and reduces input current harmonics injected to the grid, and a DC/DC converter that provides high-frequency galvanic isolation. Since there is a low-frequency ripple (second harmonic of the input ac line frequency) in the output voltage of the PFC AC/DC boost converter, the voltage loop in the conventional control system typically has a very low bandwidth to avoid distorting the input current waveform. This causes the conventional PFC controller to have slow dynamics against load variations. This paper presents a new control approach that regulates the input power of the converter instead of the output voltage by using an optimal nonlinear control approach based on the Control-Lyapunov Function (CFL). In this paper, it is shown that the proposed controller is able to eliminate the low bandwidth voltage control loop in the conventional PFC controller, thus allowing the front-end AC/DC boost PFC converter to operate with faster dynamic response than with the conventional controller approach. Experimental results from a 3 kW AC/DC converter are presented in the paper to validate the proposed control method and its superior performance.

Determining elastic–plastic properties from indentation data obtained from finite element simulations and experimental results

Various approaches have been proposed to determine the material properties of power law materials, based on dimensionless analysis and the concept of a representative strain. In this work, non-linear optimisation algorithms are developed and integrated with Finite Element (FE) analysis to determine and improve the accuracy of the elastic–plastic mechanical properties of a power-law material without the concept of dimensionless analysis and a representative strain. The optimisation approach shows that a unique set of four key material properties of a given material (Young's modulus, Poisson's ratio, yield stress and work hardening exponent) can be determined from the loading–unloading indentation curve of only a single indentation curve, without the need for using results from two or more indentations. Different geometries of indenters (Conical, Berkovich and Vickers) are used with various initial values to test the robustness of this approach. Two types of target indentation loading–unloading curves are used; simulated target curves (obtained from FE analysis) and experimental test data with some random errors. The results show that the non-linear optimisation approach produces impressive accuracy when using a simulated FE loading–unloading curve, but is less accurate when a real-life experimental loading–unloading curve is used.

Nonlinear inverse optimization approach for determining the weights of objective function in standing reach tasks

This paper presents a nonlinear inverse optimization approach to determine the weights for the joint displacement function in standing reach tasks. This inverse optimization problem can be formulated as a bi-level highly nonlinear optimization problem. The design variables are the weights of a cost function. The cost function is the weighted summation of the differences between two sets of joint angles (predicted posture and the actual standing reach posture). Constraints include the normalized weights within limits and an inner optimization problem to solve for joint angles (predicted standing reach posture). The weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 52 degree-of-freedom (DOF) human whole body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the actual standing reach posture. A total of 12 subjects (three subjects for each percentile in stature of 5th percentile female, 50th percentile female, 50th percentile male and 95th percentile male) are selected to run the experiment for 30 tasks. Among these subjects one is Turkish, two are Chinese, and the rest subjects are Americans. Three sets of weights for the general standing reach tasks are obtained for the three zones by averaging all weights in each zone for all subjects and all tasks. Based on the obtained sets of weights, the predicted standing reach postures found using the direct optimization-based approach have good correlation with the experimental results. Sensitivity of the formulation has also been investigated in this study. The presented formulation can be used to determine the weights of cost function within any multi-objective optimization (MOO) problems such as any types of posture prediction and motion prediction.

Models for fare planning in public transport

The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a nonlinear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany.

Nonlinear Risk Optimization Approach to Gas Lift Allocation Optimization

Gas lift allocation can be modeled as a nonlinear programming problem in which adjusting optimum gas injection rates and compressor pressure maximize the oil rate or other objective functions. This study describes a nonlinear programming approach to maximize daily cash flow of some gas-lifted wells in an uncertain condition for oil price. First, some solution points of each well are obtained by employing a production simulation software. Then, by use of nonlinear optimization, a model is developed for gas lift performance in each well. Then these functions are used to develop a model under capacity, pressure and other real constraints for the cash flow of production from these wells. Oil price is assumed as a triangle risk function in this model. Results show a significant increase in cash flow in comparison with old case due to appropriate gas injection parameters. Sensitivity analysis on this problem shows that oil price, compression cost and water–oil ratio variations should be considered in the long term optimization.

Hybrid Range Based Indoor Wireless Localization using Unconstrained Nonlinear Optimization for UWB Applications

In this paper, a hybrid TOA/RSSI wireless localization is proposed for accurate positioning in indoor UWB systems. The major problem in indoor localization is the effect of non-line of sight (NLOS) propagation. To mitigate the NLOS effects, an unconstrained nonlinear optimization approach is utilized to process Time-of –arrival (TOA) and Received Signal Strength (RSS) in the location system.TOA range measurements and path loss model are used to discriminate LOS and NLOS conditions. The weighting factors assigned by hypothesis testing, is used for solving the objective function in the proposed approach. This approach is used for describing the credibility of the TOA range measurement. Performance of the proposed technique is done based on MATLAB simulation. The result shows that the proposed technique performs well and achieves improved positioning under severe NLOS conditions.

Inducing unstable grassland equilibrium states due to nonlinear optimal patterns of initial and parameter perturbations: Theoretical models

Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach, in our work.

Similarities between Optimal Precursors that Trigger the Onset of Blocking Events and Optimally Growing Initial Errors in Onset Prediction

AbstractA triangular T21, three-level, quasigeostrophic global spectral model was used to investigate how precursors relate to the predictability of blocking onset when a conditional nonlinear optimal perturbation approach is used. Here the authors focused on links between the optimal precursor to blocking onset and the optimally growing initial error in onset prediction.Numerical results have shown that during the prediction of blocking events, a type-1 optimally growing initial error, which causes an overprediction of blocking onset, bears the greatest resemblance to the optimal precursor, and both are distributed primarily over the blocking and its upstream regions. A type-2 optimally growing initial error is also characterized by a similar pattern, but with the opposite sign. Further analysis reveals that a type-1 optimally growing initial error has a similar growth behavior to that of the optimal precursor, and both develop into a dipole blocking anomaly pattern with a strong positive anomaly in the north and a weak negative anomaly to the south. The evolutionary mechanism of a type-1 optimally growing initial error during blocking onset can be explained in the same manner as that of an optimal precursor triggering blocking onset. This similarity between an optimal precursor and an optimally growing initial error also suggests that targeted observations over sensitive areas may be carried out in advance to eliminate optimally growing errors (as many as possible) in the prediction of blocking onset. Thus, the improved observation network will help to better capture the spatial structure of precursors that trigger blocking onset and will increase the ability to predict blocking events.

The minimal seed of turbulent transition in the boundary layer

AbstractThis paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier–Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, $ \mrm{\Lambda} $ vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales.

Locking depth and slip-rate of the Húsavík Flatey fault, North Iceland, derived from continuous GPS data 2006-2010

SUMMARY Located at the northern shore of Iceland, the Tjornes Fracture Zone (TFZ) is a 120 km offset in the mid-Atlantic Ridge that connects the offshore Kolbeinsey Ridge to the on-land Northern Volcanic Zone. This transform zone is seismically one of the most active areas in Iceland, exposing the population to a significant risk. However, the kinematics of the mostly offshore area with its complex tectonics have not been adequately resolved and the seismic potential of the two main transform structures within the TFZ, the Grimsey Oblique Rift (GOR) and the Husavik Flatey Fault (HFF) in particular, is not well known. In summer 2006, we expanded the number of continuous GPS (CGPS) stations in the area from 4 to 14. The resulting GPS velocities after four years of data collection show that the TFZ accommodates the full plate motion as it is predicted by the MORVEL plate motion model. In addition, ENVISAT interferograms reveal a transient uplift signal at the nearby Theistareykir central volcano with a maximum line-of-sight uplift of 3 cm between summers of 2007 and 2008. We use a combination of an interseismic backslip and a Mogi model in a homogeneous, elastic half-space to describe the kinematics within the TFZ. With a non-linear optimization approach we fit the GPS observations and estimate the key model parameters and their uncertainties, which are (among others) the locking depth, the partition of the transform motion between the two transform structures within the TFZ and the slip rate on the HFF. We find a shallow locking depth of 6.3+1.7− 1.2 km and transform motion that is accommodated 34 ± 3 per cent by the HFF and 66 ± 3 per cent by the GOR, resulting in a slip velocity of 6.6 ± 0.6 mm yr−1 for the HFF. Assuming steady accumulation since the last two large M6.5 earthquakes in 1872 the seismic potential of the fault is equivalent to a Mw6.8 ± 0.1 event.

Bayesian frequency-domain blind deconvolution of ground-penetrating radar data

Enhancing the resolution and accuracy of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.

Trade-off analysis approach for interactive nonlinear multiobjective optimization

When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off analysis approach that can be connected to various multiobjective optimization methods utilizing a certain type of scalarization to produce Pareto optimal solutions. With this approach, the DM can conveniently learn about local trade-offs between the conflicting objectives and judge whether they are acceptable. The approach is based on an idea where the DM is able to make small changes in the components of a selected Pareto optimal objective vector. The resulting vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set located at the Pareto optimal solution selected. The obtained approximate Pareto optimal solutions can be used to study trade-off information. The approach is especially useful when trade-off analysis must be carried out without increasing computation workload. We demonstrate the usage of the approach through an academic example problem.

Load maximization of flexible joint mechanical manipulator using nonlinear optimal controller

In this paper, a closed loop nonlinear optimal control approach is investigated for flexible joint manipulators (FJM). The dynamic load carrying capacity (DLCC) of these manipulators is obtained via this approach. The state-dependent Riccati equation (SDRE) technique is used for solving nonlinear optimal control problem. This method uses special parameterization to develop the nonlinear system to a linear structure having state-dependent coefficient matrices. The Taylor series numerical method is addressed by approximating the solution to the SDRE. Simulations for FJM are provided to illustrate the effectiveness of this approach for designing nonlinear feedback controllers and computing DLCC of these manipulators. Also effects of change in spring factors of manipulator and control parameters on resulted trajectory of manipulator are considered. DLCC is calculated subject to the limits in actuators and tracking accuracy. Finally the results are checked by comparison with experimental results.

Nonlinear optimization of acoustic energy harvesting using piezoelectric devices

In the first part of the paper, a single degree-of-freedom model of a vibrating membrane with piezoelectric inserts is introduced and is initially applied to the case when a plane wave is incident with frequency close to one of the resonance frequencies. The model is a prototype of a device which converts ambient acoustical energy to electrical energy with the use of piezoelectric devices. The paper then proposes an enhancement of the energy harvesting process using a nonlinear processing of the output voltage of piezoelectric actuators, and suggests that this improves the energy conversion and reduces the sensitivity to frequency drifts. A theoretical discussion is given for the electrical power that can be expected making use of various models. This and supporting experimental results suggest that a nonlinear optimization approach allows a gain of up to 10 in harvested energy and a doubling of the bandwidth. A model is introduced in the latter part of the paper for predicting the behavior of the energy-harvesting device with changes in acoustic frequency, this model taking into account the damping effect and the frequency changes introduced by the nonlinear processes in the device.

Solving the Hamilton–Jacobi–Bellman equation using Adomian decomposition method

The aim of this research is to solve the Hamilton–Jacobi–Bellman equation (HJB) arising in nonlinear optimal problem using Adomian decomposition method. First Riccati equation with matrix variable coefficients, arising in linear optimal and robust control approach, is considered. By using the Adomian method, we consider an analytical approximation of the solution of nonlinear differential Riccati equation. An application in optimal control is presented. The solution in different order of approximations and different methods of approximation will be compared with respect to accuracy. Then the HJB equation, obtained in nonlinear optimal approach, is considered and an analytical approximation of the solution of it, using Adomian method, is presented.