Nonlinear Constrained Optimization Method Research Articles

Optimized selection of fluid lubricant for cylindrical roller bearings under elastohydrodynamic lubrication

Roller bearings are widely used in machinery. Keeping the contact surfaces of bearings properly lubricated strongly mitigates wear effects, improving bearing fatigue life. Therefore, systematically selecting the lubricant fluid that satisfies bearing operation conditions allows the lubricating layer to be able to carry the applied load, the operating temperature, and the roughness on contact. The nonlinear constrained optimization method is used for lubricant selection, seeking to find the fluid that best fits the bearing operation conditions. Roller bearing lubrication is characteristically elastohydrodynamic (EHL); namely, the Hertz theory describes the load applied on the contacts of a cylindrical roller bearing, and the Stribeck condition classifies the tribological condition of the surfaces in contact. This work concludes that roughness and speed are the most important parameters to consider when choosing a fluid lubricant.

An Optimization Problem for Quadcopter Reference Flight Trajectory Generation

This paper deals with the reference flight trajectory generation and planning problems for quadcopter Unmanned Aerial Vehicle (UAV). The reference flight trajectory is defined as the composition of path and motion functions. Both of them are generated by using quintic B-spline functions. Based on differential flatness approach, the quadcopter dynamical constraints are satisfied instantaneously by computing the induced aerodynamical moments and lift force. The optimal reference flight trajectory, with respect to the mission requirements and imposed constraints, is reached by manipulating the control points’ vectors of B-spline functions via a nonlinear constrained optimization method. The mission requirements are defined as a set of waypoints with their respective scheduled flight timetable. A minimum-energy cost function is developed to minimize the consumed energy and induced efforts by reference flight trajectory. For the need of the optimal overfly-times schedule, the overfly times with respect to the defined constraints and performance criteria are calculated. Numerical simulation results show the feasibility and effectiveness of the proposed optimization method.

Bayesian optimal estimation for output-only nonlinear system and damage identification of civil structures

This paper presents a new framework for output-only nonlinear system and damage identification of civil structures. This framework is based on nonlinear finite element (FE) model updating in the time-domain, using only the sparsely measured structural response to unmeasured or partially measured earthquake excitation. The proposed framework provides a computationally feasible approach for structural health monitoring and damage identification of civil structures when accurate measurement of the input seismic excitations is challenging (e.g., buildings with significant foundation rocking and bridges with piers in deep water) or the measured seismic excitations are erroneous and/or distorted by significant measurement error (e.g., malfunctioning sensors). Grounded on Bayesian inference, the proposed framework estimates the unknown FE model parameters and the ground acceleration time histories simultaneously, using the sparse measured dynamic response of the structure. Two approaches are presented in this study to solve the joint structural system parameter and input identification problem: (a) a sequential maximum likelihood estimation approach, which reduces to a sequential nonlinear constrained optimization method, and (b) a sequential maximum a posteriori estimation approach, which reduces to a sequential iterative extended Kalman filtering method. Both approaches require the computation of FE response sensitivities with respect to the unknown FE model parameters and the values of base acceleration at each time step. The FE response sensitivities are computed efficiently using the direct differentiation method. The two proposed approaches are validated using the seismic response of a 5-story reinforced concrete building structure, numerically simulated using a state-of-the-art mechanics-based nonlinear structural FE modeling technique. The simulated absolute acceleration response time histories of 3 floors and the relative (to the base) roof displacement response time histories of the building to a bidirectional horizontal seismic excitation are polluted with artificial measurement noise. The noisy responses of the structure are then used to estimate the unknown FE model parameters characterizing the nonlinear material constitutive laws of the concrete and reinforcing steel and the (assumed) unknown time history of the ground acceleration in the longitudinal direction of the building. The same nonlinear FE model of the structure is used to simulate the structural response and to estimate the dynamic input and system parameters. Thus, modeling uncertainty is not considered in this paper. Although the validation study demonstrates the estimation accuracy of both approaches, the sequential maximum a posteriori estimation approach is shown to be significantly more efficient computationally than the sequential maximum likelihood estimation approach.

인체모션 데이터 획득 장치와 최적화 기법을 사용한 로봇운동 데이터 생성과 애니메이션

This paper describes a whole-body (human body's) motion generation scheme for an android robot that uses motion capture device and a nonlinear constrained optimization method. Because the captured motion data are based on global coordinates and the actors have different heights and different upper-lower body ratios, the captured motion data cannot be used directly for a humanoid robot. In this paper, we suggest a method for obtaining robot joint angles, which allow the resultant robot motion to be as close as possible to the captured human motion data, by applying a nonlinear constrained optimization method. In addition, the results are animated to demonstrate the similarity of the motions.

A Novel Approach to Improve the Performance of Evolutionary Methods for Nonlinear Constrained Optimization

Evolutionary methods are well-known techniques for solving nonlinear constrained optimization problems. Due to the exploration power of evolution-based optimizers, population usually converges to a region around global optimum after several generations. Although this convergence can be efficiently used to reduce search space, in most of the existing optimization methods, search is still continued over original space and considerable time is wasted for searching ineffective regions. This paper proposes a simple and general approach based on search space reduction to improve the exploitation power of the existing evolutionary methods without adding any significant computational complexity. After a number of generations when enough exploration is performed, search space is reduced to a small subspace around the best individual, and then search is continued over this reduced space. If the space reduction parameters (red_gen and red_factor) are adjusted properly, reduced space will include global optimum. The proposed scheme can help the existing evolutionary methods to find better near-optimal solutions in a shorter time. To demonstrate the power of the new approach, it is applied to a set of benchmark constrained optimization problems and the results are compared with a previous work in the literature.

Primary fluid optimization in once-through steam generator

Abstract Once-Through Steam Generator (OTSG) is widely used in nuclear reactor system due to its advantages of compactness. This paper presents a double-tube Once-Through Steam Generator (OTSG) consisting of an outer straight tube and an inner helical tube. In the double-tube, the primary fluid is divided into two parts: one is in the inner tube and the other is in the shell side. This bi-channel flow brings difficulties in optimizing the flow distribution ratio of the primary water (FDRP), and affects the heat transfer and flow characteristics. In this paper, a nonlinear constrained optimization method was proposed to optimize the FDRP for keeping balance between maximizing the heat transfer rate and minimizing the pressure drop. A throttling device at the inlet of the lower pressure drop side is introduced to achieve the optimum FDRP. The theoretical analysis and analytical results show that our proposed method can be used in engineering practice for optimizing the primary flow.

Dynamic Modeling of Apoptosis and its Interaction with Cell Growth in Mammalian Cell Culture

AbstractCaspases are the key mediators of the apoptotic cascade leading to cell death in mammalian cells. Caspase activation in a Chinese Hamster Ovary (CHO) cell line producing Anti-RhD monoclonal antibody (mAb) in batch culture was simulated and measured experimentally. The model assumes that apoptosis proceeds through one of two independent pathways: the intrinsic pathway and the extrinsic pathway. Induction of the extrinsic pathway is assumed to involve cell-cell signaling by apoptotic (caspase-3 active) cells, while the intrinsic pathway is assumed to be triggered by toxic stress (ammonia). The model parameters were estimated by training the model by a nonlinear constrained optimization method embedded in MATLAB. The model provides a good fit to the experimental observations. In addition, this apoptosis model was integrated with a dynamic model of CHO culture metabolism previously obtained through metabolic flux analysis. The combined model provides good predictions of the measured metabolite profiles thus it can serve for future optimization of the culture.

A Nonlinear Constrained Optimization Method of MTD

This paper presents a nonlinear constrained optimization of the moving target detection (MTD) filter design method, which can be better designed to detect moving targets need to control the filter characteristics of the main-lobe and side-lobes, but also has less parameter constraints. Simulation results show that the MTD filters designed with a better clutter suppression performance and real-time engineering applications.

Sequential Penalty Derivative-Free Methods for Nonlinear Constrained Optimization

We consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints. We assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor explicitly approximated. Hence, every minimization procedure must use only a suitable sampling of the problem functions. These problems arise in many industrial and scientific applications, and this motivates the increasing interest in studying derivative-free methods for their solution. The aim of the paper is to extend to a derivative-free context a sequential penalty approach for nonlinear programming. This approach consists in solving the original problem by a sequence of approximate minimizations of a merit function where penalization of constraint violation is progressively increased. In particular, under some standard assumptions, we introduce a general theoretical result regarding the connections between the sampling technique and the updating of the penalization which are able to guarantee convergence to stationary points of the constrained problem. On the basis of the general theoretical result, we propose a new method and prove its convergence to stationary points of the constrained problem. The computational behavior of the method has been evaluated both on a set of test problems and on a real application. The obtained results and the comparison with other well-known derivative-free software show the viability of the proposed sequential penalty approach.

Modeling the progression of apoptosis in Chinese Hamster Ovary cells

Caspases play important roles in driving the progression of apoptosis. We developed a first principle-based population-balance model to predict the time-evolution of caspase activities in a cell culture process under different cell density conditions. As a model system, we employed a Chinese Hamster Ovary (CHO) cell line producing anti-RhD monoclonal antibody in batch culture. Caspase activity was detected by flow cytometric measurements of the initiators caspase-8, caspase-9 and the executioner caspase-3. Two models were compared. In the first model, apoptosis was assumed to be triggered by one of two independent pathways: extrinsic or intrinsic. In the second model, simultaneous activation of the two pathways was allowed. The model parameters were calibrated by fitting to training data via a nonlinear constrained optimization method. It was found that the second model outperforms the first model, providing better fit between model predictions and experimental measurements. In addition, we analyzed the origin of apoptosis-related cell-to-cell communication and found that cells with caspase-3 activity are most likely responsible for the initiation of the extrinsic pathway of apoptosis.

New Initial Parameter for the Constrained Optimization Method

In this paper, we have investigated a new initial parameter in the nonlinear constrained optimization method. The aim of this new method is to make a balance between interior and exterior method for constrained optimization. The new technique has been programmed to solve some of standard problems in the non-linear optimization. The results are too effective when compared with other standard optimization methods like interior and exterior methods.

Optimization of the optical sparse array configuration

One feature of systems with sparse optical aperture is the possible existence of zero-value regions of the optical transfer function. In using fast-convergent gradient methods for nonlinear constrained optimization with criteria based on the optical transfer function or the modulation transfer function, the gradient of the minimized function can also contain zero-value regions. Such situations can result in a suspension of the calculation if an intermediate solution falls into such a region. We show that, using gradient methods, it is possible to avoid this calculation problem if we redefine the subaperture step pupil functions—in particular, approximate them by continuously differentiable functions having no zero-value regions. This is demonstrated on examples of apertures consisting of circular and annular subapertures. This approach can be used for both types of multiaperture optical telescopes, the Michelson and Fizeau, and for both space and earth science missions.

Building thermal model reduction using nonlinear constrained optimization

The short-time-horizon modelling of building thermal response is of relevance in situations where HVAC plant and control system analyses are of interest. In this precise area of building thermal modelling issues of model accuracy and computational efficiency become important. In this work a nonlinear constrained optimization method is used for reducing the model order of building elements. The approach involves minimizing the error between the step response of a high-order reference model whilst tuning the parameters of a lower order model in order to obtain an optimized reduced-order model. Results show that a reduced model based on a 2nd-order building element gives minimal loss of accuracy but significant improvements in computational effort when treating both high and low thermal capacity modelling problems.

Improving the performance of weighted Lagrange-multiplier methods for nonlinear constrained optimization

Nonlinear constrained optimization problems in discrete and continuous spaces are an important class of problems studied extensively in artificial intelligence and operations research. These problems can be solved by a Lagrange-multiplier method in continuous space and by an extended discrete Lagrange-multiplier method in discrete space. When constraints are satisfied, these methods rely on gradient descents in the objective space to find high-quality solutions. On the other hand, when constraints are violated, these methods rely on gradient ascents in the Lagrange-multiplier space in order to increase the penalties on unsatisfied constraints and to force the constraints into satisfaction. The balance between gradient descents and gradient ascents depends on the relative weights between the objective function and the constraints, which indirectly control the convergence speed and solution quality of the Lagrangian method. To improve convergence speed without degrading solution quality, we propose an algorithm to dynamically control the relative weights between the objective and the constraints. Starting from an initial weight, the algorithm automatically adjusts the weights based on the behavior of the search progress. With this strategy, we are able to eliminate divergence, reduce oscillation, and speed up convergence. We show improved convergence behavior of our proposed algorithm on both nonlinear continuous and discrete problems.

Simulated annealing and neural networks as alternative methods for nonlinear constrained optimization

By highlighting a particular example of track fitting with geometrical and kinematical constraints of events from a particle physics experiment simulated annealing and backprop neural networks are investigated as alternative optimization methods. The two methods are different in the way that simulated annealing suffers from the enormous amount of function evaluations required while a trained neural network requires negligible computing time. This makes the former unpractical to use in analysis of large amounts of data, but we find that using any of these methods to compute start values has significant impact on the convergence of the constrained fits. Further, it enables us to reduce and estimate the effects introduced by the optimization algorithm. For our case of kinematic and geometric fitting of p p → K 0K ± π ± Monte Carlo events we find that the rate of non-convergence, in the case that the standard analytical minimization did not work using the measured values as the start values, changes up to 40% when making a second attempt with start values from a global optimizer.

Non-negative exponential splines

Two strategies to determine the tension parameters of the exponential spline are discussed. First, a nonlinear constrained optimization method is considered, which guarantees the positivity of the interpolant. The second method gives an a priori estimate of the tension parameters. Both strategies are tested on several examples where the cubic spline becomes negative.