Study of Long Baseline Navigation Optimization Solution Based on Redundancy measurement

Nonlinear optimization is becoming challengeable in information sciences and various industrial applications, but nonlinear problems solved by the classical particle swarm-based methods are usually characterized with low efficiency, accuracy, and convergence speed in specific issues. To solve these problems and enhance the nonlinear optimization performance, an improved metaheuristic particle swarm optimization (PSO) model is proposed here. First, the optimization principles and model of the new method are introduced, and algorithms of the improved PSO are presented. Then, influence of the model parameters, input dimensions, and different nonlinear problems on the PSO optimization characterizations are studied by Pareto set solving and optimization performance comparison. The analysis regarding diverse nonlinear problems and optimization methods demonstrates the feasibility of the proposed method. Finally, the performance evaluation is exhibited by the case study of nonlinear parameter optimization, CEC benchmark problems, and rank sum test, which all verify its effectiveness and reliability, as well as the significance and great application promise. Additionally, the future work is discussed.

In this paper, methods for robot inverse calibration are described. The position and orientation in space of the end effector (pose) errors of a six degrees of freedom (DOF) Puma robot are measured, using a precision co-ordinate measuring machine (CMM), at discrete locations distributed in the calibration volume. The corresponding joint corrections are obtained to compensate the pose error using a nonlinear optimisation method. This nonlinear optimisation method is more accurate and robust than the, widely-used, iterative Newton-Raphson method. However, the computation necessary for nonlinear optimisation is prohibitively expensive for online joint compensation. Therefore, an artificial neural network (NN) based approach has been developed to achieve constant-time solutions. A simple feedforward network architecture with a higher-order approximation capability is designed to ensure efficient and accurate network learning, where the training patterns are based on the results of the nonlinear optimisation method. Both simulation and experimental results are presented to show the effectiveness of the approach.

The integrated energy system has obvious economic, energy-saving and environmental protection characteristics, and is one of the important ways to achieve the carbon peak and carbon neutral strategy. The operation mode of the integrated energy system is very flexible, and the system can obtain better operation performance through scheduling optimization. To fully improve the system performance, this paper proposes a two-stage integrated energy system intraday scheduling optimization method considering equipment nonlinearity. First, to minimize the operation cost and consider the linear characteristic constraints of equipment, a linear programming model for the optimal scheduling of the intraday economy is established. Then, based on the linear optimization results and considering the nonlinear characteristics of equipment, a nonlinear optimal scheduling model is established, and the nonlinear optimization method is used to further improve the optimization accuracy of the load setting values of each equipment. Simulation results show that, compared with linear scheduling optimization, the deviation between the scheduling results and the actual operation of the system is reduced after considering nonlinear optimization, thus improving the economy, energy conservation, and environmental protection of the system.

This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variational optimization problem can be casted into a sparse linear system. Fast sparse linear solver can be adopted to generate deformation result interactively, or even in real-time. The nonlinear nature of gradient domain mesh deformation leads to the development of two categories of deformation methods: linearization methods and nonlinear optimization methods. Basically, the linearization methods only need to solve the linear least-squares system once. They are fast, easy to understand and control, while the deformation result might be suboptimal. Nonlinear optimization methods can reach optimal solution of deformation energy function by iterative updating. Since the computation of nonlinear methods is expensive, reduced deformable models should be adopted to achieve interactive performance. The nonlinear optimization methods avoid the user burden to input transformation at deformation handles, and they can be extended to incorporate various nonlinear constraints, like volume constraint, skeleton constraint, and so on. We review representative methods and related approaches of each category comparatively and hope to help the user understand the motivation behind the algorithms. Finally, we discuss the relation between physical simulation and gradient domain mesh deformation to reveal why it can achieve physically plausible deformation result.

An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion

Diffuse Optical Tomography (DOT) involves a nonlinear optimization problem to find the tissue optical properties by measuring near-infrared light noninvasively. Many researchers used linearization methods to obtain the optical image in real time. However, the linearization procedure may neglect small but sometimes important regions such as small tumors at an early stage. Therefore, nonlinear optimization methods such as gradient- or Newton- type methods are exploited, resulting in better resolution image than that of linearization methods. But the disadvantage of nonlinear methods is that they need much computation time. To solve this trade-off dilemma between image resolution and computing time, we suggest second order inverse Born expansion algorithm in this paper. It is known that a small perturbation of photon density is represented by Born expansion with respect to the perturbation of optical coefficients, which is an infinite series of integral operators having Robin function kernel. Whereas, inverse Born expansion is an implicit representation of a small perturbation of optical coefficients by an infinite series of the integral operators with respect to the photon density and its perturbation, which is appropriate series expansion for inverse DOT problem. Solving the inverse Born expansion itself and the first order approximation correspond to nonlinear and linear method, respectively. We formulated a second order approximation of the inverse Born expansion explicitly to make numerical implementation possible and showed the convergence order of the proposed method is higher than the linear method.

: A globally convergent primal-dual predictor corrector interior point algorithm for linear programming has been developed.

Laptop personal computers (LPCs) and their components are vulnerable devices in harsh mechanical environments. One of the most sensitive components of LPCs is hard disk drive (HDD) which needs to be protected against damages attributable to shock and vibration in order to have better magnetic read/write performance. In the present work, a LPC and its HDD are modeled as two degrees of freedom system and the nonlinear optimization method is employed to perform a passive control through minimizing peak of HDD absolute acceleration caused by a base shock excitation. The presented shock excitation is considered as half-sine pulse of acceleration. In addition, eleven inequality constraints are defined based on geometrical limitations and allowable intervals of lumped modal parameters. The target of the optimization is to reach optimum modal parameters of rubber mounts and rubber feet as design variables and subsequently propose new characteristics of rubber mounts and rubber feet to be manufactured for the HDD protection against shock excitation. The genetic algorithm and the modified constrained steepest descent algorithm are employed in order to solve the nonlinear optimization problem for three widely-used commercial cases of HDD. Finally, the results of both optimization methods are compared to make sure about their accuracy.

Recent studies using Principal Components Analysis (PCA) support low-dimensional models of odor space, in which one or two dimensions - with hedonic valence featuring prominently - explain most odor variability. Here we use non-negative matrix factorization (NMF) - a nonlinear optimization method - to discover an alternative, reduced-dimensional representation of the Dravnieks odor database (144 odors x 146 descriptors). NMF is theoretically well-suited for these types of analyses, as odor profiling data is inherently non-negative (e.g. descriptors either apply, or do not). We divided the dataset into training and testing halves, and found that RMSD testing error attained a minimum for subspace choice of 25, motivating this as an upper bound for odor perceptual space dimensionality. More parsimonious representations were found by comparing reconstruction errors (fraction of unexplained variance) of NMF with reconstruction errors of PCA on scrambled data (PCAsd). For subspace sizes > 10, NMF error was indistinguishable from PCAsd error, indicating no gain in retaining more than 10 perceptual dimensions. As is typical of NMF basis sets, the 10 odor dimensions we obtain are sparse (only a small subset of the 146 descriptors apply), and categorical (represent a positive valued quality). Moreover, these 10 dimensions were near-orthogonal, with a mean angle of 73 degrees between all pairs of basis vectors. Investigating the distribution of odors in this 10-dimensional space, we find marked clustering (Figure 1), with each odor being well-defined by its membership in a single dimension, and to the exclusion of others. In ongoing work, we are using graph-kernel methods to define a rudimentary mapping between physicochemical features of odorants and the 10 descriptor dimensions.

An approach is presented for the identification of modal parameters in frequency domain in an experimental modal analysis with multiple frequency response functions, using the non-linear least squares method and the optimization method. Computation time is reduced, and, stability and accuracy of results are improved compared with thone of conventional approach, when input bata are contaminated with errors. Validity and usefulness of presented approach are verified experimentally with an iron plate.

Glycan structures account for up to 35% of the mass of cardiac sodium ( Nav ) channels. To question whether and how reduced sialylation affects Nav activity and cardiac electrical signaling, we conducted a series of in vitro experiments on ventricular apex myocytes under two different glycosylation conditions, reduced protein sialylation (ST3Gal4(-/-)) and full glycosylation (control). Although aberrant electrical signaling is observed in reduced sialylation, realizing a better understanding of mechanistic details of pathological variations in INa and AP is difficult without performing in silico studies. However, computer model of Nav channels and cardiac myocytes involves greater levels of complexity, e.g., high-dimensional parameter space, nonlinear and nonconvex equations. Traditional linear and nonlinear optimization methods have encountered many difficulties for model calibration. This paper presents a new statistical metamodeling approach for efficient computer experiments and optimization of Nav models. First, we utilize a fractional factorial design to identify control variables from the large set of model parameters, thereby reducing the dimensionality of parametric space. Further, we develop the Gaussian process model as a surrogate of expensive and time-consuming computer models and then identify the next best design point that yields the maximal probability of improvement. This process iterates until convergence, and the performance is evaluated and validated with real-world experimental data. Experimental results show the proposed algorithm achieves superior performance in modeling the kinetics of Nav channels under a variety of glycosylation conditions. As a result, in silico models provide a better understanding of glyco-altered mechanistic details in state transitions and distributions of Nav channels. Notably, ST3Gal4(-/-) myocytes are shown to have higher probabilities accumulated in intermediate inactivation during the repolarization and yield a shorter refractory period than WTs. The proposed statistical design of computer experiments is generally extensible to many other disciplines that involve large-scale and computationally expensive models.

Electromagnetic imaging of inhomogeneous objects is a nonlinear inverse scattering problem which can be effectively handled by means of linear inversion methods or nonlinear optimization methods. In addition to being nonlinear, inverse scattering problems are also ill-posed which can be overcome through a regularization scheme by taking into account some kind of a priori information. However, it is not straightforward to incorporate such inhomogeneity prior information into conventional inversion methods. In this work, we propose an innovative method to solve the problem of imaging inhomogeneous objects with piecewise homogeneity. Under Born approximation (BA), this problem is cast into a linear inversion one which is then addressed by means of a hierarchical Bayesian inversion method. To account for the piecewise homogeneity of the image, a Gaussian mixture model (GMM) is developed to enforce the feature. Specifically, a hidden label variable which is associated with each pixel is introduced for the class of materials and the contrast of each pixel is modeled as a mixture of independent Gaussian priors. Then, the proposed hierarchical Bayesian inversion method incorporates the GMM to the variational Bayesian inference framework to approximate the posterior distribution of all the unknowns (the unknown contrast, hidden label variable, and other model parameters). In addition, the damped generalized approximate message passing (GAMP) is utilized to circumvent the matrix inversion, making the overall process very computationally efficient. Extensive numerical examples will be shown to demonstrate the effectiveness of the proposed method.

A Conduction cooled superconducting magnet (SM) for human magnetic resonance imaging, made of Nb3Sn superconducting coils, has been designed. The magnet features a warm bore with a diameter of 850 mm and a central field strength of 7 T. The size and positioning of a bundle of seven epoxy-impregnated coils were determined using both linear and nonlinear optimization methods. These methods ensured that the superconducting coils achieved a magnetic field uniformity of 10 ppm within a 400 mm diameter spherical volume (DSV). The magnet was designed to operate at a current of 250 A in a cryogenic system, and its temperature will be maintained below 8 K through conduction cooling provided by a Gifford-McMahon (G-M) cryocooler at its second-stage cooling capacity. The SM and its cryogenic system were designed according to a comprehensive analysis of the mechanical and thermal features of the magnet system. The design was evaluated and validated by Finite Elements simulations. The results confirmed that the magnet is capable of stable and reliable operation at low temperatures, effectively achieving conduction cooling.

Improvement of pressure-saturation changes estimations from time-lapse PP-AVO data by using non-linear optimization method

Spline and weighted random directions method for nonlinear optimization