Nonlinear Space Research Articles

Optimal Path Planning for Unmanned Aircraft Target Observation Through Constrained Urban Environments

The work herein determines the optimal flight path for a small unmanned aircraft system through a constrained urban environment. The implementation of unavoidable keep-out regions is evaluated by first solving the optimal flight path through a constrained simplex corridor and, second, minimizing incursions to keep-out regions given the same constraint field and ending on a defined orbit around a target of interest. Direct orthogonal collocation methods are combined with fast geometric path planning techniques where a triangulated mesh is used to produce a hybrid control routine, resulting in optimal flight paths through a defined triangulated corridor. Physical constraints are eliminated from the nonlinear program search space, while keep-out regions are modeled within the objective function of the optimal control problem and avoided according to a weighted distribution of the objective components. A scenario is presented for a small unmanned aircraft system to advance at constant altitude and constant speed through city building constraints while minimizing time in unavoidable keep-out regions. The path terminates outside the triangulated corridor on an orbit, encircling the target location. Results illustrate an optimal path solution through 37 polygonal constraints and 2 nonlinear, unavoidable keep-out regions with computational times on the order of 90 s.

Data Analytics Approach for Rational Design of Nanomedicines with Programmable Drug Release.

Drug delivery vehicles can improve the functional efficacy of existing antimicrobial therapies by improving biodistribution and targeting. A critical property of such nanomedicine formulations is their ability to control the release kinetics of their payloads. The combination of (and interactions among) polymer, drug, and nanoparticle properties gives rise to nonlinear behavioral relationships and large data space. These factors complicate both first-principles modeling and screening of nanomedicine formulations. Predictive analytics may offer a more efficient approach toward the rational design of nanomedicines by identifying key descriptors and correlating them to nanoparticle release behavior. In this work, antibiotic release kinetics data were generated from polyanhydride nanoparticle formulations with varying copolymer compositions, encapsulated drug type, and drug loading. Four antibiotics, doxycycline, rifampicin, chloramphenicol, and pyrazinamide, were used. Linear manifold learning methods were used to relate drug release properties with polymer, drug, and nanoparticle properties, and key descriptors were identified that are highly correlated with release properties. However, these linear methods could not predict release behavior. Nonlinear multivariate modeling based on graph theory was then used to deconvolute the governing relationships between these properties, and predictive models were generated to rapidly screen lead nanomedicine formulations with desirable release properties with minimal nanoparticle characterization. Release kinetics predictions of two drugs containing atoms not included in the model showed good agreement with experimental results, validating the model and indicating its potential to virtually explore new polymer and drug pairs not included in the training data set. The models were shown to be robust after the inclusion of these new formulations, in that the new inclusions did not significantly change model regression. This approach provides the first step toward the development of a framework that can be used to rationally design nanomedicine formulations by selecting the appropriate carrier for a drug payload to program desirable release kinetics.

Co-regularized multi-view sparse reconstruction embedding for dimension reduction

With the development of information technology, we have witnessed an age of data explosion which produces a large variety of data filled with redundant information. Because dimension reduction is an essential tool which embeds high-dimensional data into a lower-dimensional subspace to avoid redundant information, it has attracted interests from researchers all over the world. However, facing with features from multiple views, it’s difficult for most dimension reduction methods to fully comprehended multi-view features and integrate compatible and complementary information from these features to construct low-dimensional subspace directly. Furthermore, most multi-view dimension reduction methods cannot handle features from nonlinear spaces with high dimensions. Therefore, how to construct a multi-view dimension reduction methods which can deal with multi-view features from high-dimensional nonlinear space is of vital importance but challenging. In order to address this problem, we proposed a novel method named Co-regularized Multi-view Sparse Reconstruction Embedding (CMSRE) in this paper. By exploiting correlations of sparse reconstruction from multiple views, CMSRE is able to learn local sparse structures of nonlinear manifolds from multiple views and constructs significative low-dimensional representations for them. Due to the proposed co-regularized scheme, correlations of sparse reconstructions from multiple views are preserved by CMSRE as much as possible. Furthermore, sparse representation produces more meaningful correlations between features from each single view, which helps CMSRE to gain better performances. Various evaluations based on the applications of document classification, face recognition and image retrieval can demonstrate the effectiveness of the proposed approach on multi-view dimension reduction.

A Novel Integrated SVM for Fault Diagnosis Using KPCA and GA

Fault diagnosis has been more and more significant in modern factories to ensure the proper functionality of the manufacturing process and to improve product quality and efficiency. A novel integrated SVM model is developed in this paper. Since KPCA can implicitly mapped the data into a higher nonlinear feature space, it is applied in our model to extract key information of original data sets for further training of SVMs. SVM is the main part to detect and identify different kinds of faults, and GA is utilized to optimize the parameters of SVM to avoid over fitting or under fitting problems caused by wrong parameters. Compared with other fault diagnosis methods applied on Tennessee Eastman (TE) process benchmark, we can safely conclude that the proposed model can achieve good predictive accuracy in a relatively short time based on our experiment results.

Spatiotemporal data fusion and manifold reconstruction in Hall thrusters**Distribution Statement A: Approved for Public Release. Distribution is Unlimited. PA# 18635.

A critical breakthrough in the understanding of Hall effect thrusters (HETs) has been the emergence of mapping techniques to fuse multiple time-varying plasma measurements from spatially distributed probes into a unified reconstruction describing the full spatiotemporal dynamics of the HET plasma. The most basic requirement for generating such a spatiotemporal reconstruction is a robust and accurate method to build a map between a single input and a single output signal. This work describes a new nonlinear phase space based mapping technique, the shadow manifold interpolation (SMI) technique, and assesses its performance versus traditional linear FFT-based mapping. Results demonstrate the superiority of the SMI reconstruction for short, noisy and aperiodic signals. Analysis in conjunction with the convergent cross mapping methodology (Sugihara et al 2012 Science 338 496–500) provides theoretical justification for the physical relevance of SMI application to a given signal reconstruction.

An Optimized Approach for Tracing Pre- and Post-Buckling Equilibrium Paths of Space Trusses

In this paper, a novel optimization-based method is proposed to analyze steel space truss structures undergoing large deformations. The geometric nonlinearity is considered using the total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to the displacement-type constraints. The proposed approach can fully follow the equilibrium path of the geometrically nonlinear space truss structures not only before the limit point, but also after it, namely, including both the pre- and post-buckling paths. Moreover, a direct estimation of the buckling loads and their corresponding displacements is possible by using the method. Particularly, it has been shown that the equilibrium path of a structure with highly nonlinear behavior, multiple limit points, snap-through, and snap-back phenomena can be traced via the proposed algorithm. To demonstrate the accuracy, validity, and robustness of the proposed procedure, four benchmark truss examples are analyzed and the results compared with those by the modified arc-length method and those reported in the literature.

Voltage stability constrained line‐wise optimal power flow

The purpose of optimal power flow (OPF) is to optimise an objective function subject to a set of operating constraints. It remains an active research area because of using the bus-wise power balance equations, which leads to a non-linear solution space, resulting in OPF yielding local optimal solutions, thereby causing significant economic loss. In this study, first, a new line-wise OPF (LWOPF) formulation is proposed. Thereafter, a maximum loadability factor, as a voltage collapse indicator, is derived and combined with LWOPF constraints to form a voltage stability constrained LWOPF (VSCLWOPF) model. As the line-wise power balance equations are based upon the square of voltage magnitudes, it results in significant improvement in the solution space and lower-order terms in all computational steps. The LWOPF and VSCLWOPF formulations, are solved using non-linear optimisation technique, tested on several benchmark and real power systems. Results show that the proposed LWOPF is accurate, provides monotonic convergence, and scales well for large systems. It provides a better solution and is consistently faster, up to twice the speed of MATPOWER, due to reduced computational needs. Results of VSCLWOPF show that, for the same voltage stability level, the solution costs less than that obtained by classical bus-wise OPF.

Sensitivity analysis and optimization capabilities of the transparent open-box learning network in predicting coal gross calorific value from underlying compositional variables

Prediction performance and optimization attributes of the transparent open-box learning networks (TOB) applied to a large database of US coals are further explored to complement recently published base-case analysis. Nine sensitivity cases configured with the 6339 data records allocated in different ways to the TOB’s tuning, training, and testing subsets are developed. These cases demonstrate for this data set that the TOB algorithm provides robust, reliable, and repeatable predictions provided that the tuning subset contains 40 or so data records. On the other hand, increasing the number of records in the testing subset to numbers much greater than 100 does not lead to improved prediction accuracy. A comparison of the prediction performance of three optimizers applied with the TOB for each of the sensitivity cases reveals that a memetic firefly optimizer matches the optimized solutions found by Excel’s GRG Solver optimizer. The functionality of the memetic firefly optimizer enables it to be used effectively in a fully coded version of the TOB optimizer (not involving Excel cell formula for the optimizer to operate). This is an advantage when evaluating larger data sets with larger tuning subset requirements. The memetic firefly optimizer also introduces further transparency, flexibility, and control to the TOB optimization process by facilitating metaheuristic profiling that aids the tuning and customization of the optimizer for deployment with a range of data sets involving complex, non-linear feasible-solution spaces.

Regular families of kernels for nonlinear approximation

This article studies sufficient conditions on families of approximating kernels which provide N-term approximation errors from an associated nonlinear approximation space which match the best known orders of N-term wavelet expansion. These conditions provide a framework which encompasses some notable approximation kernels including splines, cardinal functions, and many radial basis functions such as the Gaussians and general multiquadrics. Examples of such kernels are given to justify the criteria. Additionally, the techniques involved allow for some new results on N-term Greedy interpolation of Sobolev functions via radial basis functions.

Shape geodesics for robust sign language recognition

In this study, a novel method of pattern recognition for static gesture recognition is proposed. To deal with this application, the authors should tackle the problem of low variability among shape classes in the gestures databases. The authors' method is based on robust registration and shape geodesics in shape space with a preliminary step of pose estimation accelerating the processing time. The different gestures are considered individual points in a non-linear shape space. Similarity between any two considered shapes can be measured by a distance metric on the shape space. For shape comparison, three distances with and without robust norm are proposed and evaluated for the target application. To cope with low shape variability among classes, the best scheme is to use robust norm in shape matching but not in shape comparison. Experiments are conducted on reference databases used in the literature to evaluate static gesture recognition. These experiments show the outperformance of the proposed scheme compared to state-of-the art methods.

High-Performance SAR Image Matching Using Improved SIFT Framework Based on Rolling Guidance Filter and ROEWA-Powered Feature

Severe speckle noise and complex local deformation in synthetic aperture radar (SAR) images degrade the performance of common scale-invariant feature transform (SIFT) based SAR image matching algorithms. To address this issue, this paper presents a new SIFT framework based algorithm by designing a novel nonlinear multiscale space construction strategy and a new local feature detector and descriptor. In the proposed algorithm, the multiscale images are generated by embedding a rolling guidance filter into the procedure of scale space construction, which can achieve better results in edge-preserving despeckling than other strategies. The improved nonlinear multiscale space construction strategy lays a solid foundation for high-quantity feature point detection with a low false ratio. For feature detection, a new feature detector, Harris–Laplace technique combined with the ratio of exponential weighted average, Harris–Laplace ratio of exponential weighted average (ROEWA), is proposed to effectively suppress the false feature points in SAR images. Moreover, a gradient location and orientation histogram powered by ROEWA is designed to obtain feature descriptors, which is robust to local deformations. Finally, the K-nearest neighbor approach is used to speed up the search for initial matching; the spatially consistent random sample consensus is adopted to remove false match points (outliers). The experimental results using simulated and real SAR images demonstrate that the proposed algorithm can achieve much better performance in terms of the matching accuracy and inlier ratio than other methods.

Sequential Laplacian regularized V-optimal design of experiments for response surface modeling of expensive tests: An application in wind tunnel testing

In an increasing number of cases involving estimation of a response surface, one is often confronted with situations where there are several factors to be evaluated, but experiments are prohibitively expensive. In such scenarios, learning algorithms can actively query the user or other resources to determine the most informative settings to be tested. In this article, we propose an active learning methodology based on the fundamental idea of adding a ridge and a Laplacian penalty to the V-optimal design to shrink the weight of less significant factors, while looking for the most informative settings to be tested. To leverage the intrinsic geometry of the factor settings in highly nonlinear spaces, we generalize the proposed methodology to local regression. We also propose a simple sequential design strategy for efficient determination of subsequent experiments based on the information from previous experiments. The proposed methodology is particularly suited for problems involving expensive experiments with a high standard deviation of the error. We apply the proposed methodology to a simulated wind tunnel testing and compare the result with an existing practice. We also evaluate the estimation accuracy of the proposed methodology using the paper helicopter case study. Finally, through extensive simulated experiments, we demonstrate the performance of the proposed methodology against classic response surface methods in the literature.

Component-Graph Construction

Component-trees are classical tree structures for grey-level image modelling. Component-graphs are defined as a generalization of component-trees to images taking their values in any (totally or partially) ordered sets. Similar to component-trees, component-graphs are a lossless image model; then, they can allow for the development of various image processing approaches. However, component-graphs are not trees, but directed acyclic graphs. This makes their construction non-trivial, leading to nonlinear time cost and resulting in nonlinear space data structures. In this theoretical article, we discuss the notion(s) of component-graph, and we propose a strategy for their efficient building and representation, which are necessary conditions for further involving them in image processing approaches.

Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg–Landau equations

In this paper, we discuss the error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex space fractional Ginzburg-Landau equations. The continuous mass and energy inequalities as well as their discrete versions are presented. Moreover, by the discrete mass and energy inequalities, the error estimate of the Fourier pseudo-spectral scheme is established, and the scheme is proved to have the spectral accuracy.

A Machine Learning Approach to Kinematic Synthesis of Defect-Free Planar Four-Bar Linkages

Synthesizing circuit-, branch-, or order-defects-free planar four-bar mechanism for the motion generation problem has proven to be a difficult problem. These defects render synthesized mechanisms useless to machine designers. Such defects arise from the artificial constraints of formulating the problem as a discrete precision position problem and limitations of the methods, which ignore the continuity information in the input. In this paper, we bring together diverse fields of pattern recognition, machine learning, artificial neural network, and computational kinematics to present a novel approach that solves this problem both efficiently and effectively. At the heart of this approach lies an objective function, which compares the motion as a whole thereby capturing designer's intent. In contrast to widely used structural error or loop-closure equation-based error functions, which convolute the optimization by considering shape, size, position, and orientation of the given task simultaneously, this objective function computes motion difference in a form, which is invariant to similarity transformations. We employ auto-encoder neural networks to create a compact and clustered database of invariant motions of known defect-free linkages, which serve as a good initial choice for further optimization. In spite of highly nonlinear parameters space, our approach discovers a wide pool of defect-free solutions very quickly. We show that by employing proven machine learning techniques, this work could have far-reaching consequences to creating a multitude of useful and creative conceptual design solutions for mechanism synthesis problems, which go beyond planar four-bar linkages.

Enhanced Artificial Coronary Circulation System Algorithm for Truss Optimization with Multiple Natural Frequency Constraints

In this paper, an enhanced artificial coronary circulation system (EACCS) algorithm is applied to structural optimization with continuous design variables and frequency constraints. The standard algorithm, artificial coronary circulation system (ACCS), is inspired biologically as a non-gradient algorithm and mimics the growth of coronary tree of heart circulation system. Designs generated by the EACCS algorithm are compared with other popular evolutionary optimization methods, the objective function being the total weight of the structures.Truss optimization with frequency constraints has attracted substantial attention to improve the dynamic performance of structures. This kind of problems is believed to represent nonlinear and non-convex search spaces with several local optima. These problems are also suitable for examining the capabilities of the new algorithms. Here, ACCS is enhanced (EACCS) and employed for size and shape optimization of truss structures and six truss design problems are utilized for evaluating and validating of the EACCS. This algorithm uses a fitness-based weighted mean in the bifurcation phase and runner phase of the optimization process. The numerical results demonstrate successful performance, efficiency and robustness of the new method and its competitive performance to some other well-known meta-heuristics in structural optimization.

Detection of Emotions Induced by Colors in Compare of Two Nonlinear Mapping of Heart Rate Variability Signal: Triangle and Parabolic Phase Space (TPSM, PPSM)

Emotions in the word mean understanding, sensing and recognizing something with one’s senses. Emotions are relatively simple responses that the body presents to external or internal stimuli. As the individual’s mental and emotional state changes, the activity of the various parts of the body also changes and increases. This applies to all cultures. So emotion detection from biological signals especially heart rate variability (HRV) signal is considered in this article. The behavior of HRV in two nonlinear phase space have been evaluated and the extracted features of these two mapping have been used for emotion detection. Triangle and Parabolic Phase Space Mapping (TPSM and PPSM) are recently introduced methods which are able to indicate hidden aspects of HRV in response to different emotions. The Lead II of electrocardiogram signal was recorded from 32 female students while they were stimulated by four main psychology colors (blue, green, red, and yellow) to induce emotions which were labeled by SAM test. The results show that the mentioned colors caused emotions pleasure, joy, anger, and sadness, respectively. After rating the results by Kruskal–Wallis test, k-nearest neighbor classifier was used for emotion classification. The obtained accuracy after 10-fold cross validation was 90.91%. The hypotheses of being a relationship between colors and emotions without awareness of subjects have been proved. Furthermore, by studying the usefulness of TPSM and PPSM as new mapping of HRV, significant results have obtained which indicate the advantages of using them. So it is suggested to use and analyze the usage of these kinds of colors in different psychological situations and for biofeedback tests.

Forecasting Model Based on Information-Granulated GA-SVR and ARIMA for Producer Price Index

The accuracy of predicting the Producer Price Index (PPI) plays an indispensable role in government economic work. However, it is difficult to forecast the PPI. In our research, we first propose an unprecedented hybrid model based on fuzzy information granulation that integrates the GA-SVR and ARIMA (Autoregressive Integrated Moving Average Model) models. The fuzzy-information-granulation-based GA-SVR-ARIMA hybrid model is intended to deal with the problem of imprecision in PPI estimation. The proposed model adopts the fuzzy information-granulation algorithm to pre-classification-process monthly training samples of the PPI, and produced three different sequences of fuzzy information granules, whose Support Vector Regression (SVR) machine forecast models were separately established for their Genetic Algorithm (GA) optimization parameters. Finally, the residual errors of the GA-SVR model were rectified through ARIMA modeling, and the PPI estimate was reached. Research shows that the PPI value predicted by this hybrid model is more accurate than that predicted by other models, including ARIMA, GRNN, and GA-SVR, following several comparative experiments. Research also indicates the precision and validation of the PPI prediction of the hybrid model and demonstrates that the model has consistent ability to leverage the forecasting advantage of GA-SVR in non-linear space and of ARIMA in linear space.

Hierarchical Multi-Geodesic Model for Longitudinal Analysis of Temporal Trajectories of Anatomical Shape and Covariates.

Longitudinal regression analysis for clinical imaging studies is essential to investigate unknown relationships between subject-wise changes over time and subject-specific characteristics, represented by covariates such as disease severity or a level of genetic risk. Image-derived data in medical image analysis, e.g. diffusion tensors or geometric shapes, are often represented on nonlinear Riemannian manifolds. Hierarchical geodesic models were suggested to characterize subject-specific changes of nonlinear data on Riemannian manifolds as extensions of a linear mixed effects model. We propose a new hierarchical multi-geodesic model to enable analysis of the relationship between subject-wise anatomical shape changes on a Riemannian manifold and multiple subject-specific characteristics. Each individual subject-wise shape change is represented by a univariate geodesic model. The effects of subject-specific covariates on the estimated subject-wise trajectories are then modeled by multivariate intercept and slope models which together form a multi-geodesic model. Validation was performed with a synthetic example on a S 2 manifold. The proposed method was applied to a longitudinal set of 72 corpus callosum shapes from 24 autism spectrum disorder subjects to study the relationship between anatomical shape changes and the autism severity score, resulting in statistics for the population but also for each subject. To our knowledge, this is the first longitudinal framework to model anatomical developments over time as functions of both continuous and categorical covariates on a nonlinear shape space.

Graph Laplacian Regularization with Sparse Coding for Image Restoration and Representation

Sparse coding is widely used in image denoising, deblurring, clustering, and classification. However, most existing approaches to sparse coding failed to consider the fact that high dimensional data naturally reside on geometrical structure of the data space. It has been shown that geometric information of the data is important for both inversion and discrimination. In this paper, we proposed a generalized framework for image restoration and representation by combining sparse coding and graph based algorithms. In image denoising and deblurring problems, an image is first decomposed into cartoon layer (piecewise-smooth contents) and texture layer (textures and sharp edges) using morphological component analysis (MCA); then optimal graph Laplacian regularizer (OGLR) algorithm and simultaneous sparse coding with Gaussian scale mixture prior (SSC-GSM) algorithm are applied to cartoon layer and texture layer, respectively; final restored image is generated by aggregating the outcomes from two algorithms. The proposed hybrid image restoration algorithm outperforms state-of-the-art image denoising algorithms, such as BM3D on natural images, measured in PSNR, and performs comparatively in image deblurring. In image clustering and classification problems, we convert our generalized framework into a novel dual graph regularized sparse coding method to transform the nonlinear data space and feature space into linear space, two efficient optimization algorithms are provided for the numerical implementation. The experimental results show that our generalized graph Laplacian and sparse coding framework performs competitively with popular denoising, deblurring, clustering, and classification methods.