Ideal Constraint Research Articles

Adaptive Feature Selection With Augmented Attributes.

In many dynamic environment applications, with the evolution of data collection ways, the data attributes are incremental and the samples are stored with accumulated feature spaces gradually. For instance, in the neuroimaging-based diagnosis of neuropsychiatric disorders, with emerging of diverse testing ways, we get more brain image features over time. The accumulation of different types of features will unavoidably bring difficulties in manipulating the high-dimensional data. It is challenging to design an algorithm to select valuable features in this feature incremental scenario. To address this important but rarely studied problem, we propose a novel Adaptive Feature Selection method (AFS). It enables the reusability of the feature selection model trained on previous features and adapts it to fit the feature selection requirements on all features automatically. Besides, an ideal l0-norm sparse constraint for feature selection is imposed with a proposed effective solving strategy. We present the theoretical analyses about the generalization bound and convergence behavior. After tackling this problem in a one-shot case, we extend it to the multi-shot scenario. Plenty of experimental results demonstrate the effectiveness of reusing previous features and the superior of l0-norm constraint in various aspects, together with its effectiveness in discriminating schizophrenic patients from healthy controls.

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on eight commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available at https://github.com/GuanxingLu/Subspace-Clustering.

Simultaneous local clustering and unsupervised feature selection via strong space constraint

Clustering is a fashion method applied in machine learning tasks. However, high dimensional data brings many obstacles for clustering approaches. To address such a problem, the unsupervised feature selection (UFS) method can be incorporated into clustering to reduce dimensionality. In general, most of the UFS methods adopt ℓ2,1-norm for subspace sparsity learning. However, its sparsity highly relies on the setting of trade-off parameter, which may lead to instability of ranking results and the difficulty in obtaining the optimal solution of projection matrix. In this paper, we propose to directly learn an absolutely row-sparsity subspace via the ℓ2,0-norm constraint, called Sparse constraint and Local learning for Unsupervised Feature Selection (SLUFS). It is an ideal sparse subspace constraint which can overcome the drawbacks of the ℓ2,1-norm. However, optimizing the ℓ2,0-norm constraint is an NP-hard problem, and at present, only some approximate solutions can be given, but the convergence can not be guaranteed. To tackle this challenge, we design a novel alternative iterative algorithm to directly optimize the ℓ2,0-norm based model. Most importantly, our strategy can obtain a closed-form solution with strict convergence guarantee. Comprehensive experiments are conducted on several real-world datasets to evaluate the performance of SLUFS with comparison to several related state-of-the-art methods.

Design, optimization and experimental testing of 2 K cryogenic plate-fin heat exchanger

2 K heat exchanger is a key component of cryogenic system at advanced superconducting accelerator. The distributed parameter method was used to design and calculate the 2 K heat exchanger with a helium flow rate of 10 g/s, and the ideal constraints and real constraints were set according to the actual test conditions. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was selected as the optimization, and two groups of Pareto front solution sets were obtained. Two optimization results from the solution sets were selected as the optimal designs, According to the adaptability of the heat exchanger under different flow conditions The Computational Fluid Dynamics (CFD) numerical simulation verification was carried out for the optimal design of the heat exchanger according to the actual constraint conditions., and the experimental test was carried out for the prototype with the same design. The experimental results show that the outlet temperature of the high-pressure side at 10 g/s is 2.983 K, and the difference from the design calculation is within 6 %, which verifies the accuracy of the design method. For the heat exchanger optimized according to the ideal constraint, the calculation results show that the outlet temperature of the high pressure side is 2.235 K. The heat transfer efficiency is 82.4 % and the pressure drop of low pressure side is 121.59 Pa.

On a Sailed Spacecraft Motion along a Handrail Fixed to Two Heliocentric Space Stations

Motion of a particle modeling a spacecraft with a solar sail along a handrail joining two heliocentric space stations is considered under the assumption that the sail is a perfect reflecting plane that can be located at any angle with respect to the direction of solar rays, the particle does not leave the plane of the orbit of the stations, the handrail is a tether that realizes an ideal unilateral constraint whose boundary is some ellipse, and the particle motion is sufficiently fast with respect to the orbital motion of the stations to neglect noninertiality of the orbital frame of reference. The equations of particle motion are written in dimensionless form without parameters, and the existence of an energy integral for the case of the sail orientation depending only on the spacecraft location is established. This integral is used for complete integration of the equations of motion for the particle relocations along the constraint boundary. The optimal length of the tether for the fastest relocation of a particle between the most remote points of the constraint boundary is computed for the case of the sail being orthogonal to the solar rays throughout the motion. Such a relocation time is computed in dimensionless form and for some real and hypothetical situations. A set of pairs of points in the constraint boundary between which relocation along the constraint boundary with zero initial and final velocities and with the invariably oriented sail is possible is constructed depending on the eccentricity of the ellipse. The result is presented as several plots that illustrate the evolution of the pairs’ regions as the eccentricity of the ellipse changes.

3D Browsing of Wide‐Angle Fisheye Images Under View‐Dependent Perspective Correction

AbstractThis paper presents a novel technique for 3D browsing of wide‐angle fisheye images using view‐dependent perspective correction (VDPC). First, the fisheye imaging model with interior orientation parameters (IOPs) is established. Thereafter, a VDPC model for wide‐angle fisheye images is proposed that adaptively selects correction planes for different areas of the image format. Finally, the wide‐angle fisheye image is re‐projected to obtain the visual effect of browsing in hemispherical space, using the VDPC model and IOPs of the fisheye camera calibrated using the ideal projection ellipse constraint. The proposed technique is tested on several downloaded internet images with unknown IOPs. Results show that the proposed VDPC model achieves a more uniform perspective correction of fisheye images in different areas, and preserves the detailed information with greater flexibility compared with the traditional perspective projection conversion (PPC) technique. The proposed algorithm generates a corrected image of 512 × 512 pixels resolution at a speed of 58 fps when run on a pure central processing unit (CPU) processor. With an ordinary graphics processing unit (GPU) processor, a corrected image of 1024 × 1024 pixels resolution can be generated at 60 fps. Therefore, smooth 3D visualisation of a fisheye image can be realised on a computer using the proposed algorithm, which may benefit applications such as panorama surveillance, robot navigation, etc.

Dynamics and control of spacecraft solar array deployment considering physical contacts between locking mechanisms

The numerical simulation of the deployment and locking process of flexible appendages is an important topic in the overall design of spacecraft. In the existing research, the connecting mechanism between the solar panels is usually regarded as an ideal revolute constraint, and the locking process is simulated by applying a virtual lock torque related to the deployment angle. However, this method cannot obtain the physical contact force history, and because the physical meaning of the stiffness term in the lock torque function is not clear, it is difficult to accurately illustrate the frequency characteristics of the flexural vibration of the panels in the post-lock phase. In fact, the locking process is a frequent contact-impact process between the lock pin and groove. In this study, a typical deployable spacecraft with torsion-spring-driven panels were investigated numerically. The locking mechanism is modeled as a physical entity, and the continuous contact force model between the lock pin and groove is established. The contact stiffness of cylindrical line-contact is given by preloading calculation using the finite element method. Based on the multibody dynamics, rigid body model and flexible body model of the solar panels are established respectively. Through the comparison between the numerical simulation results of the two models, it is found that the rigid body model will produce excessive contact force and false high-frequency vibration. Furthermore, the attitude PD controller of spacecraft is designed, and the difference of system dynamic response in the deployment process under the main-body free state and the main-body controlled state is studied. The vibration frequency under the main-body controlled state is close to the first-order natural frequency of the structural finite element analysis, which verifies the rationality of the calculation results of the model.

Relaxed magnetohydrodynamics with ideal Ohm's law constraint

The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity ‘ideal’ Ohm's law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. The augmentation combines a pointwise vector Lagrange multiplier method and global penalty function method and can be used either for iterative enforcement of the IOL to arbitrary accuracy, or for constructing a continuous sequence of magnetofluid dynamics models running between RxMHD (no IOL) and weak IMHD (IOL almost everywhere). This is illustrated by deriving dispersion relations for linear waves on an MHD equilibrium.

Diverse classes of constraints enable broader applicability of a linear programming-based dynamic metabolic modeling framework

Current metabolic modeling tools suffer from a variety of limitations, from scalability to simplifying assumptions, that preclude their use in many applications. We recently created a modeling framework, Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), that addresses a key gap: capturing metabolite dynamics and regulation while retaining a potentially scalable linear programming structure. Key to this framework’s success are the linear kinetics and regulatory constraints imposed on the system. However, while the linearity of these constraints reduces computational complexity, it may not accurately capture the behavior of many biochemical systems. Here, we developed three new classes of LK-DFBA constraints to better model interactions between metabolites and the reactions they regulate. We tested these new approaches on several synthetic and biological systems, and also performed the first-ever comparison of LK-DFBA predictions to experimental data. We found that no single constraint approach was optimal across all systems examined, and systems with the same topological structure but different parameters were often best modeled by different types of constraints. However, we did find that when genetic perturbations were implemented in the systems, the optimal constraint approach typically remained the same as for the wild-type regardless of the model topology or parameterization, indicating that just a single wild-type dataset could allow identification of the ideal constraint to enable model predictivity for a given system. These results suggest that the availability of multiple constraint approaches will allow LK-DFBA to model a wider range of metabolic systems.

Dual Empirical Orthogonal Functions Restrained Tomographic Model for Ionosphere Imaging

Extra constraints are always brought into an ionosphere tomographic model to strengthen its robustness. However, existent models using the constraints either show a weak restriction, amplifying the model’s uncertainties, or demonstrate a strong restriction, decreasing the model’s flexibility. Empirical Orthogonal Function (EOF), as a kind of basis function and generally being extracted from a prior dataset, is an ideal constraint for the tomographic model. By using EOFs as the vertical and slant constraints of the tomographic model, a dual-EOFs restrained tomographic model (DERT) is proposed. In DERT, a smooth constraint, conducted by a moving window process, is firstly imposed, and then a vertical constraint and a slant constraint, which are carried out by fitting the estimated vertical and slant profiles with their dominant EOFs via a least square method, are appended. To reduce the impacts of the errors of the slant total electron content (STEC) measurements on the processes of moving window and least square fit, an algorithm that can reject abnormal STEC values is employed before the two processes. Validations Tests are conducted to validate the DERT and compare it with the Slepian method and the IRI-2016 model. Results show that DERT outperforms the reference methods in aspects of vertical profiles, F2 layer peak density (foF2), STEC measurement and vertical total electron content (VTEC). The root mean square errors (RMSE) improvements over the Slepian method are 14.17%, 0.47%, 16.24% and 40.46% (IGS map as the truth), respectively.

Selecting The Best Route for Aerial Ladder Truck to Speed Up Response Time in High-Rise Buildings Located in Unprotected and High Fire Risk Areas

Fire outbreaks on high-rise buildings require specific techniques and equipment; one of such equipment is aerial ladder trucks. Firefighters in aerial ladder trucks must ideally arrive at the location of the fire within the ideal response time constraint in the context of fire emergency management to minimize collateral damage, be it of human lives or properties. This study aims to discover the best route traversable by aerial ladder trucks to achieve the ideal response time should a fire occur in high-rise buildings, particularly stated buildings located within unprotected and high fire risk areas in Sidoarjo Regency. The best routes were selected through a simulation using the closest facility in GIS Network Analyst based on proximal distance and travel time. The study results show that the aerial ladder trucks can traverse the recommended routes to the high-rise buildings within the ideal response time. However, the majority of these results only occur during off-peak hours. Hence, the addition of new fire stations, whose locations are within 5 km of the high-rise buildings, and the improvement or addition of street networks as an alternative to increase the fulfillment of the ideal response time of aerial ladder trucks, especially during peak hours, are recommended.

Joint Active and Passive Beamforming Design for IRS-Assisted Multi-User MIMO Systems: A VAMP-Based Approach

This paper tackles the problem of joint active and passive beamforming optimization for an intelligent reflective surface (IRS)-assisted multi-user downlink multiple-input multiple-output (MIMO) communication system under both ideal and practical IRS phase shifts. We aim to maximize the spectral efficiency of the users by minimizing the sum mean square error (MSE) of the users’ received symbols. For this, a joint non-convex optimization problem is formulated under the sum minimum mean square error (MMSE) criterion. Alternating minimization is used to break the original joint optimization problem into the separate optimization of the active precoding matrix for the base station (BS) and the matrix of phase shifts for the IRS. While the MMSE active precoder is obtained in closed-form, the IRS phase shifts are optimized iteratively using a modified version (developed in this paper) of the vector approximate message passing (VAMP) algorithm. Moreover, the underlying joint optimization problem is solved under two different models for the IRS phase shifts, namely by assuming <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> ) a unimodular (i.e., ideal) constraint on the reflection coefficients and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ii$ </tex-math></inline-formula> ) a more practical reflection elements termination by a variable reactive load (which inherently introduces the phase-dependent amplitude attenuation in the IRS phase shifts). Simulation results are presented to illustrate the performance of the proposed method under both perfect and imperfect channel state information (CSI) and to show the effect of the practical constraint on the system throughput. The results validate the superiority of the proposed method over the state-of-the-art techniques both in terms of throughput and computational complexity.

基于Udwadia-Kalaba方法的并联机器人鲁棒伺服约束控制

For the trajectory tracking control problems of 2-DOF redundant drive parallel robots, a robust servo control method based on the Udwadia-Kalaba equation was proposed. Under the influences of load, external interference and manufacturing errors, it is impossible to obtain the accurate and complete motion model for the robot, and the control performance of the robot is poor. To solve the impacts of this type of uncertainty, a robust control method was proposed to enable the system to accurately track the ideal trajectory, and ensure the uniform boundedness and the uniform ultimate boundedness of the overall system. In addition, the Udwadia-Kalaba equation was used to solve the constraint force required by the system to meet the ideal constraint in the control process. The Udwadia-Kalaba equation does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized velocities, and can handle both complete and incomplete constraints, with analytical solutions of constraint forces satisfying the trajectory obtained. The stability of this robust control method was proved theoretically with the Lyapunov function. Simulation experiments show that, the proposed robust control method can achieve high-precision tracking control along a given trajectory under non-ideal conditions.

Stability of Large-Size and High-Strength Steel Angle Sections Affected by Support Constraint

The influence of support stiffness on the effective calculated length which plays an essential role in the axial compression stability of steel memeber is always ignored due to the ideal support constraint that is difficult to achieve in the test. In this paper, the calculation method of the effective length factor was put forward by the mechanical model of the axially compressed member. The supports rotation stiffness of large-size and high-strength steel angle sections (LHS) under the test condition were measured, and the effective length of each specimen was modified. And 36 LHS members were tested under axial load. Then the stability responses for LHS members were studied using finite element analysis considering more section profiles and the wide range slenderness ratios. Moreover, the buckling strengths were compared with the current design codes. The results show that the support constraint has a significant influence on the bearing capacity of the LHS member. Considering the influence of support restraint, when the slenderness ratio is small, the stability factor is higher than the column curve in current codes; when the slenderness ratio is large, b-curves in both GB50017-2017 and Eurocode 3 are conservative, whereas other codes are marginally unsafe. Finally, a new column curve was proposed to predict LHS members’ capacity more accurately.

DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE

The Gauss's principle gives the rules to identify the real motion from the possible motion by finding the extreme value of the function, which can make the dynamic problem of the multi-body system not need to solve the differential (algebra) equation, but adopt the optimization method of solving the minimum value, therefore, how to define the appropriate Gaussian constraint function is the prerequisite for the realization of dynamic optimization method. For the ideal system, the effect of constraints on the system can be reflected by the constraint equation and so the Gaussian constraint can be expressed as a function of the particle acceleration of the system, then the dynamic problem of the system can be described as the constrained optimization problem with the objective function as the Gaussian constraint function and the optimization variable as the particle acceleration. When the non-ideal factors such as dry friction need to be taken into account in the system, the partial interaction can not be covered by the defined constraint equation and needs to be described by additional physical laws. This sort of interaction destroys the extreme value characteristics of the original Gaussian restraint function of the system. Based on Gauss's principle of the variable classification, the extreme value principle of non-ideal system is derived and proved, whose objective function is expressed by ideal constraint forces. The Gauss's principle for non-ideal system in the existing literature is discussed and it is pointed out that it is an expression of the extreme value principle given when there is no obvious function correlation between the non-ideal constraint force and the ideal constraint force. But when they have obvious function relation (such as the linear relationship between the sliding friction force and the normal constraint force in the Coulomb friction law), this form will fail. And according to the extreme value principle given, the dynamic optimization model of contact problem for multi-body system considering friction is obtained. In the examples, the optimization model and the corresponding linear complementary model are analyzed, which is found that the two are necessary and sufficient conditions for each other under the condition of satisfying the uniqueness of rigid body sliding problem, thus, the reliability of the optimization model given is proved. And the dynamic simulation is carried out by the optimization calculation method. The simulation results show the feasibility and effectiveness of combining Gaussian principle with optimization algorithm.

Wave based method for flexural vibration of thin plate with general elastically restrained edges

Wave based method is a numerical technique to predict steady-state vibration and solve vibroacoustic problems. It is a deterministic approach that is acknowledged to be more efficient than the element based methods in the mid-frequency range. The wave based method for plates with prescribed boundary conditions has been proposed and verified for the ideal constraint cases such as clamped, free and simply supported. To deal with different kind of or more realistic boundary conditions, this paper proposes a modified wave based method. The method is aimed at analyzing the flexural vibration of thin plates with general elastically restrained edges, and it can also consider the damping effect associated with the edge restraint. A number of numerical validation examples are shown, where the plate edges are uniform, non-uniform or partially supported. Within the examples, the responses of the plate under different edge conditions are compared, including elastic supports with different translational and rotational stiffness and damping parameters, rigid supports like clamped and simply supported, and free edges. For all the considered cases, the proposed method is proved to be effective, though the convergence performance is influenced by the boundary conditions. More wave functions may be required for simply supported, non-uniform or partially supported cases.

Realizing brachistochronic planar motion of a variable mass nonholonomic mechanical system by an ideal holonomic constraint with restricted reaction

The paper considers realization of the brachistochronic motion of a nonholonomic mechanical system, composed of variable mass particles, by means of an ideal holonomic constraint with restricted reaction. It is assumed that the system performs planar motion in an arbitrary field of forces and that it has two degrees of freedom. In addition, the laws of the time-rate of mass variation of the particles, as well as relative velocities of the expelled and gained particles, respectively, are known. Restricted reaction of the holonomic constraint is taken for the scalar control. Applying Pontryagin?s maximum principle and singular optimal control theory, the problem of brachistochronic motion is solved as a two-point boundary value problem (TPBVP). Since the reaction of the constraint is restricted, different types of control structures are examined, from singular to totally nonsingular. The considerations are illustrated via an example.

A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value

We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper.

Deployment and control of cable-driven flexible solar arrays

PurposeThe purpose of this study is to investigate the deployment and control of cable-driven flexible solar arrays.Design/methodology/approachFirst, dynamic model of the system is established by using the Jourdain’s velocity variation principle and the single direction recursive construction method, including the dynamic equation of a single flexible body, the kinematical recursive relation of two adjacent flexible bodies and the dynamic equation of the solar array system. Then, the contribution of joint friction to the dynamic equation of the system is derived based on the virtual power principle. A three-dimensional revolute joint model is introduced and discussed in detail. Finally, a proportion-differentiation (PD) controller is designed to control the drift of the system caused by the deployment.FindingsSimulation results show that the proposed model is effective to describe the deployment of flexible solar arrays, joint friction may affect the dynamic behavior of the system and the PD controller can effectively eliminate the spacecraft drift.Practical implicationsThis model is useful to indicate the dynamics behavior of the solar array system with friction.Originality/valueThe relationship between ideal constraint force and Lagrange multipliers is derived. The contribution of joint friction to the dynamic equation of the system is derived based on the virtual power principle. A PD controller is designed to control the drift of the system caused by the deployment of solar arrays.

Relaxing Nonholonomic Constraints to Eliminate Chattering From Time-Optimal Control Solutions

This letter presents a new approach to tackle the problem of infinite chattering , observed at bang-singular junctions of the minimum-time trajectories of car-like robots with bounded angular acceleration control. To eliminate chattering from time-optimal control solutions, we propose to relax the ideal nonholonomic constraint of no-skidding. A proof is presented to demonstrate that this relaxation eliminates chattering from the bang-singular junctions. Finally, a solution to the time-optimal synthesis under the condition of small skid angles is provided.