Redundant Constraints Research Articles

SEARCH AND ELIMINATION OF REPEATED CONNECTIONS IN THE SCHEME OF GUIDING SLIDE-CRANK MECHANISM OF THE GRIPPING DEVICE

Purpose. The article is aimed to carry out a structural analysis of the coupled straight-guiding crank-slide mechanism of variable structure gripping devices with external unilateral constraints. It is also necessary to determine the number of internal and external repeating connections in the contours of the mechanism at different stages of its functioning, to assess their possible perniciousness and to suggest ways to reduce them. Methodology. Achieving this goal is carried out based on the universal structural theory of Ozols mechanisms for analyzing the gripping device as a mechanism with geometric, internal and frictional holonomic external constraints. Ozols internal and external structural formulas are used. Findings. The eleven-link gripping device is built on the basis of coupled central parallelogram crank-slider mechanism with a driving cranks. Synchronous driving cranks act on elongated connecting rods connected to sliders and gripping clamp elements. Gripping clamp elements carry out plane-parallel movement. Structural analysis was performed using structural schemes for two states of the mechanism: before clamping the object and in the state of the clamped object. In the first state of the mechanism with kinematic pairs of class V, the one-movable scheme contains thirteen internal redundant constraints. In the second state of the mechanism, external constraints act and in the scheme another five additional external repeating constraints are formed. Their contour arrangement and possible consequences of their action are shown. Originality. Structural analysis of the coupled crank-slider mechanism of the gripping device as a mechanism of a variable structure with internal and external connections is carried out for the first time. It is performed contour analysis, search and elimination, as well as reduction of pernicious repeated connections in the internal and external contour of the mechanism. Practical value. Practical recommendations have been developed on changing the mobilities of sliding pairs to eliminate all repeated connections in the internal contours of the mechanism. To reduce the number of pernicious repeated connections, the introduction of a self-centering unloading coupling into the external contour of the mechanism is proposed.

Just-in-time two-dimensional bin packing

This paper considers the on-time guillotine cutting of small rectangular items from large rectangular bins. Items assigned to a bin define the bins’ processing time. Consequently, an item inherits the completion time of its assigned bin. Any deviation of an item’s completion time from its due date causes either earliness or tardiness penalties. This just-in-time two-dimensional bin packing problem (JITBP) combines two difficult discrete optimization problems: Bin packing and total weighted earliness tardiness single machine scheduling. It is herein modeled as an integrated constraint program, augmented with two sets of logically redundant constraints that speed the search. The first set uses the concept of dual feasible functions. It focuses on bin packing feasibility. The second is the result of a linear program that schedules filled bins on a single machine. As an alternative to this integrated model, this paper proposes two decomposition cut-and-check approaches that define the master problem (MP) as a relaxation of JITBP where the items are reduced to dimensionless entities. They then reestablish the geometric feasibility of the MPs’ solutions by iteratively augmenting MP with Benders cuts generated from the subproblems. The two approaches are similar in concept except that one implements MP as a constraint program (CP) while the second implements it as a mixed-integer program (MIP). Because JITBP is computationally challenging, we test all approaches under a number of heuristic assumptions, which include a maximum runtime for the MIP and CP solvers. The results provide computational evidence that the integrated constraint programming approach performs relatively well, and outperforms the decomposition approach whose MP is a CP. However, both approaches are outperformed by the decomposition approach whose MP is a warm-started MIP.

Deterministic global superstructure-based optimization of an organic Rankine cycle

Organic Rankine cycles (ORCs) offer a high structural design flexibility. The best process structure can be identified via the optimization of a superstructure, which considers design alternatives simultaneously. In this contribution, we apply deterministic global optimization to a geothermal ORC superstructure, thus guaranteeing to find the best solution. We implement a hybrid mechanistic data-driven model, employing artificial neural networks as thermodynamic surrogate models. This approach is beneficial as we optimize the problem in a reduced space using the optimization solver MAiNGO. We further introduce redundant constraints that are only considered for the lower-bounding problem of the branch-and-bound algorithm. We perform two separate optimizations, one maximizing power output and one minimizing levelized cost of electricity. The optimal solutions of both objectives differ from each other, but both have three pressure levels. Global optimization is necessary as there exist suboptimal local solutions for both flowsheet configuration and design with fixed configurations.

A Cognitive Joint Angle Compensation System Based on Self-Feedback Fuzzy Neural Network With Incremental Learning

Joint angle error of robotic arm has great impacts on the accuracy of the end-effector, which is critical in industrial applications. Therefore, in this article, an online cognitive joint angle error compensation method based on incremental learning is proposed to reduce joint angle error. The proposed method consists of a joint angle error solver and a compensation module, which ensure that the robot can obtain effective joint angle compensation in various situations. The joint angle error solver is used to solve joint angle error online. It uses the redundant constraint method for multilink position measurement so as to calculate the position error of the robot accurately later. The compensation module uses the self-feedback incremental fuzzy neural network (SFIFN) to predict and update the compensation in real time. SFIFN is a variant of the fuzzy neural network (FNN), which uses long short-term memory to introduce a feedback mechanism based on FNN. The incremental learning capability of SFIFN reduces the time for solving error and makes the module runs in real time. Specifically, two inertial measurement units mounted at the ends of links are used to measure pose changes of the ends of corresponding links. Both the simulated and the real experiments show that the proposed method yields good compensations to joint angle error and its potentials for smart manipulation.

Retrofit Fatigue Cracked Diaphragm Cutouts Using Improved Geometry in Orthotropic Steel Decks

Diaphragm cutouts are set to release redundant constraints and hence reduce weld fatigue at the connection of U-ribs to diaphragms in orthotropic steel decks. However, most fatigue cracks which originate from the edge of cutouts are in fact detected in the diaphragms. Therefore, a retrofit technology on cracked cutouts at the diaphragm is proposed and applied to the orthotropic steel box girder of a suspension bridge. Firstly, the stress concentration on the cutout is analyzed through refined finite element analyses. Furthermore, the fatigue cracked cutouts are retrofitted by changing their geometrical parameters. Thereafter, an optimized geometry and the size of diaphragm cutouts were confirmed and applied in the rehabilitation of a suspension bridge. On-site wheel load tests were carried out before and after retrofitting of the diaphragm cutout. The stress distributions along the edges of the cutouts and at the side of a diaphragm were measured under a moving vehicle. The stress spectra at two critical locations on the edge of a cutout was obtained under longitudinally and laterally moving vehicles. Finally, the fatigue life of the cutouts is assessed by the modified nominal stress method. The analytical and test results indicate that the wheel loads on the deck transmit stress to the diaphragms through the U-ribs, during the load transmission process, the stress flow is obstructed by diaphragm cutouts, resulting in local stress concentrations around the cutouts. In addition, the overall size of the cutouts should be small, but the radius of the transition arc should be large, thus the stress flow will not be obviously obstructed. After the retrofitting of the cutouts by improved geometry, the maximum stress decreases by 87.6 MPa, which is about 40% of the original stress. The equivalent constant amplitude stress is reduced by 55.2% when the lateral position of the wheel loads is taken into consideration. Based on the stresses obtained by finite element analysis (FEA) and experimental tests, the fatigue lives of the original cutouts are 1.7 and 4.9 years, respectively, which increase to 78.1 and 155.5 years, respectively, after the cutouts were retrofitted, which indicates that the improved geometry and retrofit technology can enhance the fatigue performance and extend the fatigue life of diaphragm cutouts with fatigue cracks.

Fast identifying redundant security constraints in SCUC in the presence of uncertainties

Security constrained unit commitment (SCUC), with renewable resources integrated into power grid, is one core function in the day-ahead market. However, it confronts with critical challenges as the heavy complicated security constraints are considered. Usually, it is observed that lots of security constraints are redundant, which can be identified and eliminated, so as to reduce the computational complexity. In this study, the authors first lift the uncertain feasible region of SCUC into a high dimensional space. Furthermore, a fast identification method is proposed to relax the original feasible region, which thus can be solved by the classical greedy algorithm. In order to prevent the over-relaxation and find more redundant constraints, an efficient feasible-based bound tightening strategy is utilised to provide a tighter bound. Numerical results on large-scale test systems verify the effectiveness of the proposed method.

Improved Stiffness Modeling for An Exechon-Like Parallel Kinematic Machine (PKM) and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy, stiffness and workspace of machining equipment. Therefore, a 5-DOF (degrees of freedom) parallel kinematic machine (PKM) with redundant constraints is proposed. Based on the kinematics analysis of the parallel mechanism using intermediate variables, the kinematics problems of the PKM are solved through equivalent kinematics model. The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM, where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis. And the stiffness model of the parallel mechanism is improved by correction coefficient matrix, each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism. The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively. The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism. To enhance the machining accuracy of the PKM, the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece. A plate workpiece taken as example is examined in the case study section, which demonstrates the effectiveness of optimization method.

A multi-constrained binary ILP method for optimal allocation of PMUs in network

This paper proposes multi-constrained binary integer linear programming (MBILP) method for optimal installation of phasor measurement units in IEEE networks considering Fast Load Voltage Stability Index (FLVSI), branch weight and redundancy constraints to minimize the cost of installation and to accomplish complete network observability. The weak buses of IEEE network are sorted based on their severity through the proposed strategy. A new FLVSI is programmed along with branch weight and redundancy constraints in MBILP to place PMUs in network. As installation cost of PMU for different buses varies with the number of branches or number of channels connected, PMUs should be allotted at bus with minimum cost. Redundancy of bus is computed to measure redundancy of bus network. Priority of PMU placement is considered at weak bus with proposed FLVSI in such a way that the cost is minimized and redundancy is adequate considering both branch weight and redundancy constraints. Ranking is proposed for PMU placement to find weak load bus in network along with the consideration of branch weight and redundancy. Zero injection (ZI) constraint modeling is recommended to minimize allocations further in system without losing observability. Contingency constraints for single-line or PMU loss are considered for allocation of PMUs. The proposed method is compared with ZI and without ZI modeling under general and line-outage or PMU loss cases to show efficacy of method. To estimate observability performance of complete network, a Complete Network Bus Observability Index is suggested. IEEE 14-, 24-, 30- and 57-bus networks are programmed with MATLAB software and compared with standard approaches to validate their efficacy.

Improved genetic algorithm with two-level multipoint approximation for complex frame structural optimization

In this paper, an improved structural topology and sizing optimization method is developed for the fast and efficient engineering design of complex frame structures where beam elements are mainly used in the structures. Discrete and continuous variables are included that the elimination or existence of beam elements are treated as discrete variables (0,1), and the continuous sizing variables of beam cross sections are considered to be continuous variables. To solve the mixed variable problem, the paper introduces a two-level multipoint approximation strategy (TMA). The first-level approximate problem is established by using the branched multipoint approximate function, which includes both two types of variables. Genetic algorithm (GA) is used to determine the absence or presence of beam members. The second-level approximate problem that only involving retained continuous size variables is made on this basis, which uses Taylor expansion and dual methods to solve the inner layer continuous optimization problem. Meanwhile, a strategy of adding a new complementary design point is adopted to expend the search scopes and improve the precision. Temporal deletion techniques are used to temporarily remove redundant constraints and local vibration modes processing techniques are used for continuum topology optimization under frequency constraints. Several representative examples are investigated to validate the effectiveness of the improved method.

Dissipative control of interval type-2 nonhomogeneous Markovian jump fuzzy systems with incomplete transition descriptions

This paper investigates the problem of designing a dissipative controller for interval type-2 nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition descriptions. To explore a generalized model for MJFSs under realistic situations, the coexistence of incompletely known transition rates and mismatched membership functions is considered in MJFS models, and the corresponding stabilization conditions are derived in terms of multi-parameterized linear matrix inequalities (M-PLMIs). In addition, to handle the problem of M-PLMIs, two novel relaxation techniques are additionally proposed such that the use of redundant constraints on multiple time-varying parameters can be significantly reduced. Finally, the validity of the proposed method is demonstrated via two illustrative examples.

Fast Screen of Redundant Transmission Constraints in Line Contingency-Constrained Dispatch

Line contingency-constrained dispatch (LCCD) problems are challenging to solve due to the large number of transmission constraints in pre- and post-contingency scenarios, yet the majority of them are never active. This letter proposes a fast method to remove redundant constraints in LCCD problems. The linear programming problems solved in the proposed method are significantly smaller than those in the known approach.

On the Study of the Basic Design Parameters of a Seven-Link Spatial Mechanism of a Part Processing Machine

A design of a spatial seven-link mechanism with rotational kinematic pairs of a part processing machine without redundant constraints is presented. The principle of operation of the mechanism is described. The mechanism structure is studied using elements of kinematic analysis and SolidWorks CAD. Expressions for the determination of rational ratios of link lengths are derived that provide failure-free operation of the mechanism.

An Optimal Generation Scheduling Approach Based on Linear Relaxation and Mixed Integer Programming

This paper proposes an optimal generation scheduling approach based on linear relaxation and mixed integer programming, which is used to solve the generation dispatch problem. The quadratic transmission loss constraint of each transmission line is converted into linear constraints by using the linear relaxation and mixed integer programming technique. Consequently, the original optimal generation scheduling problem is formulated as a quadratic programming or mixed integer quadratic programming problem that can be solved by commercial optimization solver. In order to improve the efficiency of algorithm, this paper further analyses the generation scheduling model and deletes the redundant variables and constraints. Three test systems, including IEEE 30-node system, IEEE 118-node system, and Polish 2746-node system, are employed to examine the effectiveness of the proposed method. The comparative results obtained by the proposed method, quadratically constrained quadratic programming method (QCQP), and solving constraint integer programs solver (SCIP) verify the effectiveness of the proposed method in solving the optimal generation scheduling problem.

Rattler wedging and force chain buckling: metastable attractor dynamics of local grain rearrangements underlie globally bistable shear banding regime

Grain rearrangements govern the mechanical response of granular materials under load. A comprehensive time series analysis of macroscopic stress, previously undertaken for the persistent shear banding regime, uncovered a bistable dynamical system with two interconnected attractor basins—one tied to jamming, the other to unjamming. Here we examine the state space of local fabric of a 3D granular material to uncover the underlying grain rearrangements which induce the system to switch basins and manifest macroscopic quasistationary dynamics. The fabric state space comprises metastable attractors organized according to structural determinacy: hypostatic, isostatic and hyperstatic. Although trajectories overwhelmingly favor identity transitions which preserve local fabric, rare nonidentity transitions hold the key to basin switching. Jamming basin dynamics is governed by force chain transitions in the hyperstatic region: here redundant constraints enable force reconfigurations with little to no change in the local fabric. But as force chains become overloaded, they buckle. Buckling and attendant dilatancy push grains to the isostatic region. This in turn triggers unjamming and ensuant transitions to the hypostatic region where rattlers, though few, dominate dynamics. Rattlers provide wedge-like supports to unstable misaligned particle columns, promoting force chain formation and return to the hyperstatic region. The lateral reinforcement of an isostatically constrained grain in a trimer by the addition of a contact and/or a 3-cycle is the most probable nonidentity transition during nascent force chain evolution.

Robust principal component analysis using facial reduction

We introduce a novel approach for robust principal component analysis (RPCA) for a partially observed data matrix. The aim is to recover the data matrix as a sum of a low-rank matrix and a sparse matrix so as to eliminate erratic noise (outliers). This problem is known to be NP-hard in general. A classical approach to solving RPCA is to consider convex relaxations. One such heuristic involves the minimization of the (weighted) sum of a nuclear norm part, that promotes a low-rank component, with an ell _1 norm part, to promote a sparse component. This results in a well-structured convex problem that can be efficiently solved by modern first-order methods. However, first-order methods often yield low accuracy solutions. Moreover, the heuristic of using a norm consisting of a weighted sum of norms may lose some of the advantages that each norm had when used separately. In this paper, we propose a novel nonconvex and nonsmooth reformulation of the original NP-hard RPCA model. The new model adds a redundant semidefinite cone constraint and solves small subproblems using a PALM algorithm. Each subproblem results in an exposing vector for a facial reduction technique that is able to reduce the size significantly. This makes the problem amenable to efficient algorithms in order to obtain high-level accuracy. We include numerical results that confirm the efficacy of our approach.

Towards scaling elementary flux mode computation.

While elementary flux mode (EFM) analysis is now recognized as a cornerstone computational technique for cellular pathway analysis and engineering, EFM application to genome-scale models remains computationally prohibitive. This article provides a review of aspects of EFM computation that elucidates bottlenecks in scaling EFM computation. First, algorithms for computing EFMs are reviewed. Next, the impact of redundant constraints, sensitivity to constraint ordering and network compression are evaluated. Then, the advantages and limitations of recent parallelization and GPU-based efforts are highlighted. The article then reviews alternative pathway analysis approaches that aim to reduce the EFM solution space. Despite advances in EFM computation, our review concludes that continued scaling of EFM computation is necessary to apply EFM to genome-scale models. Further, our review concludes that pathway analysis methods that target specific pathway properties can provide powerful alternatives to EFM analysis.

Оцiнки Шора для зваженого числа стiйкостi графа

Application of a technique of dual Lagrangian quadratic bounds of N.Z. Shor to studying the Maximum Weighted Independent Set problem is described. By the technique, two such N.Z. Shor’s upper bounds are obtained. These are bounds of the graph weighted independence number $ \alpha (G, w) $, which can be found in polynomial time. The first bound $ \psi (G, w) $ is associated with a quadratic model of the Maximum Weighted Independent Set problem and coincides with the known Lov\'asz number $ \vartheta (G, w) $. The second bound $ \psi_1 (G, w) $ corresponds to the same quadratic model supplemented by a family of functionally redundant quadratic constraints and is able to improve the accuracy of the upper bound $ \alpha (G, w) $ for special graph families. It is shown that, if graph is bipartite or perfect, $ \psi (G, w)= \alpha (G, w) $, while $ \psi_1 (G, w) =\alpha (G, w) $ for $ t $- or $ W_p $-perfect graphs. Based on the graph classes that were singled out, a technique is demonstrated, which enables us to form new classes of graphs for which polynomial solvability of the Maximum Weighted Independent Set problem is preserved. Thus, by an example of the Maximum Weighted Independent Set problem in a graph, it is shown how the Lagrangian bounds’ technique can be applied to solving an issue of single outing new classes of polynomial solvable combinatorial optimization problems. This approach can be used for improving known bounds of the objective function in combinatorial optimization problems as well as for justifying their polynomial solvability.

Schur Complement-based Substructuring of Stiff Multibody Systems with Contact

Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

Some methods for identifying redundant constraints in linear programming

Linear programming problems consist of two parts are objective function and inequality constraints. A redundant constraint is a constraint that does not change the feasible region. There are many methods for detecting redundant constraint. The methods for identifying redundant constraints which in the process only uses the objective function and inequality constraints, among others, Heuristic method, Llewellyn method, and Stojkovic-Stanimirovic methods. Heuristic method cannot identify weakly redundant constraints as redundant constraints. Llewellyn method comparing two constraints. Stojkovic-Stanimirovic depend on objective function. In this paper, we give some examples to recognize characteristics of these methods.

Modified Stojkovic-Stanimirovic method to find redundant constrains in linear programming problems

Important techniques in linear programming are modeling and solving practical optimization. A redundant constraint is a constraint that can be remove from a system of linear constraints without changing the feasible region. Method for identifying redundant constraints which in the process only uses the objective function and inequality constraints, i.e., Stojkovic-Stanimirovic method. In this paper we give a modified method of Stojkovic-Stanimirovic method to detect redundant constraints in linear programming problems. The advantages of employing the propose method is still to use the different objective function on linear programming associated the same feasible set have the same result. To clarify these method is given an example cannot be solve using detect Stojkovic-Stanimirovic method but can be solve using propose method.