Slope Constraints Research Articles

Emergence of capacity withholding: an agent-based simulation of a double price cap electricity market

This study analyses a double price cap electricity market using agent-based simulation and investigates the emergence of capacity withholding, the tacit collusion behind it and its effects on market outcomes. In the context of the infinitely repeated game paradigm, the authors try to demonstrate the link between market design and tacit collusion that allows firms to behave strategically, resulting in a deterioration of economic efficiency. An optimal control problem is embedded in the supply function equilibrium (SFE) modelling framework. A feature of this method is to provide firms with a tool that is capable of bidding supply curves with vertical segments. They are then prepared to deal with slope constraints imposed by the SFE modelling. A simulation using the generation portfolio of the Iranian electricity industry illuminates the nature of tacit collusion and capacity withholding.

Applying slope constrained Q-type aspheres to develop higher performance lenses

It has recently been shown that the coefficients that specify the aspheric departure from a spherical surface in high NA lithographic lenses routinely require more significant digits than are available in even double precision computers when they are described as part of a power series in aperture-squared. The Q-type aspheric description has been introduced to solve this problem. An important by-product of this new surface description is that it allows the slope of a surface to be directly constrained during optimization. Results show that Q-type aspheric surfaces that are optimized with slope constraints are not only more testable, an original motivation, but, they can also lead to solutions that are less sensitive to assembly induced misalignments for lithographic quality lenses. Specifically, for a representative NA 0.75 lens, the sensitivity to tilt and decenter is reduced by more than 3X, resulting in significantly higher lens performance in-use.

Duality results for stationary problems of open pit mine planning in a continuous function framework

Open Pit Mine Planning problems are usually considered in a Mixed Integer Programming context. Characterizing each attainable profile by a continuous function yields a continuous framework. It allows for a more detailed modeling of slope constraints and other material properties of slanted layers. Although the resulting nonlinear programming problems are in general non-convex and non-differentiable, they provide certain advantages as one can directly compute sensitivities of optimal solutions w.r.t. small data perturbations. In this work duality results are derived for the stationary problems of the continuous framework employing an additional condition called convex-likeness.

A continuous framework for open pit mine planning

This paper proposes a new mathematical framework for the open pit mine planning problem, based on continuous functional analysis. The main challenge for engineers is to determine a sequence of nested profiles maximizing the net present value of the mining operation. The traditional models for this problem have been constructed by using binary decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming problems. Instead, we use a continuous approach which allows for a refined imposition of slope constraints associated with geotechnical stability. The framework introduced here is posed in a suitable functional space, essentially the real-valued functions that are Lipschitz continuous on a given two dimensional bounded region. We derive existence results and investigate qualitative properties of the solutions.

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov–Krasovskii functional

In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities (LMIs) by constructing new Lyapunov–Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.

A note on: Spline technique for modeling roadway profile to minimize earthwork cost

The gap constraint used in A. A. Moreb, Spline technique for modeling roadway profile to minimize earthwork cost, J. Ind. Man. & Opt., 5 (2) (2009), 275-283 introduces unnecessary errors, while the slope constraint may be violated for second- and higher-order splines. In this note we amend the gap constraint, while maintaining the linearity of the model. We also present an improved slope constraint for linear and quadratic splines, and show that it becomes nonlinear for cubic and higher order splines. The improvements also apply to A. Moreb, M. Aljohani, Quadratic representation for roadway profile that minimizes earthwork cost, J. Sys. Sci. & Sys. Eng., 13 (2) (2004), 245-252.

Strain and electric field modulation of the electronic structure of bilayer graphene

We study how the electronic structure of the bilayer graphene (BLG) is changed by electric field and strain from ab initio density-functional calculations using the linear muffin-tin orbital and the linear augmented plane wave methods. Both hexagonal and Bernal stacked structures are considered. We only consider interplanar strain where only the interlayer spacing is changed. The BLG is a zero-gap semiconductor like the isolated layer of graphene. We find that while strain alone does not produce a gap in the BLG, an electric field does so in the Bernal structure but not in the hexagonal structure. The topology of the bands leads to Dirac circles with linear dispersion in the case of the hexagonally stacked BLG due to the interpenetration of the Dirac cones, while for the Bernal stacking, the dispersion is quadratic. The size of the Dirac circle increases with the applied electric field, leading to an interesting way of controlling the Fermi surface. The external electric field is screened due to polarization charges between the layers, leading to a reduced size of the band gap and the Dirac circle. The screening is substantial in both cases and diverges for the Bernal structure for small fields as has been noted by earlier authors. As a biproduct of this work, we present the tight-binding parameters for the free-standing single layer graphene as obtained by fitting to the density-functional bands, both with and without the slope constraint for the Dirac cone and keeping the hopping integral up to four near neighbors.

A parameter free Continuous Ant Colony Optimization Algorithm for the optimal design of storm sewer networks: Constrained and unconstrained approach

This paper describes the application of the newly introduced Continuous Ant Colony Optimization Algorithm (CACOA) to optimal design of sewer networks. Two alternative approaches to implement the algorithm is presented and applied to a storm sewer network in which the nodal elevations of the network are considered as the decision variables of the optimization problem. In the first and unconstrained approach, a Gaussian probability density function is used to represent the pheromone concentration over the allowable range of each decision variable. The pheromone concentration function is used by each ant to randomly sample the nodal elevations of the trial networks. This method, however, will lead to solutions which may be infeasible regarding some or all of the constraints of the problem and in particular the minimum slope constraint. In the second and constrained approach, known value of the elevation at downstream node of a pipe is used to define new bounds on the elevation of the upstream node satisfying the explicit constraints on the pipe slopes. Two alternative formulations of the constrained algorithm are used to solve a test example and the results are presented and compared with those of unconstrained approach. The methods are shown to be very effective in locating the optimal solution and efficient in terms of the convergence characteristics of the resulting algorithms. The proposed algorithms are also found to be relatively insensitive to the initial colony and size of the colony used compared to the original algorithm.

Speech confusion index (Φ): A confusion-based speech quality indicator and recognition rate prediction for dysarthria

This paper presents an automated method to help us assess the speech quality of a dysarthric speaker, in place of laborious and subjective manual methods. The assessment result can be used as a good indicator for predicting the accuracy of speech recognition. The so-called speech confusion index ( Φ ) is proposed to measure the speech disorder severity of a speaker in terms of how easily his/her speech signal may be misrecognized to other unintended words. Based on signal processing without any high-level information, the dynamic-time-warping technique incorporated with adaptive slope constraint and accumulative mismatch score is used to measure a distance between any two speech signals of a same word or two different words. Compared to the articulatory and intelligibility tests, the proposed indicator was shown to have more predictability on the recognition rates obtained from the Hidden Markov Model (HMM) and Artificial Neural Networks (ANN). Based on three evaluation criteria, namely root-mean-square difference, correlation coefficient and rank-order inconsistency, the experimental results on a phoneme-balance set showed that Φ achieved better prediction than both articulatory and intelligibility tests. Another experiment on a reduced training set is made to investigate the robustness of the proposed indicator. Finally, a detailed analysis of speech confusion is done at the phoneme level.

Active Control of a Beam for Generating Points of Zero Displacements and Zero Slopes

Piezoelectric transducers have been used extensively as the distributed actuators and sensors in active control of structural vibrations. Piezoelectric actuator/sensors are distributively bonded on or embedded in the host structure and have the inherent advantage of integrating over their surface area, which leads to potentially more robust implementations as compared to implementations that use shaker/accelerometers. For this reason piezoelectric actuator/sensors have attracted more and more attention in recent years. In this paper, a theoretical analysis is presented of the active control of a vibrating beam using collocated triangular and rectangular piezoelectric actuator/sensor pairs. The aim of this study is to generate points of zero displacements and zero slopes at any designated position. So the control systems impose a virtual clamped boundary condition at the control position on the beam, in which both displacement and slope are driven to zero. Two independent single-input single-output (SISO) control systems similar to direct velocity feedback (DVFB) are implemented, i.e. for the rectangular pair the voltage signal measured by a triangular piezoelectric sensor is electronically multiplied by a fixed gain and fed directly back to a collocated piezoelectric actuator. The triangular and rectangular piezoelectric actuator/ sensor pairs positioned at one end of the beam are used to measure and control the displacement and slope of the structure respectively. The active control systems are unconditionally stable for any type of primary disturbance acting on the structure due to the collocated actuator/sensors. It should be noted that the presented control strategy is different to DVFB. In DVFB, when the control gain is increased, the vibration energy of the beam is initially reduced at resonance frequencies because of the active damping effect. However this effect does not continue. When large control gains are implemented, the overall kinetic energy of the beam is increased to the same or even higher values than those of the beam without control systems because the vibration of the beam is rearranged into a new set of lightly damped resonance frequencies. Imposing a virtual clamped boundary condition at the control position is clearly more complicated than DVFB, because in addition to the zero displacement constraints, the zero slope constraints must also be satisfied. The proposed control system allows for certain points of the structure to remain stationary without using any rigid supports. Furthermore, such control systems have the potential to create a region of nearly zero vibration for any ‘excitation’ frequency. This means that no progressive waves or reflected waves exist in the designated region, thus significantly reducing the vibration level in that region of the beam. The control systems impose a virtual clamped boundary condition at the control position on the beam in which the displacement and slope are driven to zero. As a result, the vibration of the actively controlled beam can be described in terms of two beams clamped at the control position. A numerical analysis is then performed to verify the proposed control system. It is found that the new resonance frequencies and mode shapes seen in the simulations are consistent with the natural frequencies and natural modes of the controlled beam derived analytically. The capability of the proposed method for generating a zero-vibration region is also numerically demonstrated.

Partially constrained ant colony optimization algorithm for the solution of constrained optimization problems: Application to storm water network design

This paper exploits the unique feature of the Ant Colony Optimization Algorithm (ACOA), namely incremental solution building mechanism, to develop partially constraint ACO algorithms for the solution of optimization problems with explicit constraints. The method is based on the provision of a tabu list for each ant at each decision point of the problem so that some constraints of the problem are satisfied. The application of the method to the problem of storm water network design is formulated and presented. The network nodes are considered as the decision points and the nodal elevations of the network are used as the decision variables of the optimization problem. Two partially constrained ACO algorithms are formulated and applied to a benchmark example of storm water network design and the results are compared with those of the original unconstrained algorithm and existing methods. In the first algorithm the positive slope constraints are satisfied explicitly and the rest are satisfied by using the penalty method while in the second one the satisfaction of constraints regarding the maximum ratio of flow depth to the diameter are also achieved explicitly via the tabu list. The method is shown to be very effective and efficient in locating the optimal solutions and in terms of the convergence characteristics of the resulting ACO algorithms. The proposed algorithms are also shown to be relatively insensitive to the initial colony used compared to the original algorithm. Furthermore, the method proves itself capable of finding an optimal or near-optimal solution, independent of the discretisation level and the size of the colony used.

Modelling the driving forces of Sydney's urban development (1971-1996) in a cellular environment

This paper demonstrates a flexible implementation of rules to control the simulation of urban development of Sydney from 1971 to 1996 using a cellular automata model. Five key factors, including the self propensity for development and neighbourhood support, slope constraint, transportation support, terrain and coastal proximity attractions and urban planning support are introduced into the model in a spatially explicit format, which generated a realistic estimation of the extent and timing of Sydney’s urban development. With the flexibility of rule implementation within the model, more rules can be added as new ‘If-Then’ statements to fine-tune the model, provided that a good understanding of the rule is maintained and accurate data are collected.

Fundamental tree algorithm in optimising production scheduling for open pit mine design

Mathematical programming models are well suited to optimising long-term production scheduling of open pit mine designs; however, it is not possible in most cases to solve the scheduling problem as a mathematical programming model because the number of integer variables required becomes too large. New methods are required that will reconstruct the mining blocks and decrease the number of integer variables in scheduling without reducing the resolution of the model or optimality of the results. The fundamental tree algorithm proposed herein addresses this issue effectively. A fundamental tree is defined as any combination of blocks such that the blocks can be profitably mined, the blocks obey the slope constraints, and the chosen blocks do not have a proper subset that meets the first two conditions. A set of linear programming (LP) formulations is developed to find a set of fundamental trees (FTs) that exist for a given mine deposit. It is shown in this paper that the LP model generates FTs with the defined properties. The proposed method is illustrated in optimisation of the long-term production schedule of a multi-element large open pit copper deposit in Peru, South America. The results show that after generating FTs, the mixed integer programming (MIP) model can be used to optimise large open pit mines. The case study presented shows the financial benefits of the capabilities of MIP to consider multiprocessors and multi-elements in mine optimisation.

Analysis and enhancements to piecewise linear comparametric image registration

This correspondence details enhancements to previous work on piecewise linear comparametric image registration. The enhancements come in the form of slope constraints and knots' location selection in the comparametric modeling. An analysis of the properties of comparametric functions leads to two general slope constraints that, along with a knot location selection based on the reference image's pixel value distribution, serves to reduce error and sensitivity to the number of segments considered as well as allow for the solution to cases in which there are gaps in the comparagram. Results on real images are presented.

Correlation optimized warping and dynamic time warping as preprocessing methods for chromatographic data

AbstractTwo different algorithms for time‐alignment as a preprocessing step in linear factor models are studied. Correlation optimized warping and dynamic time warping are both presented in the literature as methods that can eliminate shift‐related artifacts from measurements by correcting a sample vector towards a reference. In this study both the theoretical properties and the practical implications of using signal warping as preprocessing for chromatographic data are investigated. The connection between the two algorithms is also discussed. The findings are illustrated by means of a case study of principal component analysis on a real data set, including manifest retention time artifacts, of extracts from coffee samples stored under different packaging conditions for varying storage times. We concluded that for the data presented here dynamic time warping with rigid slope constraints and correlation optimized warping are superior to unconstrained dynamic time warping; both considerably simplify interpretation of the factor model results. Unconstrained dynamic time warping was found to be too flexible for this chromatographic data set, resulting in an overcompensation of the observed shifts and suggesting the unsuitability of this preprocessing method for this type of signals. Copyright © 2004 John Wiley & Sons, Ltd.

Land Capability Assessment and Estimation of Pastoral Potential of Semiarid Rangeland in South Australia

An Environmental Resource Assessment and Management System (ERAMS), a computer-aided decision support system developed for determination of present and potential pastoral productivity of arid and semiarid regions, was used in this study on rangelands that have been cropped or grazed by sheep or both for 150 years. ERAMS determines productivity of mapped land units on the basis of soil-water availability. This in turn is dependent on annual rainfall, slope, soil depth, salinity, and physical and chemical constraints. Stock carrying capacity is dependent on vegetation type and condition, based on foliage cover and botanical composition, and nutritive value of the pasture. Physical and biological features are determined by field survey. ERAMS has been used to examine the likely impacts of management strategies that alter either the vegetation type, vegetation state, or degree of erosion. Six Land Capability classes were derived from combinations of rainfall, slope, soil depth, and salinity. Total dry matter production was calculated and ranged from 58 kg−1 ha−1 to 1980 kg−1 ha−1 Rainfall use efficiency (kg−1 ha−1 of total dry matter mm−1 of mean annual rainfall) ranged from 3.05 to 4.07. Comparison of present and potential production indicates the likely benefits of programs designed to increase carrying capacity through improved vegetation cover and land stability.

온라인 서명자동인식을 위한 개선된 DTW

Dynamic Programming Matching(DPM)은 순차적으로 구성된 문제를 수학적으로 최적화 시키는 기술로서 패턴인식 분야에서 다년간 중요한 역할을 해왔다. 서명인식을 위한 대부분의 실제적 적용에서는 Sakoe and Chiba [9]의 실제구현 버전이 기반이 되어 왔는데, 일반적으로 slope constraint p = 0의 방법이 적용되어 왔다. 이 논문에서는 이 경우에는 전진탐색에 의한 휴리스틱한 방법을 적용한 MDPM이 상당한 처리 시간의 단축 뿐만 아니라 약간의 인식능력 향상을 가질 수 있음을 보여준다. Dynamic Programming Matching (DPM) is a mathematical optimization technique for sequentially structured problems, which has, over the years, played a major role in providing primary algorithms in pattern recognition fields. Most practical applications of this method in signature verification have been based on the practical implementational version proposed by Sakoe and Chiba [9], and is usually applied as a case of slope constraint p = 0. We found, in this case, a modified version of DPM by applying a heuristic (forward seeking) implementation is more efficient, offering significantly reduced processing complexity as well as slightly improved verification performance.

Constrained torsion of prismatic bars

A theory is developed that allows the determination of three-dimensional displacements and stresses within finite length prismatic bars of arbitrary cross-section experiencing restrained torsion. This restraint arises from the twisting of a bar where one of its cross-sections is subject to displacement and slope constraints. The deformations within this bar are represented by an exponentially decaying residual solution superimposed on the classical Saint-Venant solution. Galerkin's method is used to solve the boundary value problem resulting from a simultaneous system of three quadratic eigenproblems subject to the stress free boundary condition due to the traction-free lateral surface of the bar. A three-dimensional finite element model is used for validation.

Efficacy of Drilling Degrees of Freedom in the Finite Element Modeling of P-and SV-Wave Scattering Problems

ABSTRACTThis paper deals with a hybrid finite element method for wave scattering problems in infinite domains. Scattering of waves involving complex geometries, in conjunction with infinite domains is modeled by introducing a mathematical boundary within which a finite element representation is employed. On the mathematical boundary, the finite element representation is matched with a known analytical solution in the infinite domain in terms of fields and their derivatives. The derivative continuity is implemented by using a slope constraint. Drilling degrees of freedom at each node of the finite element model are introduced to make the numerical model more sensitive to the transverse component of the elastodynamic field. To verify the effects of drilling degrees freedom and slope constraints individually, reflection of normally incident P and SV waves on a traction free half space is considered. For P-wave incidence, the results indicate that the use of a slope constraint is more effective because it suppresses artificial reflection at the mathematical boundary. For the SV-wave case, the use of drilling degrees of freedom is effective in reducing numerical error at the irregular frequencies.

Stochastic-Optimization Annealing of an Intelligent Open Pit Mine Design

Optimized pit layouts are used to extract mineable reserves with minimum waste under geological, geotechnical and property boundary constraints and to develop strategic and tactical production plans for achieving corporate goals. Pit design and optimization algorithms are limited in dealing with the random field properties of these layouts resulting in sub-optimal results. Database changes require complete rerun of these algorithms resulting in long CPU times with no allowance for incorporating operating strategies. In this study, the authors develop an intelligent pit optimizer, IPOP, to solve these problems. It combines stochastic models of ore reserves and commodity prices to generate economic block and target values. The error backpropation algorithm is used to train the neural network for block pattern recognition and partitioning based on the target values. The PITSEARCH program is then used to search for the optimized layout under the pit slope constraints. Stochastic-optimization annealing is carried out to examine the random field properties of the optimized pit value. IPOP is used to optimize Section SBHP 860001 of the Sabi open pit in Zimbabwe, and the results are compared with that from the 2D Lerchs-Grossmann's algorithm. The two algorithms yield the same value of Z$3.58 million for the optimized Section SBHP 860001. In addition, IPOP provides analysts with the risks associated with the optimized value of this section with a reduced CPU time.