An efficient BE iterative-solver-based substructuring algorithm for 3D time-harmonic problems in elastodynamics

This work is concerned with the development of an efficient and general algorithm to solve frequency-domain problems modelled by the boundary element method based on a sub-region technique. A specific feature of the algorithm discussed here is that the global sparse matrix of the coupled system is implicitly considered, i.e. problem quantities are not condensed into interface variables. The proposed algorithm requires that only the block matrices with non-zero complex-valued coefficients be stored and manipulated during the analysis process. In addition, the efficiency of the technique presented is improved by using iterative solvers. The good performance of pre-conditioned iterative solvers for systems of equations having real-valued coefficients, well demonstrated in the literature, is confirmed for the present case where the system matrix coefficients are complex. The efficiency of the algorithm described here is verified by analysing a soil–machine foundation interaction problem. CPU time and accuracy are the parameters used for estimating the computational efficiency.     

Lot sizing algorithms with applications to engineering and economics

This paper presents two new solution procedures for a deterministic lot size problem, a matrix algorithm and a heuristic matrix method. The algorithm is based on the dual of a linear programming model formulation of the lot size problem, and it provides optimal solutions even in the general case of time-varying parameters. A comparison of the efficiency of the new solution procedures with well-known methods is developed. New applications of the techniques described within the fields of engineering (optimal design of a pump-pipe system) and economics (a model for import-planning) are referred to.     

非比例阻尼结构参数识别算法的研究

在地下结构的地震响应中,无限地基的辐射阻尼起着重要的影响,然而其阻尼形式同结构的比例阻尼假定不同。同样,对于施加隔振、减震措施的建筑结构,其系统阻尼也不再满足比例阻尼假定,在结构参数识别中将阻尼阵假定为与刚度阵形式相似的方法不能反映实际结构参数。从研究结构的阻尼模型发发,引入了节点堆积阻尼,这样形成的阻尼与刚度、质量既有一定的联系,又有一定的独立性。以剪切型结构为例对此做了详细说明,结果表明,引入堆积阻尼后,进行参数识别的结构动力学方程是一个非线性识别问题,在此基础上提出了基于最小二乘平均的非线性迭代识别算法。     

Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

This article presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a ‘hybrid’ Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its efficacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested on the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the hybrid Bernstein global optimization algorithm delivers satisfactory performance in terms of solution optimality.     

LFTB: An Efficient Algorithm to Bound Linear Fractional Transformations

This work presents an efficient algorithm to solve a structured semidefinite program (SDP) with important applications in the analysis of uncertain linear systems. The solution to this particular SDP gives an upper bound for the maximum singular value of a multidimensional rational matrix function, or linear fractional transformation, over a box of n real parameters. The proposed algorithm is based on a known method for solving semidefinite programs. The key features of the algorithm are low memory requirements, low cost per iteration, and efficient adaptive rules to update algorithm parameters. Proper utilization of the structure of the semidefinite program under consideration leads to an algorithm that reduced the cost per iteration and memory requirements of existing general-purpose SDP solvers by a factor of O(n). Thus, the algorithm in this paper achieves substantial savings in computing resources for problems with a large number of parameters. Additional savings are obtained when the problem data includes block-circulant matrices as is the case in the analysis of uncertain mechanical structures with spatial symmetry.     

Internal variable formulations of elastic-plastic dynamic problems

The paper reviews work that has been carried out in recent years in the Centre for Research in Computational and Applied Mechanics (CERECAM) at the University of Cape Town on the compact internal variable formulation of the problem of an elastic-plastic body subject to incremental loading. The fundamental problem is expressed as a convex nonlinear programming problem. The simplest two step algorithm for the solution of this programming problem is shown to be the standard Newton-Raphson algorithm, and the formulation permits a discussion of the convergence of the iterative solution procedure. It is shown that this static formulation is readily extended to include inertia and linear damping terms, leading to an identical basic formulation in which the stiffness matrix and the residual are redefined for the dynamic problem. The static problem, and hence any software written for its solution, can thus be simply modified to include dynamic effects. The essential analogy between the static and dynamic problems was first presented as a master's thesis (R.D. Isted, 1988); subsequently there have been a number of additional contributions to the basic formulation for static problems, in which the internal variable framework was extended and clarified. Further contributions have also been made in respect of the dynamic problem, and these developments are summarised. Some of this later work has been directed at improvements in the implicit solution algorithms. These aspects will not be discussed in detail, however, the main purpose of this review is to demonstrate the formal relationship between the static and dynamic problems.     

SSP algorithm for linear and non-linear dynamic response simulation

A direct integration algorithm to solve the spatially discretized equations of motion of a structure is proposed. This algorithm formulates the equations of motion in state space and uses their analytical solution to derive a recursive discrete-time equation. The proposed structural state procedure (SSP) can be considered as a generalization for multi-degree-of-freedom systems of the Duhamel's integral used for single-degree-of-freedom systems. It can be noted that the proposed SSP algorithm does not need a previous modal uncoupling of the equations of motion and consequently it does not require any hypothesis about damping. SSP is shown to be stable and to give accurate results with a reasonable computation time. Stability and accuracy essentially depend on the computation of the system matrix. The SSP algorithm is combined with an iterative scheme to obtain the response of structures with non-linear behaviour. Two examples of application of SSP are included: seismic response of a building structure with linear behaviour and free vibration of a non-linear system with imposed initial conditions.     

A new boundary element formulation for wave load analysis

A new boundary element (BEM) formulation is proposed for wave load analysis of submerged or floating bodies. The presented formulation, through establishing an impedance relation, permits the evaluation of the hydrodynamic coefficients (added mass and damping coefficients) and the coefficients of wave exciting forces systematically in terms of system matrices of BEM without solving any special problem, such as, unit velocity or unit excitation problem. It also eliminates the need for scattering analysis in the evaluation of wave exciting forces. The imaginary and real parts of impedance matrix give, respectively, added mass and damping matrices whose elements describe the fluid resistance against the motion of the body. The formulation is explained through the use of a simple fluid-solid system under wave excitations, which involves a uniform fluid layer containing a solid cylindrical body. In the formulation, the solid body is taken first as deformable, then, it is specialized when it is rigid. The validity of the proposed method is verified by comparing its result with those available in literature for rigid submerged or floating bodies.     

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.     

Evaluation of added mass by a cloning algorithm

In problems of structure interaction with infinite surrounding of incompressible, inviscid fluid media, added mass matrices on wet surfaces have been considered for modelling the effects of outgoing waves. For an arbitrary geometry of the wet surface, an expression for the added mass matrix is derived according to a finite element procedure which utilizes the force-displacement relations of representative elements on the boundary. In the element mass matrix a certain symmetry, which characterizes interactions between the interior and exterior surfaces, helps reduce the quadratic matrix equation of the cloning algorithm to a linear eigenvalue problem. A benchmark example is included to establish the numerical accuracy of the proposed formulation.     

子空间预测控制算法在主动噪声振动中的应用

为解决主动噪声和振动控制中的执行器饱和约束条件问题,本文在子空间系统辨识的基础上,研究了一种新颖的子空间预测控制方法。该控制方法联合了系统辨识和控制器设计,直接由输入-输出数据得到将来时刻的输出预测值,自动校正系统中的参数,克服了传统的模型预测控制中繁琐的系统辨识环节。同时子空间预测控制允许执行器机构出现饱和现象,在考虑由饱和现象导致的约束条件时,利用线性矩阵不等式将约束优化问题转化为无约束优化问题。采用椭球优化算法迭代地产生一系列体积逐渐减小的椭球序列,该序列最终能收敛到一个最优解。在椭球算法的基础上推导了该算法达到收敛时所需要迭代次数的一个上界。这在智能优化算法中是很难求得到的。最后以直升机悬停状态时发生的颤振为例,利用本文中的子空间预测控制和椭球优化算法设计闭环系统的反馈控制器,验证闭环系统的输出响应能较好地跟踪期望值,从而得出本文方法的有效性。     

On the equivalence of dynamic relaxation and the Newton‐Raphson method

Dynamic relaxation is an iterative method to solve nonlinear systems of equations, which is frequently used for form finding and analysis of structures that undergo large displacements. It is based on the solution of a fictitious dynamic problem where the vibrations of the structure are traced by means of a time integration scheme until a static equilibrium is reached. Fictitious values are used for the mass and damping parameters. Heuristic rules exist to determine these values in such a way that the time integration procedure converges rapidly without becoming unstable. Central to these heuristic rules is the assumption that the highest convergence rate is achieved when the ratio of the highest and lowest eigenfrequency of the structure is minimal. This short communication shows that all eigenfrequencies become identical when a fictitious mass matrix proportional to the stiffness matrix is used. If, in addition, specific values are used for the fictitious damping parameters and the time integration step, the dynamic relaxation method becomes completely equivalent to the Newton‐Raphson method. The Newton‐Raphson method can therefore be regarded as a specific form of dynamic relaxation. This insight may help to interpret and improve nonlinear solvers based on dynamic relaxation and/or the Newton‐Raphson method.     

Probability and Random Processes for Electrical Engineering

This article considers deterministic computer experiments with real-valued tuning parameters which determine the accuracy of the numerical algorithm. A prominent example is finite-element analysis with its mesh density as the tuning parameter. The aim of this work is to integrate computer outputs with different tuning parameters. Novel nonstationary Gaussian process models are proposed to establish a framework consistent with the results in numerical analysis. Numerical studies show the advantages of the proposed method over existing methods. The methodology is illustrated with a problem in casting simulation. Supplementary material for this article is available online.     

Scheduling dynamically positioned tankers for offshore oil offloading

The operation of offshore oil fields entails transferring oil that accumulates in Floating Production Storage and Offloading Units to onshore terminals. To this end, a fleet of dynamically positioned tankers is deployed for transferring oil from large oil fields, which should be scheduled to meet operational constraints while minimising costs and economic losses. This work presents a mixed-integer linear programming (MILP) formulation for the problem of scheduling shuttle tankers that accounts for the essential constraints. Combined with an MILP solver, the model serves as a decision support tool to guide engineers in daily operations. A family of valid inequalities is proposed to strengthen the MILP formulation and reduce solving time with state-of-the-art solvers. Computational results are also reported on the application of the proposed model in tandem with a rolling horizon strategy.     

Neural networks for adaptive control coordination of PSSs and FACTS devices in multimachine power system

The paper develops a new design procedure for online control coordination which leads to adaptive power system stabilisers (PSSs) and/or supplementary damping controllers of flexible ac transmission system (FACTS) devices for enhancing the stability of the electromechanical modes in a multimachine power system. The controller parameters are adaptive to the changes in system operating condition and/or configuration. Central to the design is the use of a neural network synthesised to give in its output layer the optimal controller parameters adaptive to system operating condition and configuration. A novel feature of the neural-adaptive controller is that of representing the system configuration by a reduced nodal impedance matrix which is input to the neural network. Only power network nodes with direct connections to generators and FACTS devices are retained in the reduced nodal impedance matrix. The system operating condition is represented in terms of the measured generator power loadings, which are also input to the neural network. For a representative power system, the neural network is trained and tested for a wide range of credible operating conditions and contingencies. Both eigenvalue calculations and time-domain simulations are used in the testing and verification of the dynamic performance of the neural-adaptive controller.     

Sparse hierarchical solvers with guaranteed convergence

Solving sparse linear systems from discretized partial differential equations is challenging. Direct solvers have, in many cases, quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and efficient. Approximate factorization preconditioners such as incomplete LU factorization provide cheap approximations to the system matrix. However, even a highly accurate preconditioner may have deteriorating performance when the condition number of the system matrix increases. By increasing the accuracy on low-frequency errors, we propose a novel hierarchical solver with improved robustness with respect to the condition number of the linear system. This solver retains the linear computational cost and memory footprint of the original algorithm.     

Optimisation-based control coordination of PSSs and FACTS devices for optimal oscillations damping in multi-machine power system

An optimal procedure for designing co-ordinated controllers of power system stabiliser and flexible ac transmission system devices is developed for achieving and enhancing small-disturbance stability in multi-machine power systems. A constrained optimisation approach is applied for minimising an objective function formed from selected eigenvalues of the power systems state matrix. The eigenvalue-eigenvector equations associated with the selected modes form a set of equality constraints in the optimisation. There is no need for any standard eigenvalue calculation routines, and the use of sparse Jacobian matrix in the case of large system for forming the eigenvalue-eigenvector equations leads to the sparsity formulation. Inequality constraints include those for imposing bounds on the controller parameters. Constraints which guarantee that the modes are distinct ones are derived and incorporated in the control coordination formulation using the property that eigenvectors associated with distinct modes are linearly independent. The robustness of the controllers is achieved very directly through extending the sets of equality constraints and inequality constraints in relation to selected eigenvalues and eigenvectors associated with the state matrices of power systems with loading conditions and/or network configurations different from that of the base case. Simulation results of a multi-machine power system confirm that the procedure is effective in designing controllers that guarantee and enhance the power system small-disturbance stability.     

Modified Damping Scheduling Proximate Time Optimal Servomechanism for Improvements in Short Strokes in Hard Disk Drives

Proximate time-optimal servomechanism (PTOS) has been widely used as a point-to-point motion control algorithm in many control systems, especially in hard disk drives, because of its simplicity and good performance. A great deal of research for improving PTOS has been reported; however, most of it is complex or needs a time-consuming tuning process. Damping scheduling PTOS (DSPTOS), which maintained the simplicity of PTOS and showed faster settling in long strokes by scheduling a closed-loop damping coefficient, was proposed previously. In this paper, we propose a modified DSPTOS which can schedule a closed-loop damping coefficient not only in long strokes, but also in short strokes. The proposed algorithm improves seek and settling performances significantly in short strokes. The effectiveness of the proposed algorithm is verified through simulations and real-time experiments. Consequently, we achieved over a 25% settling time improvement for a short stroke (10 tracks).     

Nonstationary random vibrations of yielding multi-degree-of-freedom systems: Method of effective envelope functions

Summary This paper is concerned with non-stationary random vibrations of yielding shear-wall buildings approximated by multi-degree-of-freedom elastic-plastic oscillators in the plastic hinge model. The initial strain formulation of plasticity is applied to render a linear system under effective and updated non-stationary random loading: Noting the complete analogy to a linear system driven by the earthquake excited ground acceleration as well as by the nonlinear drift processes, the excitation of the totally associated linear problem is alternated by assuming the power spectral density of the input to be given in the form of an effective envelope function including frequency dependence. This fictitious evolutionary excitation of the linear system with fixed stiffness and damping behaviour is taken into account using a time-stepping procedure.With 6 Figures     

A network flow algorithm for optimal resource allocation

This paper introduces a network flow method for manpower scheduling and resource allocation. The network formulation of the problem permits the development of an algorithm that determines the minimal flow of resources through the network. The method presented here corresponds to the Simplex method, for in both methods the value of the objective function is optimized while the capacity limitations are preserved. The procedure proposed here, however, uses a more economical problem representation and is computationally more efficient. The efficacy of the minimal flow algorithm and its use is illustrated for a production system but the applicability of the procedure is sufficiently broad for it to work in other problem situations just as well.