Dynamic Response Optimization Research Articles

Simultaneous topology and size optimization of a 3D variable-length structure described by the ALE–ANCF

An efficient optimization approach is proposed to simultaneously optimize the topology and geometrical sizes of a three-dimensional (3D) variable-length structure. First of all, in a unified global coordinate system, a flexible multibody system (FMBS) model is established to describe the extension and contraction dynamics of a variable-length structure. The variable-length flexible structure is meshed by the proposed arbitrary Lagrangian–Eulerian (ALE) solid elements of absolute nodal coordinate formulation (ANCF). To consider the variable-length behaviors, the classic equivalent static loads (ESL) is redefined by introducing the concept of virtual design domain. With the help of the ESL, the dynamic response optimization of the variable-length structure is turned into a static one. A simultaneous topology and size optimization approach is initially proposed via the moving morphable components (MMC). By appropriately arranging the initial configuration of the components and linking all or part of the design variables of a component with others’, the variable-length structure can be designed as a homogeneous or heterogeneous periodic structure. The approach is numerically implemented via an additional constraint that modifies the sensitivities with respect to some design variables. Finally, three numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed optimization approach.

A frequency domain dynamic response approach to optimize the dynamic performance of grinding machine spindles

The dynamic performance of the grinding machine spindle determines its ultimate vibration resistance and the machining accuracy. To gain better dynamic performance of the grinding machine spindle system, the integrated evaluation and optimization method should take both manufacturing process and machine tool into account. In this paper, a frequency domain dynamic response approach is proposed to study the optimization. This approach considers the dynamic grinding force from the view of spindle imbalance and frequency response function (FRF) by means of modal frequency and dynamic stiffness. The dynamic grinding force is analyzed experimentally to verify the vibration excitation force in process. Furthermore, the optimization process by finite element method is conducted with the intermediate dynamic parameter improvement by structural optimum design. Applying on a high-speed machine tool, the case studies are illustrated to demonstrate the implementation of the proposed method; the dynamic response optimization approach results shows, to achieve the vibration response in grinding process, it is necessary and priority to improve the dynamic stiffness of the spindle.

Optimization of the operation of a flywheel to support stability and reduce generation costs using a Multi-Contingency TSCOPF with nonlinear loads

Multi-Contingency Transient Stability Constrained Optimal Power Flow (MC-TSCOPF) models optimize the economic dispatch of power systems while ensuring their stability after a series of reference incidents. This paper proposes a MC-TSCOPF model that represents the power balance at each node of the system and at each sample time. The proposed model includes non-linear loads, synchronous generators, a windfarm, and a Flywheel Energy Storage system (FESS). The model is written on GAMS and solved using a standard Interior Point algorithm. This study focuses on the Fuerteventura-Lanzarote insular grid in Spain, where stability problems and load shedding cause high additional costs due to the low inertia of the system. A FESS has been recently installed in the system to improve its stability, taking advantage of its high-power capacity and rapid response. The proposed TSCOPF model has been applied to optimize the operation of the FESS to support stability in the event of a contingency. The results of the study show that 1) a proper model of non-linear loads is essential in TSCOPF studies; 2) the proposed MC-TSCOPF provides a tool for minimizing the generation costs while ensuring transient and frequency stability; and 3) it is possible to further reduce the generation costs by using the proposed model to calculate an optimal dynamic response of the FESS.

A design methodology for structural and control systems of a prosthetic leg

A design methodology is proposed to optimize a prosthetic leg considering the structural and control aspects. Previous studies mainly focused on each of a structural design problem or a control problem. The structural design variables of a prosthetic leg are determined in a structural design problem while the trajectory tracking based on the human gait cycle is found to be a control problem. The two problems have been separately solved. However, they should be simultaneously considered to obtain a better design. Then the problem would be nonlinear dynamic response optimization of structural and control systems. An optimization method was recently developed for a linear system of structural and control design problems using the equivalent static loads (ESLs). In this study, a design methodology for the prosthetic leg is presented by expanding the equivalent static loads method (ESLM) to nonlinear dynamic systems. A simple example is solved to validate the proposed methodology, and then a prosthetic leg is optimized to reduce the weight and energy consumption.

Efficient design optimization strategy for structural dynamic systems using a reduced basis method combined with an equivalent static load

This paper presents an efficient structural design optimization strategy that combines the reduced basis method (RBM) with the equivalent static load (ESL). In dynamic response optimization using ESL, the computation of a static system optimization is repeatedly executed under multiple static loads. In this process, we propose parametrizing the static system and employing the RBM with global proper orthogonal decomposition (POD). In general, the snapshots for the sampling procedure under multiple loads increase proportionally to the number of loads, which results in an inefficient computational procedure. Thus, we propose taking snapshots with a proper orthogonal mode (POM) of the multiple loads rather than for the multiple loads themselves. The number of snapshots then decreases, and the original system can be efficiently reduced. We directly employ the framework of the proposed RBM with the POM of multiple loads to ESL-based design optimization, and the results indicate that the proposed method is more efficient than conventional ESL-based optimization as well as a full order model. Various numerical examples, including comparisons of relative errors and the dynamic response optimizations, support the strength of the proposed strategy.

Design of curved composite panels for optimal dynamic response using lamination parameters

Abstract In this paper, dynamic response of composite panels is investigated using lamination parameters as design variables. Finite element analyses are performed to observe the individual and combined effects of different panel aspect ratios, curvatures and boundary conditions on the dynamic responses. Fundamental frequency contours for curved panels are obtained in lamination parameters domain and optimal points yielding maximum values are found. Subsequently, forced dynamic analyses are carried out to calculate equivalent radiated power (ERP) for the panels under harmonic pressure excitation. ERP contours at the maximum fundamental frequency are presented. Optimal lamination parameters providing minimum ERP are determined for different excitation frequencies and their effective frequency bands are shown. The relationship between the designs optimized for maximum fundamental frequency and minimum ERP responses is investigated to study the effectiveness of the frequency maximization technique. The results demonstrate the potential of using lamination parameters technique in the design of curved composite panels for optimal dynamic response and provide valuable insight on the effect of various design parameters.

Effect of Fe and Co doping on ethanol sensing property of powder-based ZnO nanostructures prepared by sol–gel method

Iron and cobalt doped zinc oxide were prepared by the sol–gel method. The doping concentration was varied between 5 and 10 wt.%. Structural and morphological features of the samples were investigated comparatively by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM) and Fourier transform infrared spectroscopy (FTIR). They were also placed in an electric circuit and their sensing characteristics toward ethanol vapors were studied. It was found that, the gas response was impressed by doping. The optimal operating temperature, dynamic response, sensitivity and response and recovery times of the samples have been measured. The operating temperature and the time of response and recovery of the sensor were generally reduced after doping. According to our results, by considering the time of rising/ falling, the doped samples have a relatively better status than pure zinc oxide sample and in particular, the sample with 10% cobalt doped (ZC10) had a competitive attitude compared to pure zinc oxide due to significant reduction in response/recovery times.

Optimization of dynamic mechanical response of a composite plate using multi-field coupling with thermal constraints

• Nonlinear PDE-constrained optimization multiphysics problem is considered. • Plate vibrations due to mechanical and electromagnetic loads are studied. • Optimal characteristics of an electromagnetic field minimizing vibrations are found. • Joule heating is controlled through introduction of a thermal constraint. We consider the problem of optimizing the dynamic response of a mechanically loaded, rectangular, electrically conductive anisotropic composite plate by applying an electromagnetic field, which exploits the electro-magneto-mechanical field coupling phenomenon. An important aspect of the formulated nonlinear partial differential equation (PDE)-constrained optimization model is the presence of a thermal constraint that prevents polymer matrix degradation in the composite material due to Joule heating produced by the electromagnetic field. A black-box optimization approach based on the active set algorithm is employed. A system of governing PDEs is solved using a series of sequential numerical procedures that includes the method of lines, Newmark time-stepping scheme, quasilinearization, integration of two-point boundary-value problems, and a superposition method followed by orthonormalization. Implementation in hyper-dual arithmetics facilitated automatic differentiation and computation of the gradient. Optimization results show that application of an electromagnetic field with optimal characteristics enables one to significantly reduce the amplitude of the plate vibrations while controlling for Joule heating.

The equivalent static loads method for structural optimization does not in general generate optimal designs

The Equivalent Static Loads Method (ESLM) is an algorithm intended for dynamic response structural optimization. The algorithm attempts to solve a sequence of static response structural optimization problems approximating the original problem. It is argued in several published articles that if the ESLM converges, then it finds a KKT point of the considered dynamic structural response optimization problem. The theoretical convergence properties of the ESLM are however not as strong as previously reported. We propose and analyze easily reproducible counter examples based on a two-bar truss illustrating that the ESLM in general fails in finding optimal designs to the considered dynamic response problem.

Dynamic response and mooring optimization of spar-type substructure under combined action of wind, wave, and current

Floating wind turbines (FWTs) have become the preferred structures to exploit offshore winds since a large part of the offshore wind resource is located in deep water zones. In the harsh marine environment, a spar-type substructure is the most promising substructure for FWTs with good structure stability and economic advantages. In this study, the surge, heave, and pitch motions of the spar-type substructure under combined action of wind, wave, and current are analyzed by using the AQWA module of ANSYS. Besides, the effects of different parameters, namely, the mooring line distribution form, fairlead position, and line number of mooring systems, on the spar-type substructure motion response are also investigated. Based on the calculation results, a new spar-type substructure with an optimized mooring system is put forward and analyzed. It can be found that both the dynamic response and the mooring tension of the new spar-type substructure are significantly improved relative to the non-optimized structure. The results of this paper could offer reference for further development of spar-type FWTs in real marine environments.

System-wise equivalent static loads for the design of flexible mechanisms

Structural optimization of flexible multibody systems (MBS) is a challenging design problem which has received increased attention in the last decade. The weakly coupled method is a powerful method to solve this design problem as it transforms the underlying dynamic response optimization problem into a static response optimization problem subject to multiple load cases. These load cases can be conveniently defined using the so-called Equivalent Static Load (ESL) method. With the usual ESL method, ESLs are defined at a component-level assuming that each component is isolated from the rest of the system. Thus, this method cannot account for design functions involving the global response of the system but it is restricted to optimization problems that are solely formulated in terms of local responses within the components. In order to get rid of this restriction, a system-wise extension of the ESL method is proposed. It is shown that the solutions of the equivalent static optimization problem and of the initial MBS optimization problem are equivalent and that the ESL formulation naturally leads to a weakly coupled solution algorithm. Standard benchmarks exemplify the proposed method.

Optimizing information processing in neuronal networks beyond critical states.

Critical dynamics have been postulated as an ideal regime for neuronal networks in the brain, considering optimal dynamic range and information processing. Herein, we focused on how information entropy encoded in spatiotemporal activity patterns may vary in critical networks. We employed branching process based models to investigate how entropy can be embedded in spatiotemporal patterns. We determined that the information capacity of critical networks may vary depending on the manipulation of microscopic parameters. Specifically, the mean number of connections governed the number of spatiotemporal patterns in the networks. These findings are compatible with those of the real neuronal networks observed in specific brain circuitries, where critical behavior is necessary for the optimal dynamic range response but the uncertainty provided by high entropy as coded by spatiotemporal patterns is not required. With this, we were able to reveal that information processing can be optimized in neuronal networks beyond critical states.

Fixed Switching Frequency Generalized Peak Current Control (GPCC) of DC–AC Converters

A fast and robust fixed switching frequency peak current controller for DC–AC converters is presented. The proposed method tends to mimic the switching behavior of pulse width modulation (PWM) techniques, so it features all the advantages of peak current controllers (such as simplicity, fast transient, and optimum dynamic response), with the superiority of fixed switching frequency and harmonic free output. The proposed method is a generalized approach that can be applied to different PWM schemes. The method is specifically elaborated for single-phase distributed generation applications, using various inverter topologies and mimicking different PWM schemes. Moreover, adaptive bands are proposed to provide active damping for the controller, to extend use of the proposed method for inverters with LCL output filters. Feasibility and performance of the controller is shown by means of simulations and experiments.

Multi-objective robust optimization design for powertrain mount system of electric vehicles

A multi-objective robust optimization scheme for the powertrain mount system of an electric vehicle is proposed in this paper. A permanent magnet synchronous motor model is established by taking account of the effects of magnetic saturation and space harmonics, in which the d–q-axis inductance and the flux linkage excited by permanent magnet were obtained by finite element method. The rippled output torque of the permanent magnet synchronous motor mixed with harmonic components is obtained with the New European Driving Cycle as the running condition of the electric vehicle. A six degree-of-freedoms (DOFs) powertrain mount system is established and the response of the system is obtained with the rippled torque as the excitation input. A multi-objective optimization model of the powertrain mount system is built with the stiffness’s of the mounts as the design variables, and with the goal of maximizing the decoupling rates and minimizing the dynamic reaction forces of the mounts acting on the car body. Genetic algorithm is used to conduct the global optimization and all the Pareto optimal solutions are found out based on the optimization theory, and the solution with the optimal robustness of dynamic reaction force is obtained by Latin hypercube sampling method. The results show that with the proposed multi-objective robust optimization scheme applied for the parameters optimization of the motor mount system, the decoupling rates increase obviously, the dynamic reaction force decreases apparently, and the optimization result shows good robustness. The optimization results can make the powertrain mount system of electric vehicles processing of optimal dynamic response characteristics correspondingly.

Infinite-time linear–quadratic optimal control of the BLDC motor exploiting a nonlinear finite element model

PurposeThis paper aims to present a nonlinear finite element model (FEM) of the Brushless DC (BLDC) motor and the application of the optimal linear–quadratic control-based method to determine the excitation voltage and current waveform considering the minimization of the energy injected to the input circuit and energy lost. The control problem is designed and analyzed using the feedback gain strategy for the infinite time horizon problem.Design/methodology/approachThe method exploits the distributed parameters, nonlinear FEM of the device. First, dynamic equations of the BLDC motor are transformed into a suitable form that makes an ARE (algebraic Riccati equation)-based control technique applicable. Moreover, in the controller design, a Bryson scaling method is used to obtain desirable properties of the closed-loop system. The numerical techniques for solving ARE with the gradient damping factor are proposed and described. Results for applied control strategy are obtained by simulations and compared with measurement.FindingsThe proposed control technique can ensure optimal dynamic response, small steady-state error and energy saving. The effectiveness of the proposed control strategy is verified via numerical simulation and experiment.Originality/valueThe authors introduced an innovative approach to the well-known control methodology and settled their research in the newest literature coverage for this issue.

On Path Oscillations Analysis of Mechanical Multi-body and Hydrostatical Driving Units Coupled System

This research deals with the path dynamics of the multi-body systems embedding hydrostatically actuating units. The main purpose of this analysis consists by an optimal dynamic response of the mechanic and hydraulic coupled ensemble, taking into account the characteristic requirements for the final path of the working tool. Theoretical background contains elements both for the multi-body dynamics of mechanical parts, and for the hydraulic driving systems. The forward analysis in terms of command – action connection, and the reverse analysis in terms of system response evaluation and actuating system control frame the main research problem of this study. A computational application developed within Matlab-SimScape software was provided, and a comparative analysis between simulation data and experimental test results was presented. A practical example was developed based on the excavating equipment with a single bucket.

Computational Dynamics of the Rotational Heavy Loads Mastered by Hydrostatical Driving Systems

This research deals with the transitory dynamics within the hydrostatical driving systems, for the case of rotational mechanical loads with the consistent moment of inertia. Optimal dynamic response of the mechanic and hydraulic coupled system is the main purpose of this study. Theoretical background provides elements both for the multi-body dynamics of mechanical parts, and for the hydraulic driving systems, with the common aspects in evaluation and control of the system response. Reducing the transitory phases, in the same time with diminishing of the primary power supply level, frame the goal of this study. The authors present a computational approach based on Matlab-SimScape© software implementations, which is able to provide both the analysis of different stages of load motion and actuating dynamics, and the evaluation of variable control techniques for driving system. Real data was used to verify the computer simulations. A comparative analysis of the results was provided and an errors evolution was estimated. The relevance of the model was underlined in case of simulations of different types and characteristics of rotational heavy-loads driven by hydrostatic systems. In addition, the model is useful within the hydraulic scheme optimization analysis and, also, for tuning of controlling algorithm of driving parameters according with required dynamic parameters at working body.

Topology optimization based on level set for a flexible multibody system modeled via ANCF

A topology optimization methodology is proposed for the flexible multibody system undergoing both large overall motion and large deformation. The system of concern is modeled via the absolute nodal coordinate formulation. The equivalent static load method is employed to transform the topology optimization of the nonlinear dynamic response of the system into a static one, and evaluated to adapt to the absolute nodal coordinate formulation by splitting the elastic deformations of the flexible components from the overall motions of those components. During the static topology optimization, the material interface is implicitly described as the zero level set of a higher-dimensional scalar function. Then, the semi-implicit level set method with the additive operator splitting algorithm is employed to solve the corresponding Hamilton-Jacobi partial differential equation. In addition, the expert evaluation method of weights based on the grey theory is utilized to define the objective function, and a modified augmented Lagrange multiplier method is proposed to treat the inequality volume constraint so as to avoid the oscillation and drift of the volume. Finally, two numerical examples are provided to validate the proposed methodology.

Structural optimization of flexible components in a flexible multibody system modeled via ANCF

The paper presents how to optimize the flexible components in a flexible multibody system undergoing both large overall motion and large deformation by using the Absolute Nodal Coordinate Formulation (ANCF) and the equivalent static load (ESL) method. Before the structural optimization, the flexible multibody system is modeled via ANCF first so as to describe the coupled overall motion and large deformation accurately. During the structural optimization, the elastic deformation of the flexible component to be optimized is split from the overall motion of the flexible component, and then the equivalent static loads are determined by using the ESL method such that the structural optimization of nonlinear dynamic response can be transformed into a static one. In addition, the nonlinear interior point method is adopted to solve the corresponding structural optimization problem of nonlinear static response. The paper gives three numerical examples to validate the above optimization procedure. The final example of optimizing the arms in a rigid-flexible grasping robot shows that the proposed optimization procedure enables one to deal with realistic engineering systems.

Study of the fractional order proportional integral controller for the permanent magnet synchronous motor based on the differential evolution algorithm

A tuning method of the fractional order proportional integral speed controller for a permanent magnet synchronous motor is proposed in this paper. Taking the combination of the integral of time and absolute error and the phase margin as the optimization index, the robustness specification as the constraint condition, the differential evolution algorithm is applied to search the optimal controller parameters. The dynamic response performance and robustness of the obtained optimal controller are verified by motor speed-tracking experiments on the motor speed control platform. Experimental results show that the proposed tuning method can enable the obtained control system to achieve both the optimal dynamic response performance and the robustness to gain variations.