Robust Design Method Research Articles

A robust optimization design method for sheet metal roll forming and its application in roll forming circular cross-section pipe

Sheet metal roll forming (SMRF) is affected by many factors, including forming speed, forming passes, roller diameter, and material properties. It is easy to produce quality defects, such as longitudinal bending, edge wave, and springback, which eventually lead to poor quality stability of SMRF. At present, SMRF design relies mainly on the experience of engineers and its technological parameters must be adjusted repeatedly through experiments, resulting in a long product design cycle and difficult quality stability control. This paper discusses a mathematical model for a robust optimization design for SMRF. Support vector machine (SVM) classification and support vector regression (SVR) are adopted to construct a model of the response surface and to separate feasible variables and infeasible variables. High-dimensional robust optimization problems in SMRF are solved. Using roll forming of a circular cross-section pipe as an example, the result shows that the roundness error standard deviation of the robust optimization design method is 62.2% less than the roundness error standard deviation of the deterministic optimization design method, along with significant improvement in reliability probability. The method is validated as effective in reducing quality defects, including longitudinal bending, edge wave, and springback. This robust optimization design method can improve the quality stability of SMRF.

Life-Cycle Optimization of a Chiller Plant with Quantified Analysis of Uncertainty and Reliability in Commercial Buildings

Conventional and most optimal design methods for chiller plants often address the annual cooling load distribution of buildings and their peak cooling loads based on typical meteorological year (TMY) data, while the peak cooling load only appears a few times during the life-cycle and the sized chiller plant usually operates within its low efficient region. In this paper, a robust optimal design method based on life-cycle total cost was employed to optimize the design of a chiller plant with quantified analysis of uncertainty and reliability. By using the proposed design method, the optimized chiller plant can operate at its highly efficient region under various cooling load conditions, and provide sufficient cooling capacity even alongside some equipment/systems with failures. The minimum life-cycle total cost, which consists of the capital cost, operation, and availability-risk cost, can be achieved through optimizing the total cooling capacity and the numbers/sizes of chillers. A case study was conducted to illustrate the detailed implementation process of the proposed method. The performance of this design method was evaluated by comparing with that of other design methods.

Robust optimization of aerodynamic loadings for airfoil inverse designs

For the modern design of more realistic aerodynamic shapes, disturbances caused by uncertain operating conditions must be conveniently considered, since they can affect significantly the performance of the designed systems. In this situation, the concept of robust design in conjunction with optimization tools is strongly recommended, since the interest is to maximize the performance and its robustness, simultaneously. Clearly, the great number of exact evaluations normally required to compute the robustness makes the robust optimization in aerodynamics computationally prohibitive, particularly when direct methods are chosen. To overcome this drawback, inverse methods appear as an interesting option, provided a robust aerodynamic loading can be furnished previously at low computational costs. However, few works have been dedicated to this subject in the open literature, which motivates the present study. The focus is to apply the robustness concept to optimize the velocity (or pressure) distributions for airfoil inverse designs, using a boundary layer method to predict the aerodynamic coefficients prior to the knowledge of the final airfoil shape. Here, the velocity distribution is parameterized using B-spline polygons with a set of control points, where the design variables are the ordinates of these points in the parameterization. The resulting robust multiobjective optimization problem involves the performance of the airfoil as a first objective function and its robustness introduced as additional objective to be optimized simultaneously. To illustrate the usefulness of the proposed robust design method, an example of drag minimization for an isolated airfoil is addressed and the aerodynamic coefficients for the optimal airfoils are compared with the corresponding obtained by experiments from the open literature.

Robust design method for mechanical characteristics of power turbine rotor structural system

Robust design method for mechanical characteristics of power turbine rotor structural system

Uncertainty Analysis and Robust Design for a Hybrid Rocket Upper Stage

An uncertainty analysis is performed for a hybrid rocket engine, and a robust design method is proposed and applied to a liquid-oxygen/paraffin–based fuel hybrid rocket engine that powers the third stage of a Vega-like launcher. An indirect method is used to optimize a mission-specific objective function, which takes into account both the payload mass and the ability of the rocket to reach the required final orbit despite uncertainties. First, a screening of uncertain model parameters is performed using the Morris method. The screening shows that three groups can be distinguished: parameters with negligible or no effect on model outputs, parameters with small linear effect on model outputs, and parameters with large nonlinear effect on model outputs. The robust optimization design process is then carried out by a particle swarm optimization algorithm considering only the uncertainties of the latter group, which includes six parameters. A fractional factorial design of experiment techniques is considered to characterize the robust performance index. Average launcher performance is considered and the best solution is found by means of Box–Behnken’s array. Finally, the identified robust solution is checked against the second group of parameters uncertainties previously neglected in the robust optimization procedure. The scattering of the robust solution is small, and the robustness of the selected optimal solution is confirmed.

Robust fixture design of compliant assembly process based on a support vector regression model

Fixtures are used to locate and clamp parts and subassemblies during the compliant assembly process of automotive body parts. As a result, the assembly quality of compliant sheet metal parts is mainly determined by fixture locating layouts and variation sources, such as manufacturing variation of parts and fixture locating variation. This paper proposes a robust fixture design method of the compliant assembly process based on a support vector regression model. Firstly, an assembly variation modeling method of compliant sheet metal parts is discussed during the assembly subprocesses of fixture locating, welding gun clamping, weld finishing, and welding gun releasing. The combined assembly variation model describes a numeric relationship between the assembly variation of key measurement points and all variation sources under a certain fixture locating layout. Further, to solve the difficulty of directly obtaining the parameter model between the assembly variation and fixture design layouts under a certain variation source level, a response surface modeling method based on a support vector regression model is presented. And a whole assembly robust objective function is presented to realize the combining consideration of the whole assembly quality control with different assembly quality controls of different areas. Finally, a taillight bracket assembly is used to demonstrate the robust fixture design method. Results show that the proposed method is feasible and the assembly quality under the robust fixture locating layout has been greatly increased.

Kharitonov’s theorem: A good starting point for robust control

Advanced robust controller design methods such as: [Formula: see text], [Formula: see text] synthesis, or linear matrix inequality require advanced mathematics which makes these techniques difficult topics for final year projects. A robust controller (for plants with parametric uncertainty) can be designed with the aid of Kharitonov’s theorem, which has simpler mathematical machinery. This paper studies the robust control of DC–DC converters with the aid of Kharitonov’s theorem. It presents a tutorial exposition of robust controller design based on Kharitonov’s theorem. Kharitonov’s theorem provides a good starting point for BSc students who wish to continue their future studies in robust control.

Active Disturbance Rejection Based Robust Trajectory Tracking Controller Design in State Space

This paper proposes a new active disturbance rejection (ADR) based robust trajectory tracking controller design method in state space. It can compensate not only matched but also mismatched disturbances. Robust state and control input references are generated in terms of a fictitious design variable, namely differentially flat output, and the estimations of disturbances by using differential flatness (DF) and disturbance observer (DOb). Two different robust controller design techniques are proposed by using Brunovsky canonical form and polynomial matrix form approaches. The robust position control problem of a two mass-spring-damper system is studied to verify the proposed ADR controllers.

Robust Circuit Parameters Design for the CLLC-Type DC Transformer in the Hybrid AC–DC Microgrid

CLLC-type dc transformer (CLLC-DCT) is very popular in the hybrid ac–dc microgrid thanks to its high-power density advantage and good bidirectional power transfer capacity. In the hybrid ac/dc microgrid, the open-loop control is always utilized by the CLLC-DCT to cooperate with the bidirectional interlinking converter to realize the power and voltage conversion between the ac and dc bus. This paper first studies the circuit parameters design of the open-loop controlled CLLC-DCT with consideration of such a realistic problem: The real inductors/capacitors values are actually different with their theoretically designed values due to the operation power and temperature variation. To solve this problem, a robust circuit parameters design scheme is proposed for the CLLC-DCT in this paper. With the proposed scheme, the designed CLLC-DCT exhibits good power transmission and voltage regulation ability in the hybrid ac/dc microgrid even when its actual inductors/capacitors values vary with the practical power and temperature. The robust design method is experimentally verified in a hybrid ac/dc microgrid prototype.

Robust optimization design of structures based on the specular reflection algorithm

The nominal values of structural design parameters are usually calculated using a traditional deterministic optimization design method. However, owing to the failure of this type of method to consider potential variations in design parameters, the theoretical design results can be far from reality. To address this problem, the specular reflection algorithm, a recent advancement in intelligence optimization, is used in conjunction with a robust design method based on sensitivity. This method not only is able to fully consider the influence of parameter uncertainty on the design results but also has strong applicability. The effectiveness of the proposed method is verified by numerical examples, and the results show that the robust design method can significantly improve the reliability of the structure.

A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals

We present a multiscale continuous Galerkin (MSCG) method for the fast and accurate stochastic simulation and optimization of time-harmonic wave propagation through photonic crystals. The MSCG method exploits repeated patterns in the geometry to drastically decrease computational cost and incorporates the following ingredients: (1) a reference domain formulation that allows us to treat geometric variability resulting from manufacturing uncertainties; (2) a reduced basis approximation to solve the parametrized local subproblems; (3) a gradient computation of the objective function; and (4) a model and variance reduction technique that enables the accelerated computation of statistical outputs by exploiting the statistical correlation between the MSCG solution and the reduced basis approximation. The proposed method is thus well suited for both deterministic and stochastic simulations, as well as robust design of photonic crystals. We provide convergence and cost analysis of the MSCG method, as well as a simulation results for a waveguide T-splitter and a Z-bend to illustrate its advantages for stochastic simulation and robust design.

Analysis of a Polynomial Chaos-Kriging Metamodel for Uncertainty Quantification in Aerodynamics

New aerospace aerodynamic bodies increasingly require robust design methods that demand data of the key problem variables in the presence of uncertainty. When these bodies are subject to complex physics, such as turbulence, separation, or secondary flows, the uncertainty data become more difficult to produce economically. Metamodels (surrogate models) can be used to produce data in the presence of uncertainty more efficiently by propagating the uncertainty from the model parameters to the outputs. However, the chief difficulty of metamodels is in consistently producing statistical data of the full system from a sparse number of evaluations. Recently, the polynomial chaos and kriging metamodeling approaches have been combined to take advantage of both their benefits. This research explores the combined method’s effectiveness on airfoil and aircraft engine nacelle examples. It demonstrates that, although the combined method can produce more accurate results than either method alone, there is always a compromise between accuracy and efficiency.

Control allocation-based fault tolerant control

This paper describes a novel scheme for fault tolerant control using a robust optimal control design method. This scheme can also be employed as actuator redundancy management for over-actuated linear systems. In contrast to many existing methods in the literature, this scheme can be applied to systems whose control input matrix cannot be factorised into two matrices whose ranks are equal and less than the minimum of the number of columns and rows of the input matrix. The so-called virtual control, in this scheme, is calculated using a robust ℋ2-based feedback design approach constructed to be robust against uncertainties emanating from visibility of the control allocator to the controller and imperfection in the estimated effectiveness gain. Then, using a new control allocation scheme along with a novel Tikhonov-based re-distributor mechanism, the obtained virtual control signal is re-distributed among remaining (redundant or non-faulty) set of actuators. As the proposed scheme is modular-based, it can be employed as a real-time fault tolerant control scheme with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed scheme is demonstrated by a numerical example.

Distributed Control of HVDC Links for Primary Frequency Control of Time-Delay Power Systems

This paper considers high voltage direct current (HVDC) links for the primary frequency control of interconnected time-delay power systems with electric vehicles (EVs). Novel distributed control of HVDC links is proposed to minimize the differences in the frequency deviations between the connected power areas. A power system with EVs, HVDC links and multiple time delays is first presented. Then, we propose a new robust distributed HVDC controllers design method to stabilize the closed-loop system with a guaranteed $H_{\infty }$ performance. The design method can be flexibly extended to design static output feedback controllers of various structures to cater for different power system topologies. The performance and usefulness of our proposed controller design method is validated by extensive simulations.

Robust controller design for uncertain delayed systems and its applications to hypersonic vehicles

AbstractThe longitudinal dynamics of hypersonic flight vehicles involves strong nonlinearity and coupling, uncertainties including parametric uncertainties, unmodeled uncertainties, external disturbances, and time‐varying input and state time delays. In this paper, a robust controller design method is proposed for the longitudinal stabilization of these vehicles by the signal‐compensation‐based control idea. Theoretical analysis is given to prove the robustness properties of the designed closed‐loop control system subject to multiple time‐varying uncertainties and time‐varying input and state delays. Simulation results are performed to show the validness and advantages of the proposed robust control approach.

Hybrid genetic algorithm for multi-objective flow shop scheduling problem with sequence dependent setup time: parameter design using Taguchi's robust design method

This paper determines optimal parameters of the proposed hybrid genetic algorithm for solving the multi-objective flow shop scheduling problem with sequence dependent setup time. The objectives considered in this study are minimisation of makespan and mean tardiness. In order to achieve these objectives, genetic algorithm is used in combination with a local search method to obtain Pareto-optimal solutions. The best parameters of the proposed algorithm are determined using the Taguchi's robust design method and the concept of utility index value. The set of parameters corresponding to the highest utility value is selected as the optimal parameters for the proposed algorithm. The analysis of results reveals that crossover type is the most influential parameter. The other parameters in the order of importance are mutation probability, crossover probability, mutation type and initial population. The hybrid genetic algorithm is applied to the benchmark problems of flow shop scheduling with sequence dependent setup time.

Framework for Robust Design and Reliability Methods to Develop Frugal Manufacturing Systems

Emerging markets are rapidly growing. Manufacturing systems in these markets have to be cost-effective but still of high quality. In addition they are often exposed to harsh conditions e.g. climate, infrastructure and lack of knowledge. Consequently, local conditions as well as reliability and robustness methods must be explicitly taken into account during the development process to successfully develop high quality yet cost-effective manufacturing systems for these specific markets. This paper shows different views on robustness and reliability to overcome the geographical and cultural distance of emerging markets for industrial equipment manufacturers from industrialized countries. In addition, framework conditions for robust design and reliability methods are derived in order to develop frugal manufacturing systems, aiming to improve sustainable usage in emerging markets.

Hybrid genetic algorithm for multi-objective flow shop scheduling problem with sequence dependent setup time: parameter design using Taguchi's robust design method

Hybrid genetic algorithm for multi-objective flow shop scheduling problem with sequence dependent setup time: parameter design using Taguchi's robust design method

Novel Robust Methodology for Controller Design Aiming to Ensure DC Microgrid Stability Under CPL Power Variation

In recent years, dc microgrid (MG) is increasing rapidly in electric power grids and other isolated systems, integrating more efficiency and suite better some of the renewable energy sources, storage units, and dc loads. However, dc MG stability analysis becomes a challenge when constant power loads (CPLs) are applied to dc bus, which introduces destabilizing effects in the system due to its negative impedance characteristics. This paper presents a novel robust controller, based on linear programming based on the Chebyshev theorem as a robust control technique considering the Kharitonov’s theorem that ensures the minimization of the total deviation from the desired performance in a closed-loop system, specified by a family of characteristic polynomials. The purpose of the proposed controller is to tightly regulate the dc bus voltage, ensuring MG stability due to the effects of power variation on CPLs. The simulation and experimental tests are performed by using a MATLAB/Simulink simulator and a developed prototype of the DC MG system, respectively, to ratify the robustness and effectiveness of the proposed method of robust controller design.

Recent developments in metamodel based robust black-box simulation optimization: An overview

In the real world of engineering problems, in order to reduce optimization costs in physical processes, running simulation experiments in the format of computer codes have been conducted. It is desired to improve the validity of simulation-optimization results by attending the source of variability in the model’s output(s). Uncertainty can increase complexity and computational costs in Designing and Analyzing of Computer Experiments (DACE). In this state-of the art review paper, a systematic qualitative and quantitative review is implemented among Metamodel Based Robust Simulation Optimization (MBRSO) for black-box and expensive simulation models under uncertainty. This context is focused on the management of uncertainty, particularly based on the Taguchi worldview on robust design and robust optimization methods in the class of dual response methodology when simulation optimization can be handled by surrogates. At the end, while both trends and gaps in the research field are highlighted, some suggestions for future research are directed.