Robust Parameter Design Research Articles

Sliding Mode Observer-Based Phase-Locking Strategy for Current Source Inverter in Weak Grids

The current source inverter (CSI) has become the main grid-connected interface of distributed generation systems due to its advantages, such as boost capability, current controllability, and short-circuit protection capability. However, in weak grids, the grid-connected CSI that uses a phase-locked loop to achieve grid voltage synchronization has problems, such as instability in the fundamental positive-sequence voltage phase detection at the point of common coupling and instability in the current loop control, which seriously hamper the promotion and application of the CSI and its interconnected systems. For this reason, this paper proposes a sliding mode observer-based phase-locking strategy for the CSI. The strategy proposes a sliding mode observer for grid voltage phase detection, so that the grid current can directly follow the grid voltage, solving the problem of inconsistency or distortion between the voltage phase of the point of common coupling and the grid voltage phase in weak grids. On this basis, the grid impedance is regarded as part of the CL filter, and a robust parameter design method is proposed for the grid current closed-loop control in weak grids, which achieves robust operation of a CSI in weak grids. Finally, an experimental platform for a single-phase grid-connected CSI is built to verify the effectiveness and feasibility of the proposed scheme.

Bayesian modeling and optimization for split-plot experiments with multiple responses

In many industrial processes, cost or time constraints make some input variables harder to change or control than others. An appropriate experimental design method is restricted randomization, which results in split-plot experiments. Empirical models that connect multiple quality characteristics with input variables play a crucial role in robust parameter design for split-plot experiments. At present, many modeling methods typically adopt the single response model for analyzing industrial processes in the split-plot experiments without considering correlation among multiple responses, correlation among whole plots, and uncertainty of model parameters. However, ignoring these issues can lead to poor product or process design. To solve these issues, this paper suggests a novel Bayesian modeling and optimization approach. We first construct a Bayesian multi-response linear mixed-effects model and obtain the posterior distribution for model parameters by employing Bayesian theorem. Then, the Gibbs sampling procedure is employed for the estimation of model parameters. Finally, the overall weighted desirability optimization function meeting the specification is developed to avoid acquiring ideal input settings with outliers. A simulation and an engineering case study demonstrate the validity of the proposed method. In comparison to existing methods, the optimization results given the proposed method are more robust and reliable.

Dynamic Robust Parameter Design Using Response Surface Methodology based on Generalized Linear Model

Purpose: When designing an input-output system susceptible to noise, engineers assume a functional relation between the input and the output. The Taguchi method, which uses a dynamic, robust parameter design (RPD) to evaluate the robustness of the input-output relation against noise, is employed. This study aims to address extending the scope of use of a dynamic RPD. Methodology/Approach: A target system in a typical dynamic RPD can be interpreted as one in which the relation between the input and the output is a linear model, and the output error follows a normal distribution. However, an actual system often does not conform to this premise. Therefore, we propose a new analysis approach that can realize a more flexible system design by applying a response surface methodology (RSM) based on a generalized linear model (GLM) to dynamic RPD. Findings: The results demonstrate that 1) a robust solution can be obtained using the proposed method even for a typical dynamic RPD system or an actual system, and 2) the target function can be evaluated using an adjustment parameter. Research Limitation/implication: Further analysis is required to determine which factor(s) in the estimated process model largely contribute(s) to changes in the adjustment parameter. Originality/Value of paper: The applicability of typical dynamic RPD is limited. Hence, this study’s analytical process provides engineers with greater design flexibility and deeper insights into dynamic systems across various contexts. Category: Research paper Keywords: robust parameter design; dynamic system; generalized linear model; response surface methodology; Taguchi method

Online robust parameter design using sequential support vector regression based Bayesian optimization

Traditional robust parameter design (RPD) is an effective offline quality improvement method, but it cannot update the optimal settings in a timely manner. To resolve the drawback of traditional one-time modeling methods, online RPD comes into being. In online RPD, when the setting for controllable factor is unreasonable, it can be regarded as a new sample to update the optimal setting, which improves the efficiency of constructing response surface. Now, one of the mainstream approaches is to use support vector regression (SVR) as a response surface for online RPD. However, in the process of adding samples and updating the response surface, the parameters of the model are not updated. If the parameters do not change after adding samples, the accuracy of the model may decrease, which is obviously not desirable. To address this problem, this paper proposes Bayesian optimization sequential SVR based on online RPD (BOSSVR-RPD) strategy, which can simultaneously update the parameters and response surface in real time. In the proposed strategy, we can use the optimal setting of previously controllable factors, the currently observed noise factor and the corresponding response as new samples to add to the response surface to improve the accuracy of the response surface, and at the same time use the Bayesian optimization method to optimize the parameters of the model. By repeating this process, we can find the desirable optimal setting for controllable factor. This paper verifies the method through four cases, proving that the proposed BOSSVR-RPD strategy can find the optimal setting for controllable factors. Compared with the existing method without parameter optimization, the model proposed in this paper is more accurate, so the optimal setting for controllable factors can be found faster and the controllable factors obtained are more reliable.

Robust Parameter Design on Dual Stochastic Response Models With Constrained Bayesian Optimization

In engineering system design, minimizing the variations of the quality measurements while guaranteeing their overall quality up to certain levels, namely the robust parameter design (RPD), is crucial. Recent works have dealt with the design of a system whose response-control variables relationship is a deterministic function with a complex shape and function evaluation is expensive. In this work, we propose a Bayesian optimization method for the RPD of stochastic functions. Dual stochastic response models are carefully designed for stochastic functions. The heterogeneous variance of the sample mean is addressed by the predictive mean of the log variance surrogate model in a two-step approach. We establish an acquisition function that favors exploration across the feasible and optimality-improvable regions to effectively and efficiently solve the stochastic constrained optimization problem. The performance of our proposed method is demonstrated by the extensive numerical and case studies. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many manufacturing processes involve undesirable variations, which create variations in the final products. For example, many emerging manufacturing processes, such as nanomanufacturing, involve complex physical and chemical dynamics and transformation, creating variations in the manufacturing output. In such processes, it is crucial to design the manufacturing processes or products so that they have minimum variations in their quality. Meanwhile, it is also important to maintain the overall quality of the designed processes or products. Furthermore, acquiring data from many advanced manufacturing processes is often very costly, especially in the designing stage. In this work, we propose a data-driven method that automatically finds the best setting of manufacturing processes or products with the minimum variations of quality and a given constraint on the average quality satisfied. Our proposed method is used before conducting every experiment; It analyzes the historical data from previous experiments and provides a setting to be used in the next experiment. Our proposed method efficiently utilizes the historical data, and thus finds the best robust setting by conducting only a small number of experiments.

A Study of the Impacts of Measurement errors on Robust Parameter Design for Multi-response

Robust parameter design is a principle in quality improvement methodologies that is directed towards reducing the effects of errors which are either poised by the noise factors or the control factors. Response surface methodology is an effective approach to robust parameter design. Previous studies discussed Robust parameter design based on the response surface model by considering measurement errors in control variables for a single response variable. However, in process design, determining optimal levels of control variables is an important issue in some problems with different outputs. This study therefore investigates the impacts of measurement errors in the levels of control variables on processes with multiple quality characteristics (responses). Different variances of error were tested on the levels of control variables and the analysis of response surface modeling and optimization was performed. The result showed that as measurement errors in the levels of control variables increase, the coefficient of determinations for the multi-response and the expected quality loss deviates from what is obtainable in the initial state. It can be concluded based on the result however, that measurement errors in the levels of control variables exert impacts on robust parameter design for multi-response.

Robust parameter design of the procedure for determining the chemical composition of copper alloys by X-ray fluorescence

Robust parameter design of the procedure for determining the chemical composition of copper alloys by X-ray fluorescence

Multi-response robust parameter design based on Bayesian mixed effects model

In robust parameter design for blocked experiments, the correlation of response observations within each block and model parameter uncertainty often impact acquiring ideal operating conditions. In this paper, a Bayesian mixed regression-based multi-response surface modeling and optimization method is suggested to address the above issues. Firstly, the mixed effects model is incorporated into the Bayesian framework, and posterior distributions of the model parameters are derived using Bayes' theorem. Secondly, the hybrid Monte Carlo algorithm is employed to calculate the model parameters. Thirdly, the expected quality loss function satisfying the specification is constructed to lessen the impact of outliers on the results of optimization, and the optimal factor settings are obtained by the hybrid genetic algorithm. In addition, the posterior probability is used to assess the conformance of the optimization results. Finally, a simulated study and real-world example of the additive manufacturing process are used to illustrate the viability of the proposed method. Compared with the current techniques, the proposed method can reduce the impact of model uncertainty on the modeling and optimization results, leading to more conformant and robust optimization results.

Robust parameter design of the measurement procedure for determining the chemical composition of copper alloys by X-ray fluorescence

A brief overview of contemporary methods for determining the chemical composition of copper alloys and the analytical control methods used is given. It has been shown that to obtain reliable and comparable results of measuring the mass fractions of copper alloys elements in wide ranges of values, the most suitable procedures are based on the X-ray fluorescence method, implemented using portable X-ray fluorescence spectrometers. In order to select the optimal values of the influencing quantities when determining the chemical composition of copper alloys, a robust parameter design of a quantitative chemical analysis procedure was carried out on the X-50 Mobile X-ray fluorescence spectrometer. The use of robust parameter design, as opposed to conducting a full factorial experiment when developing a measurement procedure, makes it possible to optimize measurement conditions and obtain results of the required accuracy with a limited number of experiments and a maximum number of control factors. An example of drawing up an experimental plan for the parameter design of this procedure is given and a statistical analysis of the measurement results is carried out. The optimal measurement conditions (influencing quantities) were analyzed and selected, under which the minimum error in the results of measuring the mass fraction of elements is ensured. The selection of optimal values of the influencing quantities based on the results of robust parameter design of the quantitative chemical analysis procedure made it possible to increase the accuracy of the results of determining the chemical composition of copper alloys and, as a consequence, the reliability of the results of product quality control at relatively low costs for its implementation. This approach can be recommended to analytical laboratories developing procedures of quantitative chemical analysis for metallurgical industry enterprises.

A multi-objective robust evolutionary optimization approach applied to the multivariate helical milling process of super duplex steel

This work presents an approach for multivariate modeling and multi-objective robust evolutionary optimization for processes presenting as inputs control and noise variables and as outputs a set of correlated responses regarding process performance and product quality. Factor analysis is applied to obtain a transformed output set that is uncorrelated and retains most part of the information of the original outputs. Models that are robust regarding noise variables relating this transformed output set with the control variables are obtained through robust parameter design. Response models in the function of process and noise variables are obtained through the least squares method. Mean and variance models as a function of process variables are obtained through error propagation. Robust mean square error models are obtained to model the bias and variance of each latent variable. Finally, multi-objective evolutionary optimization is performed. Three evolutionary algorithms were applied and compared through hypervolume. The approach is applied in the helical milling of super duplex stainless steel UNS S32760. Tool overhang length, hole depth, and lubri-cooling flow rate were set as noise factors. Cutting forces were monitored, while roughness and roundness were measured to evaluate process performance and product quality. The three factors, obtained to represent the six outputs, guaranteed dimensionality reduction and minimized the redundancy in output space. The mean square error models obtained to these three factors as a function of control variables minimize both bias and variance regarding noise factors. The AGE-MOEA multi-objective evolutionary algorithm obtained the best performance considering the hypervolume. Some solutions with high trade-off were selected through pseudo-weights to aid the decision-making.

Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

Mathematical model development for multivariate decision-making problems (i.e., multiple parameter and response optimization problems) has received significant attention and has been investigated by many researchers and practitioners. Although many different optimization models and methods, including priority and weight allocation problems, have been proposed in the literature, there is significant room for improvement. The majority of existing optimization methods may have difficulties in determining reliable priorities and weights for practical industrial situations. In addition, because they often focus on tradeoffs only among multiple output responses, these methods may not incorporate the multiple priority and/or weight effects directly from input factors to output responses (i.e., quality characteristics). To address these problems, the primary objective of this research is to propose a new multi-objective optimization approach by integrating a game theory principle (i.e., the Stackelberg leadership game) into a robust parameter design model to determine the optimal factor settings. First, a multi-response robust design optimization (RDO) problem was formulated using a mean squared error model and response surface methodology. A Stackelberg leadership game is then integrated into this RDO problem, where multiple responses play the role of game participants. Second, the integrated RDO model using the Stackelberg game-based multi-response (SGMR) formulation approach is analyzed by decomposition into various sequential optimization models in terms of different leader–follower relationships. Finally, non-dominated solutions are obtained from the proposed model by evaluating the overall quality loss (OQL). A pharmaceutical numerical example was performed to demonstrate the proposed integrated model and to examine whether this model can determine the most efficient solutions when the relative importance among multiple responses is unidentified. In addition, a comparative study associated with the conventional multi-objective optimization methods and the newly proposed RDO model is presented, and the proposed RDO model provided significantly better solutions than the conventional methods in the relevant comparative study.

Is designed data collection still relevant in the big data era? – A discussion

Is designed data collection still relevant in the big data era? – A discussion

Structural and Functional Picosecond Laser Modification of the Nimonic 263 Superalloy in Different Environmental Conditions and Optimization of the Irradiation Process.

In this experimental study, picosecond laser treatment was performed on a nickel-based superalloy Nimonic 263, aiming to investigate the surface effects induced by irradiation in different atmospheric conditions and, concerning changes in surface composition, regarding the possibility for improvement of its functionality. Besides the varying laser parameters, such as a number of pulses and pulse energy, environmental conditions are also varied. All surface modifications were carried out in standard laboratory conditions and a nitrogen- and argon-rich atmosphere. The resulting topography effects depend on the specific laser treatment and could be categorized as increased roughness, crater formation, and formation of the laser-induced periodic surface structures (LIPSS). Changes in the chemical surface composition are distinguished as the potential formation of the protective oxides/nitrides on the sample surface. Numerous characterization techniques analyse the resulting effects on the topography and surface parameters. The multi-response parametric optimization of the picosecond laser process was performed using an advanced statistical method based on Taguchi's robust parameter design. Finally, the optimal parameter conditions for Nimonic 263 modification are suggested.

多変量解析法とロバスト設計を適用した樹脂射出成形プロセス条件の最適化

In recent years, the demand for plastic products has increased, and along with the deepening of academics, mass production, weight reduction, and high precision are progressing. In the fields of design development and production technology, there are many issues related to quality assurance such as molding defects and product strength. In particular, in the resin molding process, there is a high degree of freedom in product shape and mold structure, and it is an important issue to create quality functions that apply analysis of complex multidimensional information. In this study, the important factors of the resin molding process related to the optimization of resin strength are extracted by applying the multivariate analysis method and robust parameter design. As a result of verification of the proposed method, it is clarified that uniformization of the resin filling density in the mold is extremely important for stabilizing the resin strength.

Device Voltage Stress From Ground Leakage Current in Medium-Voltage Solid-State Transformer

Grounding related issues are critical for safe and reliable operation of solid-state transformer (SST) in medium-voltage (MV) applications, e.g., solar photovoltaic and energy storage integration, date center, electric vehicle fast charging, etc. This article presents for the first time the issue of additional device voltage stress due to grounding-loop current in current-source SST, using the soft-switching solid-state transformer (S4T) as an example. The S4T features single-stage isolated ac–ac, ac–dc, or dc–dc conversion with full-range ZVS, derived from flyback converter or current-source converter (CSC). However, the flyback operation for CSC-based SST means that magnetizing current flows through the reverse-blocking devices on only one side of the medium-frequency transformer (MFT) at a time. Then, the voltages across the devices, especially those on the other side of the MFT, can be influenced by parasitic current. A parasitic model of a modular S4T (M-S4T) prototype is developed from direct measurements and datasheets. Using the developed parasitic model and equivalent circuits, the causes of the voltage stress are analyzed. A voltage-stress mitigation scheme of connecting additional grounding capacitors is proposed. Damping resistors are also installed to damp out the grounding-loop resonance. A robust parameter design of the proposed scheme is given. The existence of the voltage stress issue and the effectiveness of the proposed scheme are verified experimentally on an MV SiC M-S4T prototype with inherent parameter variations among the five modules in the prototype. Both single-module and stacked-module operation are demonstrated during steady state and dynamic conditions up to 4 kV peak.

Integrated parameter and tolerance design for multiple response optimization

Robust parameter design and tolerance design are effective approaches for continuous product quality improvement. However, the traditional two-stage design approach of parameter design followed by tolerance design is time-consuming. The tolerance levels determined in the tolerance design stage typically affect quality loss; therefore, the parameter levels obtained in the parameter design may be suboptimal. In this paper, we propose an integrated parameter and tolerance design model, and then a criteria importance through intercriteria correlation-based grey relational analysis technique is adopted to obtain the optimal parameter and tolerance levels. A case study is conducted to validate the proposed method. Comparison results show that the parameter levels and tolerance levels of controllable factors obtained using the proposed method are more reliable and enable a better tradeoff among quality loss, tolerance cost and predicted loss.

An online approach for robust parameter design with incremental Gaussian process

Robust parameter design (RPD), an important method for quality improvement, can effectively mitigate the negative impact of fluctuations on product quality. Traditional RPD adopts offline design, that is, the optimal level of parameter combination is fixed by one-time modeling throughout the production process. This strategy is obviously unreasonable. Online RPD breaks through the limitation of traditional offline design, which can update the optimal setting by utilizing the new sample when the current optimal setting of controllable factors is not suitable. However, there are still some problems in the current version of online RPD, such as poor data fitting ability of response surface model and low efficiency of parameter design. In this paper, a new online RPD method based on Gaussian process (GP) is proposed. The GP model is used to construct the response surface, which has the capacity of dealing with high-dimensional nonlinear data. But traditional GP method adopts batch learning, it cannot update the model online with new samples. So this paper proposes an incremental Gaussian process model (IGP), which can update the response surface in real-time. In the proposed IGP based online robust parameter design method (IGP-RPD), an effective optimization strategy is used to find the optimal setting of controllable factors, and a reasonable selection criterion is used to determine the noise factor setting for the next stage. The optimal setting of the controllable factor in the previous stage and the currently observed noise factor are used as input, and the corresponding quality characteristic is taken as the output. The input and output form a new sample to update the response surface model. In this way, the RPD process can be redone continuously until the desirable optimal setting of the controllable factor is found. Three cases are used to verify the IGP-RPD method and compare it with the existing methods. The experiments manifest that the IGP-RPD method has better performance in both accuracy and efficiency.

Incremental Huber-Support vector regression based online robust parameter design

In the response surface based RPD, the optimal setting of the controllable factor is highly dependent on the accuracy of the response surface. Classically, in order to improve the accuracy of the response surface, it is necessary to add more samples. The larger the number of samples, the higher the accuracy. Traditional RPD usually uses a one-shot modeling method to construct a response surface. Whenever the number of samples increases, all samples need to be learned from the beginning to rebuild the response surface. However, The one-shot modeling method significantly increases the time of model training and the complexity of model training. We present an incremental strategy to build response models. Our solution is based on the Huber-support vector regression machine. In this article, the incremental Huber-SVR model is proposed to construct the response surface in robust parameter design. The proposed algorithm can continuously integrate new sample information into the already built model. In incremental HSVR-RPD, we can use the optimal settings of the previous controllable factors, the currently observed noise factor and the corresponding response to improve the accuracy of the response surface, so as to obtain more reliable recommended settings in the next stage.

Robust parameter design of mixed multiple responses based on a latent variable Gaussian process model

Traditional robust parameter design methods mainly focus on the optimization of quantitative quality characteristics. However, computer experiments involving qualitative and quantitative mixed input and output occur frequently in the manufacturing industry, which prompted the authors to develop an effective meta-modeling and optimization technique for such experiments. This article combines the latent variable Gaussian process (LVGP) model and fuzzy set theory to create a mixed multi-response LVGP (MMR-LVGP) model involving qualitative and quantitative mixed input and output. Then, the optimization scheme is established by comprehensively weighing the location and dispersion effects of each quality characteristic to find the joint optimal solution of qualitative and quantitative factors. Numerical and industrial cases are used to illustrate the validity of the proposed method in the modeling and optimization of experimental data with qualitative and quantitative mixed input and output or spatio-temporal structure. The comparison results indicate that the proposed method is preferred over existing methods.

Robust optimization with uncertainty using a stochastic multivariate Gaussian process model

In robust parameter design (RPD), estimating the response surface model from the noisy experimental data is critical for parameter optimization. The multivariate Gaussian process (MGP) model has become a popular tool for response surface modelling. However, most existing MGP models may not effectively evaluate the uncertainty of noisy data. This article proposes a stochastic MGP for efficient emulation and robust optimization by considering uncertainty. Firstly, the hierarchical modelling technique is adopted to estimate the relationship model with noisy data. Secondly, the hyperparameters are estimated by the Gibbs technique, and the Bayesian averaging method is used to measure the parameter uncertainty. Finally, a novel optimization model integrated with the Bayesian averaging and quality loss function is developed to find the optimal solution. Two case studies are used to illustrate the effectiveness of the proposed method. The results show that the proposed approach obtains smaller quality loss than the existing ones.