Operation Of Nuclear Power Plants Research Articles

Seismic fragility analysis of nuclear containment structure with Bayesian cloud analysis framework

Nuclear containment structure plays a critical role in safe operation of nuclear power plants. Seismic safety of nuclear power plant structures has become a hot issue in nuclear engineering community following Fukushima nuclear accident. Seismic fragility analysis, as a key element in probabilistic safety assessment of nuclear power plants, is widely used in nuclear power plant structures. This study presents an innovative method for seismic fragility analysis of engineering structures. The proposed methodology combines conventional Cloud analysis method and Bayesian framework. The accuracy and efficiency of the proposed methodology were demonstrated by a single-degree-of-freedom system, heavy computational efforts but high accuracy seismic fragility analysis method was adopted for comparison. Seismic fragility analysis of a typical prestressed concrete nuclear containment structure was analyzed using the proposed method. Results indicated that method proposed in this study can improve the accuracy of seismic fragility analysis. Furthermore, with the enhance of performance level, the increasing ratios for median seismic capacity of the nuclear containment structure was decreasing.

A Novel Approach for Predicting the Mid–Long-Term Radiation Dose in the Case of a Hypothetical STSBO Nuclear Accident for an Operating Nuclear Power Plant

Four severe nuclear accident scenarios have been identified for operating nuclear power plants (ONPPs). However, there is a research gap in predicting the mid–long-term radiation doses for these scenarios. This study aims to address this gap by proposing a novel approach for predicting the mid–long-term radiation dose in the case of a hypothetical short-term station blackout (STSBO) scenario, one of the aforementioned scenarios. Firstly, the Weather Research and Forecasting (WRF) model was coupled with the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) (WRF-HYSPLIT) model to establish an atmospheric transport and diffusion model for airborne radionuclides, and the regularity of the atmospheric transport and diffusion for the airborne radionuclides was determined. Subsequently, the Residual Radioactive Material Guidelines (RESRAD) OFFSITE (RESRAD-OFFSITE) code was utilized to establish a radiation dose model for predicting the mid–long-term radiation dose resulting from the airborne radionuclides, and the evolution of the mid–long-term radiation dose was analyzed. Finally, the proposed approach was applied to an ONPP, and the results were used to predict the mid–long-term public radiation dose. The results indicated that the total radiation dose would be lower than the dose limit recommended by the International Commission on Radiological Protection (1 mSv/yr) from the second month to the 100th year after the hypothetical STSBO nuclear accident, and the total radiation dose would decrease slowly over time. Recommendations are made for offsite emergency response measures. These research findings can assist ONPPs in analyzing their environmental impacts in the event of an STSBO scenario.

Effect of Constant Cyclic Stress Coupling on the Fatigue Behavior of 304LN Stainless Steel

The stress state of the primary circuit main pipeline is very complex mixed constant stress and periodic cyclic stress during the operation of nuclear power plants, which often affects the failure behavior of the stainless steel (SS) pipe. The fatigue behavior of 304LN SS under mixed constant stress and cyclic stress was investigated, and it was found that the coupling effect of constant stress and cyclic stress has a significant collaborative acceleration on the fatigue behavior. The research results showed that the cracks in the 304LN SS did not propagate even after 78 days under both constant load conditions of 5 KN and 7.5 KN, while the crack growth rate (CGR) of the specimen increased by about an order of magnitude when coupled with a cyclic fatigue load. The fatigue life of 304LN SS was the longest under 200 °C high-temperature water, and its life was roughly the same under 250 °C and 300 °C water. In a 300 °C high-temperature water environment, the fatigue life under the coupling of constant stress and cyclic fatigue stress is significantly lower than that under symmetric cyclic stress alone. There is a synergistic acceleration effect on the fatigue life of 304LN SS when constant stress is coupled with periodic cyclic stress, which is attributed to the combined effect of a corrosion environment and mechanical factors.

Remaining useful life prediction of nuclear reactor control rod drive mechanism based on dynamic temporal convolutional network

The control rod drive mechanism (CRDM) is a critical equipment of the nuclear reactor, and the prediction of its remaining useful life (RUL) is important for the efficient maintenance and ensuring the safe, reliable operation of nuclear power plants. In this paper, a novel framework for the RUL prediction of CRDM is proposed, which is a dynamic temporal convolution network (DTCN) based on dynamic activation function and attention mechanism. Firstly, the temporal convolution network (TCN) is used as the backbone of the prediction model, to extract the temporal dependence of the input data. Next, the dynamic activation function DReLU is integrated into the TCN, which can dynamically activate features and capture variable degradation information. Then, introducing the attention mechanism improves the influence of important high-level features extracted by the network on RUL prediction, thereby improving the efficiency of feature extraction in the network. Finally, the DTCN outputs the predicted RUL by performing non-linear mapping on the extracted features. The CRDM accelerated life test platform is established and a series of experiments are conducted using the collected CRDM full-life vibration dataset. The results demonstrated the performance and advantages of the proposed method.

Low-level ionizing radiation-induced DNA responses in the Asian green mussel Perna viridis

Cesium-137 (Cs-137) is a radioactive isotope present in marine environments due to the operation of nuclear power plants and weapons testing. Radiocesium poses a potential risk to marine life due to its long half-life and bioaccumulation. This study evaluated the genotoxicity of low doses of Cs-137 in the Asian green mussel Perna viridis, a sentinel species for marine pollution monitoring, by performing the comet assay and micronucleus test on hemolymph samples. Genotoxicity was assessed after exposing mussels to Cs-137 at dose rates of 0, 5, 10, and 15 μGy/h for 48 h. Cs-137's organ-specific distribution was also determined using HPGe gamma spectrometry. Even at low radiation doses, Cs-137 was found to exert genotoxic effects. Significant increases in DNA strand breaks (%Tail DNA) and micronucleus formation (MNF) were observed at all tested dose rates compared with the levels in controls, with dose-dependent responses. Cs-137 predominantly accumulated in the soft tissues, specifically the gills and digestive gland. The findings support the recommended safety level of 10 μGy/h for aquatic organisms, suggesting its appropriateness as a fundamental criterion for developing the national marine water quality standard for Cs-137 in Thailand.

Assessment of Power Equipment Operational Safety in the Sustainable Management of Residual Lifespan

Introduction. Ensuring the safe operation of energy facilities is a critical issue at all life cycle stages. It is associated with the adoption of management decisions when rescheduling and assessing the remaining resources, which are made based on a comprehensive assessment of the technical condition of the equipment, taking into account the economic efficiency and environmental requirements for further operation, which is the basis for technical and economic assessments. Aim and tasks. This study aims to develop a technical and economic assessment of the safe operation of power equipment to ensure sustainable management of the remaining service lifespan. Results. An algorithm for assessing pipeline system elements by the coolant environment is proposed, which allows for the pipeline load and changes in erosion and corrosion caused by coolant movement. It was proposed that the equipment be systematised by safety class and coolant. When conducting a technical and economic assessment, these parameters and the costs of extending the service life and upgrading the existing equipment were considered in the standard calculations of a certain type of equipment. For this purpose, mathematical models for calculating the residual life for each type, obtained and confirmed based on empirical studies, are proposed. Research findings into ensuring the reliability and safety of operation with various heat carriers have shown that it is necessary to consider low-cycle and high-cycle loads and erosion processes. It was found that the erosive wear rate is 0.3-0.4 mm/year for bending sections of the main circulation pipeline, where maximum loads occur relative to low-cycle and vibration loads, and the stress is 212.5 MPa when assessing the residual life of 7 years. Conclusions. The cost-effectiveness of reassigning the service life is reasonable, as it does not require additional investment in upgrading or replacing equipment subject to annual technical diagnostics. The systematisation of pipelines, improved codifiers, lifespan assessment models, and algorithms for evaluating the remaining life under various loadings enhance the regulatory framework for safe nuclear power plant operations and support technical and economic evaluations for extending their lifespan.

EVALUATION OF TECHNOLOGICAL PLASTICITY OF HIGH BORON CORROSION-RESISTANT STEEL DURING HOT DEFORMATION OF PIPES USED FOR SPENT NUCLEAR FUEL STORAGE

Statement of the problem. The sustainable development of the global nuclear power industry in the future depends on how effectively the problems of radiation safety and nuclear proliferation are addressed. Such problems occur, among other things, at the final stage of the nuclear fuel cycle – spent fuel management. This task is currently on the agenda of both the international community and national governments of countries that develop or intend to develop nuclear energy [1−3]. Today, in connection with ensuring the safety of nuclear energy, boron-containing steels are widely used in the world practice as a material for biological protection and for the manufacture of special equipment parts. This is due to the fact that the B10 isotope in steels provides neutron capture [4]. Hexagonal pipes made of high-boron steel were needed to shield the support cover of the compacted spent fuel storage facility at nuclear power plants. Corrosion-resistant steels alloyed with boron are widely used in the nuclear power industry due to their special nuclear properties. During the operation of nuclear power plants, fuel assemblies that have served their useful life must be stored in special storage facilities using containers – hexagonal tubes made of 04Сr14Ti3B2V steel. To reduce costs during in the construction and operation of NPPs, part of the spent nuclear fuel management should be performed at Ukrainian enterprises. This will provide a significant import substitution effect. To manufacture hexagonal tubes from 04Сr14Ti3B2V steel according to the ingot-hot deformation-profiling-heat treatment scheme, it is necessary to develop the parameters of hot deformation and subsequent technological operations. The use of these pipes in compacted spent fuel storage facilities of NPPs will allow to increase the storage capacity by 2 times, which will give a significant national economic effect Material and methods of research. Material used for the study was steel 04Сr14Ti3B2V (CS-82), smelted using two variants (vacuum-induction – “VI” and vacuum-induction followed by vacuum-arc remelting – (“VD”). Steel grade 04Сr14Ti3B2V belongs to high-alloy, corrosion-resistant ferritic steels with a high boron content of up to 2 %. The method of differential thermal analysis was used to study the phase transformation temperatures in the steel. X-ray diffraction and micro-X-ray spectral analysis were used to assess the phase state. The steel samples were tested for weldability After cooling, the welded samples were subjected to X-ray transmission [5]. Hot twisting tests and mechanical tests at high temperatures were also performed. The macro- and microstructure of the metal was studied. Results. The macro- and microstructure of steel was evaluated depending on the smelting method. The phase composition of the steel was studied. The study of the plastic properties of steel ChS-82 by means of penetration and hot twisting tests showed that the temperature range of maximum plasticity is in a wide range (from 1 025 to 1 150 0C) with a rather low resistance to deformation. During hot deformation in the temperature range of 1 175 0C and above, metal fracture was observed along the grain boundaries at the melting points of the Cr−Fe−B boride phase. The optimal temperature range for hot deformation of steel ChS-82 is 1 000−1 050 ⁰С. Scientific novelty. For corrosion-resistant high boron steel used for spent nuclear fuel storage, the temperature range of hot deformation was selected and the structural and phase composition was estimated, which will allow deforming the metal on the piercing mill and manufacturing pipes.

The protection of nuclear installations in time of armed conflict – Old rules, new challenges

AbstractIn 2022, for the first time in some while, the public around the world was confronted with an armed conflict between states, which directly involved a nuclear facility, specifically a nuclear power plant in operation. Unfortunately, the situation following Russia's armed attack on Ukraine on 24 February 2022 and the acts of war around the Zaporizhzhya nuclear power plant once again draw attention to the need to protect nuclear facilities during armed conflicts. Therefore, this paper reviews the relevant rules of public international law and scrutinizes the norms that have been established through international legislation and soft law mechanisms to protect and guarantee the nuclear safety and security of nuclear installations.

Explainable, Deep Reinforcement Learning–Based Decision Making for Operations and Maintenance

This paper presents research that integrates condition monitoring and prognostics with decision making for nuclear power plant operations and maintenance aimed at reducing lifetime maintenance and repair costs. Additionally, a focal point of this research is to make the decisions explainable to operators, improving the trustworthiness of the decisions from what can be considered a black box model. In this work, we develop and evaluate an explainable, online asset management methodology to help reduce lifetime maintenance and repair costs. Using the latest advancements in condition monitoring, inventory management, deep reinforcement learning, and explainable artificial intelligence methods, we create a predictive maintenance methodology that can optimize the maintenance and spare part management of a repairable nuclear power plant system. To demonstrate these methods, preliminary studies were conducted on a representative maintenance system undergoing a stochastic degradation process that requires repairs or replacement to continue operation. Using deep reinforcement learning, we were able to reduce maintenance spending by approximately 50% compared to optimized, time-based maintenance strategies for the chosen system. A key component of our methodology is the integration of Shapley values to quantify the contribution of various factors to the decision-making process. This addition enhances the explainability and trustworthiness of our decisions, providing operators with transparent and understandable insights into the rationale behind maintenance strategies. The robustness and resiliency of our decision policy against observation noise were also thoroughly evaluated, demonstrating its effectiveness in uncertain operational environments.

Research on Assessment Method for Cognitive Influence Factors of Nuclear Power Plant Operators Based on Fuzzy Analytic Hierarchy Process and Deep Learning of Electroencephalogram Signals

This study explores the factors influencing the cognitive processes of operators in digital nuclear power plants, with a focus on the correlation between these factors and electroencephalogram (EEG) features. Initially, based on expert consultations, seven factors were considered: stress, time, fatigue, procedural complexity, user interface experience, procedural clarity, and efficiency. From these, four were identified as the most crucial for each stage of the cognitive process, highlighting their significant roles in influencing cognitive performance and potentially correlating with distinct EEG characteristics. These were assessed using the fuzzy analytic hierarchy process (FAHP) to determine the weightings of influences across the cognitive stages of monitoring, decision making, and execution. Employing a simulated scenario of a steam generator tube rupture, subjective questionnaires were utilized to gauge participant perceptions of influencer impacts at each stage, calculating human factors fuzzy synthetic values. Concurrently, EEG signals were segmented by operational steps, extracting around 114 features across the time, frequency, and time-frequency domains, which were then dimensionally reduced to 17 principal components via adaptive principal components analysis (APCA). A correlation analysis was performed between the human factors fuzzy synthetic values and the APCA-reduced EEG features of participants. Subsequently, the EEG feature columns of the eight selected participants were used as inputs to construct a transformer-based self-attention network model to evaluate the participants’ human factors fuzzy comprehensive values. The findings confirm the transformer model’s efficacy in assessing these values, evidencing a significant correlation between the EEG features and human factors fuzzy synthetic values. Integrating FAHP with machine learning methodologies, this model proficiently estimated operators’ cognitive states during various cognitive processes, significantly enhancing human-machine interface design and the operational safety and efficiency at nuclear power plants.

Comprehensive assessment of the effectiveness of the hydrogen production and transportation system

Based on the energy development strategy of Russia until 2035, the article substantiates the prospect for the development of nuclear energy, according to which nuclear plants are planned to be forced to unload in the range of up to 50% of the rated power while participating in the regulation of daily unevenness of the electrical load. In addition, nuclear power plants will be involved in primary frequency regulation, which is also associated with the unloading mode of operation of nuclear power plants. All these circumstances force us to look for ways to provide nuclear power plants with base load. Along with pumped storage power plants, the article considers an alternative option in the form of using a hydrogen complex based on the electrolysis production of hydrogen, which satisfies the concept of its carbon-free production. The article presents the global dynamics of the introduction of electrolyzers, and in addition to the increase in the share of electrolysis hydrogen produced at nuclear power plants. The hydrogen complex in this case is a means of providing the nuclear power plant with a base load, which involves the consumption of unclaimed electricity at cost. This allows hydrogen to be produced at a competitive price compared to individual producers on the market. The resulting hydrogen is in great demand as a useful product in a number of industries. The article provides examples of hydrogen consumption in various areas of consumption depending on purity, taking into account the requirements of GOST. A number of consumer industries use hydrogen of a special degree of purity, i.e., more than 99.999% vol. In this regard, additional hydrogen purification on palladium membranes was taken into account. A comprehensive assessment of the efficiency of the hydrogen production system was carried out, taking into account its additional purification and delivery to the consumer in various ways, mastered and in demand in world practice. A comparison has been made of the methods of delivering hydrogen to the consumer in comparison with the production of hydrogen by electrolysis at the point of consumption. A comparison was made using the criterion of net present value for the option of third-party consumers who do not have their own hydrogen production.

Verification and Validation of CFD analysis for 1/7th scale model of APR1400 for CVAP

This paper presents a methodology for analyzing the internal flow of the APR1400 Reactor Vessel Internals (RVI) using Computational Fluid Dynamics (CFD). The Comprehensive Vibration Assessment Program (CVAP) is performed to verify the structural integrity of reactor internals for flow-induced vibrations prior to the commercial operation of nuclear power plants. To classify the APR1400 as a valid prototype, it is necessary to demonstrate through successful CVAP that there are no adverse effects. In this study, CFD is used to calculate the local velocity and flow distribution to generate the forcing functions caused by turbulent flow for analysis programs in the CVAP. The Verification &Validation (V&V) procedure recommended by the American Society of Mechanical Engineers (ASME) is performed to verify the accuracy of CFD based on reliability, and it is compared with tests on a scale model. This paper provides valuable insights into the analysis and V&V process for CVAP using CFD, which can help ensure the safe and reliable operation of nuclear power plants.

Harmonic characteristics analysis and power quality requirements of Light-Emitting Diode lamps used in nuclear power plant lighting system

Abstract This article conducts an in-depth study of the application of LED (Light-Emitting Diode) lamps in nuclear power plant lighting systems and conducts a comprehensive analysis of its impact on the power quality of the plant’s low-voltage AC power system. First of all, through a detailed discussion of the harmonic characteristics of LED lamps and the power quality requirements of nuclear power plants, it is pointed out that the harmonics of LED lamp drivers will inevitably have an impact on the power quality of low-voltage AC power systems. Therefore, the harmonic characteristics of LED lamps must comply with certain constraints. Subsequently, the application of LED lamps under different capacity transformers was analyzed and combined with relevant standards and specifications, and application suggestions for LED lamps in nuclear power plant lighting systems were put forward. Finally, measures to improve the total harmonic distortion rate of LED lamp current were discussed, emphasizing the importance of power factor correction technology. In summary, this article provides important reference and guidance for the application of LED lamps in nuclear power plants, helping to ensure the safe and stable operation of nuclear power plants.

Development of an integrated framework to implement the nuclear safety goals with various safety criteria

The question “How safe is safe enough?” has been raised since the start of nuclear power plant (NPP) operations in the 1950s, and to address this issue, the Nuclear Regulatory Commission (NRC) of the United States (U.S.) introduced the concept of safety goals in the mid-1980s. In the U.S., the safety goal is called the 0.1 % rule because it requires that the additional risk imposed on individuals and society by the operation of a new NPP should not exceed one-tenth of one percent (0.1 %) of the total risk resulting from other factors to which members of the U.S. population are generally exposed. Nordic countries Sweden and Finland have taken a different approach to setting safety goals for NPPs than the U.S. by introducing requirements for the amount and frequency of cesium-137 (Cs-137) releases. In the case of the Republic of Korea, the regulatory body introduced nuclear safety goals following amendments to the Nuclear Safety Act in 2016. Korea adopted the same safety goal of the 0.1 % rule of the U.S. and simultaneously introduced the Cs-137-related safety goal, which requires that the total frequency of NPP accidents in which the release of Cs-137 exceeds 100 TBq is less than or equal to 1.0E-6 per year. The latter was introduced as a safety goal to protect the environment. Furthermore, while Canada, which has also formally adopted the Cs-137-related safety goal, and Finland require this goal to be applied only to new NPPs, the Korean regulatory body requires the Cs-137-related safety goal to be applied to both operating and new NPPs. Thus, various safety criteria are used in the Korean nuclear safety goals. The use of various safety criteria as in the Korean nuclear safety goals might cause several issues in the practical application of those safety criteria. In this paper, I examine these issues from three main perspectives: (1) consistency, (2) assessment framework, and (3) practical application. I propose several methods to resolve these issues, and also recommend a new integrated framework to implement the safety goals with various safety criteria based on the proposed methods.

LSTM-GCN based multidimensional parameter relationship analysis and prediction framework for system level experimental bench

In nuclear power plants (NPPs) operations, the prediction of multi-dimensional parameters is found to help operators to grasp the condition of the system. However, majority of existing studies are focused on single-dimensional parameter prediction. In this study, a multi-dimensional parameter prediction framework of NPPs based on Long Short-Term Memory Network and Graph Convolution Network (LSTM-GCN) and a multi-model integrated parameter correlation analysis framework (PCAF) are proposed, in which PCAF is used to build a parameter correlation network for GCN, and LSTM-GCN is used to predict multi-dimensional parameter of NPPs. To verify the feasibility of the LSTM-GCN framework, multi-dimensional parameter prediction researches are conducted using data from a thermohydraulic experimental bench that simulates the operation of NPPs. Results indicate that compared to traditional prediction models, LSTM-GCN framework enhances the prediction accuracy of multi-dimensional parameter, which benefits from the ability of LSTM-GCN to utilize the temporal dependencies and spatial correlations of parameters.

An estimation method for bias error of measurements by utilizing process data, an incidence matrix and a reference instrument for data validation and reconciliation: Part 2 Extension to the energy balance relation

Abstract Ensuring data reliability is becoming increasingly important for further applications of AI, IoT, and digital twins. One promising technology for ensuring data reliability is data validation and reconciliation (DVR), which minimizes the uncertainty of measurements based on statistics. DVR has been widely used for the operation and maintenance of nuclear power plants in Europe and the United States in recent years. The most important input for DVR analysis is measurement uncertainty. The catalog value provided by sensor manufacturers includes the measurement uncertainty, but in reality, the actual measurement uncertainty is often smaller. Previous studies have proposed several methods for evaluating the actual measurement uncertainty based on process data, which have been confirmed to be effective for evaluating random errors. It is important to note that bias errors also contribute significantly to the measurement uncertainty. In our previous paper, we proposed a method for estimating bias error using process data, an incidence matrix, and a reference instrument. The proposed method was limited to a mass balance relation, i.e., flow rate measurements. In this paper, we extend the method to include an energy balance relation by considering energy conservation in addition to mass conservation. This extension enables the evaluation of measurement uncertainty for flow rate and temperature. The proposed method was validated with two benchmark problems. It was found to be applicable to various flow conditions, including physically fluctuating flow, such as that observed in the feedwater flow in nuclear power plants.

Digital engineering implementation in nuclear demonstration and nonproliferation projects at Idaho National Laboratory

Digital engineering and digital twins are increasingly being used in nuclear energy projects with important impacts. At Idaho National Laboratory, these approaches have been applied in a variety of nuclear energy research, development, and demonstration projects, with key lessons and evolutions occurring for each. In this paper, we describe the use of digital engineering and digital twins in the Versatile Test Reactor design, National Reactor Innovation Center test beds, and nonproliferation analysis of the AGN-201 reactor design. We share key lessons learned for these projects related to tool selection, adoption and training, and working with existing assets versus beginning at the design phase. We also share highlights of future potential uses of digital twins and digital engineering, including using artificial intelligence to perform repetitive design tasks and digital twins to move towards semiautonomous nuclear power plant operations.

Exploring signal interactions in PWR nuclear power plants through noise-based signal processing

Nuclear power plants operate as complex, interconnected systems with tightly interlinked variables. Monitoring systems within such plants gather data from various process parameters. This paper systematically analyzes key signals in a typical PWR power plant. We develop a dynamic model of the PWR plant encompassing mathematical models for the reactor core, steam generator, pressurizer, turbine, and condenser. This model is rigorously validated against reference data. We use this model to analyze signal perturbations in hypothetical scenarios, employing both time-domain and frequency-domain analyses. Our results demonstrate that noise in one signal noticeably impacts others. Furthermore, the extent of this impact varies depending on the nature of their connection. Direct connections exhibit a higher susceptibility to noise-induced interference, whereas intermediate connections typically show a diminished impact. Through signal analysis, we identify correlated signal pairs, offering insights into processes during abnormal conditions. These findings have implications for enhancing the safety and reliability of nuclear power plant operations.

Current Progress in the Application of Artificial Intelligence for Nuclear Power Plant Operation

Current Progress in the Application of Artificial Intelligence for Nuclear Power Plant Operation

A computationally efficient approach of tuned mass damper design for a nuclear cabinet based on two-step machine learning and optimization methods

Enhancing nuclear power plant (NPP) safety is demanded because of the recent beyond-design-basis earthquake near a NPP. Therefore, research on improving the seismic performance of the electrical cabinet, which ensures the safe operation of NPPs, is needed. In this paper, a tuned mass damper (TMD) is employed to control the seismic response of cabinet. To design the TMD, we employ existing design equations or perform numerical model–based optimization. However, limitations, such as inconsistencies with targeted control of the load and structure, the possibility of converging a local solution, and the high cost of numerical analysis. Therefore, this paper proposes a two-step machine learning and optimization method. Such an approach is utilized to find the optimal global design solution and reduce numerical analysis costs. Each step involves the design of experiment (DOE), response surface, and optimization. Notably, range setting in the DOE accounts for the difference between each step. In the first step, the sampling range is widened to determine the relationship between the design variables and the cabinet's response, and in the second step, the sampling range is narrowed depending on the result of the first step. Consequently, the proposed method reduced the cabinet's response by 35.4 % on average and numerical analysis cost declined by 1/3.