Sobol Method Research Articles

Optimization of Submersible LNG Centrifugal Pump Blades Design Based on Support Vector Regression and the Non-Dominated Sorting Genetic Algorithm Ⅱ

Optimizing the impeller blade design of submersible LNG centrifugal pump significantly enhances mechanical efficiency, reducing energy consumption and carbon emissions during LNG storage and transportation. This study focuses on optimizing blades of the centrifugal pump, combining Bezier blade design, CFD simulations, optimal Latin Hypercube sampling, Support Vector Regression (SVR), and Non-Dominated Sorting Genetic Algorithm Ⅱ(NSGA-II) multi-objective optimization into a systematic method. During the development of this optimization method, it was found that directly applying sampled CFD simulation data for machine learning led to poor overall predictive performance of the models. To address this, a data augmentation method based on Gaussian noise was proposed. Through Bayesian optimization of the machine learning model’s hyperparameters, the R2 of the predictive model was successfully increased from below 0.8 to above 0.99. The optimized design improved the prototype pump's efficiency from 70% to 77.8% under rated flow and head conditions. This efficiency gain is due to the significant reduction in flow separation vortices between blades and decreased turbulent kinetic energy between the impeller and diffuser vanes. Additionally, sensitivity and linear relationship analyses using the Sobol method and Pearson correlation provided valuable insights for blade optimization design.

Using the basic reproduction ratio to quantify transmission and identify data gaps for epizootic haemorrhagic disease virus.

Epizootic haemorrhagic disease virus (EHDV) is an arbovirus transmitted by Culicoides biting midges that has recently emerged in Europe. Here, the basic reproduction ratio (R 0) was used to quantify the transmission of EHDV and its dependence on temperature for cattle and deer. Using data from the published literature the parameters needed to calculate R 0 were estimated with Bayesian methods to incorporate uncertainty in the calculations. The Sobol method of sensitivity analysis was used to determine the parameters having the greatest influence on R 0 and, hence, to identify important data gaps. Depending on the strain, the maximum R 0 for EHDV varied from 0.7 to 2.5 in cattle and 1.3 to 4.3 in deer. The maximum R 0 occurred at temperatures between 22 and 25°C, while the lowest temperature at which R 0 exceeded one was between 16 and 20°C. The sensitivity analysis identified the threshold temperature for virus replication, the probability of transmission from host to vector and the vector- to- host ratio as the most important parameters influencing R 0. Furthermore, there are only limited data on EHDV in European deer species and on transmission in wildlife and at the livestock/wildlife interface. These data gaps should be the focus of future research.

Numerical and sensitivity analysis of hydraulic characteristics of triangular labyrinth side weir

Triangular labyrinth side weirs have significantly more discharge capacity than traditional nonlinear weirs, and the complex hydraulic parameter interaction mechanism has been the research focus. This study used Computational Fluid Dynamics (CFD) to analyze the side weir's flow characteristics. Then, the Bayesian optimization algorithm and Extreme Learning Machine (BELM) developed a prediction model for the side weir's discharge coefficient. Finally, Sobol's method performed a sensitivity analysis for hydraulic parameters. The results show that the main channel's streamline is evenly distributed and begins to shift when it is close to the side weir. The overflow front is increasing and secondary flow also increases. BELM's Mean Absolute Percentage Error and Root Mean Square Error are 8.793 % and 0.455 in the testing stage, respectively, declined by about 56.24 % and 32.29 % compared with ELM; Froude number Fr, weir crest angle θ and the ratio of overflow front length to weir head l/h1 are the most critical hydraulic parameters affecting the discharge coefficient, the global sensitivity coefficients are 0.4393, 0.4218 and 0.4152, respectively.

Integrated learning model for water intake capacity of Tyrolean weirs under supercritical flow

ABSTRACT Tyrolean weir can be used as an effective solution to address floatation and sediment deposition in runoff hydropower stations. To improve the efficiency and accuracy of calculating this structure's water intake capacity. The integrated learning algorithm random forest (RF), the firefly algorithm (FA), and the exponential distribution algorithm (EDO) are utilized to develop the algorithm that can be used for the Tyrolean weir Cd and (qw)i/(qw)T prediction models. Sobol's method and SHAP theory are introduced to analyze the above parameters quantitatively and qualitatively. It is shown that EDO-RF is the optimal prediction model for the Tyrolean weir's discharge coefficient and the Froude number Fr has the greatest influence on the Cd prediction results; when Fr < 30, the greater the negative influence of Fr on the model prediction results. When Fr > 30, the greater the positive influence of Fr on the model prediction results. FA-RF is the optimal prediction model for the Tyrolean weir water capture capacity (qw)i/(qw)T, with the ratio of bar length to bar spacing L/e being the largest; When L/e < 20, the greater the negative influence of L/e on the model prediction results. When L/e > 20, the more significant the positive impact of L/e on the model prediction results.

Implementation of monitoring and certification with the developed China heavy-duty vehicle energy consumption and carbon emission calculation model

Owing to escalating concerns regarding global warming, there has been a heightened focus on greenhouse gases emitted by vehicles. To effectively monitor and certify the fuel consumption and CO2 emissions of heavy-duty vehicles, this study proposes a calculation model named the China Heavy-Duty Vehicle Energy Consumption and Carbon Emission Calculation Model (CHECM). The CHECM is a simulation tool based on longitudinal dynamics. A classification learner was utilised to obtain shifting strategies, achieving accuracies of 92.9% and 93.5% under regulated driving cycles. A fuel-consumption model was incorporated to predict the transient performance of the engine and transmission. In addition, the Sobol method was used to assess the sensitivities of rolling resistance, air drag and rotational mass conversion coefficients to the driving force and a method was proposed to obtain the road resistance correction factor. The test results of three China-6 heavy-duty vehicles over two regulatory test cycles were obtained and used for model accuracy evaluation. The results showed that the deviations between the measured and calculated fuel consumption were 1.25–3.57%, whereas those between the measured and calculated CO2 emissions using the Chinese World Transient Vehicle Cycle were 3.23–4.16%. The CHECM has the potential to accurately replicate various driving conditions and vehicle configurations, particularly when specific sources of uncertainty are constrained.

Joint sensitivity analysis method of impeller aerodynamic performance to key geometric errors of five-axis machine tool

As a high-performance workpiece, an impeller must ensure both dimensional accuracy and aerodynamic performance. A five-axis machine tool has various geometric errors, which seriously influence the impeller processing quality, hence it is crucial to identify the key error items and compensate them. In this study a joint sensitivity analysis method for the key geometric errors of a five-axis machine tool is proposed that focuses on the aerodynamic performance of an impeller. First, a volumetric error model and an aerodynamic performance model were built, representing the relationships between the tool center point volumetric errors and each of the geometric errors and the impeller aerodynamic performance. Then, the improved Sobol method was implemented to compute the total sensitivity index of each variable in the two models, from which two sensitivity distribution matrices were obtained. Finally, a joint sensitivity analysis was performed on these two matrices to identify the key geometric errors. Experiments were executed to ascertain the impact of compensation strategies on the impeller aerodynamic performance. The results showed that after compensating for the key errors, the total pressure ratio and isentropic efficiency loss rate of the impeller are reduced by 72.2% and 55.8% under the design parameters. The significant improvement in the aerodynamic performance of the impeller demonstrates the accuracy of key geometric error identification.

Influence of materials and surface parameters on the moisture buffering in office buildings: A sensitivity analysis of China

The management of indoor humidity through equipment consumes massive energy, leading to the growing interest in passive regulation of indoor humidity via moisture buffering. Numerous factors may impact the performance of interior finishing material during moisture regulation, thus identifying the dominant parameters is critical for moisture buffering effect optimization. This study analyzes the influence of five moisture and surface parameters, which are directly related to the moisture transfer of the interior finishing layer, on the thermal loads in a typical office building under typical climates in China. The analysis employs scatter plots and sensitivity indices based on Sobol's method. The results show that the material thickness plays a decisive role under different climates. The importance of sorption isotherm varies with climates and load types. The vapor diffusion resistance factor of the material only affects the latent heat loads, while the effect of the surface vapor transfer resistance is negligible. Finally, this study puts forward suggestions for interior finishing material selection to achieve low-load performance based on the characteristics of parameter combinations.

Reliability-based Design Optimization (RBDO) Study Applied to the Thermal Management of a Multi-Led Chip Package

Solid-state lighting based on LEDs is used in various applications, including display, communications, etc. However, the high junction temperature is still challenging due to the LED chip’s reduced light output and lifetime. To face this challenge, a thermal study was done to determine junction temperature TJ of a multi-led chip package. Then, a sensitivity analysis of different materials was performed using the Sobol method to identify the parameters that most influence the junction temperature. To calculate the probability of failure of the model, the FORM-SORM and Monte Carlo methodologies were employed in this study. It was obtained that the probability of failure of the LED package is roughly 20%. An optimum design was created using reliability-based design optimization (RBDO) to lower this percentage. After application of this method, the junction temperature was lowered by 11% and the reliability level increased from 80% to 91%.

Modelling and optimization method for energy saving of computer numerical control machine tools under operating condition

The widespread application of machine tools in industry results in very high energy consumption. In order to save energy, it is an effective means to reduce the processing power while improving the processing efficiency of machine tools. Since milling parameters directly affect machine performance, the selection of suitable milling parameters is particularly important. In this regard, this study proposes an integrated modelling and optimization method for energy saving of computer numerical control (CNC) machine tools under operating condition. Firstly, the operating condition of the CNC machine are analyzed and the processing power and efficiency mathematical models are established based on the four milling parameters (n, fz, ae, ap). Subsequently, the Pareto optimal solution is introduced to establish an optimization model integrating the processing power and time. To solve the optimization problem, an adaptive chaotic multi-objective chimp algorithm with fast convergence and satisfactory optimization is proposed considering three aspects: search space, convergence factor, and chaotic mapping. Afterwards, further degrees of freedom and sensitivity analyses were carried out on the constructed model using the Sobol method. Finally, comparative analysis and validation are conducted through simulation cases and actual processing experiments, respectively. The results show that both validation scenarios have the same conclusion. Compared with three existing algorithms, the proposed method reduces the processing power by 5.63 %, 4.65 % and 4.51 % and improves the processing efficiency by 27.88 %, 15.11 % and 15.31 %, respectively. Based on the above enhancements, the energy consumption is reduced by 58.21 %, 45.54 % and 41.45 % respectively.

Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

In this article, we apply the sensitivity analysis method to capture the influence of various parameters on the inflation pressure, axial force, and the deformation for an inflated and axially stretched cylinder. The material consists of an isotropic ground substance material reinforced with fibers that undergo a continuous and mechano-sensitive remodeling process. The input parameters of the mechanical system are assumed to be distributed according to the uniform probability distribution function. In the sensitivity analysis, we apply the Sobol method to determine how the variations of input parameters affect the inflation as well as the axial force in the cylinder. Special attention is given to the fiber remodeling process associated with a homeostatic balance between the constant fiber creation process and the strain-stabilized fiber dissolution. The results may help to understand the importance of the effect of material parameter changes, for example, due to remodeling processes in the context of diseases or recovering processes, on the overall tissue behavior.

Parametric Sensitivity Analysis of Stability Margins of Holos-Quad Microreactor

An analysis of the stability margins of the innovative Holos-Quad microreactor design is presented. This high-temeprature gas-cooled reactor (HTGR) system is designed to operate fully autonomously with passive safety mechanisms. Therefore, the inherent stability of the reactor is of great importance. Using a point-reactor model, which couples point kinetics to thermal-hydraulic heat balance equations and includes reactivity feedback effects of the fuel and moderator temperatures, the closed-loop transfer function of the reactor is derived. Applying the approach of linear systems and control theory, both the gain and phase margins of the Holos-Quad design are obtained. The analysis demonstrates that the design is stable, with an infinite gain margin and a finite phase margin. A parametric uncertainty quantification study is also performed using a total Monte Carlo approach. The stability of the reactor for different power levels, such as during reactor startup or load-following transients, is also explored. Finally, two sensitivity analysis methods are applied, namely, multiple regression (deriving standardized regression coefficients) and variance-based sensitivity analysis (known as the Sobol method), to study the contribution of each of the parameters to the stability margins’ uncertainty. This analysis improves our understanding of the role of each of the parameters in the stability of the reactor.

Theoretical model and parameter sensitivity analysis of concrete slab vibration in concrete-face rockfill dams during underwater nuclear explosions

Large reservoir dams, which are carriers of energy and resources, have historically been the main targets of military conflict and terrorist attacks. A concrete-face rockfill dam (CFRD) is a competitive hydraulic structure widely used in large-scale water conservancy projects. However, the vibration response and damping paths of CFRDs under the influence of underwater explosion shock waves remains insufficiently understood. In this study, we created a theoretical model of slab vibration with four-sided free boundaries using Cole’s formula and the motion differential equation of a slab on an elastic foundation. Furthermore, a global sensitivity analysis of the vibration model parameters on the slab displacement was performed based on the Kriging surrogate model and Sobol method. The results showed that the antiseepage slabs experienced a void phenomenon, resulting in overall instability. The explosive distance and normal stiffness of the slab had the greatest influence on the void displacement of the slab, whereas the dam height and concrete density had insignificant effect. Moreover, increasing the dam height of the CFRD did not increase the risk of slab voids during underwater explosions, which was not the case under strong seismic loads. Therefore, the key factors for active and passive defense against blast resistance in CFRDs were identified, which can provide theoretical support for the blast-resistant design and research on CFRDs. In this study, the reliability of the theoretical model was verified by establishing a numerical analysis model.

An Improved Sobol Sensitivity Analysis Method

The Sobol method is a variance-based global sensitivity analysis method that evaluates single-input and multiple-input interaction effects by calculating the contribution of a single input to the output variance and the contribution of multiple inputs to the output variance. The Sobol method requires each input to obey a uniform distribution of U [0,1], but it is difficult to meet the requirements in practice. Taking the sum function as an example, this paper analyzes the inapplicability of the existing Sobol method when the input does not obey the uniform distribution U [0,1]. To solve the inapplicability of the Sobol method and broaden the application scope, an improved Sobol sensitivity analysis method is proposed. First, the effect of the joint probability density function not 1 on sensitivity calculation is studied; second, the input parameters are changed to uniform distribution U [0,1] through variable substitution; finally, a complete algorithm model is presented and logical sensitivity analysis results are obtained. Application verification shows that the improved Sobol method is more scientific, applicable and practical.

Complementing Drawability Assessment of Deep-Drawn Components With Surrogate-Based Global Sensitivity Analysis

Abstract In the early-stage development of sheet metal parts, key design properties of new structures must be specified. As these decisions are made under significant uncertainty regarding drawing configuration changes, they sometimes result in the development of new parts that, at a later design stage, will not be drawable. As a result, there is a need to increase the certainty of experience-driven drawing configuration decisions. Complementing this process with a global sensitivity analysis (GSA) can provide insight into the impact of various changes in drawing configurations on drawability, unveiling cost-effective strategies to ensure the drawability of new parts. However, when quantitative global sensitivity approaches, such as Sobol's method, are utilized, the computational requirements for obtaining Sobol indices can become prohibitive even for small application problems. To circumvent computational limitations, we evaluate the applicability of different surrogate models engaged in computing global design variable sensitivities for the drawability assessment of a deep-drawn component. Here, we show in an exemplary application problem, that both a standard Gaussian process regression (GPR) model and an ensemble model can provide commendable results at a fraction of the computational cost. We compare our surrogate models to existing approaches in the field. Furthermore, by comparing drawability measures we show that the error introduced by the surrogate models is of the same order of magnitude as that from the choice of drawability measure. In consequence, our surrogate models can improve the cost-effective development of a component in the early design phase.

ESTAN—A toolbox for standardized and effective global sensitivity-based estimability analysis

The development of accurate and reliable mathematical models is the cornerstone for the modeling and optimization of processes. However, most of the existing models suffer from weak prediction capabilities due to poor data information content and poor parameter estimation methodologies. Several estimability approaches have been developed and increasingly implemented to address some of these issues. However, the wider adoption of these methods is still hampered by the lack of standardized and robust methodologies. In this paper, we present a Matlab Toolbox, called ESTAN, designed and developed to make estimability analysis accessible to non-specialist users. It uses a Quasi-Monte Carlo sequence to sample the main unknown parameters within their variation spaces. Then, depending on whether the studied model is computationally cheap or expensive, sensitivity indices are calculated either using the Sobol method or Fourier Amplitude Sensitivity Test (FAST). The calculated sensitivities are finally used within an orthogonalization algorithm to rank the parameters from the most to less estimable ones and to determine the estimable and non-estimable ones based on an estimability cut-off criterion. Various case studies are used to validate the toolbox and guide the users. The first one deals with the non-dynamic Toth adsorption model, while the second one deals with a dynamic batch cooling crystallization model. The main challenge with these two case studies is to show the importance of estimability analysis in the interpolation/extrapolation of model prediction capabilities. The last case addresses a computationally expensive thermodynamic model. The results for all the case studies are found to be promising, showing how the presented toolbox simplifies the investigation of the estimability analysis.

A Computationally Efficient Method for Parameter Sensitivity Analysis of Microbially Explicit Biogeochemical Models Accounting for Long‐Term Behavior

AbstractMicrobial ecological models become increasingly complex owing to the incorporation of many parameters and multiple biotic and abiotic processes. However, little attention has been paid to the variations in the parameter sensitivity during long‐term versus short‐term simulations. Here, we developed a Multi‐Objective Parameter Sensitivity Analysis (MOPSA) method to efficiently identify the important parameters in complex microbial ecological models with multiple response variables of interest in terms of short‐ and long‐term model simulations. We found that MOPSA was more computationally efficient for complex microbial ecological models than Sobol's method because of MOPSA's reliability and low computational sample size. In addition, we address the increased significance of microbial physiology in mediating long‐term than short‐term soil C‐N cycling, indicating that experiment‐model integration practices should examine model behaviors beyond the conventional short‐term experimental period. The outcomes of this study provide an efficient global sensitivity analysis method for parameterization and the scientific foundation for microbial physiology in mediating long‐term microbial ecological processes.

Optimal design method for geometric errors of horizontal machining center based on Sobol method and IPSO

Optimal design method for geometric errors of horizontal machining center based on Sobol method and IPSO

Automatic calibration of SWMM parameters based on multi-objective optimisation model

Abstract To address the issue of low accuracy and inefficiency in the traditional parameter calibration methods for the SWMM model, this paper constructs an automatic parameter calibration model based on multi-objective optimisation algorithms. Firstly, the Sobol method and GLUE method are utilised to determine sensitive parameters and their ranges, aiming to narrow down the solution space and expedite the model-solving speed. Secondly, the NSGA-3 multi-objective optimisation algorithm based on the Pareto theory is applied for the optimisation and calibration of sensitive parameter sets. The model is validated in the rainwater drainage system with independent runoff in a residential area in a northwestern city in China. The results show that parameters such as N-Imperv and KSlope are highly sensitive to the model output under the land-use conditions of the study area. The simulation accuracy of the multi-objective continuous optimisation algorithm is significantly better than that of the single-objective genetic algorithm. The simulation results of the SWMM model under multi-objective optimisation demonstrate a certain level of reliability and stability. The research findings can provide technical support for the automatic calibration of SWMM model parameters, accurate model simulation, and application.

Simultaneously maximizing microalgal biomass and lipid productivities by machine learning driven modeling, global sensitivity analysis and multi-objective optimization for sustainable biodiesel production

Simultaneous enhancement in the productivities of microalgal biomass and lipids that are inversely correlated to each other has been a long-standing challenge before the scientists engaged in algal biodiesel research and innovation. This study, develops an Artificial Neural Network (ANN) model and uses multi-objective optimization approach to determine the process parameters, namely, light intensity, CO2%, air flow rate, and C/N ratio to maximize biomass and lipid productivities of microalga, Chlorella sorokiniana, simultaneously. Experimental data based on central composite design (CCD) were used to train a feed-forward multilayer ANN with four critical parameters. The global sensitivity analysis was performed on the trained ANN model using Sobol's method to assess the relative significance of the four process variables. Since the objectives of maximizing biomass and lipid productivities conflict with each other, multi-objective optimization approach was used for deriving the optimal process parameters, experimental validation of which resulted in approximately 3 times increase in biomass productivity and 7 times increase in lipid productivity. On transesterification of the lipid, the biodiesel product with saturated to unsaturated fatty acids ratio of 48:52 conformed very well to the international standards, ASTM D6751 and EN14214, thereby making it an environment friendly green biofuel. Thus, the present study showcases the successful application of machine learning tool in analysing the global sensitivity analysis of process variables, and employ it for multi-objective optimization towards achieving maximum microalgal biomass and lipid productivities concomitantly for potentially sustainable production of biodiesel.

Electrochemical Parameter Identification for Lithium-Ion Battery Sources in Self-Sustained Transportation Energy Systems

Lithium-ion battery (LIB) sources have played an essential role in self-sustained transportation energy systems and have been widely deployed in the last few years. To realize reliable battery maintenance, identifying its electrochemical parameters is necessary. However, the battery model contains many parameters while the measurable states are only the current and voltage, inducing the identification inherently an ill-conditioned problem. A parameter identification approach is proposed, including the experiment, model, and algorithm. Electrochemical parameters are first grouped manually based on the physical properties and assigned to two sequenced tests for identification. The two tests named the quasi-static test and the dynamic test, are compressed on time for practical implementation. Proper optimization models and a sensitivity-oriented stepwise (SSO) optimization algorithm are developed to search for the optimal parameters efficiently. Typically, the Sobol method is applied to conduct the sensitivity analysis. Based on the sensitivity indexes, the SSO algorithm can decouple the mixed impacts of different parameters during the identification. For validation, numerical experiments on a typical NCM811 battery at different life stages are conducted. The proposed approach saves about half the time finding the proper parameter value. The identification accuracy of crucial parameters related to battery degradation can exceed 95%. Case study results indicate that the identified parameters can not only improve the accuracy of the battery model but also be used as the indicator of the battery SOH.