Sensitivity Analysis Techniques Research Articles

A fast analysis algorithm for structural vibration modal sensitivity

Vibration modal sensitivity analysis has a wide range of applications in structural optimization design, model correction, fault detection, and reliability analysis. The existing methods for calculating modal sensitivity mainly include modal superposition method, Nelson’s method, and some improved algorithms derived from them. However, the existing algorithms have the drawback of low computational efficiency when applied to modal sensitivity analysis of the large-scale structures. In view of this, the objective of this work is to develop a fast modal sensitivity analysis method that can more efficiently calculate the modal sensitivity of the large structures with thousands of degrees of freedom. This new sensitivity analysis technique integrates Sherman-Morrison-Woodbury formula, subspace iteration and forward-difference to achieve the goal of fast calculation. The innovations of the proposed method mainly include the following aspects. Firstly, the Sherman-Morrison-Woodbury formula is used to quickly calculate the perturbed flexibility matrix due to the minor modification in the structure. Then, the perturbed flexibility matrix is introduced into the subspace iteration method to calculate the perturbed modal parameters. Finally, the forward-difference algorithm is used to calculate the modal sensitivity. Two numerical examples are used to verify the superiority of the proposed modal sensitivity algorithm. Taking the 1952-bar structure as an example, the calculation time of the proposed algorithm is only 8.3 % and 18.2 % of that of the existing approximate modal superposition method and the improved Nelson’s method, respectively. In terms of calculation accuracy, the results obtained by the proposed method are exactly the same as the exact solution when the perturbation scale is set to 10−5. It is found that the proposed method significantly reduces computation time compared to the existing methods on the premise that the calculation accuracy is basically unchanged.

Active Learning of Ensemble Polynomial Chaos Expansion Method for Global Sensitivity Analysis

Global sensitivity analysis (GSA) techniques, especially Sobol indices, have gained prominence in assessing the impact of uncertainty across all input variables on the variation of model response. However, GSA can incur intensive computational costs, particularly when dealing with time-consuming models. To address this issue, an ensemble polynomial chaos expansion (EPCE) surrogate model based on an active learning hybrid (ALH) criterion is proposed. The proposed method integrates a weighted combination of multiple sparse PCE surrogate models to formulate the EPCE method. To enhance the performance, the ALH criterion, which balances local exploitation and global exploration, is developed to sequentially select samples for updating the EPCE model. In terms of local exploitation, the model correlation and sensitivity pursuit criteria are derived to identify the local region displaying both the largest discrepancy among multiple sparse PCE methods and the most substantial contribution to the total variance. The ALH criterion also incorporates a minimum distance-based measure for global exploration. The performance of the proposed method is evaluated by four benchmark functions and an engineering application. The numerical studies demonstrate that the proposed method exhibits favorable performance for conducting GSA.

Deterministic mathematical modeling, sensitivity analysis, and dynamic optimization of cross-flow ultrafiltration systems for concentration of monoclonal antibody solutions

This manuscript proposes a general new framework for mathematical modeling, extended sensitivity analysis and dynamic optimization of tangential flow filtration (TFF) systems for concentration of monoclonal antibody (mAb) products and, potentially, other biologics. This framework is comprised of four major components: (I) a new first-principles-inspired TFF model; (II) dedicated parameter estimation strategies for automated model training; (III) new extended sensitivity analysis techniques for enhancing TFF phenomenological understanding and providing general guidance on TFF process development; and (IV) novel mono-objective and multi-objective dynamic optimization strategies for optimal TFF design and operation. The application of this framework to Bovine immunoglobulin γ (IgG) – a mAb analog in terms of physicochemical properties – shows the potential benefits it may offer in terms of overall TFF performance and rapid TFF development for new mAb candidates, compared to the current state of the art.

Sensitivity Analysis of the Square Cup Forming Process Using PAWN and Sobol Indices

This study investigates the sensitivity of the square cup forming process. It analyses how the uncertainties in the material properties, friction and process conditions affect the results of the square cup, such as equivalent plastic strain, geometry change, thickness reduction, punch force and springback. The cup flange and the die curvature region are identified as highly affected areas, while the cup bottom is least affected by the uncertainties. Two sensitivity analysis techniques, PAWN and Sobol indices, are compared. In particular, the study shows that PAWN indices require a significantly smaller number of simulations than Sobol indices, making them a more efficient choice for sensitivity analysis. While both PAWN and Sobol indices generally give comparable results, discrepancies arise in the analysis of springback, where PAWN indices show superior accuracy, particularly when dealing with multimodal distributions. This observation highlights the importance of selecting the appropriate sensitivity analysis method based on the nature of the data being analysed. These results provide insights for optimizing stamping processes to reduce production time and costs.

Partial derivative-based dynamic sensitivity analysis expression for non-linear auto regressive with exogenous (NARX) model[sbnd]case studies on distillation columns and model's interpretation investigation

Constructing the reliable dynamic sensitivity profile for the output variable using the machine learning model is a challenging task; however, the dynamic sensitivity trends are helpful to understand the impact of the input variables on the system's performance. In this paper, we have derived the partial-derivative approach-based sensitivity analysis expression for the non-linear auto regressive with exogenous (NARX) model for the first time. The engineering systems-based case studies, i.e., two distillation columns with five and ten stages, respectively are taken which are commonly found in the chemical processing plants. Two output variables, i.e., liquid composition in tray 2 and tray 4 (Y2 and Y4) of a five-stage distillation column, and liquid composition in tray 7 (Y7) of a ten-stage (higher) distillation column are modelled by NARX with respect to time, feed concentration (Xf) and feed flow rate (Lf). The dynamic sensitivity profiles of the output variables with respect to Xf and Lf for the two distillation columns are plotted by the derived partial derivative-based sensitivity expression on the NARX model. Furthermore, the forward difference method of sensitivity analysis (first principle method) is also applied on the ordinary differential equations of the distillation columns to compute the sensitivity values of the output variables. A good agreement in the dynamic sensitivity values of the output variables with respect to the input variables is found for the two sensitivity analysis techniques thereby demonstrating the effectiveness of the partial-derivative approach for the improved NARX's interpretability performance. This research presents the explicit partial-derivative based sensitivity analysis expression for the NARX model which can be utilised for time-series applications and can provide the insights about the model's interpretation performance.

Genetically predicted high serum sex hormone-binding globulin levels are associated with lower ischemic stroke risk: A sex-stratified Mendelian randomization study

ObjectiveCross-sectional and cohort studies have found insufficient evidence of a causal relationship between sex hormone-binding globulin and ischemic stroke, only associations. Here, we performed a sex-stratified, bidirectional, two-sample Mendelian randomization analysis to evaluate whether a causal relationship exists between sex hormone-binding globulin and ischemic stroke. MethodsSingle-nucleotide polymorphisms associated with sex hormone-binding globulin and ischemic stroke were screened from genome-wide association studies summary data as instrumental variables to enable a bidirectional, two-sample Mendelian randomization study design. Inverse-variance weighted analysis was used as the main method to evaluate potential causality, and additional methods, including the weighted median and MR-Egger tests, were used to validate the Mendelian randomization results. Cochran's Q statistic, MR-Egger intercept test, and Mendelian Randomization-Pleiotropy Residual Sum and Outlier global test were used as sensitivity analysis techniques to assure the reliability of the results. Multivariable analysis was used to show the robustness of the results with key theorized confounders. ResultsInverse-variance weighted analysis showed that genetically predicted higher serum sex hormone-binding globulin levels were associated with significantly decreased risk of ischemic stroke in males (odds radio = 0.934, 95 % confidence interval = 0.885-0.985, P = 0.012) and females (odds radio = 0.924, 95 % confidence interval = 0.868-0.983, P = 0.013). In an analysis of ischemic stroke subtypes, genetically predicted higher serum sex hormone-binding globulin levels were also associated with significantly decreased risk of small-vessel occlusion in both males (odds radio = 0.849, 95 % confidence interval = 0.759-0.949, P = 0.004) and females (odds radio = 0.829, 95 % confidence interval = 0.724-0.949, P = 0.006). The association remained in sensitivity analyses and multivariable analyses. The reverse analysis suggested an association between genetically predicted risk of cardioembolism and increased serum sex hormone-binding globulin in females (Beta = 0.029 nmol/L, Standard Error = 0.010, P = 0.003). ConclusionOur findings provide new insight into the etiology of ischemic stroke and suggest that modulating serum sex hormone-binding globulin may be a therapeutic strategy to protect against ischemic stroke.

A two-level optimisation approach for underground natural ventilation based on CFD and building energy simulations

Natural ventilation is a historical and promising passive design for conserving building energy. However, a noticeable scarcity exists in design strategies and academic studies on underground natural ventilation. This study introduces a two-level optimisation approach for underground natural ventilation, considering form and environmental characteristics. At the initial level, computational fluid dynamics simulations were employed to quantify and visualise the momentary ventilation performances of various passive strategies. These simulations also furnished precise wind pressure coefficients. Subsequently, at the second level, this study predicted the annual energy savings of the proposed prototype by integrating an airflow network model with building energy simulations. To adapt design parameters, sensitivity analysis and multi-objective optimisation techniques were applied. These numerical models underwent validation against measured data from analogous studies. The results reveal that the ‘inlet buried pipe + outlet shaft’ led to a 6.9 % reduction in energy consumption for heating, ventilation, and air-conditioning in underground hybrid ventilation compared to underground mechanical ventilation. Moreover, it achieved a 28.8 % decrease compared to aboveground mechanical ventilation. Optimising air temperatures following climate, soil conditions, and building characteristics is imperative, aligning with design standards. This study contributes a quantitative and visual approach to support underground natural ventilation and addresses the limitations of empirical designs, providing a foundation for future research and practical applications.

Analyzing dynamics and stability of single delay differential equations for the dengue epidemic model

This paper introduces a mathematical model that simulates the transmission of the dengue virus in a population over time. The model takes into account aspects such as delays in transmission, the impact of inhibitory effects, the loss of immunity, and the presence of partial immunity. The model has been verified to ensure the positivity and boundedness. The basic reproduction number R0 of the model is derived using the advanced next-generation matrix approach. An analysis is conducted on the stability criteria of the model, and equilibrium points are investigated. Under appropriate circumstances, it was shown that there is local stability in both the virus-free equilibrium and the endemic equilibrium points when there is a delay. Analyzing the global asymptotic stability of equilibrium points is done by using the appropriate Lyapunov function. In addition, the model exhibits a backward bifurcation, in which the virus-free equilibrium coexists with a stable endemic equilibrium. By using a sensitivity analysis technique, it has been shown that some factors have a substantial influence on the behavior of the model. The research adeptly elucidates the ramifications of its results by effortlessly validating theoretical concepts with numerical examples and simulations. Furthermore, our research revealed that augmenting the rate of inhibition on infected vectors and people leads to a reduction in the equilibrium point, suggesting the presence of an endemic state.

Application of uncertainty and sensitivity analysis in dose assessment during a postulated LBLOCA for VVER-1000 nuclear reactor

A key element in the process of accident analysis for the event of a severe nuclear emergency such as the large break loss of coolant accident (LBLOCA) is to properly quantify safety margins using reliable tools. Assessing the consequences of radioactive material release and the equivalant dose after the LBLOCA can provide clarity about the accident. Reliable safety analysis methods for nuclear power plants (NPPs) can be used to obtain relatively realistic outcomes considering the complex uncertainties of NPP events. In this study, an appropriate technique for sensitivity and uncertainty analysis is employed to develop a methodology for performing dose assessment within a postulated LBLOCA including uncertainties. Considering the approved reliability over the years and safety aspects, VVER reactor is among the most widely used nuclear reactors, which is selected as the case study in this article. The main problem that the study aims to solve is to illustrate whether the inordinate deviation of the input parameters from their reference values lead to violation of the allowed TEDE value by conducting uncertainty analysis. For performing calculations of total effective dose equivalent (TEDE), the environmental contamination with radioactive materials has been simulated using HotSpot code and the obtained results were compared with the solutions of JRODOS program. To obtain the most influential parameters on the obtained TEDE values in different distances from the NPP, an appropriate sensitivity analysis has been carried out, following which the Wilks’ statistical method is used to generate 59 data samples with uncertainty propagation and 95 % confidence. The resulting uncertainty bands demonstrate that the maximum TEDE values of calculated data lie within about 7 to 15 mSv in the postulated LBLOCA scenario, which are below the threshold limit of 50 mSv recommended by International Atomic Energy Agency.

Carbon cycle responses to climate change across China's terrestrial ecosystem: Sensitivity and driving process

Investigations into the carbon cycle and how it responds to climate change at the national scale are important for a comprehensive understanding of terrestrial carbon cycle and global change issues. Contributions of carbon fluxes to the terrestrial sink and the effects on climate change are still not fully understood. In this study, we aimed to explore the relationship between ecosystem production (GPP/SIF/NDVI) and net ecosystem carbon exchange (NEE) and to investigate the sensitivity of carbon fluxes to climate change at different spatio-temporal scales. Furthermore, we sought to delve into the carbon cycle processes driven by climate stress in China since the beginning of the 21st century. To achieve these objectives, we employed correlation and sensitivity analysis techniques, utilizing a wide range of data sources including ground-based observations, remote sensing observations, atmospheric inversions, machine learning, and model simulations. Our findings indicate that NEE in most arid regions of China is primarily driven by ecosystem production. Climate variations have a greater influence on ecosystem production than respiration. Warming has negatively impacted ecosystem production in Northeast China, as well as in subtropical and tropical regions. Conversely, increased precipitation has strengthened the terrestrial carbon sink, particularly in the northern cool and dry areas. We also found that ecosystem respiration exhibits heightened sensitivity to warming in southern China. Moreover, our analysis revealed that the control of terrestrial carbon cycle by ecosystem production gradually weakens from cold/arid areas to warm/humid areas. We identified distinct temperature thresholds (ranging from 10.5 to 13.7 °C) and precipitation thresholds (approximately 1400 mm yr−1) for the transition from production-dominated to respiration-dominated processes. Our study provides valuable insights into the complex relationship between climate change and carbon cycle in China.

A framework for parameter estimation, sensitivity analysis, and uncertainty analysis for holistic hydrologic modeling using SWAT+

Abstract. Parameter sensitivity analysis plays a critical role in efficiently determining main parameters, enhancing the effectiveness of the estimation of parameters and uncertainty quantification in hydrologic modeling. In this paper, we demonstrate an uncertainty and sensitivity analysis technique for the holistic Soil and Water Assessment Tool (SWAT+) model coupled with new gwflow module, spatially distributed, physically based groundwater flow modeling. The main calculated groundwater inflows and outflows include boundary exchange, pumping, saturation excess flow, groundwater–surface water exchange, recharge, groundwater–lake exchange and tile drainage outflow. We present the method for four watersheds located in different areas of the United States for 16 years (2000–2015), emphasizing regions of extensive tile drainage (Winnebago River, Minnesota, Iowa), intensive surface–groundwater interactions (Nanticoke River, Delaware, Maryland), groundwater pumping for irrigation (Cache River, Missouri, Arkansas) and mountain snowmelt (Arkansas Headwaters, Colorado). The main parameters of the coupled SWAT+gwflow model are estimated utilizing the parameter estimation software PEST. The monthly streamflow of holistic SWAT+gwflow is evaluated based on the Nash–Sutcliffe efficiency index (NSE), percentage bias (PBIAS), determination coefficient (R2) and Kling–Gupta efficiency coefficient (KGE), whereas groundwater head is evaluated using mean absolute error (MAE). The Morris method is employed to identify the key parameters influencing hydrological fluxes. Furthermore, the iterative ensemble smoother (iES) is utilized as a technique for uncertainty quantification (UQ) and parameter estimation (PE) and to decrease the computational cost owing to the large number of parameters. Depending on the watershed, key identified selected parameters include aquifer specific yield, aquifer hydraulic conductivity, recharge delay, streambed thickness, streambed hydraulic conductivity, area of groundwater inflow to tile, depth of tiles below ground surface, hydraulic conductivity of the drain perimeter, river depth (for groundwater flow processes), runoff curve number (for surface runoff processes), plant uptake compensation factor, soil evaporation compensation factor (for potential and actual evapotranspiration processes), soil available water capacity and percolation coefficient (for soil water processes). The presence of gwflow parameters permits the recognition of all key parameters in the surface and/or subsurface flow processes, with results substantially differing if the base SWAT+ models are utilized.

A study of integrated pest management models with instantaneous and non-instantaneous impulse effects.

The occurrence of pests and diseases during agricultural production affects the quality and quantity of agricultural products. It is important to evaluate the impact of various factors on pests to achieve optimal results of integrated pest management (IPM) during its implementation. In this paper, we considered the transient and non-transient effects of chemical control on pests and the effects on natural enemies at different times, and developed a corresponding pest control model. Detailed studies and comparisons were conducted for spraying pesticides either more or less frequently as compared to strategies for releasing natural enemies. The threshold conditions for global asymptotic stabilization of the pest extinction period solution was obtained. Using two-parameter and sensitivity analysis techniques, the parameters affecting the variation of the threshold were discussed. By comparing these two pest control strategies, we found the existence of optimal application and release frequencies. Finally, in order to control pests below the economic threshold level, the state-dependent pest model was numerically investigated. The results show that the presence or absence of chemical control of pests can depend on the values taken for the parameters in the model. Based on this information, pest control experts can make decisions about the best spraying time and the best release rate.

Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence

In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.

Sensitivity analysis for a thermohydrodynamic model: Uncertainty analysis and parameter estimation

This paper proposes an efficient computational strategy to deal with uncertainty propagation problems for the Navier–Stokes equations coupled with a temperature equation based on a sensitivity analysis technique model. Sensitivity analysis allows one to investigate how the model response in a point is affected by a change in the boundary conditions on the temperature, the heat capacity, the thermal conductivity, and the thermal diffusivity under the hypothesis of a small variance of the input parameters. The variance can be estimated with just one simulation of the state and as many simulations of the sensitivity as there are uncertain parameters. We focused on the benchmark problem of natural convection in a square cavity, also known as the de Vahl Davis problem. Various areas of the domain were analysed to determine the relative influence of each parameter on temperature and velocity. We use the open-source code TrioCFD to simulate the state equations and a specific module is developed for the sensitivity equations.

Efficient sensitivity analysis for biomechanical models with correlated inputs.

In most variance-based sensitivity analysis (SA) approaches applied to biomechanical models, statistical independence of the model input is assumed. However, often the model inputs are correlated. This might alter the interpretation of the SA results, which may severely impact the guidance provided during model development and personalization. Potential reasons for the infrequent usage of SA techniques that account for input correlation are the associated high computational costs, especially for models with many parameters, and the fact that the input correlation structure is often unknown. The aim of this study was to propose an efficient correlated global sensitivity analysis method by applying a surrogate model-based approach. Furthermore, this article demonstrates how correlated SA should be interpreted and how the applied method can guide the modeler during model development and personalization, even when the correlation structure is not entirely known beforehand. The proposed methodology was applied to a typical example of a pulse wave propagation model and resulted in accurate SA results that could be obtained at a theoretically 27,000× lower computational cost compared to the correlated SA approach without employing a surrogate model. Furthermore, our results demonstrate that input correlations can significantly affect SA results, which emphasizes the need to thoroughly investigate the effect of input correlations during model development. We conclude that our proposed surrogate-based SA approach allows modelers to efficiently perform correlated SA to complex biomechanical models and allows modelers to focus on input prioritization, input fixing and model reduction, or assessing the dependency structure between parameters.

Inverse design of high entropy alloys using a deep interpretable scheme for materials attribution analysis

High entropy alloys (HEAs) have gained significant attention due to their unique combinations of properties and extensive compositional space. However, designing HEAs with specific properties has become increasingly complex and challenging. To address this issue, a Deep Interpretable Scheme for Material Attribution Analysis (DISMAA) was developed to systematically uncover the composition-structure-property (CSP) relationships of HEAs and generate novel compositions. The approach combines a deep generative model, trained with limited data, to create a continuous composition space of AlCoCrFeMnNi high entropy alloys, and additional deep learning models, trained with more data, to predict the corresponding phase and properties. Attribution and sensitivity analysis techniques are used to analyze the contribution of each element to different materials properties and phases. The distributions of composition, phase, mechanical property, and contribution of elements are visualized in the latent space, providing a novel and intuitive approach to analyze CSP relationships using deep learning. The efficacy of the method was validated, demonstrating the interpretability and rationality of the deep neural network model for material inverse design applications. This approach can be applied to tailor multiple properties and manufacturing parameters in various materials systems, providing scientists with a comprehensive context for designing HEAs.

Evaluation of response characteristics using sensitivity analysis and TLBO technique of powder mixed wire EDM of Ti6Al4V alloy

The development of Powder Mixed Wire Electric Discharge Machining (PMWEDM) aims to enhance both precise dimension and surface quality, making it a more efficient method for the cost-effective production of precise dies and tools compared to conventional Wire Electric Discharge Machining (WEDM. This approach effectively eliminates the need for secondary operations. The present study is focused on the parametric influence of surfactant with powder mixed WEDM process parameters during die corner cutting on Ti6Al4V material in the presence of surfactant and powder with dielectric. A sensitivity analysis was conducted to determine the significant influence of machining parameters and powder properties in conjunction with the dielectric. To empirically explore these variables, a central composite full factorial design based on response surface methodology was utilized. The design involved varying the pulse on-time (Ton) within the range of 30–90 µs, pulse off-time (Toff) within 3–11 µs, gap voltage (GV) within 40–80 V, and powder concentration (PC) within 2–10 g/L. The mathematical model was developed to predict the responses such as corner inaccuracy (CI) and surface roughness (SR) using RSM. The results conclude that the sensitiveness of powder concentration is highest. Apart from this, positive sensitiveness towards surface roughness is determined for three inputs: pulse on time, pulse off time, and powder concentration. In comparison, powder concentration shows positive sensitiveness towards corner inaccuracy. An artificial intelligence technique namely, Teaching learning-based optimization (TLBO) algorithm has been used to determine the best output. The minimum output for both responses, i.e. corner inaccuracy of 12982.67 µm2 and surface roughness of 1.199 µm, was obtained using TLBO technique. Further improvement for surface finish and corner accuracy in addition powder (3 g/L) with dielectric in WEDM process is found to be a value of 50.77% and 23.01%, respectively, compared with conventional WEDM process. SEM was employed to observe and analyze the topographical changes that occurred during powder mixed and without powder mixed in WEDM process.

Modeling the dynamics of leptospirosis in India.

Leptospirosis, a formidable zoonotic threat spawned by Leptospira, plagues tropical and subtropical realms. This study delves deep into tropical Indian states, namely, Kerala, Gujarat, Karnataka, Maharashtra, and Tamil Nadu, unraveling the dynamics of leptospirosis through a comprehensive mathematical model that embraces temperature-driven growth rates of Leptospira. Sensitivity analysis and parameter estimation techniques fortified the model's accuracy, unraveling the factors shaping leptospirosis transmission. Notably, the numerical results highlight the significant impact of rainfall, fishing, climate, mining, agriculture, and cattle farming on leptospirosis prevalence in the endemic states of India. Finally, our study urges resolute preventive action to control and combat leptospirosis in India. Strengthening surveillance, impactful awareness campaigns, targeted interventions, and improved hygiene practices among high-risk individuals are vital. Embracing these proactive strategies will alleviate the burden of leptospirosis and enhance public health in India and beyond.

On the selection of Morris trajectories for parametric sensitivity analysis in spectroscopic ellipsometry modeling

Spectroscopic ellipsometry and some other optical metrology techniques, such as reflectometry and scatterometry, are model-based optical measurements and, therefore, require appropriate modeling to determine the geometric and material properties of substrates, thin films, and multilayer structures. Parametric sensitivity analysis (SA) provides essential assistance in the model-building process to quantify the relative importance of model parameters for model output and to identify those with high/little influence. SA can be performed in a variety of ways, and this article discusses an application of the Morris or elementary effect (EE) method, a screening type SA procedure, to spectroscopic ellipsometry modeling. The method is a global SA technique and uses a stepping of m parameters along certain so-called “trajectories” or sequences of points in parameter space, randomly constructed in order to maximally fill the volume of the m-dimensional parameter space. However, it was thought that the EE method relies greatly on a sampling strategy or a way of selecting “optimized trajectories” in the parameter space, i.e., a necessary number of trajectories chosen to be well spread over the space to properly cover the entire realistic ranges of all input factors. Here, we use two sampling methods for selecting trajectories with possibly different distributions and investigate their effects on the estimation of various sensitivity measures in spectroscopic ellipsometry data modeling. The SA results indicate that the performance of the sampling strategy should not be judged only by maximizing the trajectory spread but also include some additional convergence criteria for the sensitivity measures.

Utilizing the Sobol’ Sensitivity Analysis Method to Address the Multi-Objective Operation Model of Reservoirs

The operation of reservoirs has significantly influenced the river ecological system. Upholding the ecological integrity of rivers during reservoir operations has been the focus of research over the years. When the Dahuofang reservoir project started, focus moved to ecological goals to address the Biliuhe reservoir’s environmental issues. The water strategy limits usage for various purposes and outlines the diversion route, complicating Biliuhe operations. In this study, to comprehend the effects of individual water level guidelines and their combined influence on these goals, the Sobol’ sensitivity analysis was introduced as an initial measure to tackle the optimization challenge. The results show that removing the insensitive water levels during specific periods of reservoir scheduling lines and beginning with sensitive water levels for local optimization to identify viable solutions, and then moving to wider optimization, significantly enhances the search efficiency, solution quality, and operational speed compared with an exhaustive search without any preceding steps. This sensitivity analysis technique is crucial for fine-tuning multi-objective reservoir operations.