Sensitivity Indices Of Parameters Research Articles

Efficient Methods for Reliability Sensitivity Analysis of Distribution Parameters and Their Application

To efficiently evaluate the influence of the distribution parameters of the input variables on the failure probability of engineering structures and improve the reliability and safety of engineering structures in a targeted manner, new methods for the global reliability sensitivity analysis (RSA) of distribution parameters are proposed in this study based on the cubature formula (CF), surrogate sampling probability density function (SSPDF), and quasi-Monte Carlo (QMC) method. By introducing CF, the proposed methods can effectively improve the computational efficiency of the nested expectation and variance operators in the reliability sensitivity indices of the distribution parameters. Based on the concept of SSPDF, a surrogate importance sampling probability density function was developed. This not only overcomes the problem of the computational effort of propagating parameter uncertainty to the failure probability function (FPF), which depends on the dimensionality of the parameters; it also further improves the efficiency of the RSA of the parameters in the case of a small failure probability. Finally, by incorporating the idea of the QMC method, the process of calculating the reliability sensitivity indices of the parameters is reduced from a double-loop to a single-loop one. Three engineering examples are used in this study to demonstrate the efficiency and accuracy of the new algorithms.

Parameter sensitivity analysis and parameter identifiability analysis of electrochemical model under wide discharge rate

The increasing demand for electric vehicles, grid stability, and high pulse power loads has driven the development of new high-power lithium-ion batteries (LIBs) that are capable of discharging at extremely high C-rates. Accurately identifying physical parameters in electrochemical models is crucial for the rational design and optimization of these new high-power LIBs. Since high-rate discharge can significantly reduce discharge time, it is essential to investigate the impact of double-layer capacitors. In this study, we present a P2D coupled double-layer capacitor model and conduct a comprehensive analysis of the sensitivity of all 32 physical parameters to terminal voltage during constant current discharge over a wide rate range of 1C to 40C. This is the first time such an analysis has been performed. We classified the parameters into three groups based on their normalized parameter sensitivity index: high sensitivity, sensitive, and insensitive, and identified 14 physical parameters that can be recognized under constant current discharge conditions. We used a genetic algorithm to identify these parameters, achieving a root mean square error below 13 mV and an average absolute error below 10 mV between the simulation results of the model and the experimental data. This work provides guidance and inspiration for the parameter identification of high-power LIBs electrochemical models.

Process Interactions Can Change Process Ranking in a Coupled Complex System Under Process Model and Parametric Uncertainty

AbstractFor a complex hydrologic system with multiple processes and process interactions, global sensitivity analysis is often used to identify important or influential parameters for model development and improvement. The identification is complicated by process model uncertainty, when a system process can be represented by multiple process models. This study develops a new total‐effect process sensitivity index to identify influential processes under model uncertainty. This is done by extending Sobol's total‐effect parameter sensitivity index for one system model to total‐effect process sensitivity index for multiple system models to account for uncertainty in process models and model parameters. The total‐effect process sensitivity index includes not only the first‐order process sensitivity index for measuring the importance of individual processes but also higher‐order indices that account for process interactions. The total‐effect process sensitivity index can identify an influential process that itself and its interactions with other processes influence a model output. The total‐effect process sensitivity index is applied to two numerical examples: (a) Sobol's G*‐functions with analytical solutions of first‐order and total‐effect process sensitivity indices, and (b) groundwater flow models with interactions between recharge, geology, and snowmelt processes. The second evaluation shows that, due to second‐order and higher‐order process interactions, the first‐order and total‐effect process sensitivity indices give different process ranking. It is thus necessary to estimate both first‐order and total‐effect process sensitivity indices to appreciate the difference between the first‐order impact of a process alone and the overall total‐effect impact of the process itself and its interactions with other processes on a model output.

Diurnal Extrema Timing—A New Climatological Parameter?

We address the following question: Are turning points of daily air temperature function a piece of relevant climatological information worth recording and analyzing? Diurnal Extrema Timing (DET) are daily occurrence times of air temperature minimum and maximum. Although unrecognized and unrecorded as a meteorological variable, the exact timing of daily temperature extrema plays a crucial role in the characterization of air temperature variability. In this study, we introduce the DET concept and assess the plausibility of this potential parameter in detecting temperature extrema timing changes. Conceptualization of the DET parameter has, for a primary goal, the supplementation of vital spatial information to the daily measurements of air temperature extrema. The elementary analysis of annual trends of daily DET examines the significance of this parameter in describing changes in the time domain of air temperature variability. The introduction of the new Climate Parameter Sensitivity Index (CPSI) for evaluating the susceptibility of climate parameters to climate change directs attention to the importance of the systematic acquisition of the timing of daily extrema in climate observations. The results of this study reveal the timing of daily air temperature maximum as the most vulnerable to climate change among temperature and timing extrema indices.

Mathematical modelling of root causes of hyperglycemia and hypoglycemia in a diabetes mellitus patient

The rapid increase of diabetes patients in the world has attracted many researchers’ efforts to find the best way of managing the disease. However, lack of clear etiology in some types of the diseases such as Idiopathic Type 1 Diabetes hinders the effort. Here we present a mathematical model that demonstrates some possible causes of hyperglycemia and hypoglycemia. Sufficient and necessary conditions for hyperglycemia and hypoglycemia were newly formulated to guide the screening of the diabetes’s root causes. Apart from insulin resistance and insufficient insulin secretion, our study reveals that other factors such as abnormalities in hepatic glucose absorption, endogenous glucose production, glucagon resistance, and beta-cells responsiveness can possibly cause hyperglycemia or hypoglycemia. In an attempt to quantify an influence of each parameter to plasma glucose, it was observed that sensitivity indices of parameters with respect to plasma glucose do vary with plasma glucose concentration; however, plasma glucose was frequently observed to be most sensitive to insulin-dependent glucose uptake rate. The new established conditions for hyperglycemia and hypoglycemia cast some light on the etiological studies of the diseases; they call for more empirical research work on the disease’s etiology beyond insulin resistance and inadequate insulin secretion.

Model updating method for hybrid simulation based on global sensitivity analysis

AbstractThe hybrid simulation (HS) is a cost‐effective and promising method for investigating the seismic performance of structures. This paper proposes a model updating method for HS to improve incomplete boundary conditions and model error, and develops criteria to select the updated parameters. First, an actual HS model updating is conducted to verify the effectiveness of uniform design as a parameter estimation method. This experiment shows that parameter sensitivity has a significant relationship with the update effect. Then, the Sobol global sensitivity analysis (GSA) method is applied to the HS model updating to obtain the sensitivity indices of parameters that change with time, which provides a sound basis for parameter selection and the determination of the search range. Following this, a whole‐structure module for dynamic time history analysis is proposed to improve the boundary conditions, simplify the implementation, and refine the numerical models. The errors in six boundary conditions of the traditional HS are then analyzed. The proposed method of model updating based on GSA is then obtained by integrating the above ideas. In the case of multiple inputs of ground motion, four strategies are developed to verify the effectiveness of the method. The results of a total of 216 numerical cases under different working conditions show that the proposed method can improve the accuracy of HSs and the identified parameters.

Parameter sensitivity analysis of electrochemical model-based battery management systems for lithium-ion batteries

Accurate identification of physical parameters of a lithium-ion electrochemical model is of critical importance for next-generation battery management systems. The complexity of the electrochemical model increases the difficulty of the identification process, and hence the analysis of parameter identifiability is the cornerstone for accurate parameter identification. The overarching goal of this paper is to analyze the parameter sensitivity of an electrochemical model under both the charging process and real-world driving cycles. The boundaries for the sensitivity analysis of 26 physical parameters are determined with a systematic benchmarking of published parameters for lithium Nickel-Manganese-Cobalt-Oxide/graphite cells. In particular, the sensitivity of the parameters is analyzed not only for terminal voltage but also for essential states in an electrochemical model-based battery management system, e.g., cathode bulk state of charge, cathode surface state of charge and anode potential. The sensitivity matrices of the parameters under different C-rates and depth of discharge regions clearly show their different influences on capacity-related parameters and other parameters. Furthermore, the rankings of the normalized parameter sensitivity index provide us the identifiability of the parameters, as well as the influence of parameter inaccuracy on the main functionalities in an electrochemical model-based battery management system.

Parameter sensitivity analysis of a 5-DoF parallel manipulator

Abstract With the capability of determining main/subordinate parameters, parameter sensitivity analysis plays an important role in eliminating unimportant parameters and simplifying performance analysis and optimization model. Taking a 5 degree-of-freedom parallel manipulator (T5 PM) as an example, the effects of joint stiffness/compliance coefficients and parameters of cross section to the mass and stiffness performance are investigated through parameter sensitivity analysis based on response surface method and performance reliability. By selecting experimental strategy and implementing accuracy assessment, the response surface method is adopted to establish the mapping model of parameters and performance with high efficiency and accuracy. In the light of reliability sensitivity, the performance reliability to parameter mean value and variance are simultaneously considered by the global parameter sensitivity index, which is the principle for determining the impact extent of parameters. Moreover, how the parameters affect the targeted performance can be evaluated through RSAV, RSPC and RSNC defined by the performance reliability to the parameter mean value. After verifying the sensitivity analysis approach by SolidWorks simulation, the parameter discussion of T5 PM is carried out. 15 parameters are selected from the original 39 parameters and effects of these parameters are clearly demonstrated, which provide reference for the future optimization process.

Trajectory sensitivity analysis of first order and second order on position control system of highly integrated valve-controlled cylinder

A Highly-integrated valve-controlled cylinder (HIVC) that has the advantage of large power weight ratio and fast response is widely applied in many fields. To ensure high performance of HIVC, control strategy selection and structure parameters optimization are essential; thus, performance-influenced main parameters and secondary parameters should be well-grasped to target control compensation and structure optimization. Trajectory sensitivity analysis (TSA), a branch of sensitivity analysis, can be adapted to research on the effects of control and structure parameter variation on system performance; the analysis conclusions can be used to improve system performance and the analysis has been applied in many applications in various fields. In this paper, based on the mathematical model of the First-order trajectory sensitivity analysis (FOTSA), the mathematical model of Second trajectory sensitivity analysis (SOTSA) is further derived; the general expression of the second-order trajectory sensitivity equations and the special expression that is applicable to each system parameter sensitivity analysis of HIVC are built respectively. Furthermore, based on the position control system of the nonlinear mathematical model of HIVC involved with servo valve dynamic characteristics, flow-pressure nonlinearity, initial piston position of servo cylinder, and friction nonlinearity, the coefficient items and the free items matrices of the special expression are calculated. Moreover, the First-order trajectory sensitivity function (FOTSF) and the Second trajectory sensitivity function (SOTSF) of the 17 main parameters in HIVC are computed on the MATLAB/Simulink platform under nine typical working conditions of the displacement step response. Then, the dynamic change rules and the differences and similarities of each parameter sensitivity analysis results are obtained through FOTSA and SOTSA under different working conditions with different parameter variations; each parameter sensitivity variation histogram based on the two kinds of sensitivity indexes, including the maximum value of the percentage absolute value and the absolute value summation within the sampling time, are given. Furthermore, differences and similarities of each parameter sensitivity index change rule and value are quantitatively analyzed. Finally, the sensitivity index change rules and values of the four parameters in the position control system of HIVC, including system supply oil pressure, proportion gain, initial piston position of servo cylinder, and load are experimentally verified. All above studies indicate that each parameter SOTSA result of HIVC vary under different working conditions. When parameter variation is significant, the differences in certain parameter sensitivity analysis between FOSTA and SOTSA are relatively significant; and SOTSA results are more similar to the test results, which illustrates that SOTSA results are more accurate.

Important population viability analysis parameters for giant pandas (Aliuropoda melanoleuca).

Population viability analysis (PVA) is a tool to evaluate the risk of extinction for endangered species and aid conservation decision-making. The quality of PVA output is dependent on parameters related to population dynamics and life-history; however, it has been difficult to collect this information for the giant panda (Aliuropoda melanoleuca), a rare and endangered mammal native to China, confined to some 30 fragmented habitat patches. Since giant pandas are long-lived, mature late, have lower reproductive rates, and show little sexual dimorphism, obtaining data to perform adequate PVA has been difficult. Here, we develop a parameter sensitivity index by modeling the dynamics of six giant panda populations in the Minshan Mountains, in order to determine the parameters most influential to giant panda populations. Our data shows that the giant panda populations are most sensitive to changes in four female parameters: initial breeding age, reproductive rate, mortality rate between age 0 and 1, and mortality rate of adults. The parameter sensitivity index strongly correlated with initial population size, as smaller populations were more sensitive to changes in these four variables. This model suggests that demographic parameters of females have more influence on the results of PVA, indicating that females may play a more important role in giant panda population dynamics than males. Consequently, reintroduction of female individuals to a small giant panda population should be a high priority for conservation efforts. Our findings form a technical basis for the coming program of giant panda reintroduction, and inform which parameters are crucial to successfully and feasibly monitoring wild giant panda populations.

Sensitivity analysis of pharmacokinetic and pharmacodynamic systems: I. A structural approach to sensitivity analysis of physiologically based pharmacokinetic models.

Based on a frequency response approach to the sensitivity analysis of pharmacokinetic models, the concept of structural sensitivity is introduced. The core of this concept is the factorization of the system sensitivity into two multipliers. The first one, called structural sensitivity index, has an analytical form, which depends solely on the structure and connectivity of the system and does not depend on the drug administered or the factor perturbed. The second multiplier, the parameter sensitivity index, depends on the drug properties, the tissue of interest and the parameter perturbed, but is largely independent of the structure of the system. The structural and parametric sensitivity indices can be evaluated and analyzed separately. The most important feature of the proposed approach is that the conclusions drawn from the analysis of the structural sensitivity index are valid across all mammalian species, as the latter share a common anatomical and physiological structure. The concept of structural sensitivity is illustrated on the commonly used structure of the whole body physiologically based pharmacokinetic models by showing that the factorization of the sensitivity carried out arises naturally from the mechanism of the distribution of perturbations throughout the organism. The concept of structural sensitivity has interesting practical implications. It enables the formal proof of relationships and facts that have been observed previously. Moreover, the conclusions drawn introduce in fact a ranking of the tissues or subsystems with respect to their impact on the model outputs. From this ranking, direct recommendations regarding the design of experiments for whole-body physiologically based pharmacokinetic models are derived.