Global Sensitivity Analysis for the determination of parameter importance in bio‐manufacturing processes

The design space (DS) is defined as the combination of materials and process conditions that provides assurance of quality for a pharmaceutical product. A model-based approach to identify a probability-based DS requires costly simulations across the entire process parameter space (certain) and the uncertain model parameter space and material properties space. We demonstrate that application of global sensitivity analysis (GSA) can significantly reduce model complexity and reduce computational time for identifying and quantifying a probabilistic DS by screening out nonimportant uncertain parameters. The novelty of this approach is that the use of an indicator function, which takes only binary values as a model function, allows application of a straightforward GSA based on Sobol' sensitivity indices and avoids using more costly Monte Carlo filtering or GSA for constrained problems. We consider a chemical reaction example to illustrate how this formulation results in a model reduction and a significant decrease of model runs.

Unraveling the complex dynamics of temporal moments for multispecies contaminant transport in saturated porous media: A global sensitivity analysis approach

The aim of sensitivity analysis (SA) is to ascertain how much the uncertainty in the output of a model is influenced by the uncertainty in its input factors. An SA can be performed using different methods, which are classified according to various criteria. One possible classification is that in which global and local approaches are identified. This paper strengthens the role of global SA methods and suggests their use in the context of MCDA. Useful applications of global SA already exist in a variety of fields where numerical models are considered, e.g. in economics, engineering and chemistry. Global SA is quite different in its formulation and application from local SA, which is seen more frequently in the literature. The global sensitivity indices adopted are derived from a variance decomposition scheme: they can be estimated by alternative computational strategies, such as the extended FAST or the method proposed by Sobol’. A truly global SA is capable of apportioning the output uncertainty according to any subgroup of input factors. Hence, the output uncertainty of an MCDA can, for instance, be decomposed into a part due to uncertain model inputs and a part due to poorly defined (or variable) weights attached to the criteria. This information could be useful to the decision maker (DM) since it explains synthetically how much the assessment of an MCDA study is biased by the assessor judgements. Alternative regrouping of the uncertain input elements might shed light on other features of the problem addressed by the DM. Copyright © 1999 John Wiley & Sons, Ltd.

Determination of an optimal measurement configuration in optical scatterometry using global sensitivity analysis

Application of global sensitivity analysis to statistical energy analysis: Vehicle model development and transmission path contribution

The main focus of this thesis is the uncertainty propagation (UP) and global sensitivity analysis (GSA) in complex hydrogeological numerical models. Various methods are presented with applications on numerical models for the groundwater flow and mean lifetime expectancy (MLE) in the scope of Andra's (French National Radioactive Waste Management Agency) project for the geological disposal of high-level and intermediate-level long-lived radioactive wastes in a highly impermeable layer from Callovo-Oxfordian age (COX) in France. <br> A state of the art is provided for the theory of uncertainty propagation and for the methodologies of sensitivity analyses in a broad sense. Methods for UP are provided from 2-levels Factorial Designs to quasi-random samplings. GSA techniques encompass screening methods such as the Morris Measures and the Derivative-based Global Sensitivity Measures (DGSM), and also the so-called Sobol' indices based upon the variance decomposition of the response of interest. Meta-modelling techniques such as polynomial regression and Polynomial Chaos Expansions (PCE) meta-models are employed as surrogate models for UP and GSA purpose at negligible computational-costs. A comparison of GSA techniques upon various complex analytical test-functions was undertaken with the purpose of determining a relevant method to be employed in the context of “screening” out unimportant variables in computer-intensive, high-dimensional models. <br> A numerical model of groundwater flow and lifetime expectancy is employed for assessing the effect of uncertain advection-dispersion parameters and their spatial distributions upon the MLE from a target zone inside the domain. The model is a 2-dimensions synthetic cross-section of the eastern region of the Paris Basin (Meuse/Haute-Marne sector). This model was used as an exploratory tool for sensitivity analysis methods applied upon numerous sets of uncertain hydrodynamic and dispersion parameters in 15 layers. The uncertainty characterizing the permeability-porosity values in aquifer formations encompassing the COX have proved to add much of variability to the MLE calculated from the target zone. The model also served at exploring the effect of the spatial variability of permeability-porosity parameters in two main aquifer sequences on the groundwater flow rates and MLE in the model. The variabilities of the output responses are mainly due to the uncertainty upon the means and variances of the permeability-porosity distributions, as well as the longitudinal correlation lengths, in each sequence. <br> Then, a 3-dimensions high-definition hydrogeological model representing the Meuse/Haute-Marne sector in the eastern region of the Paris Basin is a more comprehensive numerical model incorporating realistic geometries, fractures, heterogeneities and discontinuities encountered on field. A sensitivity analysis of the MLE from a given zone located in the middle of the COX layer was performed by perturbing the hydraulic conductivities and porosities values in fourteen hydrogeological formations. The uncertain permeability-porosity parameters in the aquifer formations from Bathonian in the Dogger sequence, and Rauracian-Sequanian in the Oxfordian sequence, have strong and rather non-linear effects on the variability of the output response of interest. <br> The methodologies for UP and GSA employed in the present thesis have proved to be very efficient when applied to large hydrogeological models of groundwater flow and MLE. In particular, quasi-random sampling methods offer a flexible frame for providing the uncertainty distribution of the output response of interest at low computational costs. Screening techniques provide a fast estimation for the overall contribution of each input variable to the variability of the output. Meta-modelling techniques such as PCE proved highly accurate in individualising the low- and high-order effects of each input variable upon the output response of interest.

This paper presents the use of Global Sensitivity Analysis (GSA) methods to analyze the sensitivity level of the performance of the impedance measurement algorithm of SEL-421 distance relay protection when used to perform transmission line protection with compensation circuit. This GSA technique was developed to see the dominance effect of system uncertainty (or factors). Two techniques that might be used for sensitivity analysis using GSA are Quasi-Monte Carlo (QMC) and data sampling with Sobol technique. Experimental is done with DIgSILENT software to do modeling of the power system, simulation, and calculation of impedance and algorithm error. The testing is carried out automatically with the help of the developed algorithm using DPL (DIgSILENT Programming Language). SIMLAB software, in this case, (with Sobol technique) is applied to generate some non-linear factor data and analyze the output of variations in impedance measurement errors.

Tree-based ensemble methods for sensitivity analysis of environmental models: A performance comparison with Sobol and Morris techniques

We consider parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs. We illustrate these techniques for a dynamic HIV model but note that the parameter selection and verification framework is applicable to a wide range of biological and physical models. To accommodate the nonlinear input to output relations, which are typical for such models, we focus on global sensitivity analysis techniques, including those based on the Pearson correlation coefficient, Sobol indices based on second-order model representations, and Morris indices, as well as a parameter selection technique based on standard errors. A significant objective is to provide verification strategies to assess the accuracy of those techniques, which we illustrate in the context of the HIV model.

This paper presents a step-by-step procedure to study the impact of each thermal phenomenon occurring in electric machines on their internal temperature distribution. First, the Monte-Carlo method is chosen as a global sensitivity analysis technique. This method is applied on a thermal network of a prototype consisting of a permanent magnet based integrated starter-generator machine (ISG). Accordingly, the variation of electric machine critical temperatures in windings and rotor's permanent magnets is evaluated. In addition, a sensitivity index is defined for identifying network parameters that cause significant variation in the machine critical temperatures and should therefore be the focus of attention when designing electric machines. Finally, experimental tests are performed on the prototype and the difference between simulated and a measured temperature is presented.

ABSTRACTBiosorption of Pb and Cd from aqueous solution by biomass of Chara aculeolata was studied in a continuous packed bed column. C. aculeolata in the fixed bed column is capable of decreasing Pb and Cd concentrations from 10 mg/L to a value below the detection limit of 0.02 mg/L. Selective uptake of Pb and Cd in a binary solution resulted in Pb having much higher relative affinity than Cd. The experiments were conducted to study the effects of column design parameters, bed depth, and flow rate on the metal biosorption. Pb uptake capacity of C. aculeolata increased with increased bed depth and decreased flow rate, while Cd uptake capacity increased with increased bed depth but remained constant at any flow rate. The Thomas model was found in a suitable fitness with the experiment data for Pb and Cd (R2 > 0.90). The efficiency of biosorbent regeneration achieved by 0.1 M HCl was very high, that was, 98% for Pb and 100% for Cd in the third reused cycle. It can be concluded that C. aculeolata is a good biosorbent for treating wastewater having low concentrations of Pb and Cd contamination.

Experimental and theoretical studies were carried out to investigate the performance of a batch, fluidized/expanded ion-exchange system. Exchange of phenylalanine on cation exchange resin was studied in the linear velocity range 5.5-39.8 cm/min. The breakthrough curves were obtained at various design and operating conditions with changes of column size, distributor, bed type, bed height, flow rate, and number of stages. The breakthrough data were analyzed by two theoretical models. A CSTR-type model which we called a lumped model fitted the data well when bed aspect ratio (bed height/bed diameter) was less than 1.5 and column diameter was less than 4 cm. We considered the fluidized bed as a bed that can be well simulated by the lumped model (uniform mixing), and the expanded bed as a bed where the lumped model fails because of reduced backmixing. Another model, which is adapted from a packed bed model (VERSE) with axial dispersion, film diffusion, and intraparticle diffusion, fitted the data for both fluidized beds and expanded beds successfully. Experimental and theoretical results showed the bed type changed from a fluidized bed to an expanded bed as the bed aspect ratio increases. The breakthrough curves for the expanded bed and a packed bed were almost identical except at very short times. When sieve plates were used as liquid distributors, the plate with more holes of a smaller size was most efficient. Mass transfer at different flow rates and the effects of bed type and multiple stages are discussed

Fluid Catalytic Cracking (FCC) process is a vital unit to produce gasoline. In this research, a feed forward ANN model was developed and trained with industrial data to investigate the effect of operating variables containing reactor temperature feed flow rate, the temperature of the top of the main column and the temperature of the bottom of the debutanizer tower on quality and quantity of gasoline, LPG flow rate and process conversion. Eventually, validated ANN model and firefly algorithm which is an evolutionary optimization algorithm were applied to optimize the operating conditions. Three different optimization cases including maximization of RON (as the parameter which demonstrates the quality of the gasoline), gasoline flow rate and conversion were investigated. In order to obtain the maximum level of targeted output variables, inlet reactor temperature, temperature of the top of the main column, temperature of the bottom of debutanizer column and feed flow rate should respectively set at 525,138, 169oC and 43000 bbl/day. Also, sensitivity analysis between the input and output variables were carried out to derive some effective rule-of- thumb to facilitate the operation of the process under unsteady state conditions. The result introduces a methodology to compensate for the negative effect of undesirable variation in some operating variables by manipulating the others.

Removal of Pb(II) ions from electroplating wastewater of Bursa, an industrial city in Turkey, was investigated in fixed‐bed column. The experiments were conducted to study the effect of important design parameters such as column bed height and flow rate. The breakthrough profiles were obtained in these studies. At a bed height of 14 cm and flow rate of 6 mL/min, the metal‐uptake capacity of poly(ethylene glycol dimethacrylate‐1‐vinylimidazole) [poly(EGDMA‐VIM)] beads for Pb(II) ions was found to be 90 mg/g. Bed Depth Service Time (BDST) model was used to analyse the experimental data and evaluate the performance of adsorption column. For various flow rates, adsorption capacity per unit bed volume (N0) and adsorption rate constant (ka) are in the range of 2370–3560 mg/mL and 0.0225–0.0616 L/mg h, respectively. The saturated column was easily regenerated by 0.1 M HNO3 and the poly(EGDMA‐VIM) beads in fixed‐bed column could be reused for Pb(II) ions removal.

In the present study, continuous fixed bed column runs were carried out in an attempt to evaluate the feasibility of using bone char for the removal of manganese from acid mine drainage (AMD). Tests using a laboratory solution of pure manganese at typical concentration levels were also performed for comparison purposes. The following operating variables were evaluated: column height, flow rate, and initial pH. Significant variations in resistance to the mass transfer of manganese into the bone char were identified using the Thomas model. A significant effect of the bed height could only be observed in tests using the laboratory solution. No significant change in the breakthrough volume could be observed with different flow rates. By increasing the initial pH from 2.96 to 5.50, the breakthrough volume was also increased. The maximum manganese loading capacity in continuous tests using bone char for AMD effluents was 6.03 mg g-1, as compared to 26.74 mg g-1 when using the laboratory solution. The present study also performed desorption tests, using solutions of HCl, H2SO4, and water, aimed at the reuse of the adsorbent; however, no promising results were obtained due to low desorption levels associated with a relatively high mass loss. Despite the desorption results, the removal of manganese from AMD effluents using bone char as an adsorbent is technically feasible and attends to environmental legislation. It is interesting to note that the use of bone char for manganese removal may avoid the need for pH corrections of effluents after treatment. Moreover, bone char can also serve to remove fluoride ions and other metals, thus representing an interesting alternative material for the treatment of AMD effluents.