Multi-parameter Sensitivity Analysis and Application Research in the Robust Optimization Design for Complex Nonlinear System

The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-dimensional curve or robust control design is used to find an accurate robust solution. However, there may exist complex interaction between parameters and practical engineering system. With the increase of the number of parameters, it is getting hard to determine high-dimensional curves and robust control methods, thus it＇s difficult to get the robust design solutions. In this paper, a method of global sensitivity analysis based on divided variables in groups is proposed. By making relevant variables in one group and keeping each other independent among sets of variables, global sensitivity analysis is conducted in grouped variables and the importance of parameters is evaluated by calculating the contribution value of each parameter to the total variance of system response. By ranking the importance of input parameters, relatively important parameters are chosen to conduct robust design analysis of the system. By applying this method to the robust optimization design of a real complex nonlinear system-a vehicle occupant restraint system with multi-parameter, good solution is gained and the response variance of the objective function is reduced to 0.01, which indicates that the robustness of the occupant restraint system is improved in a great degree and the method is effective and valuable for the robust design of complex nonlinear system. This research proposes a new method which can be used to obtain solutions for complex nonlinear system robust design.

Uncertainty and sensitivity analysis of in-vessel phenomena under severe accident mitigation strategy based on ISAA-SAUP program

The phenomenology involved in severe accidents in nuclear reactors is highly complex.Currently,integrated analysis programs used for severe accident analysis heavily rely on custom empirical parameters,which introduce considerable uncertainty.Therefore,in recent years,the field of severe accidents has shifted its focus toward applying uncertainty analysis methods to quantify uncertainty in safety assessment programs,known as“best estimate plus uncertainty(BEPU).”This approach aids in enhancing our comprehension of these programs and their further development and improvement.This study concentrates on a third-generation pressurized water reactor equipped with advanced active and passive mitigation strategies.Through an Integrated Severe Accident Analysis Program(ISAA),numerical modeling and uncertainty analysis were conducted on severe accidents resulting from large break loss of coolant accidents.Seventeen uncertainty parameters of the ISAA program were meticulously screened.Using Wilks'formula,the developed uncertainty program code,SAUP,was employed to carry out Latin hypercube sampling,while ISAA was employed to execute batch calculations.Statistical analysis was then conducted on two figures of merit,namely hydrogen generation and the release of fission products within the pressure vessel.Uncertainty calculations revealed that hydrogen production and the fraction of fission product released exhibited a normal distribution,ranging from 182.784 to 330.664 kg and from 15.6 to 84.3%,respectively.The ratio of hydrogen production to reactor thermal power fell within the range of 0.0578–0.105.A sensitivity analysis was performed for uncertain input parameters,revealing significant correlations between the failure temperature of the cladding oxide layer,maximum melt flow rate,size of the particulate debris,and porosity of the debris with both hydrogen generation and the release of fission products.

A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

Seismic response comparison and sensitivity analysis of pile foundation in liquefiable and non-liquefiable soils

Case history investigations have shown that pile foundations are more critically damaged in liquefiable soils than non-liquefiable soils.This study examines the differences in seismic response of pile foundations in liquefiable and non-liquefiable soils and their sensitivity to numerical model parameters.A two-dimensional finite element(FE)model is developed to simulate the experiment of a single pile foundation centrifuge in liquefiable soil subjected to earthquake motions and is validated against real-world test results.The differences in soil-pile seismic response of liquefiable and non-liquefiable soils are explored.Specifically,the first-order second-moment method(FOSM)is used for sensitivity analysis of the seismic response.The results show significant differences in seismic response for a soil-pile system between liquefiable and non-liquefiable soil.The seismic responses are found to be significantly larger in liquefiable soil than in non-liquefiable soil.Moreover,the pile bending moment was mainly affected by the kinematic effect in liquefiable soil,while the inertial effect was more significant in non-liquefiable soil.The controlling parameters of seismic response were PGA,soil density,and friction angle in liquefiable soil,while the pile bending moment was mainly controlled by PGA,the friction angle of soil,and shear modulus of loose sand in non-liquefiable soil.

Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM

Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation.

Seismic Liquefaction Resistance Based on Strain Energy Concept Considering Fine Content Value Effect and Performance Parametric Sensitivity Analysis

Liquefaction is one of the most destructive phenomena caused by earthquakes,which has been studied in the issues of potential,triggering and hazard analysis.The strain energy approach is a common method to investigate liquefaction potential.In this study,two Artificial Neural Network(ANN)models were developed to estimate the liquefaction resistance of sandy soil based on the capacity strain energy concept(W)by using laboratory test data.A large database was collected from the literature.One group of the dataset was utilized for validating the process in order to prevent overtraining the presented model.To investigate the complex influence of fine content(FC)on liquefaction resistance,according to previous studies,the second database was arranged by samples with FC of less than 28%and was used to train the second ANN model.Then,two presented ANN models in this study,in addition to four extra available models,were applied to an additional 20 new samples for comparing their results to show the capability and accuracy of the presented models herein.Furthermore,a parametric sensitivity analysis was performed through Monte Carlo Simulation(MCS)to evaluate the effects of parameters and their uncertainties on the liquefaction resistance of soils.According to the results,the developed models provide a higher accuracy prediction performance than the previously publishedmodels.The sensitivity analysis illustrated that the uncertainties of grading parameters significantly affect the liquefaction resistance of soils.

Sensitivity Analysis of Multi-phase Seepage Parameters Affecting the Clayey Silt Hydrate Reservoir Productivity in the Shenhu Area,South China Sea

Natural gas hydrate(NGH)is an important future resource for the 21st century and a strategic resource with potential for commercial development in the third energy transition.It is of great significance to accurately predict the productivity of hydrate-bearing sediments(HBS).The multi-phase seepage parameters of HBS include permeability,porosity,which is closely related to permeability,and hydrate saturation,which has a direct impact on hydrate content.Existing research has shown that these multi-phase seepage parameters have a great impact on HBS productivity.Permeability directly affects the transmission of pressure-drop and discharge of methane gas,porosity and initial hydrate saturation affect the amount of hydrate decomposition and transmission process of pressure-drop,and also indirectly affect temperature variation of the reservoir.Considering the spatial heterogeneity of multi-phase seepage parameters,a depressurization production model with layered heterogeneity is established based on the clayey silt hydrate reservoir at W11 station in the Shenhu Sea area of the South China Sea.Tough+Hydrate software was used to calculate the production model;the process of gas production and seepage parameter evolution under different multi-phase seepage conditions were obtained.A sensitivity analysis of the parameters affecting the reservoir productivity was conducted so that:(a)a HBS model with layered heterogeneity can better describe the transmission process of pressure and thermal compensation mechanism of hydrate reservoir;(b)considering the multi-phase seepage parameter heterogeneity,the influence degrees of the parameters on HBS productivity were permeability,porosity and initial hydrate saturation,in order from large to small,and the influence of permeability was significantly greater than that of other parameters;(c)the production potential of the clayey silt reservoir should not only be determined by hydrate content or seepage capacity,but also by the comprehensive effect of the two;and(d)time scales need to be considered when studying the effects of changes in multi-phase seepage parameters on HBS productivity.

Prediction and sensitivity analysis of the surface quality in Ni60/WC coatings

For laser cladding a large temperature gradient easily weakened the surface quality by generating cracks and irregular coating surfaces,which in turn affected the bearing capacity and corrosion resistance of coatings in the rapid heating and cooling process.The response surface methodology(RSM)was used to predict coating cracks by changing the powder ratio,energy density,and preheating temperature,which obtained the relevant mathematical model.After that,the sensitivity of the crack length to process parameters was analyzed based on the sensitivity analysis method.The effect of Ni60/WC composite powder process parameters on the surface quality was revealed in laser cladding.The crack length first decreased and then increased,and the Smooth decreased with the increased powder ratio.The crack length and Smooth increased with the increased energy density.The crack length decreased and Smooth increased with the increased preheating temperature.Sensitivity analysis showed that the crack length and Smooth were the most sensitive to the powder ratio.Therefore,the process parameters were reasonably selected to control the surface quality.The mathematical model and sensitivity analysis method in the work could improve the surface quality,which provided a theoretical basis for the prediction and control of laser cladding cracks.

A New Sensitivity Analysis Approach Using Conditional Nonlinear Optimal Perturbations and Its Preliminary Application

Simulations and predictions using numerical models show considerable uncertainties,and parameter uncertainty is one of the most important sources.It is impractical to improve the simulation and prediction abilities by reducing the uncertainties of all parameters.Therefore,identifying the sensitive parameters or parameter combinations is crucial.This study proposes a novel approach:conditional nonlinear optimal perturbations sensitivity analysis(CNOPSA)method.The CNOPSA method fully considers the nonlinear synergistic effects of parameters in the whole parameter space and quantitatively estimates the maximum effects of parameter uncertainties,prone to extreme events.Results of the analytical g-function test indicate that the CNOPSA method can effectively identify the sensitivity of variables.Numerical results of the theoretical five-variable grassland ecosystem model show that the maximum influence of the simulated wilted biomass caused by parameter uncertainty can be estimated and computed by employing the CNOPSA method.The identified sensitive parameters can easily change the simulation or prediction of the wilted biomass,which affects the transformation of the grassland state in the grassland ecosystem.The variance-based approach may underestimate the parameter sensitivity because it only considers the influence of limited parameter samples from a statistical view.This study verifies that the CNOPSA method is effective and feasible for exploring the important and sensitive physical parameters or parameter combinations in numerical models.

HVAC Optimal Control Based on the Sensitivity Analysis:An Improved SA Combination Method Based on a Neural Network

Aiming at optimizing the energy consumption of HVAC,an energy conservation optimization method was proposed for HVAC systems based on the sensitivity analysis(SA),named the sensitivity analysis combination method(SAC).Based on the SA,neural network and the related settings about energy conservation of HVAC systems,such as cooling water temperature,chilled water temperature and supply air temperature,were optimized.Moreover,based on the data of the existing HVAC system,various optimal control methods ofHVAC systems were tested and evaluated by a simulated HVAC system in TRNSYS.The results show that the proposed SA combination method can reduce significant computational load while maintaining an equivalent energy performance compared with traditional optimal control methods.

Sensitivity analysis and probability modelling of the structural response of a single-layer reticulated dome subjected to an external blast loading

The structural response of a single-layer reticulated dome to external explosions is shaped by many variables,and the associated uncertainties imply non-deterministic results.Existing deterministic methods for predicting the consequences of specific explosions do not account for these uncertainties.Therefore,the impact of the uncertainties associated with these input variables on the structures’response needs to be studied and quantified.In this study,a parametric uncertainty analysis was conducted first.Then,local and global sensitivity analyses were carried out to identify the drivers of the structural dynamic response.A probabilistic structural response model was established based on sensitive variables and a reasonable sample size.Furthermore,some deterministic empirical methods for explosion-resistance design,including the plane blast load model of CONWEP,the curved blast load model under the 50%assurance level,and the 20%mass-increased method,were used for evaluating their reliability.The results of the analyses revealed that the structural response of a single-layer reticulated dome to an external blast loading is lognormally distributed.Evidently,the MB0.5 method based on the curved reflector load model yielded results with a relatively stable assurance rate and reliability,but CONWEP did not;thus,the 1.2MB0.5 method can be used for making high-confidence simple predictions.In addition,the results indicated that the structural response is very sensitive to the explosion parameters.Based on these results,it is suggested that for explosion proofing,setting up a defensive barrier is more effective than structural strengthening.

Sensitivity analysis of factors affecting gravity dam anti-sliding stability along a foundation surface using Sobol method

The anti-sliding stability of a gravity dam along its foundation surface is a key problem in the design of gravity dams.In this study,a sensitivity analysis framework was proposed for investigating the factors affecting gravity dam anti-sliding stability along the foundation surface.According to the design specifications,the loads and factors affecting the stability of a gravity dam were comprehensively selected.Afterwards,the sensitivity of the factors was preliminarily analyzed using the Sobol method with Latin hypercube sampling.Then,the results of the sensitivity analysis were verified with those obtained using the Garson method.Finally,the effects of different sampling methods,probability distribution types of factor samples,and ranges of factor values on the analysis results were evaluated.A case study of a typical gravity dam in Yunnan Province of China showed that the dominant factors affecting the gravity dam anti-sliding stability were the anti-shear cohesion,upstream and downstream water levels,anti-shear friction coefficient,uplift pressure reduction coefficient,concrete density,and silt height.Choice of sampling methods showed no significant effect,but the probability distribution type and the range of factor values greatly affected the analysis results.Therefore,these two elements should be sufficiently considered to improve the reliability of the dam anti-sliding stability analysis.

Parameter sensitivity analysis for a biochemically-based photosynthesis model

A challenge for the development of Land Surface Models(LSMs) is improving transpiration of water exchange and photosynthesis of carbon exchange between terrestrial plants and the atmosphere, both of which are governed by stoma in leaves. In the photosynthesis module of these LSMs, variations of parameters arising from diversity in plant functional types(PFTs) and climate remain unclear. Identifying sensitive parameters among all photosynthetic parameters before parameter estimation can not only reduce operation cost, but also improve the usability of photosynthesis models worldwide. Here, we analyzed 13 parameters of a biochemically-based photosynthesis model(FvCB), implemented in many LSMs, using two sensitivity analysis(SA) methods(i.e., the Sobol’ method and the Morris method) for setting up the parameter ensemble. Three different model performance metrics, i.e.,Root Mean Squared Error(RMSE), Nash Sutcliffe efficiency(NSE), and Standard Deviation(STDEV) were introduced for model assessment and sensitive parameters identification. The results showed that among all photosynthetic parameters only a small portion of parameters were sensitive, and the sensitive parameters were different across plant functional types: maximum rate of Rubisco activity(Vcmax25), maximum electron transport rate(Jmax25), triose phosphate use rate(TPU) and dark respiration in light(Rd) were sensitive in broad leafevergreen trees(BET), broad leaf-deciduous trees(BDT) and needle leaf-evergreen trees(NET), while only Vcmax25and TPU are sensitive in short vegetation(SV), dwarf trees and shrubs(DTS), and agriculture and grassland(AG). The two sensitivity analysis methods suggested a strong SA coherence;in contrast, different model performance metrics led to different SA results. This misfit suggests that more accurate values of sensitive parameters, specifically, species specific and seasonal variable parameters, are required to improve the performance of the FvCB model.

Dynamic Modeling and Sensitivity Analysis for an MEA-Based CO_(2) Capture Absorber

The absorber is the key unit in the post-combustion monoethanolamine(MEA)-based carbon dioxide(CO_(2))capture process.A rate-based dynamic model for the absorber is developed and validated using steady-state experimental data reported in open literature.Sensitivity analysis is performed with respect to important model parameters associated with the reaction,mass transport and phy-sical property relationships.Then,a singular value decomposition(SVD)-based subspace parameter estimation method is proposed to improve the model accu-racy.Finally,dynamic simulations are carried out to investigate the effects of the feed rate of lean MEA solution and the flue inlet conditions.Simulation results indicate that the established dynamic model can reasonably reflect the physical behavior of the absorber.Some new insights are gained from the simulation results.

A Processor Performance Prediction Method Based on Interpretable Hierarchical Belief Rule Base and Sensitivity Analysis

The prediction of processor performance has important referencesignificance for future processors. Both the accuracy and rationality of theprediction results are required. The hierarchical belief rule base (HBRB)can initially provide a solution to low prediction accuracy. However, theinterpretability of the model and the traceability of the results still warrantfurther investigation. Therefore, a processor performance prediction methodbased on interpretable hierarchical belief rule base (HBRB-I) and globalsensitivity analysis (GSA) is proposed. The method can yield more reliableprediction results. Evidence reasoning (ER) is firstly used to evaluate thehistorical data of the processor, followed by a performance prediction modelwith interpretability constraints that is constructed based on HBRB-I. Then,the whale optimization algorithm (WOA) is used to optimize the parameters.Furthermore, to test the interpretability of the performance predictionprocess, GSA is used to analyze the relationship between the input and thepredicted output indicators. Finally, based on the UCI database processordataset, the effectiveness and superiority of the method are verified. Accordingto our experiments, our prediction method generates more reliable andaccurate estimations than traditional models.

Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Global sensitivity analysis of wheat grain yield and quality and the related process variables from the DSSAT-CERES model based on the extended Fourier Amplitude Sensitivity Test method

A crop growth model,integrating genotype,environment,and management factor,was developed to serve as an analytical tool to study the influence of these factors on crop growth,production,and agricultural planning.A major challenge of model application is the optimization and calibration of a considerable number of parameters.Sensitivity analysis(SA) has become an effective method to identify the importance of various parameters.In this study,the extended Fourier Amplitude Sensitivity Test(EFAST) approach was used to evaluate the sensitivity of the DSSAT-CERES model output responses of interest to 39 crop genotype parameters and six soil parameters.The outputs for the SA included grain yield and quality(take grain protein content(GPC) as an indicator) at maturity stage,as well as leaf area index,aboveground biomass,and aboveground nitrogen accumulation at the critical process variables.The key results showed that:(1) the influence of parameter bounds on the sensitivity results was slight and less than the impacts from the significance of the parameters themselves;(2) the sensitivity parameters of grain yield and GPC were different,and the sensitivity of the interactions between parameters to GPC was greater than those between the parameters to grain yield;and(3) the sensitivity analyses of some process variables,including leaf area index,aboveground biomass,and aboveground nitrogen accumulation,should be performed differently.Finally,some parameters,which improve the model’s structure and the accuracy of the process simulation,should not be ignored when maturity output as an objective variable is studied.

Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Global analysis of sensitivity of bioretention cell design elements to hydrologic performance

Analysis of sensitivity of bioretention cell design elements to their hydrologic performances is meaningful in offering theoretical guidelines for proper design. Hydrologic performance of bioretention cells was facilitated with consideration of four metrics： the overflow ratio, groundwater recharge ratio, ponding time, and runoff coefficients. The storm water management model （SWMM） and the bioretention infiltration model RECARGA were applied to generating runoff and outflow time series for calculation of hydrologic performance metrics. Using a parking lot to build a bioretention cell, as an example, the Morris method was used to conduct global sensitivity analysis for two groups of bioretention samples, one without underdrain and the other with underdrain. Results show that the surface area is the most sensitive element to most of the hydrologic metrics, while the gravel depth is the least sensitive element whether bioretention cells are installed with underdrain or not. The saturated infiltration rate of planting soil and the saturated infiltration rate of native soil are the other two most sensitive elements for bioretention cells without underdrain, while the saturated infiltration rate of native soil and underdrain size are the two most sensitive design elements for bioretention cells with underdrain.