Meeting of the Steering Group on Simulation (SGS) Defining the simulation plan in the Kriging meta-model development Thessaloniki, 07 February 2014 Biagio.Ciuffo@jrc.ec.europa.eu Alessandro.Marotta@jrc.ec.europa.eu Georgios.Fontaras@jrc.ec.europa.eu

Need for a simulation plan Once the simulation models are ready a plan is required in order to cover all the vehicles of a specific segment with all the necessary technology combinations It requires Knowing the parameters of the model that characterize a vehicle in terms of CO2 difference between WLTP and NEDC Knowing the technology packages to involve in the simulation Define a strategy to combine parameters and technologies to cover the market

Parameter selection Expert judgment Pros Cheap and fast Cons Leave some uncertainties (especially for rather unexplored issues like the WLTP/NEDC correlation) Difficult to foresee interactions Global sensitivity analysis of the model All the inputs are taken into consideration All their interactions are checked Computationally expensive (it requires many simulation)

Global sensitivity analysis Family of theories and techniques aimed at defining how “the uncertainty in the model outputs can be apportioned to the different sources of uncertainties in the model inputs” Important to: uncover technical errors in the model identify critical regions in the inputs domain simplify models Variance-based methods Output variance as a proxy of output uncertainty Variance decomposition formulas as sensitivity analysis tools

Variance-based methods (Cukier, 1973; Sobol, 1990; Homma and Saltelli, 2000)

First order effect

Variance decomposition

Sobol sensitivity indices An efficient (numerical) evaluation of Sobol indices requires the application of techniques based on QMC methods (Saltelli et al 2012)

Sensitivity analysis of Cruise Select a vehicle configuration (e.g. Opel Astra) Identify all the Cruise parameters that characterize the model Define ranges of variability for each parameter (in order to consider the variability in the segment) Design a simulation plan for the evaluation of the sensitivity indices Perform the simulations Check for unfeasible combinations Evaluate the sensitivity indices Rank the parameters on the basis of their effect Define a threshold before influential vs. non-influential

Definition of representative vehicle segments Sensitivity Analysis of model outputs Two validated vehicle configurations modeled with PHEM Vehicle parameters are then set to change in 60% (on average ±30%) range From these ranges, more that 1.000 parameters combinations have been evaluated in order to evaluate first order and total order sensitivity indices

Definition of representative vehicle segments Sensitivity Analysis results Gasoline Diesel Power Power Gear-box Gear-box Mass Mass Can be fixed to whatever value

Quasi-Monte Carlo Simulation Plan Monte Carlo framework using Sobol quasi-random sequences: “Quasi Monte Carlo” methods If the sequence of random numbers keeps “low-discrepancy” whatever the number of dimensions, the size of the Monte Carlo experiment decreases Discrepancy: a measure of deviation from uniformity Prof. I.M.Sobol has devoted big part of his life in studying LDS properties

Some properties of Sobol sequences (1)

Some properties of Sobol sequences (2) In integral calculation, error e: Sobol sequence (for N=2k) Other LDS Random numbers

Conclusions Quasi-random experimental design can be used in building the simulation plan Coverage of the input-space depends on the number of inputs Global Sensitivity Analysis can be used to reduce the number of inputs in an effective way The number of simulations to estimate each meta-model is defined by the accuracy level required in the study