Design of a control system model in SimulationX using calibration and optimization Dynardo GmbH 1 © Dynardo GmbH Notes • Please let your microphone muted • Use the chat window to ask questions • During short breaks we will answer your questions Supported versions • From version 4.1 optiSLang supports SimulationX since version 3.5 Design of a control system model in SimulationX 2 using calibration and optimization © Dynardo GmbH 1. Introduction 2. Process integration 3. Sensitivity 4. Optimization analysis 5. Trainings & Contact Design of a control system model in SimulationX 3 using calibration and optimization © Dynardo GmbH 1. Introduction 2. Process integration 3. Sensitivity 4. Optimization analysis 5. Trainings & Contact Design of a control system model in SimulationX 4 using calibration and optimization © Dynardo GmbH Dynardo • Founded: 2001 (Will, Bucher, CADFEM International) • More than 60 employees, offices at Weimar and Vienna • Leading technology companies Daimler, Bosch, E.ON, Nokia, Siemens, BMW are supported Software Development CAE-Consulting • Mechanical engineering • Civil engineering & Dynardo is engineering specialist for Geomechanics CAE-based sensitivity analysis, • Automotive industry optimization, robustness evaluation • Consumer goods industry and robust design optimization • Power generation Design of a control system model in SimulationX 5 using calibration and optimization © Dynardo GmbH Application of Multi-disciplinary Optimization • Virtual prototyping is an interdisciplinary process • Multidisciplinary approach requires to run different solvers in parallel and to handle different types of constraints and objectives • Arbitrary engineering software with complex non-linear analysis have to be connected • The resulting optimization problem may become very noisy, very sensitive to design changes or ill conditioned for mathematical function analysis (e.g. non-differentiable, non-convex, non-smooth) Design of a control system model in SimulationX 6 using calibration and optimization © Dynardo GmbH Excellence of optiSLang • algorithmic toolbox for • sensitivity analysis, • optimization, • robustness evaluation, • reliability analysis • robust design optimization (RDO) • complete functionality of stochastic analysis to run real world industrial applications • optiSLang advantages: • easy and reliable application, • predefined workflows, • algorithmic wizards and • robust default settings Design of a control system model in SimulationX 7 using calibration and optimization © Dynardo GmbH Example: design of a control system dynamic system • control loop consisting of a dynamic system and a controller • system transfer function should fit with a measured one from a real system • consequence is a difference between input and output signal • controller has to minimize the difference between both signals Design of a control system model in SimulationX 8 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Design parameters Responses Task • System gain • Output signal • Minimize the difference • Delay time between output signal • 2 time constants and measured reference signal SimulationX model measured reference signal Design of a control system model in SimulationX 9 using calibration and optimization © Dynardo GmbH 1. Introduction 2. Process integration 3. Sensitivity 4. Optimization analysis 5. Trainings & Contact Design of a control system model in SimulationX 10 using calibration and optimization © Dynardo GmbH Process Integration Parametric model as base for • User defined optimization (design) space • Naturally given robustness (random) space Design variables Entities that define the design space Response variables The CAE process Outputs from the Generates the system Scattering variables results according Entities that define the to the inputs robustness space Design of a control system model in SimulationX 11 using calibration and optimization © Dynardo GmbH Input and Response Variables • Scalar design variables with continuous, discrete and binary resolution and real, integer or string type • Scattering variables with continuous resolution • Scalar responses with continuous resolution • Vector responses with continuous resolution having variable length • Signal responses having variable length and several channels Design of a control system model in SimulationX 12 using calibration and optimization © Dynardo GmbH optiSLang Integrations Connection of arbitrary ASCII file based solvers Direct integrations Ansys Workbench Matlab Python Excel SimulationX Supported connections Ansys Abaqus Adams Design of a control system model in SimulationX 13 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Definition of the Input Parameters • The input parameters and its properties can be defined directly in the SimulationX integration node Design of a control system model in SimulationX 14 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Definition of the Reference Signal • The reference signal is given in an ASCII text file Design of a control system model in SimulationX 15 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Definition of the Error Measure and Responses • The SimulationX and the reference signal are compared in an ETK node • The resulting error measure is used as scalar response within the objective function Design of a control system model in SimulationX 16 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Definition of the Objective and Constraint • The objective function is defined as a minimization criterion • Constraints are not necessary Design of a control system model in SimulationX 17 using calibration and optimization © Dynardo GmbH The Integration Flow Parametric System • SimulationX node with loaded model system.isx • Text ETK node to read the reference signal from text file and to compute the signal difference Design of a control system model in SimulationX 18 using calibration and optimization © Dynardo GmbH 1. Introduction 2. Process integration 3. Sensitivity 4. Optimization analysis 5. Trainings & Contact Design of a control system model in SimulationX 19 using calibration and optimization © Dynardo GmbH The Sensitivity Flow Design of a control system model in SimulationX 20 using calibration and optimization © Dynardo GmbH Scanning the Design Space Inputs Design of Experiments Model evaluation Outputs • Uniform distribution of inputs is represented by Latin Hypercube Sampling • Minimum number of samples (variants) should represent statistical properties, cover the input space optimally and avoid clustering • For each design all responses are calculated Design of a control system model in SimulationX 21 using calibration and optimization © Dynardo GmbH Metamodel of Optimal Prognosis (MOP) • Approximation of model output by fast surrogate model • Reduction of input space to get best compromise between available information (variants) and model representation (number of inputs) • Determination of optimal approximation model • Assessment of approximation quality • Evaluation of variable sensitivities Design of a control system model in SimulationX 22 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Sensitivity with Respect to the Objective • The signal difference is mainly influenced by two parameters • Moving Least Squares approximation is a sufficient meta-model • Small values of the system gain results in strong signal deviations Design of a control system model in SimulationX 23 using calibration and optimization © Dynardo GmbH 1. Introduction 2. Process integration 3. Sensitivity 4. Optimization analysis 5. Trainings & Contact Design of a control system model in SimulationX 24 using calibration and optimization © Dynardo GmbH The Optimization Flow • Flow contains the existing sensitivity and an additional optimization • Due to the small number of design parameters, the simplex algorithm is a good choice • As start design automatically the best design of the sensitivity analysis is considered Design of a control system model in SimulationX 25 using calibration and optimization © Dynardo GmbH optiSLang Optimization Algorithms Gradient-based Gradient-free Nature inspired Methods Methods Optimization • Most efficient method if • Attractive methods for • GA/EA/PSO imitate gradients are accurate a small set of mechanisms of nature to enough continuous variables improve individuals • Consider its restrictions • Method of choice if • Method of choice if like local optima, only gradient-based fails gradient-based or continuous variables gradient-free fails and noise • Very robust against numerical noise, non- linearity, number of Start variables,… Design of a control system model in SimulationX 26 using calibration and optimization © Dynardo GmbH Decision Tree for Optimizer Selection • optiSLang automatically suggests an optimizer depending on the parameter properties, the defined criteria and user specified settings Design of a control system model in SimulationX 27 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Optimization Downhill Simplex Method • Convergence criteria fulfilled after 160 variants • Small improvement after 81 variants Design of a control system model in SimulationX 28 using calibration and optimization © Dynardo GmbH Step 1: calibration of the dynamic system Final