Design of a control system model in SimulationX using calibration and optimization. Dynardo GmbH

Transcription

1 Design of a control system model in SimulationX using calibration and optimization Dynardo GmbH 1

2 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 2

3 1. Introduction 2. Process integration 3. Sensitivity analysis 4. Optimization 5. Trainings & Contact 3

4 1. Introduction 2. Process integration 3. Sensitivity analysis 4. Optimization 5. Trainings & Contact 4

5 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 Dynardo is engineering specialist for CAE-based sensitivity analysis, optimization, robustness evaluation and robust design optimization Mechanical engineering Civil engineering & Geomechanics Automotive industry Consumer goods industry Power generation 5

6 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) 6

7 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 7

8 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 8

9 Step 1: calibration of the dynamic system Design parameters System gain Delay time 2 time constants Responses Output signal Task Minimize the difference between output signal and measured reference signal SimulationX model measured reference signal 9

10 1. Introduction 2. Process integration 3. Sensitivity analysis 4. Optimization 5. Trainings & Contact 10

11 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 Scattering variables Entities that define the robustness space The CAE process Generates the results according to the inputs Response variables Outputs from the system 11

12 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 12

13 optislang Integrations Connection of arbitrary ASCII file based solvers Direct integrations Ansys Workbench Matlab Python Excel SimulationX Supported connections Ansys Abaqus Adams 13

14 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 14

15 Step 1: calibration of the dynamic system Definition of the Reference Signal The reference signal is given in an ASCII text file 15

16 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 16

17 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 17

18 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 18

19 1. Introduction 2. Process integration 3. Sensitivity analysis 4. Optimization 5. Trainings & Contact 19

20 The Sensitivity Flow 20

21 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 21

22 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 22

23 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 23

24 1. Introduction 2. Process integration 3. Sensitivity analysis 4. Optimization 5. Trainings & Contact 24

25 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 25

26 optislang Optimization Algorithms Gradient-based Methods Most efficient method if gradients are accurate enough Consider its restrictions like local optima, only continuous variables and noise Start Gradient-free Methods Attractive methods for a small set of continuous variables Method of choice if gradient-based fails Nature inspired Optimization GA/EA/PSO imitate mechanisms of nature to improve individuals Method of choice if gradient-based or gradient-free fails Very robust against numerical noise, nonlinearity, number of variables, 26

27 Decision Tree for Optimizer Selection optislang automatically suggests an optimizer depending on the parameter properties, the defined criteria and user specified settings 27

28 Step 1: calibration of the dynamic system Optimization Downhill Simplex Method Convergence criteria fulfilled after 160 variants Small improvement after 81 variants 28

29 Step 1: calibration of the dynamic system Final variant The signal difference is reduced from 0.96 to 0.2 System transfer function fits well with the measured one from the real system The optimal parameter set is obtained 29

30 Step 2: controller design SimulationX model Design parameters Controller gain Integration time Responses Control time System output Overshoot Task Minimize the control time having a maximum overshoot of 5 % SimulationX model Input and output signal without using a controller 30

31 Step 2: controller design optislang workflow 31

32 Step 2: controller design Sensitivity results During Sensitivity Analysis only 7 variants (black) fulfill the constraint condition having control times between 3.5 s and 20 s A subsequent optimization using Simplex algorithm is performed 3.5 s 32

33 Step 2: controller design Optimization results The control time is reduced from 3.5 to 2.55 s using 61 simulation runs The final overshoot of 0.12 % is inside the given range of maximum 5 % The optimal parameter set is obtained and a fast controller is constructed 2.55 s 33

34 1. Introduction 2. Process integration 3. Sensitivity analysis 4. Optimization 5. Trainings & Contact 34

35 optislang Training optislang and SimulationX 1 day introduction to the integration of SimulationX models in a optislang solver chain, signal extraction, sensitivity analysis, optimization and calibration optislang 4 Basics 3 day introduction to process integration, sensitivity, optimization, calibration and robustness analysis Parameter Identification 1 day seminar on basics of model calibration, application of sensitivity analysis and optimization to calibration problems Robust Design and Reliability Analysis 1 day seminar on basics of probability, robustness and reliability analysis, robust design optimization See our website: 35

36 Visit our homepage for more information about software, trainings and webinars 36