Investigation of Uncertainties Associated with Actuation Modeling Error and Sensor Noise on Real

Time Hybrid Simulation Performance

Amin Maghareh, Shirley J. Dyke, Ge Ou, and Yili Qian

School of Civil Engineering, Purdue UniversitySchool of Mechanical Engineering, Purdue University

{amaghare, sdyke, gou, qian26}@purdue.edu

2

Objective:

Reduce impacts of dynamic loading on infrastructures

Real-time Hybrid Simulation

Earthquake

Tsunami

Wind

3

Shake Table Testing

Real-time Hybrid Simulation

xi+1

R4

R3 Ri+1

Displacements imposed in Real

time

gx

x2(t)

x1(t)m1

m2

c2

c1

k2

k1Experimental sub-structure

k4

k3

Numerical integration

Numerical sub-structure

x4(t)

x3(t)m3

m4

c4

c3

k4

k3

Numerical s

ub-

structu

re

Figures from “Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback” by B. F. Spencer Jr. and Brian M. Phillips

1111 iiii FRxCxM x

tti ti+1

xi xi+1

5

Outline

• Real-time Hybrid Simulation (RTHS)

• RTHS Components

• Uncertainties in RTHS– Numerical uncertainties

– Experimental uncertainties

• Actuation Misidentification and Sensor Noise

• Evolution of Uncertainties in RTHS

• Case study

• Conclusions

RTHS

What is RTHS? Real-time hybrid simulation is a cyber-physical technique of partitioning a structure into physical and numerical substructures to study the dynamic performance of complex engineering structures under dynamic loading

Why RTHS? It would facilitate low-cost and broader evaluation of new structural components and systems

Components: • Cyber Components

Distributed Real-time Control SystemVisualization and Control Dashboard

• Physical Components Reaction Mounting System Sensing and Actuation System

RTHS Components

RTHS Components

Load Cell Servo-valve LVDT

Speedgoat xPC Target System SC6000 Servo-hydraulic Control System

Reaction Mounting System + Exp. Substructure

gx

Uncertainties in Real-time Hybrid Simulation

Uncertainties are classified into two subcategories:

• Numerical uncertainties Structural Modeling Idealization Numerical Integration Scheme

• Experimental uncertainties

Numerical uncertainties

Structural Modeling Idealization• Structural modeling idealization leads to losing some dynamics of the prototype

structure.

• Modeling idealization error in hybrid simulation refers to discretization of the continuous equation of motion of a structural model which is just an approximate representation of the dynamics of the structure.

• However, it should be noted that there is always a trade-off between accuracy of the model and feasibility of the number of degrees of freedom controllable with available actuators.

Numerical Integration Scheme• To solve the idealized equation of motion, approximate numerical integration

schemes are utilized.

• Based on what scheme is utilized and how fine time steps are, stability and accuracy of the numerical method adopted for a hybrid simulation is determined.

Experimental uncertainties

• Random noise generated by the force and displacement measurement instrumentations can be challenging since these can excite spurious lightly-damped modes of the RTHS system.

• Depending upon what the frequency bandwidth of interest is, and the level of nonlinearity of actuators, developing tracking error in RTHS is inevitable.

• Moreover computation time delay, communication time delay, and actuator lag are other sources of experimental uncertainty.

Uncertainties in RTHS

0 50 100 150 200 250 300 350 400 450 500-105

-100

-95

-90

-85

-80

-75

-70

-65

-60

-55

Frequency (Hz)

Pow

er/

frequency (

dB

/Hz)

Welch Power Spectral Density Estimate

Actuation Misidentification and Sensor Noise

Ideal Case

RTHS with Actuator Misidentification and Measurement Noise

Evolution of Uncertainties in RTHS

• Excitation of the spurious modes by the input acceleration• Excitation of the spurious modes by measurement noises • Excitation of the actual modes of the system by measurement noises

Displ. Measurement Noise Force Measurement Noise

Where

Important Points

• The poles of the closed-loop system are associated with the eigenvalues of , the actual system, and the eigenvalues of which are slightly different.

• Since the compensator is designed based on the dynamics of , and not , the overall RTHS error system ends up having some closely separated poles and zeros (imperfect cancellation) causing some spurious lightly-damped poles.

• These lightly damped poles play a significant role in the propagation of error in the system.

• Depending upon whether these spurious poles are at low frequency or high frequency, they will be dominantly excited by either ground acceleration input or measurement noise signals, respectively.

Important Points

• Ground acceleration inputs have much higher power in a low frequency bandwidth compared to measurement noise signals.

Wavelet Transformation of the 1994 Northridge EQ

• If the spurious poles are located in the excitation bandwidth of ground acceleration, the quality of RTHS results will be significantly degraded.

Case Study

Case Study

Case

ICa

se II

Case Study Results

Case Study ResultsCa

se I

Case

II

Low Freq. ErrorHigh Freq. Error

Conclusions

• Hybrid simulation is a cyber-physical technique of partitioning a structure into physical and numerical substructures to study and enhance the dynamic performance of complex engineering structures under dynamic loading

• It would facilitate low-cost and broader evaluation of new structural components and systems

• In this study, evolution of uncertainties sourced from actuation misidentification and sensor noise is formulated.

• Better understanding of the evolution of uncertainties in RTHS will help us design the closed-loop more effectively as shown in the case study.

22

Acknowledgements

• This material is based in part upon work supported by the  National Science Foundation under Grant Numbers NSF-1136075 and CMMI-1011534.

23

Thank You!

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