P12

Bayesian Optimization Approach for Parameter Calibration of Constitutive Models in Liquefaction
Analysis〇Gyuchan Choi, Ueda Kyohei, Uzuoka Ryosuke

Introduction

LEAP (Liquefaction Experiment and Analysis Project)

The Finite Element (FEM) Method is a program thatwas selected for the calibration target. The CDSS test

is widely used to analyze or predict the dynamic

is one of the cyclic loading tests to objectively define

behaviors of the soil or structures in the geotechnicalthe soil's dynamic properties. The Ottawa F-65 soil, afield. Especially for analyzing the dynamic behavior,fine particle of sandy soil, was used for the test. σv =the FEM analysis is evaluated as an efficient tool with

40 kPa, 𝐷𝑟 = 66% of soil condition was chosen forhigh reliability and low cost.

the target to optimize.

The procedures of the FEM analysis start from theFLIPROSE and the Strain space multiple mechanism

calibration work. And the only calibration work ismodel were utilized for the FEM program platform andpromising work to implement the dynamic behavior of

the constitutive model of the soil, respectively.

the soil in the FEM. It is usually done manually by

Bayesian optimization (BO)adjusting the soil parameters to fit the simulation result

Bayesian optimization is a technique widely used in

into the measured data. However, manually calibrating

data science to adjust the hyper-parameters of thethe soil cannot quantify the data and reflect the previous

coefficients in the machine learning model. The BO isknowledge robustly and may produce biased data

based on the Gaussian Process (GP) to build theaccording to the person.

surrogate model and the acquisition function. The

Objective of the study

surrogate model is an unknown function that the GPTherefore, this study embarked on establishing aninfers by updating the surrogate model. The acquisition

automated parameter identification code for calibrating

function is an algorithm that decides the next point to

the dynamic behavior of the soil in the element test

explore by comparing the exploit and the explore

phase of a FEM Program using the Bayesian(trade-off).

optimization technique. The ultimate objective of thisThe Botorch and AX were utilized to compose thestudy is to obtain the liquefaction parameter sets in theBO loop. The Botorch is a program made for

FEM program that perfectly matches with measured

composing the BO loop, and the AX is a program thatliquefaction resistance curve and the time history ofmodularizes a Botorch’s program to apply it with ease.

strain data. As a first step to reach the ultimate objective,

How the BO works with the FEM?

this paper attempts to match one liquefaction criteria of

Schematic flows of how the loop works are described

the liquefaction resistance curve with the measured andin Figure 1. The input & output files of the FLIPROSE

simulation data.

consist of the text format (.txt), and the FEM

CDSS Test and FEM setup

calculating program is an execute file format (.exe).

The Cyclic Direct Simple Shear (CDSS) test thatGeorge Washington University provided during theTherefore, a computer code was made to govern theFEM program in the framework of the BO loop.

Symbol

FLIP

Set Range

Guideline

Numberof digits

𝜀𝑑𝑐𝑚

0.1~0.2

0.10~0.402

𝛾𝜀𝑑𝑐

0.5~1.0

0.01~5.00

2𝑟𝜀𝑑𝛾𝜀𝑑𝑐 × 𝑟𝜀𝑑0.001~5.000

3= 1.0Figure 1. Interaction algorithm with BO and FEM
Optimization loop setupq11.0~10

1.00~10.00

2q2

0.0~2.0

0.01~2.00

2c1

1.0~

1.00~5.00

2𝜙𝑝

28°

20.00~37.99

2Results & Discussion

Mean Squared Error (MSE) and the Mean Absolute
Error (MAE) functions were used to express thediscrepancy between the measured and simulated data.
(Eq 1 and Eq 2.) This methodology takes advantage ofmaking a number of values into one scalarized value
for the metric to evaluate, making the problem
regarding computational cost simple.
𝑁1𝑀𝑆𝐸 = ∑(𝑦𝑖 − 𝑦̂)2 ,𝑁𝑖=1𝑁

1𝑀𝐴𝐸 = ∑|𝑦𝑖 − 𝑦̂|𝑁𝑖=1

Therefore, the objective of the BO in this metric is tominimize the metric.

Figure 3. The best ten parameters set
Figure 3 presents the best ten parameters set with themeasured data. The MSE was used for the metrics. The
best match liquefaction resistance curve (LRC) data
were derived from the 1818 trial, which showed 1.60
MSE with a 3.23 standard error value. However, since
the time history of the strain or excess pore waterpressure was not considered, the match of the strain,
Excess pore water pressure ratio (E.P.W.P) showed
inconsistencies between the measured and theFigure 2. Interact algorithm

simulated data (example: Figure 4.).

Besides, in order to reduce the computational cost,parameter domains (liquefaction parameters) wereconstrained by setting the range and the number ofdigits by referring to the FLIP guidelines, as shown
below in Table 2. Lastly, the expected improvement
method was chosen for the acquisition function. One
thousand samples were generated for prior knowledge
through the SOBOL algorithm, and 1000 BO wereconducted.
Table 2. Designated parameter domain for BO loop

Figure 4. Example of Inconsistencies
Reference1. Iai, S., Tobita, T., Ozutsumi, O, & Ueda, K. (2011). Dilatancy of
granular materials in a strain space multiple mechanism
model. International Journal for Numerical and Analytical Methods inGeomechanics, 35(3), 360-392. 2. BALANDAT, Maximilian, et al.
BoTorch: A framework for efficient Monte-Carlo Bayesian
optimization. Advances in neural information processing systems, 2020,33: 21524-21538.