from uqpylab import sessions
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import Image

# Start the session
mySession = sessions.cloud()
# (Optional) Get a convenient handle to the command line interface
uq = mySession.cli
# Reset the session
mySession.reset()

Processing .

.

 done!

 uqpylab.sessions :: INFO     :: This is UQ[py]Lab, version 1.00, running on https://uqcloud.ethz.ch. 
                                 UQ[py]Lab is free software, published under the open source BSD 3-clause license.
                                 To request special permissions, please contact:
                                  - Stefano Marelli (marelli@ibk.baug.ethz.ch).
                                 A new session (909ff192edcf4c4497285d594c1350dc) started.

 uqpylab.sessions :: INFO     :: Reset successful.

uq.rng(100, 'twister');

Image(filename='SimplySupportedBeam.png')

ModelOpts = {
    'Type': 'Model', 
    'ModelFun':'SimplySupportedBeam.model',
    'isVectorized': True
}

myForwardModel = uq.createModel(ModelOpts)

PriorOpts = {
  "Marginals": [
    {
      "Name": "b",            # beam width
      "Type": "Constant",
      "Parameters": [0.15],   # (m)
    },
    {
      "Name": "h",            # beam height
      "Type": "Constant",
      "Parameters": [0.3],    # (m)
    },
    {
      "Name": "L",            # beam length
      "Type": "Constant",
      "Parameters": [5],      # (m) 
    },
    {
      "Name": "E",            # Young's modulus
      "Type": "LogNormal",
      "Moments": [30e9,4.5e9] # (Pa)
    },
    {
      "Name": "p",            # uniform load
      "Type": "Gaussian",
      "Moments": [12000,600]   # (N/m)
    }
  ]
}

myPriorDist = uq.createInput(PriorOpts)

MetaOpts = {
    'Type': 'Metamodel',
    'MetaType': 'PCE',
    'ExpDesign': {
        'NSamples': 50
    }
}

mySurrogateModel = uq.createModel(MetaOpts)

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: SimplySupportedBeam.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((50,))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

myData = {
    "y": (np.array([12.84, 13.12, 12.13, 12.19, 12.67])/1000).tolist(),
    "Name": "Mid-span deflection",
}

BayesOpts = {
    "Type" : "Inversion",
    "Data" : myData,
    'Solver': {
        'Type': 'MCMC',
        'MCMC': {
            'Sampler': 'AM', 
            'Steps': 100,    # Note: Realistic cases require order of 10,000 steps.
            'NChains': 300, 
        }
    }
}

BayesOpts['ForwardModel'] = {
    'Model': myForwardModel['Name']
}

myBayesianAnalysis_fullModel = uq.createAnalysis(BayesOpts)

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: SimplySupportedBeam.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((300,))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: SimplySupportedBeam.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((278,))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

uq.print(myBayesianAnalysis_fullModel)

%----------------------- Inversion output -----------------------%
   Number of calibrated model parameters:         2
   Number of non-calibrated model parameters:     3

   Number of calibrated discrepancy parameters:   1

%------------------- Data and Discrepancy
%  Data-/Discrepancy group 1:
   Number of independent observations:            5

   Discrepancy:
      Type:                                       Gaussian
      Discrepancy family:                         Scalar
      Discrepancy parameters known:               No

   Associated outputs:
      Model 1: 
         Output dimensions:                       1

%------------------- Solver
   Solution method:                               MCMC

   Algorithm:                                     AM
   Duration (HH:MM:SS):                           00:01:49
   Number of sample points:                       3.00e+04

%------------------- Posterior Marginals
---------------------------------------------------------------------
| Parameter | Mean    | Std     | (0.025-0.97) Quant. | Type        |
---------------------------------------------------------------------
| E         | 2.7e+10 | 4e+09   | (2.1e+10 - 3.7e+10) | Model       |
| p         | 1.2e+04 | 6.1e+02 | (1.1e+04 - 1.3e+04) | Model       |
| Sigma2    | 2.2e-05 | 3.4e-05 | (2.3e-07 - 0.00012) | Discrepancy |
---------------------------------------------------------------------

%------------------- Point estimate
----------------------------------------
| Parameter | Mean    | Parameter Type |
----------------------------------------
| E         | 2.7e+10 | Model          |
| p         | 1.2e+04 | Model          |
| Sigma2    | 2.2e-05 | Discrepancy    |
----------------------------------------

%------------------- Correlation matrix (model parameters)
------------------------
|   |  E        p      |
------------------------
| E |  1        0.081  |
| p |  0.081    1      |
------------------------

BayesOpts['ForwardModel']['Model'] = mySurrogateModel['Name']

myBayesianAnalysis_surrogateModel = uq.createAnalysis(BayesOpts)

uq.print(myBayesianAnalysis_surrogateModel)

%----------------------- Inversion output -----------------------%
   Number of calibrated model parameters:         2
   Number of non-calibrated model parameters:     3

   Number of calibrated discrepancy parameters:   1

%------------------- Data and Discrepancy
%  Data-/Discrepancy group 1:
   Number of independent observations:            5

   Discrepancy:
      Type:                                       Gaussian
      Discrepancy family:                         Scalar
      Discrepancy parameters known:               No

   Associated outputs:
      Model 1: 
         Output dimensions:                       1

%------------------- Solver
   Solution method:                               MCMC

   Algorithm:                                     AM
   Duration (HH:MM:SS):                           00:00:01
   Number of sample points:                       3.00e+04

%------------------- Posterior Marginals
---------------------------------------------------------------------
| Parameter | Mean    | Std     | (0.025-0.97) Quant. | Type        |
---------------------------------------------------------------------
| E         | 2.6e+10 | 3.5e+09 | (2.1e+10 - 3.5e+10) | Model       |
| p         | 1.2e+04 | 6.5e+02 | (1.1e+04 - 1.3e+04) | Model       |
| Sigma2    | 2.1e-05 | 3.4e-05 | (2.1e-07 - 0.00013) | Discrepancy |
---------------------------------------------------------------------

%------------------- Point estimate
----------------------------------------
| Parameter | Mean    | Parameter Type |
----------------------------------------
| E         | 2.6e+10 | Model          |
| p         | 1.2e+04 | Model          |
| Sigma2    | 2.1e-05 | Discrepancy    |
----------------------------------------

%------------------- Correlation matrix (model parameters)
----------------------
|   |  E       p     |
----------------------
| E |  1       0.12  |
| p |  0.12    1     |
----------------------

uq.display(myBayesianAnalysis_surrogateModel);

mySession.quit()

 uqpylab.sessions :: INFO     :: Session 909ff192edcf4c4497285d594c1350dc terminated.

True

INVERSION: SURROGATE MODEL ACCELERATED CALIBRATION¶

Package imports¶

Start a remote UQCloud session¶

Set the random seed for reproducibility¶

Forward model¶

Prior distribution of the model parameters¶

Surrogate model¶

Measurement data¶

Bayesian analysis¶

Terminate the remote UQCloud session¶