from uqpylab import sessions
import pprint; pp = pprint.PrettyPrinter(depth=2)

# Start the session
mySession = sessions.cloud()
# (Optional) Get a convenient handle to the command line interface
uq = mySession.cli
# Set the timeout
mySession.timeout = 2000
# 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 (0e6cd96d2cc24bdca5bab9ad250c6489) started.

 uqpylab.sessions :: INFO     :: Reset successful.

uq.rng(100,'twister');

ModelOpts = { 
    'Type': 'Model', 
    'ModelFun':'Hat.model',
    'isVectorized': True
}
myModel = uq.createModel(ModelOpts)

InputOpts = {
    "Marginals": [
        {"Name":"X1",
         "Type":"Gaussian",
         "Parameters":[0.25,1]
        },
        {"Name":"X2",
         "Type":"Gaussian",
         "Parameters":[0.25,1]
        }
    ]
}

myInput = uq.createInput(InputOpts)
uq.print(myInput)

==============================================================
Input object name: Input 1
Dimension(M): 2

Marginals:

Index | Name | Type     |  Parameters             | Moments              
--------------------------------------------------------------------------
1     | X1   | Gaussian |  2.500e-01, 1.000e+00   | 2.500e-01, 1.000e+00
2     | X2   | Gaussian |  2.500e-01, 1.000e+00   | 2.500e-01, 1.000e+00


Copula:

Type: Independent
Dimension: 2
Variables coupled: [1 2]
==============================================================

MCSOpts = {
    "Type":"Reliability",
    "Method":"MCS",
    "Simulation": { 
        "MaxSampleSize":1.0E+6,
        "BatchSize":1.0E+5,
        "TargetCoV":0.01
    }
}

MCSAnalysis = uq.createAnalysis(MCSOpts)

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((100000,))...

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

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((100000,))...

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

uq.print(MCSAnalysis)

---------------------------------------------------
Monte Carlo simulation
---------------------------------------------------
Pf               3.9600e-04       
Beta             3.3556           
CoV              0.0502           
ModelEvaluations 1000000          
PfCI             [3.5700e-04 4.3500e-04]
BetaCI           [3.3295e+00 3.3841e+00]
---------------------------------------------------

uq.display(MCSAnalysis);

SubsetSimOpts = {
    "Type":"Reliability",
    "Method":"Subset",
    "Simulation": {
        "BatchSize": 10000
    }
}

SubsetSim = uq.createAnalysis(SubsetSimOpts)

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((10000,))...

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

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((944,))...

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

uq.print(SubsetSim)

---------------------------------------------------
Subset simulation
---------------------------------------------------
Pf               3.8250e-04       
Beta             3.3652           
CoV              0.0918           
ModelEvaluations 35155            
PfCI             [3.1365e-04 4.5135e-04]
BetaCI           [3.3192e+00 3.4195e+00]
---------------------------------------------------

uq.display(SubsetSim);

AKMCSOpts = {
    "Type": "Reliability",
    "Method":"AKMCS",
    "Simulation": {
        "MaxSampleSize": 1e6    # Specify the size of the Monte Carlo sample set used for the Monte Carlo simulation
    },
    "AKMCS": {
        "MaxAddedED": 20,       # Specify the maximum number of sample points added to the experimental design
        "IExpDesign": {         # Specify the initial experimental design
            "N": 20,  
            "Sampling": "LHS"
        },
        "Kriging": {            # Specify the options for the Kriging metamodel (note that all Kriging options are supported)
            "Corr": {
                "Family": "Gaussian"
                }
        },
        "Convergence": "stopPf",  # Specify the convergence criterion for the adaptive experimental design algorithm (here, it is based on the failure probability estimate):
        "LearningFunction": "EFF" # Specify the learning function (here, it is the expected feasibility function (EFF))
    }
}

AKMCSAnalysis = uq.createAnalysis(AKMCSOpts)

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((20,))...

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

Processing . done!

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((1,))...

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

uq.print(AKMCSAnalysis)

---------------------------------------------------
AK-MCS
---------------------------------------------------
Pf               4.1200e-04       
Beta             3.3446           
CoV              0.0493           
ModelEvaluations 33               
PfCI             [3.7223e-04 4.5177e-04]
BetaCI           [3.3190e+00 3.3727e+00]
PfMinus/Plus     [4.0000e-04 4.3000e-04]
---------------------------------------------------

uq.display(AKMCSAnalysis);

APCKOpts = {
    "Type": "Reliability",
    "Method": "AKMCS",
    "AKMCS": {
        "MetaModel": "PCK",
        "PCK": {
            "Kriging": {
                "Corr": {
                    "Family": "Gaussian"
                }
            }
        },
        "IExpDesign": {
            "N": 5
        }
    },
    "Simulation": {
        "MaxSampleSize": 1.0E+6
    }
}

myAPCKMCSAnalysis = uq.createAnalysis(APCKOpts)

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((5,))...

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

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((1,))...

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

uq.print(myAPCKMCSAnalysis)

---------------------------------------------------
AK-MCS
---------------------------------------------------
Pf               3.7000e-04       
Beta             3.3743           
CoV              0.0520           
ModelEvaluations 11               
PfCI             [3.3231e-04 4.0769e-04]
BetaCI           [3.3475e+00 3.4038e+00]
PfMinus/Plus     [3.7000e-04 3.7000e-04]
---------------------------------------------------

uq.display(myAPCKMCSAnalysis);

SSEROpts = {
    "Type": "Reliability",
    "Method": "SSER",
    "SSER": {
        "ExpDesign": {
            "NEnrich": 20    # Set the number of samples to be added in every refinement domain
        },
        "ExpOptions": {
            "Degree": [0, 1, 2, 3, 4]   # Select the polynomial degree of the residual expansion
        }
    }
}

mySSERAnalysis = uq.createAnalysis(SSEROpts)

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((40,))...

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

Processing . done!

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

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

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

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((20,))...

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

uq.print(mySSERAnalysis)

---------------------------------------------------
Stochastic spectral embedding-based reliability
---------------------------------------------------
Pf               4.1680e-04       
Beta             3.3414           
CoV              0.0000           
ModelEvaluations 160              
PfCI             [4.1680e-04 4.1680e-04]
BetaCI           [3.3414e+00 3.3414e+00]
---------------------------------------------------

uq.display(mySSERAnalysis);

Processing .

.

.

.

.

 done!

mySession.quit()

 uqpylab.sessions :: INFO     :: Session 0e6cd96d2cc24bdca5bab9ad250c6489 terminated.

True

RELIABILITY: TWO-DIMENSIONAL HAT FUNCTION¶

1 - INITIALIZATION¶

Package imports¶

Start a remote UQCloud session¶

Set the random seed for reproducibility¶

2 - COMPUTATIONAL MODEL¶

Create a limit state function model based on the hat function using a string, written below in a vectorized operation:¶

3 - PROBABILISTIC INPUT MODEL¶

Specify the marginals of the two input random variables:¶

Create an INPUT object based on the specified marginals and print its properties¶

4 - STRUCTURAL RELIABILITY¶

4.1 Monte Carlo simulation (MCS)¶

4.2 Subset Simulation¶

4.3 Adaptive-Kriging-Monte-Carlo-Simulation (AKMCS)¶

4.4 Adaptive-Polynomial-Chaos-Kriging-Monte-Carlo-Simulation (APCK-MCS)¶

4.5 Stochastic spectral embedding-based reliability (SSER)¶

Terminate the remote UQCloud session:¶