Use the Directional Sampling Algorithm¶

In this example we estimate a failure probability with the directional simulation algorithm provided by the `DirectionalSampling` class.

Introduction¶

The directional simulation algorithm operates in the standard space based on:

1. a root strategy to evaluate the nearest failure point along each direction and take the contribution of each direction to the failure event probability into account. The available strategies are: - RiskyAndFast - MediumSafe - SafeAndSlow

2. a sampling strategy to choose directions in the standard space. The available strategies are: - RandomDirection - OrthogonalDirection

Let us consider the analytical example of the cantilever beam described here.

```from openturns.usecases import cantilever_beam
import openturns as ot
import openturns.viewer as viewer

ot.Log.Show(ot.Log.NONE)
```

We load the model from the usecases module :

```cb = cantilever_beam.CantileverBeam()
```

We load the joint probability distribution of the input parameters :

```distribution = cb.distribution
```

We load the model giving the displacement at the end of the beam :

```model = cb.model
```

We create the event whose probability we want to estimate.

```vect = ot.RandomVector(distribution)
G = ot.CompositeRandomVector(model, vect)
event = ot.ThresholdEvent(G, ot.Greater(), 0.30)
```

Root finding algorithm.

```solver = ot.Brent()
rootStrategy = ot.MediumSafe(solver)
```

Direction sampling algorithm.

```samplingStrategy = ot.OrthogonalDirection()
```

Create a simulation algorithm.

```algo = ot.DirectionalSampling(event, rootStrategy, samplingStrategy)
algo.setMaximumCoefficientOfVariation(0.1)
algo.setMaximumOuterSampling(40000)
algo.setConvergenceStrategy(ot.Full())
algo.run()
```

Retrieve results.

```result = algo.getResult()
probability = result.getProbabilityEstimate()
print("Pf=", probability)
```
```Pf= 4.216513551377014e-07
```

We can observe the convergence history with the drawProbabilityConvergence method.

```graph = algo.drawProbabilityConvergence()
graph.setLogScale(ot.GraphImplementation.LOGX)
view = viewer.View(graph)
```