Bayesian Belief Networks (BBNs)

Going back to my post on Bayesian Networks, generating assurance case using BBNs using python is a simple task.

A BBN is a graphical model that represents probabilistic relationships among a set of variables. Nodes in the graph represent random variables, and edges represent dependencies between the variables. The conditional probability distributions associated with each node given its parents are used to model the joint probability distribution of the entire network.

This node structure can be created using the pybbn library where the BBN is defined as a pair, G, P, where

G is a directed acylic graph (DAG)
P is a joint probability distribution and G satisfies the Markov Condition (nodes are conditionally independent of non-descendants given its parents) according to pybbn documentation.

Generating a BBN

bbn = BBN(n_experiments=n_experiments)
mission_success = bbn.create_bbn_node(
    GoalNode(0, "Meeting requirements", n_children=3)
)
mission_all_waypoints = bbn.create_bbn_node(
    node_type=MinThresholdNode(
        id=1,
        name=f"Robot Nav Terrain under Threshold",
        n_experiments=bbn.n_experiments,
        threshold=nav_threshold,
    )
)
mission_times_navigable_terrain = bbn.create_bbn_node(
    node_type=SuccessNode(
        2,
        "P(robot on navigable terrain)",
        n_experiments=bbn.n_experiments,
        probability_of_success=p_correct_navigation,
    ),
)
mission_no_collision = bbn.create_bbn_node(
    MaxThresholdNode(
        3,
        f"Robot Collision under Threshold",
        n_experiments=bbn.n_experiments,
        threshold=collision_threshold,
    )
)
mission_times_collision = bbn.create_bbn_node(
    SuccessNode(
        4,
        "P(robot not collide)",
        n_experiments=bbn.n_experiments,
        probability_of_success=p_no_collision,
    )
)
mission_pose_in_threshold = bbn.create_bbn_node(
    MinThresholdNode(
        5,
        f"Robot Pose under Threshold",
        n_experiments=bbn.n_experiments,
        threshold=pose_threshold,
    )
)
mission_times_pose_within_threshold = bbn.create_bbn_node(
    SuccessNode(
        6,
        "P(robot pose within region)",
        n_experiments=bbn.n_experiments,
        probability_of_success=p_correct_pose,
    )
)
bbn.create_edge(mission_times_navigable_terrain, mission_all_waypoints)
bbn.create_edge(mission_all_waypoints, mission_success)
bbn.create_edge(mission_times_collision, mission_no_collision)
bbn.create_edge(mission_no_collision, mission_success)
bbn.create_edge(mission_times_pose_within_threshold, mission_pose_in_threshold)
bbn.create_edge(mission_pose_in_threshold, mission_success)
bbn.set_join_tree()

Once the BBN structure has been established, an assurance case in GSN notation from a YAML format to a scalable vector graphics (SVG) image can be generated using the gsn2x program available on Github here.

assurance_case

Design of Experiments (DoE)

Using DoE, it is easier to determine the conditions which would provide greater belief/assurance in achieving the claims put forth by the assurance case.