p5so that the path
../librefers to the directory containing the Budd library routines.
make dxwill compile all of the files in the
libsubdirectory and also the
p5directory that describe an automobile diagnosis problem:
car.netgives the Bayesian network structure corresponding to the network shown in the slides.
car.dxindicates which nodes are observable and repairable and what the observation and repair costs are.
6 BatteryState ( ok weak ) ( 5 ) (11) (6 5) .99 .80 .01 .20Each node (also called a variable or a component) has an index number. This is node 6. The nodes must appear in numerical order in the network file. The name of the node is
BatteryState. All nodes are assumed to take on two values. Internally, the values are represented by the integers 0 and 1. Externally, the values have the names
ok(for 0) and
weak(for 1). We have followed the rule that correct functioning is represented by the value 0 and faulty functioning by the value 1 for all nodes.
The next entry is a list of the incoming arrows to this node. There is an incoming arrow from node 5. The next entry is a list of the outgoing arrows from this node. There is a single outgoing arrow to node 11.
On the next line, we have the probability table. The first entry is a list (6 5) of the index numbers of the variables involved in this table (this is a conditional probability table giving the probability of node 6 given node 5). The four numbers are the four probabilities. They appear in the order corresponding to the following:
P(node6=0 | node5=0) P(node6=0 | node5=1) P(node6=1 | node5=0) P(node6=1 | node5=1)In other words, the node with the smallest index is varied most rapidly (counting in binary).
You should not need to modify the network file at all. However, you
will need to modify the diagnosis file
to work the third part of the assignment. The contents of this
file are as follows:
18 13 0 SparkPlugs 1 15 1 10 1 Distributor 1 15 1 20 2 FuelPump 1 30 1 40 3 Leak2 1 5 1 60 4 Starter 1 10 1 40 5 BatteryAge 1 5 1 20 6 BatteryState 0 0 0 0 7 Alternator 0 0 1 50 8 FanBelt 1 5 1 15 9 Leak 1 30 1 60 10 Charge 1 10 0 0 11 BatteryPower 1 10 0 0 12 EngineCranks 1 2 0 0 13 Starts 1 2 0 0 14 Radio 1 1 0 50 15 GasInTank 0 0 1 10 16 GasGauge 1 1 0 0 17 Lights 1 1 0 20The first line gives the number of nodes and the index of the problem-defining node (i.e., the node that has the value 0 if the whole device is functioning properly).
On each of the remaining lines, the following fields appear:
diagnose car.net car.dxThe program will ask a series of questions and eventually declare the device to be working properly. In its present state, the program can only handle variables that are repairable or are observable and repairable. It does not handle multiple faults or purely observable variables.
The program accepts two flag arguments
-d flag turns on some tracing to
show the estimated probabilities of each of the faults. This is
useful for understanding the reasoning of the program. When a
component has probability 0, the program has proved to itself that
that component cannot possibly be faulty. Similarly, you sometimes
see a component with probability 1, meaning that the program has
inferred that this component must be faulty. The
gives an internal trace of the probability calculations. This is
extremely verbose, and you probably don't ever want to see it.
In each scenario you should assume that exactly one component is broken. There are ten components that can break (BatteryAge, Alternator, FanBelt, Leak, GasInTank, FuelPump, Distributor, SparkPlugs, Starter, Leak2). To generate a scenario, choose one of these. Suppose you choose BatteryAge. If the BatteryAge is bad (i.e., old), then you should assume that the BatteryState is bad, the BatteryPower is bad, and therefore the Radio and Lights don't work. Also, the GasGauge will not show any gas and EngineCranks will be false. This is what will prevent the car from starting. In constructing this line of reasoning, you should assume that if a node is bad, it causes all of its children (the nodes on its outgoing links) to be bad also.
You will then run the
diagnose program and answer the
questions that it asks according to this line of reasoning. When it
eventually finds and repairs the fault, it will report the total cost.
You should enter that cost into a table. The rows of the table should
correspond to the various breakable components of the car. The
columns should correspond to the various scenarios. For example, a
scenario in which the SparkPlugs are broken and this causes the car
not to start should look something like this (where the ???? should be
replaced with the actual cost repair for this scenario).
Component: Scenarios: 0 SparkPlugs 1 1 Distributor 0 2 FuelPump 0 3 Leak2 0 4 Starter 0 5 BatteryAge 0 6 BatteryState 0 7 Alternator 0 8 FanBelt 0 9 Leak 0 10 Charge 0 11 BatteryPower 0 12 EngineCranks 0 13 Starts 1 14 Radio 0 15 GasInTank 0 16 GasGauge 0 17 Lights 0 Cost ????You should add nine more columns to this table corresponding to the other 9 possible broken components. Within each column, enter a 1 if the corresponding variable should give a "bad" observation in that scenario. Run each scenario on the
car.dxfile showing the smallest modification that changed the first step of the repair policy.