4.5 Automated Generation of Sensor Sets

4.5.1 Genetic Algorithm

The automated generation of sensor sets in the PHM module utilizes a genetic algorithm. The algorithm is used to identify combinations of sensor locations with the primary goal of maximizing sensor set utility (utility refers to satisfying the input criteria). In its application to MADE, this essentially means maximizing sensor set coverage and minimizing the number of test points in the set.

A genetic algorithm is an optimization technique used to identify sensor sets that best match the user criteria. A methodology that mimics nature's evolutionary process, a genetic algorithm is a form of heuristic that can generate high quality solutions over a large potential solution space. Heuristics are often used to provide solutions for problems where it is not feasible to calculate the globally optimal solution.

Evolution in a genetic algorithm is an iterative process that performs a search through the potential solutions. The genetic algorithm initially randomly generates several candidate solutions which evolve into better solutions with each iteration. Every iteration, the highest fitness candidate solutions are selected to produce the next generation of solutions. The selection process gives preference to the solutions that best meet the criteria. In MADE, preference is given to solutions with high coverage and low sensor count, as specified within the user's analysis preferences (i.e. criteria). The selected solutions are combined and modified to produce the next generation. This process continues until the specified iteration limit has been reached.

The application of a genetic algorithm in MADE identifies potential sensor locations that in combination form sensor sets. The process will result in a list of Sensor Sets that are able to uniquely identify the failure responses found in the Propagation Table.

4.5.2 What Happens When a Sensed Flow Parameter is Excluded

Excluding a sensed flow parameter removes the potential for that flow parameter to be considered in any subsequent analysis. The column representing that flow parameter is removed from the propagation table. The implication when excluding a flow parameter is that it is impossible, infeasible, or undesirable to sense that flow parameter. Excluding flow parameters will stop sensors being automatically placed upon that flow when generating sensor sets in an Analysis Sensor Set.

Excluding a sensed flow parameter may not have a direct impact upon the calculation of coverage, as it does not change the number of failures in the system being considered. However, excluding flow parameters may make achieving maximal coverage more difficult or impossible, as certain failure responses in the system cannot be sensed.

4.5.3 Analysis Parameters

4.5.3.1 Coverage

Allows the user to define a minimum acceptable coverage for the produced sensor sets, biasing the genetic algorithm away from lower coverage sets (that may be more ideal in certain situations due to a reduced number of test points).

4.5.3.2 Test Points

Allows the user to specify a target number of sensors. Early in the sensor set design process, the specifics of the sensors being used may not be known. As such, a basic metric for optimizing sensor set design is the number of sensors that could be practically applied. The sensor sets output from the sensor set generation will be biased to fall within the specified range of test points.

4.6 Diagnostic Rule Generation

A sensor set, once generated, will have a set of sensor locations or test points that, when used in combination, will be able to identify any of the covered failures. However, not all sensor readings will be needed to detect and isolate each specific failure in the system. Diagnostic rule generation takes sensor sets previously created and outputs a simplified rule base for detecting each failure, which may be used in an onboard diagnostics system or for maintenance personnel.

Diagnostic rules are the combinations of sensor readings that can be used to determine where in the system a failure has occurred. Each row in the propagation table provides a breakdown of all the responses in the system to expect when a specific failure has occurred. All these responses collectively form what could be considered the "signature of failure"; however, all the responses do not need to be observed to isolate or confirm that the specific failure was the one that occurred.

The goal of diagnostic rules is to calculate the combinations of sensor responses which can be used to uniquely identify each failure in the propagation table. A set of responses that identifies a failure is called a diagnostic rule. A diagnostic rule can be simplified using a process of binary minimization to have the minimal number of responses. This minimization of the diagnostic rules to their simplest form is available in the diagnostics rules tab.

The diagnostic rules in MADE are based on an existing sensor set. The process for calculating the minimal diagnostic rules is:

1. A logical expression is created for each failure in the propagation table. The logical expression defines which sensor locations are required to uniquely identify the failure.
2. This logical expression is reduced to smaller (having fewer terms), equivalent expressions.
3. The group of expressions for a failure are called the diagnostic set.

Example: Output Diagnostic Rules

Using the same propagation table and sensor sets discussed in the Sensor Set Analysis chapter (Failures A, B, C, D; Test Points TP1, TP2, TP3):

• The selected sensor set has test points at TP1 and TP2. As such, responses at TP3 have been removed from consideration (greyed out).
• Both sensors are required to adequately cover all four failures.
• However, to know that a specific failure has occurred, both responses may not necessarily be required.
• A failure can be isolated given its observable response is unique when compared to the other failures' responses at the same test point.
• For example, Failure D can be isolated (determined to have been the cause of failure) using only TP1, as the "low" response is unique compared to Failures A, B, and C (2× "high", and "nominal" respectively).

Full diagnostic rules for this sensor set:

Failure	Diagnostic Rule
A	TP1 = High AND TP2 = Nominal
B	TP1 = High AND TP2 = Low
C	TP1 = Nominal AND TP2 = Low
D	TP1 = Low OR TP2 = High

(Note: the source PDF table's row-to-rule mapping was compressed/interleaved during text extraction — the extracted text lists the four diagnostic rules as a contiguous block below the four failure letters without perfectly explicit per-row delimiters. The mapping above (A, B, C, D each paired with one rule, in the same top-to-bottom order as they appear) is the most consistent reading given the surrounding explanatory text, particularly the explicit statement that "Failure D can be isolated ... using only TP1" — which matches the final rule "TP1 = Low OR TP2 = High" (TP1 alone being Low is sufficient). Treat this table as a faithful best-effort reconstruction, not a pixel-verified transcription.)

4.7 Outcomes of the PHM Module

4.7.1 Sensor Placement

Placement of sensors across the system to maximize coverage (failure isolation) and minimize test points (number of sensors).

4.7.2 Optimisation of Sensor Set

Optimisation through selection of sensor sets and allocation of specific sensors to test points based on comparisons of sensor cost, ongoing cost of monitoring, sensor set weight, and probability of detection.

4.7.3 Diagnostic Rules

Combining sensor readings to develop a diagnostic rule base for detecting and isolating failures.