Graph Feature Fusion-Driven Fault Diagnosis of Complex Process Industrial System Based on Multivariate Heterogeneous Data

Algorithm 1

MCGFF.

(A)	PSG Construction.
	Input: Sliced data , Coordinate of sensor .
	Output: graph set .
(1)	Obtain the normalized signal ;
(2)	Calculate the feature data: , ;
(3)	Separate feature data , ;
(4)	Calculate the Euclidean distance: ;
(5)	Obtain the k closest neighbors nodes set of node : if is k-th smallest;
(6)	Establish the edge connections for every node;
(7)	Embed , , as node features;
(8)	Output graph set .
(B)	PKG Construction.
	Input: original feature matrix , training epoch M for the GPK.
	Output: PKG GPK with high-level feature matrix F.
(1)	Obtain the normalized signal ;
(2)	Calculate the feature matrix: ;
(3)	Calculate the Mahalanobis distance: ;
(4)	Obtain the k closest neighbors node set of node : , if , is k-th smallest;
(5)	Establish the edge connections for every node;
(6)	Obtain original graph and original feature matrix ;
(7)	for i = 1, 2, …, M:
	Train the GCN model for M epochs:
	and ;
	end for
(8)	Output the PKG .
(C)	Fault diagnosis using MCGFF.
	Input: and GPK.
	Output: The health label Z.
(1)	Divide the training set and testing set: Vtrain, Vtest;
(2)	Train the GCN model;
(3)	for V in Vtrain do:
	MCGFF(V) ⟶ Z;
	⟶ CE loss;
	Update with backward propagation;
	end for
(4)	Output the health label: MCGFF(Vtest) ⟶ Z.