An Adaptive Smoothing-Constrained Broad Learning System for Truck-Scale Weighing

. 2026 Sep 14;26(18):5827. doi: 10.3390/s26185827

Algorithm 1 The PSO-MCC-SCBLS Algorithm for Truck-Scale Weighing

1:
Data preprocessing.
2:
for $i = 1$ ; $i \leq n$ do.
3:
Randomly initialize the parameters $W_{e}$ and $β_{e}$ of the feature mapping layer;
4:
Calculate $Z_{i} = ϕ (X W_{e i} + β_{e i}), i = 1, \dots, n$ ;
5:
end
6:
Construct feature-node matrix $Z^{n} = [Z_{1}, Z_{2}, \dots, Z_{n}]$ ;
7:
for $j = 1$ ; $j \leq m$ do
8:
Randomly initialize the parameters $W_{h}$ and $β_{h}$ of the enhancement-mapping layer
9:
Calculate $H_{j} = ξ (Z^{n} W_{h j} + β_{h j}), j = 1, \dots, m$ ;
10:
end
11:
Construct enhancement-node matrix $H^{m} = [H_{1}, H_{2}, \dots, H_{m}]$ ;
12:
Concatenate node matrices to form $A = [Z^{n} ∣ H^{m}]$ ;
13:
Compute the adjacency matrix S and the Laplacian matrix L using Equations (15) and (16);
14:
for $t_{1} = 1$ ; $t_{1} \leq T_{1}$ do
15:
Initialize output-weight matrix W and construct state matrix A based on Equations (3)–(6);
16:
Compute diagonal matrix $Λ_{w}$ according to Equation (21);
17:
Update output-weight matrix W according to Equation (22);
18:
if $∥ W_{t + 1} - W_{t} ∥_{2} < ε$ ;
19:
break
20:
end
21:
Output-weight matrix W;
22:
for $t_{2} = 1$ ; $t_{2} \leq T_{2}$ do
23:
Evaluate fitness of each particle;
24:
Update personal best and global best positions;
25:
Update particle velocity and position using Equations (8) and (9);
26:
end
27:
Output the optimized structural parameters of SCBLS;
28:
Train the model using the optimal parameters;
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Output Y;
30:
return Y