To achieve non-destructive testing for small size weld beads of metal workpieces, we developed a new testing method of closed magnetic circuit reluctance measurement. According to the shape and volume of the small size weld defects of the metal workpiece, a reluctance detection model was established in the detection environment of alternating magnetic field. The relationship between different weld defects and closed magnetic circuit reluctance was quantitatively analyzed to achieve the identification of weld defects. A particle swarm optimization algorithm (PSO) was applied to optimize the cost-sensitive support vector machine (CS-SVM), which effectively reduced the coupling errors caused by the limitation of the workpiece coupling size. This new method was used to verify the weld bead detection of representative carbide saw blades. Compared with the basic support vector machine, the improved cost-sensitive support vector machine has better performance in the classification of unbalanced samples. The experimental results showed this new method can detect the weld bead of carbide saw blade with the correct rate to 98.2%. It reduced the interference of coupling error effectively. The improved cost-sensitive support vector machine not only improved the detection accuracy, but also avoided the possibility that the defective weld workpiece samples are misclassified into qualified workpieces. This study provides a guarantee for safe production and has great significance in engineering applications. The new method provides an effective solution for the application of reluctance testing technology in small size weld bead detection. INDEX TERMS Closed magnetic circuit, cost-sensitive support vector machine, coupling error, particle swarm optimization, reluctance measurement, small size weld bead.