As a solid foundation for gradually establishing and improving the teaching quality assurance system, ensuring the standardized conduct of the teaching process, and enhancing teaching quality, teaching supervision work in higher education institutions plays a crucial role in strengthening the management of teaching processes. To improve the objectivity, scientific rigor, and rationality of teaching quality in higher education institutions, this study first conducted a principal component analysis on 26 factors influencing teaching quality to extract the principal components of these factors. PSO algorithm parameters were set, and the particle swarm optimization algorithm was used to search for the optimal input weights and hidden layer neuron thresholds of the extreme learning machine (ELM) model, thereby proposing an educational quality evaluation model that integrates principal component analysis, particle swarm optimization, and extreme learning machine (PCA-PSO-ELM). Compared to the ELM model, the ELM model optimized by PCA and PSO algorithms has lower error rates and more reliable prediction results. In terms of educational quality grading, the results of the 34 tested datasets fully align with actual outcomes. Finally, based on the fsQCA analysis results, four reform pathways were proposed to enhance higher education quality.