# Urban Quarry Ground Vibration Forecasting: A Matrix Factorization Approach
## 8 Conclusions  
In this study, we proposed a PPV (Peak Particle Velocity) prediction method using Weighted Non-negative Matrix Factorization (WNMF) based on measurement data from urban crushed stone sites. The method was further enhanced by normalization with Artificial Neural Networks (ANNs) to improve PPV prediction accuracy. This approach is particularly useful in scenarios where extensive measurement data are unavailable or contain missing values. The effectiveness of the proposed method was verified through various experiments, leading to the following key findings:  
Normalization with ANN resulted in higher accuracy compared to non-normalized methods. The PPV prediction error (root mean square error--RMSE) improved from 0.2219 to 0.1426.  
The method demonstrated high accuracy even with reduced measurement data (60 points) for ANN learning, decreasing the PPV prediction error from 0.1759 (with 100 points) to 0.1378 (with 60 points).  
The accuracy decreased when using extremely small amounts of measurement data (20 points), with the PPV prediction error increasing from 0.1759 (100 points) to 0.3630 (20 points).  
Moreover, our proposed method is versatile, capable of predicting any parameter within the matrix. This feature can extend its application beyond PPV prediction. For instance, it can estimate the amount of explosives within a specific vibration value or predict the reach of vibrations over distance. We anticipate its future role as a valuable tool in blasting design for blasters. Further research should concentrate on enhancing the predictive accuracy and functional aspects of this method as a system.  
Previous PPV prediction models, which relied on experimental, statistical methods, and ANN, faced issues like low prediction accuracy or the necessity for extensive data for accurate modeling. This study's comprehensive verification of our method using actual data from urban crushed stone sites suggests a potential resolution to these longstanding challenges.  
Nevertheless, our proposed method can be improved, particularly in establishing a rank estimation method for WNMF execution. The current practice of testing all conceivable ranks to select the one with the smallest prediction error is impractical due to its time and computational demands. Future research should aim to establish a more efficient rank estimation method, refining our approach into a highly accurate and universally applicable tool.  
Conceptualization, H.I., M.T. and T.A.; methodology, H.I., E.P. and Y.K.; software, H.I. and H.T.; validation, H.I., E.P. and B.B.S.; formal analysis, H.I. and H.T.; investigation, H.I., M.T. and B.B.S.; resources, H.I.; data curation, H.I.; writing--original draft preparation, H.I.; writing--review and editing, H.I., E.P. and Y.K.; visualization, H.I.; supervision, E.P. and Y.K.; project administration, E.P. and Y.K.; funding acquisition, M.T. and T.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
No new data were created in this study.  
We wish to extend my sincere thanks to Toseki Material Co. for allowing the use of the Mikurahana quarry site. Their generous support was crucial for the success of our research.  
The authors declare no conflict of interest.