Analysis of Residents’ Understanding of Encroachment Risk to Water Infrastructure in Makause Informal Settlement in the City of Ekurhuleni
Abstract
1. Introduction
2. The Aim of the Study
3. Objectives
- To design and train an Artificial Neural Network (ANN) model that predicts levels of the resident understanding of encroachment risks to water infrastructure.
- To evaluate the predictive accuracy and performance of the Artificial Neural Network model in classifying the resident understanding of encroachment risks.
- To interpret the relative importance of input variables in shaping resident awareness and risk perception using Artificial Neural Network techniques.
- To provide data-driven insights to policymakers and urban planners for targeted awareness campaigns and infrastructure protection in informal settlements.
4. Research Question
- To what extent can an Artificial Neural Network (ANN) accurately model and predict residents’ understanding of encroachment risks?
- How can insights from the Artificial Neural Network analysis inform risk communication and urban planning strategies for informal settlements?
5. Research Methodology
6. Equations and Models Used
- (i)
- Sample determination:The sample size was calculated using standard formulae for unknown populations based on the methods of [24,25]. To ensure statistical reliability, a confidence level of 95 and an acceptable margin of error were applied (see Appendix A for formulae).
- (ii)
- Correlation and Model Accuracy:Correlation coefficients, determination coefficients (R2), and the root mean square error (RMSE) were calculated to assess relationships between variables and the accuracy of predictive models. The detailed equations used in these calculations are provided in Appendix A.
- (iii)
- ReliefF Algorithm:The ReliefF algorithm was used to identify the most important predictors of encroachment risk. In simple terms, ReliefF updates the importance of each factor based on how well it distinguishes between different response categories. The core logic is as follows:
- -
- If two observations belong to the same group, the importance score of factors decreases with the similarity.
- -
- If they belong to different groups, the importance score increases with the difference.Detailed update and distance equations are presented in Appendix A.
- (iv)
- Neural Network Transfer Function:A logistic sigmoid transfer function was used in the neural network model to predict the risk of encroachment. The Levenberg–Marquardt algorithm was used for training. The complete mathematical expressions can be found in Appendix A.
- (v)
- Statistical Significance: To determine significance, the p-values were calculated based on the t-statistics derived from the correlation coefficients. Details on the calculation of the t-values and the degrees of freedom can be found in Appendix A.
7. Workplace Site Exposure Sample Determination
7.1. Data Collection Methods
7.2. Ethics and Community Positioning
7.3. Sampling Procedure and Possible Biases
7.4. Pilot Testing and the Validation of the Scale
8. Validity and Reliability
9. Data Analysis
10. Findings and Discussion
10.1. The Analysis of the Questionnaires on the Encroachment Risk for Residents
10.2. Encroachment Risk
10.3. The One-Way ANOVA Test for the Inputs on Encroachment Risk
10.4. Multiple Comparisons Among Groups
10.5. Relief Tests Used in the Rankings of the Inputs
10.6. Training Neural Network Using Input and Output Datasets
10.7. The ANOVA to Confirm the Accuracy of the Artificial Neural Network Model
11. Policy and Practical Relevance
12. Discussion and Conclusions
13. Recommendations
13.1. Predicting Encroachment
13.2. Mitigating Infrastructure Vandalism
13.3. Education and Training of Local Communities
- Artificial intelligence, such as Gamified apps and simulations, to educate residents on how encroachment and vandalism impact services.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Detailed Mathematical Formulas
Appendix A.1. Sample Size Determination
Appendix A.2. Correlation and Determination Coefficients
Appendix A.3. Model Accuracy: Root Mean Square Error (RMSE)
Appendix A.4. ReliefF Algorithm Equations
- ➢
- If and are in the same class, then Equation (A6) is applied
- ➢
- If and are in different classes, then Equation (A7) is employed
- ➢
- For the discrete, the equation is expressed as in Equation (A8)
- ➢
- For the continuous the equation is expressed as in Equation (A9)
Appendix A.5. Statistical Significance (t-Test for Correlation Coefficient)
Appendix A.6. Neural Network Transfer Function
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ANOVA Table | |||||
---|---|---|---|---|---|
Source | SS | df | MS | F | Prob > F |
Columns | 15,240.4 | 2 | 7620.2 | 24.45 | 2.15 × 10−8 |
Error | 17,765.3 | 57 | 311.67 | ||
Total | 33,005.7 | 59 |
Samples | MSE | R | |
---|---|---|---|
Training | 10 | 5.59 × 10−8 | 0.999 |
Validation | 5 | 1.082 | 0.990 |
Testing | 5 | 3.09 | 0.965 |
Source | Sum of Square (SS) | Degree of Freedom (df) | Mean Square (MS) | F-Statistic | Prob > F |
---|---|---|---|---|---|
Columns | 0.09 | 1 | 0.0876 | 0.0 | 0.9609 |
Error | 1366.53 | 38 | 35.9613 | ||
Total | 1366.62 | 39 |
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Ndawo, M.N.; Dzansi, D.; Tangwe, S.L. Analysis of Residents’ Understanding of Encroachment Risk to Water Infrastructure in Makause Informal Settlement in the City of Ekurhuleni. Urban Sci. 2025, 9, 294. https://doi.org/10.3390/urbansci9080294
Ndawo MN, Dzansi D, Tangwe SL. Analysis of Residents’ Understanding of Encroachment Risk to Water Infrastructure in Makause Informal Settlement in the City of Ekurhuleni. Urban Science. 2025; 9(8):294. https://doi.org/10.3390/urbansci9080294
Chicago/Turabian StyleNdawo, Mpondomise Nkosinathi, Dennis Dzansi, and Stephen Loh Tangwe. 2025. "Analysis of Residents’ Understanding of Encroachment Risk to Water Infrastructure in Makause Informal Settlement in the City of Ekurhuleni" Urban Science 9, no. 8: 294. https://doi.org/10.3390/urbansci9080294
APA StyleNdawo, M. N., Dzansi, D., & Tangwe, S. L. (2025). Analysis of Residents’ Understanding of Encroachment Risk to Water Infrastructure in Makause Informal Settlement in the City of Ekurhuleni. Urban Science, 9(8), 294. https://doi.org/10.3390/urbansci9080294