case study development of iskandar malaysia

• DOI: 10.23958/IJSSEI/VOL07-I03/278
• Corpus ID: 233825938

The Urbanization and Growth of Malaysia: Case Study of Iskandar Region

• M. Y. Yasin , J. Abdullah , +1 author N. M. Noor
• Published 4 March 2021
• Geography, Economics

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Towards a Sustainable Regional Development in Malaysia: The Case of Iskandar Malaysia

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Urban planners by duty play the role of developing functional and aesthetically pleasing cities with the most optimal use of land. At the same time, they ensure that the cities planned for are ecologically friendly, and that they develop low CO 2 emissions. The planning of the proposed high growth region, South Johor Economic Region (SJER), now commonly known as the Iskandar Malaysia, provides a good opportunity to achieve such a purpose. This chapter reexamines the concept of low carbon cities and explores the perspective and scenarios towards transforming the Iskandar Malaysia into an environmentally sustainable urban region.

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Ho, CS., Fong, WK. (2011). Towards a Sustainable Regional Development in Malaysia: The Case of Iskandar Malaysia. In: Wong, TC., Yuen, B. (eds) Eco-city Planning. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0383-4_10

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Towards Sustainable Regional Economic Development -The case study of Iskandar Malaysia

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Effects of tuning decision trees in random forest regression on predicting porosity of a hydrocarbon reservoir. A case study: volve oil field, north sea

First published on 8th August 2024

Machine learning (ML) has emerged as a powerful tool in petroleum engineering for automatically interpreting well logs and characterizing reservoir properties such as porosity. As a result, researchers are trying to enhance the performance of ML models further to widen their applicability in the real world. Random forest regression (RFR) is one such widely used ML technique that was developed by combining multiple decision trees. To improve its performance, one of its hyperparameters, the number of trees in the forest ( n_estimators ), is tuned during model optimization. However, the existing literature lacks in-depth studies on the influence of n_estimators on the RFR model when used for predicting porosity, given that n_estimators is one of the most influential hyperparameters that can be tuned to optimize the RFR algorithm. In this study, the effects of n_estimators on the RFR model in porosity prediction were investigated. Furthermore, n_estimators ’ interactions with two other key hyperparameters, namely the number of features considered for the best split ( max_features ) and the minimum number of samples required to be at a leaf node ( min_samples_leaf ) were explored. The RFR models were developed using 4 input features, namely, resistivity log (RES), neutron porosity log (NPHI), gamma ray log (GR), and the corresponding depths obtained from the Volve oil field in the North Sea, and calculated porosity was used as the target data. The methodology consisted of 4 approaches. In the first approach, only n_estimators were changed; in the second approach, n_estimators were changed along with max_features ; in the third approach, n_estimators were changed along with min_samples_leaf ; and in the final approach, all three hyperparameters were tuned. Altogether 24 RFR models were developed, and models were evaluated using adjusted R 2 (adj. R 2 ), root mean squared error (RMSE), and their computational times. The obtained results showed that the highest performance with an adj. R 2 value of 0.8505 was achieved when n_estimators was 81, max_features was 2 and min_samples_leaf was 1. In approach 2, when n_estimators’ upper limit was increased from 10 to 100, there was a test model performance growth of more than 1.60%, whereas increasing n_estimators’ upper limit from 100 to 1000 showed a performance drop of around 0.4%. Models developed by tuning n_estimators from 1 to 100 in intervals of 10 had healthy test model adj. R 2 values and lower computational times, making them the best n_estimators’ range and interval when both performances and computational times were taken into consideration to predict the porosity of the Volve oil field in the North Sea. Thus, it was concluded that by tuning only n_estimators and max_features , the performance of RFR models can be increased significantly.

1. Introduction

ML application in reservoir characterization has significantly increased over the last couple of decades due to its ability to tackle regression and classification-type problems. 5–7 With the evolution of ML, a notable number of algorithms have been introduced. The artificial neural network (ANN), which uses a parallel processing approach and was developed based on the function of a neuron of a human brain, has been utilized in petrophysical parameter prediction. 8,9 Support vector regression (SVR) is another algorithm developed in the initial stages of the ML timeline, and it can handle non-linear relationships between a set of inputs and an output. Moreover, SVR has been utilized widely in reservoir characterization. 10–13 The least absolute shrinkage and selection operator (LASSO) regression and Bayesian model averaging (BMA) have also been extensively used in ML-related studies in the literature. 14 BMA uses Bayes theorem and LASSO uses residual sums of squares to build a linear relationship between the inputs and the output. BMA and LASSO regressions have been used in permeability modelling in recent studies. 5 Apart from petrophysical parameter predictions, ML models have also been used in lithofacies classification. 15 Generally, these studies utilized ML approaches to model lithofacies sequences as a function of well-logging data to predict discrete lithofacies distribution at missing intervals. 16–18 Besides permeability prediction, water saturation estimation, and lithofacies classification, ML models have been used in reservoir porosity estimation, which is the parameter of focus in this study. ML algorithms, such as ANN, deep learning, and SVR, have been used to predict porosity using logging data, seismic attributes, and drilling parameters. 19–21

Apart from the mentioned ML models, the ML approach known as ensemble learning has been applied in many recent studies. Here, ML base models (weaker models) are strategically combined to produce a high-performing and efficient model as shown in Fig. 1 . Ensemble ML models have become a popular tool among researchers to predict petrophysical properties due to their ability to reduce overfitting and underfitting. 22–26 RFR is one such popular ensemble ML model that was developed by amalgamating multiple decision trees. 27

Hyperparameter tuning is a process that is implemented to fine-tune ML algorithms to obtain optimal models. 28–30 Several hyperparameters can be controlled in an RFR model, such as n_estimators , max_features , min_samples_leaf , maximum depth of the tree ( max_depth ), fraction of the original dataset assigned to any individual tree ( max_samples ), minimum number of samples required to split an internal node ( min_samples_split ), maximum leaf nodes to restrict the growth of the tree ( max_leaf_nodes ).

Hyperparameter optimization has been utilized in recent studies related to reservoir characterization. Wang et al. developed an RFR model to predict permeability in the Xishan Coalfield, China. 24 Five hyperparameters, n_estimators , max_features , max_depth , min_samples_leaf and min_samples_split , were tuned during hyperparameter optimization. Zou et al. estimated reservoir porosity using a random forest algorithm. 31 During the hyperparameter optimization stage, n_estimators , max_features , min_samples_leaf , min_samples_split and max_depth were tuned. Rezaee and Ekundayo tuned n_estimators , min_samples_leaf , min_samples_split , and max_depth during the development of the RFR model used to predict the permeability of precipice sandstone in the Surat Basin, Australia. 32

Even though hyperparameters have been tuned during the hyperparameter optimization phase of an ensemble ML model development, the literature lacks studies that specifically focus on the effects of hyperparameter tuning in ensemble learning when predicting petrophysical properties in reservoir characterization. Addressing this research gap, in this study, the authors investigated the influence of one of the most utilized hyperparameters in the literature, namely, the n_estimators of RFR, when predicting the porosity of a hydrocarbon reservoir. Also, the effects of n_estimators were studied along with another two widely used hyperparameters, max_features and min_samples_leaf , when predicting the porosity of the Volve oil field in the North Sea. The study considered a supervised learning regression approach. The workflow of the study consisted of data preprocessing, RFR model development, and model analysis. Several RFR models were developed, including tuning n_estimators , tuning n_estimators along with max_features , tuning n_estimators along with min_samples_leaf , and tuning all three hyperparameters at once under four approaches by integrating grid search optimization and K-fold cross-validation. The models’ performances were evaluated based on the adjusted coefficient of determination (adj. R 2 ), root mean squared error (RMSE), and computational time. Only the three aforementioned hyperparameters were considered due to processing capacity limitations; however, this study is expected to be a solid initiation towards the development of future studies on the effects of hyperparameters in ML algorithms in reservoir characterization.

2. Methodology

2.1 geological setting and dataset.

The Hugin Formation is 153 m thick and oil-bearing and was penetrated at 3796.5 m, approximately 60 m deeper than expected. The total oil column in the well was 80 m, but no clear oil–water contact was observed. 38,40 The reservoir section was made up of highly variable fine to coarse-grained, well to poorly-sorted subarkosic arenite sandstones with good to excellent reservoir properties. The Hugin Formation of the area consists of a shallow marine shoreface, coastal plain/lagoonal, channel, and possibly mouth bar deposits. The underlying Skagerrak Formation was completely tight due to extensive kaolinite and dolomite cementation. The current study used data from well 15/9-19A. The well was drilled through the Skagerrak Formation and terminated approximately 30 m into the Triassic Smith Bank Formation. To fully utilize the available data, the study considered data from the 3666.59 to 3907.08 m depth interval. This depth interval ran through three formations, namely, Draupne, Heather, and Hugin. The stratigraphic column and description of the vertical facies distribution of the section are shown in Fig. 3 .

2.2 Data preprocessing

Feature scaling is also a common practice implemented during data preprocessing. There are two widely used feature scaling approaches in the literature, namely, normalization and standardization. However, in this study feature scaling was neglected since RFR is a tree-based ML model where splits do not change with any monotonic transformation. 52

2.3 Machine learning model development

The inequality shown by eqn (6) highlights what is required for accurate RFR, which is having a low correlation between residuals of differing tree members of the forest and low prediction error for the individual trees. The model's performance can be further enhanced by tuning its hyperparameters.

During the study, RFR models were developed using the Python programming language. The cleaned dataset obtained during the data preprocessing stage was loaded into Python, then split into training and testing. The Python-based scikit-learn library's RandomForestRegressor was used to develop the RFR algorithm. The RandomForestRegressor comes with default hyperparameters built into it. Default values assigned to some of the main hyperparameters of RFR in scikit-learn are given in Table 1 .

However, rather than using the default hyperparameters assigned by the scikit-lean library, to achieve the primary objectives of the study, hyperparameter optimization was implemented. Hyperparameter optimization is a commonly used practice to build robust ML models. 56,57 The hyperparameters of RFR were tuned using the grid search optimization (GSO) approach. For this, the GridSearchCV optimization algorithm in the scikit-learn library was used. GSO was considered since it runs through all the possible combinations in the hyperparameter space, thus selecting the best combination of the space. 57,58 The hyperparameter space was predefined by including the possible values and it was fed into the GSO algorithm.

GSO was implemented along with random subsampling cross-validation. An approach known as the K-fold cross-validation was used. During the K-fold cross-validation, the training dataset is divided into K number of same-sized portions (folds), and K − 1 of the portions are used for training and the remainder are used for validation. 59,60 This is repeated until each fold gets the chance to be the validation set. For this study, a 5-fold cross-validation was implemented as shown in Fig. 5 . Therefore, the training set was divided into five portions and during each split, four portions were used for training and one portion was used for validation.

Tuning was done under 4 approaches as shown in Fig. 6 to investigate the effects of the considered hyperparameters. In the first approach, n_estimators was changed from 1 to 10, 1 to 100, and 1 to 1000 in different intervals. The notation used to demonstrate the n_estimators change is shown in Table 2 .

In the second approach, n_estimators was changed from 1 to 1000 in the same way as approach 1 along with max_features . Here, max_features was changed from 10% to 100% of total features in increments of 10%. In the third approach, n_estimators was changed in the same way along with min_samples_leaf . In this case, min_samples_leaf was changed from 1 to 20 in intervals of 1. In the fourth approach, all 3 hyperparameters, i.e. , n_estimators , max_features and min_samples_leaf were varied at the same time in the above-mentioned intervals. In each approach, values of all the other hyperparameters of RFR were kept at their default values assigned by the scikit-learn library. The link to the GitHub folder with the developed codes is given in the appendix.

2.4 Results analysis

In eqn (7) and (8) , y i is the actual value, ŷ is the predicted value, ȳ is the mean value of the distribution, n is the number of data points and m is the number of input features.

3. Results and discussion

Interestingly, when the upper limit of the n_estimators range was pushed beyond 100, the performance of the model did not show any noticeable increase in all training validation and testing adj. R 2 values. When n_estimators changed from 1 to 100 in intervals 1 and 10 (models M12 and M13) and n_estimators changed from 1 to 1000 in intervals 1 and 10 (models M14 and M15), the models showed the same performance, i.e. a training score of 0.9760, validation score of 0.8367 and a testing score of 0.8202. However, when the n_estimators changed from 1 to 1000 in intervals of 100, the training and testing scores of the M16 model showed a slight increase in performance, yielding an adj. R 2 of 0.9799 and 0.8218, respectively. However, the validation score showed a slight decrease, which was negligible.

The highest computational time of 6932.55 seconds was shown by the model M14 where n_estimators changed from 1 to 1000 in increments of 1. The results from approach 1 showed that after a certain n_estimators value, the models’ performances increased drastically and the performance was maintained at a constant value over a certain n_estimators range showing that the performance of the RFR when n_estimators was tuned was efficient within a certain range. Since the range and interval at which the n_estimators values are tuned affect the computational time, an effective range and an interval for n_estimators should be decided upon, taking computational time into account.

In approach 2, max_features were also tuned along with n_estimators . Results obtained using approach 2 of the methodology are tabulated in Table 4 . As observed in approach 1, clear spikes in training, validation, and testing adj. R 2 values were observed when the upper limit of n_estimators was increased from 10 to 100. The training score had an increase of 1.36%, the validation score had an increase of 1.92%, and the test score had an increase of 1.60%. This clear jump in performance is noticeable in Fig. 7 . Interestingly, the performances of the models developed in approach 2 were significantly higher than the performance of the corresponding “ n_estimators change” in approach 1. This is quite visible in Fig. 8 . Further, going from approach 1 to 2, the average validation score increased by 2.24% and the testing score increased by 3.52%, which was significant. This increase in adj. R 2 values is an indication that tuning max_features has a major impact on predicting the porosity using RFR. Model M21, where n_estimators were changed from 1 to 10 in intervals of 1 and max_features were changed from 0.1 to 1 in intervals of 0.1, showed the least performance with a training score of 0.9672, validation score of 0.8381, and a testing score of 0.8366. On the other hand, model M23 showed the highest testing performance with an adj. R 2 of 0.8505 where n_estimators changed from 1 to 100 in intervals of 10 and max_features changed from 0.1 to 1 in intervals of 0.1. The model M23 yielded its best test model when n_estimators was 81 and max_features were 0.5. It should be noted that even though model M23 had the highest testing score, the training, and validation scores were not the best out of all the models developed in approach 2. The highest training score of 0.9823 was shown by models M24, M25, and M26. The highest validation scores were shown by models M24 and M25. However, it is more meaningful to select model M23 as the best-performing model since the testing set represents an independent dataset that had never been seen by the model before.

The anomaly in the validation score observed when the n_estimators were changed from 1 to 1000 in intervals of 100 in approach 1 was also observable in approach 2. The difference in train–test scores provides an idea about the generalizability of the model. The smaller the train–test difference, the higher the generalizability of the model. Overall, the train–test difference in approach 2 was noticeably less than that of approach 1. The average train–test difference decreased by 15.51% on going from approach 1 to 2. This showed that the generalizability of the models improved when max_features was introduced into the hyperparameter space. Similar to approach 1, the highest runtime was shown when the n_estimators changed from 1 to 1000 in increments of 1.

In approach 3, n_estimators was investigated with the alteration of min_samples_leaf , and the results obtained are tabulated in Table 5 . Notably, all the performance results obtained for all the RFR models except the runtimes were the same as that of approach 1, as seen in Fig. 7 and 8 . This was because the optimum value selected by the grid search optimization of the min_samples_leaf was the same as the default value assigned by the scikit-learn library for the RFR algorithm, hence the best testing adj. R 2 was shown by model M34 when the n_estimators was changed from 1 to 1000 in intervals of 100. Computational times were longer than those obtained in approach 1 since models developed in approach 3 had a larger hyperparameter space as compared to approach 1.

Table 7 shows the RMSE values of approaches 1, 2, 3, and 4. While the adj. R 2 values give an idea about the correlation between the actual porosities and the predicted porosities, the RMSE values provide an idea about the difference (or the error) between the two. Therefore, RMSE is also an important parameter in ML model performance evaluation. The pattern in which RMSE values fluctuated in the 4 approaches was similar to that of adj. R 2 . The smallest RMSEs were shown by model M16 with a training model RMSE of 0.9988 and a testing model RMSE of 2.8312. The improvement in the results when max_features was introduced into the hyperparameter space was also evident based on the RMSE values obtained in approach 2. There was a clear decrease in RMSE values in both training and testing models in approaches 2 and 4 where max_features was tuned.

Runtime and grid search combinations had a positive relationship, i.e. , when the number of combinations in the grid search space was the largest, the runtime of the model was the highest, and vice versa . Further, it was observed that from approach 1 to approach 3, the increase in computational times was roughly proportional to each other as seen in Fig. 9 . However, in approach 4 where n_estimators was changed along with the tuning of max_features and min_samples_leaf , an anomaly was observed when n_estimators was changed from 1 to 1000 in intervals of 10.

Even though the primary objective of the study was to investigate the influences of n_estimators along with max_features and min_samples_leaf on the performance of RFR, having an overall picture of the variation of the actual and predicted porosity and their relationship is important to understand the model's applicability in porosity prediction. To achieve this, depth-porosity graphs and correlation plots were plotted. Fig. 10 shows one such depth-porosity graph and a correlation plot developed for the best-performing RFR test model (model M23) of the study. The depth-porosity plot indicated that most of the time, the predicted porosity followed the pattern of the actual porosity. The correlation plot showed that the majority of the points were scattered around the perfect correlation line, which is an indication of a high correlation between the actual values and the predicted values.

4. Conclusions

• Overall, based on both the performance and computational time, the RFR model with n_estimators at 81 and max_features at 2 (while keeping all the other hyperparameters at their default values), which was developed in approach 2, produced the most effective model for predicting the porosity of the Volve oil field in the North Sea with a testing model adj. R 2 of 0.8505, a testing model RMSE of 2.5875, and a computational time of 30.2 seconds.

• There was a notable increase in performance when the upper limit of the n_estimators increased from 10 to 100. On the other hand, the performance of the models did not increase significantly when the upper limit of n_estimators increased from 100 to 1000. This phenomenon indicated that identifying an effective n_estimators range that is not too low (which will make the performance significantly low) and not too high (which will increase the computational time) is important to produce an efficient RFR model during porosity prediction.

• A range of 1 to 100 changed in intervals of 10 can be suggested for n_estimators when developing an RFR model to predict the porosity of the Volve oil field since these models showed higher performances and lower computational times in all four approaches. When the n_estimators range of 1 to 100 was changed in intervals of 10, it always yielded a high adj. R 2 value (in approaches 2 and 4, it yielded the highest testing model adj. R 2 value) for the model and had the second least computational time.

• When n_estimators was tuned along with max_features in approach 2, the results improved drastically as compared to approach 1 where only n_estimators was tuned. There was an average validation score increase of 2.24% and a testing score increase of 3.52% on going from approach 1 to 2. This improvement of the scores (adj. R 2 ) showed that max_features has a significant influence on the RFR model's performance.

• It was observed that computational time was largely affected by the number of hyperparameters altered, their range, and interval. Of all the approaches, the longest computational time was when n_estimators was tuned from 1 to 1000 in intervals of 1 along with max_features and min_samples_leaf .

Based on the results, only by adjusting n_estimators and max_features can an RFR model be developed with a robust prediction power to estimate the porosity in the Volve oil field.

Recommendations

Abbreviation.

Author contributions

Data availability, conflicts of interest, acknowledgements.

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