Limited Historical Data Research Articles

Investigations on machine learning-based control-oriented modeling using historical thermal data of buildings

Machine learning-based control-oriented modelling is a promising solution to model the complex system dynamics of buildings. It can benefit learning-based controllers, e.g., Model Predictive Control and Reinforcement Learning. However, obtaining reliable models is non-trivial, especially when only limited historical data generated by the baseline controller is available. This paper analyses the modelling tasks and identifies the sources of prediction error to obtain suitable machine learning models, and then proposes a training framework to provide a well-designed training procedure, mitigating the reducible errors. Six typical machine learning methods are evaluated using simulated and real-world datasets using in- and out-of-distribution data. Comprehensive evaluation metrics are also proposed. The results of absolute error and prediction interval coverage percentage indicate that purely point estimation is not enough to provide reliable predictions, and uncertainties must be quantified. Further results from analysis of the out-of-distribution data show that although some models have satisfactory predictions on in-distribution data, their capability of interpolation and extrapolation is poor. Some predictions may deviate from the targets. Point estimation may provide over-confident results. It is, therefore, essential to quantify the uncertainty caused by the lack of data to ensure that the true value falls into the prediction interval with high probability. The decomposition of the total uncertainty provides more information and detects out-of-distribution data. These investigations demonstrated the importance of accurate point estimation and uncertainty quantification for models' reliability.

Two-stage distributionally robust optimization for joint system design and maintenance scheduling in high-consequence systems

The failures of high-consequence systems can cause serious harm to humans, including loss of human health, life security, finance, and even social chaos. To protect high-consequence systems, both optimal system design and maintenance activities contribute to improving system reliability and social safety. The existing works generally optimize these two problems sequentially and assume that the degradation process of components is precisely known. However, sequential optimization often results in significant losses due to redundancies, and such a presumption usually cannot be guaranteed in practice, due to limited historical data or a lack of expert knowledge, referred to as epistemic uncertainty. To fill this gap, in this article, we consider an integrated optimization of system design and maintenance scheduling for multi-state high-consequence systems in which the component’s degradation is known with limited distributional information. To address this issue, we utilize the framework of distributionally robust optimization to provide a risk-averse decision to decision-makers even under the worst realizations of random parameters, and develop a two-stage integer distributionally robust model with moment-based ambiguity set to determine the system design and maintenance scheduling simultaneously. The proposed model can be converted to a tractable approximation as an integer linear stochastic programming problem. In order to solve large-scale problems, we develop a sample-based adaptive large neighborhood search algorithm to find the optimal system designs. In the numerical experiments, we present a case study on feedwater heating systems in nuclear power plants and demonstrate that an integrated optimization consideration creates significant benefits in profitability. We also present the out-of-sample performance of the distributionally robust design to avoid extreme risk.

Optimizing sustainable biomass–coal co-firing power plant location problem under ambiguous supply

Promoting biomass–coal co-firing power generation technology in existing coal-fired power plants is a practical and relatively low-cost short-run choice for the coal-fired power industry to reduce carbon emissions and develop sustainably. However, the uncertainty of biomass supply complicates the location of co-firing power plants among existing coal-fired plants. To address the challenge that only limited historical data of uncertain supply are available, this paper proposes a new ambiguity distribution set to characterize the uncertain supply capacity, supply price, and supply quality (i.e., energy conversion coefficient). Accordingly, a novel bi-objective distributionally robust fuzzy optimization model is developed for the sustainable co-firing power plant location (SCPPL) problem to balance conflicting objectives of minimizing total cost and maximizing carbon emission reduction. Subsequently, the computationally tractable counterpart of the proposed model is derived against the worst-case distribution by reformulating the distributionally robust credibility objective and constraints as their solvable equivalent forms. Furthermore, the Pareto optimal solutions of the proposed bi-objective model are generated using the augmented ϵ-constraint method. Finally, a realistic case study of Heilongjiang Province in China is conducted to verify the feasibility and effectiveness of the proposed optimization method. The experimental results demonstrate that the proposed model can hedge against the distributional ambiguity of uncertain parameters and provides a robust co-firing power plant location strategy. By comparison with the nominal distribution model and analysis of the sensitivity of selected parameters, management insights are summarized for decision-makers.

Lupus activity and outcomes in lupus patients undergoing maintenance dialysis.

Lupus activity has long been considered to decline after initiation of maintenance dialysis (MD). This assumption is based on limited historical data. We aimed to describe the natural history of lupus in patients undergoing MD. We assembled a national retrospective cohort of lupus patients who started dialysis between 2008 and 2011, included in the REIN registry with a 5-year follow-up. We analysed healthcare consumption from the National Health Data System. We evaluated the proportion of patients 'off-treatment' (i.e. receiving 0-5 mg/d of corticosteroids, without any immunosuppressive therapy) after the start of MD. We describe the cumulative incidences of non-severe and severe lupus flares, cardiovascular events, severe infections, kidney transplantation and survival. We included 137 patients (121 females and 16 males), with a median age of 42 years. The proportion of patients 'off-treatment' at dialysis initiation was 67.7% (95% CI: 61.8, 73.8%), and increased to 76.0% (95% CI: 73.3, 78.8) at 1 year and 83.4% (95% CI: 81.0, 85.9%) at 3 years, with a lower proportion in younger patients. Lupus flares mainly occurred in the first year after MD initiation, and at 12 months 51.6% of patients had presented a non-severe lupus flare and 11.6% a severe lupus flare. In addition, 42.2% (95% CI: 32.9, 50.3%) and 23.7% (95% CI: 16.0, 30.7%) of patients at 12 months had been hospitalized for cardiovascular events or infections, respectively. The proportion of lupus patients off-treatment increases after MD initiation, but non-severe and severe lupus flares continue to occur, mainly during the first year. This calls for the continued follow-up of lupus patients by lupus specialists after dialysis initiation.

Two unsupervised learning algorithms for detecting abnormal inactivity within a household based on smart meter data

We study the problem of detecting abnormal inactivities within a single-occupied household based on smart meter readings. Such abnormal events include immobilizing medical conditions or sudden deaths of elderly or disabled occupants who live alone, the delayed discovery of which poses realistic social concerns as the population ages. Two novel unsupervised learning algorithms are developed and compared: one is based on nested dynamic time warping (DTW) distances and the other based on Mahalanobis distance with problem-specific features. Both algorithms are able to cold-start from limited historical data and perform well without extended parameter tuning. In addition, the algorithms are small profile in terms of data usage and computational need, and thus are suitable for implementation on smart meter hardware. The proposed methods have been thoroughly validated against real data sets with simulated target scenarios and have exhibited satisfactory performance. An implementation scheme on smart meter hardware is also discussed.

Scientific and Regulatory Policy Committee Points to Consider: Sampling, Processing, Evaluation, Interpretation, and Reporting of Test Article-Related Ganglion Pathology for Nonclinical Toxicity Studies.

Certain biopharmaceutical products consistently affect dorsal root ganglia, trigeminal ganglia, and/or autonomic ganglia. Product classes targeting ganglia include antineoplastic chemotherapeutics, adeno-associated virus-based gene therapies, antisense oligonucleotides, and anti-nerve growth factor agents. This article outlines "points to consider" for sample collection, processing, evaluation, interpretation, and reporting of ganglion findings; these points are consistent with published best practices for peripheral nervous system evaluation in nonclinical toxicity studies. Ganglion findings often occur as a combination of neuronal injury (e.g., degeneration, necrosis, and/or loss) and/or glial effects (e.g., increased satellite glial cell cellularity) with leukocyte accumulation (e.g., mononuclear cell infiltration or inflammation). Nerve fiber degeneration and/or glial reactions may be seen in nerves, dorsal spinal nerve roots, spinal cord, and occasionally brainstem. Interpretation of test article (TA)-associated effects may be confounded by incidental background changes or experimental procedure-related changes and limited historical control data. Reports should describe findings at these sites, any TA relationship, and the criteria used for assigning severity grades. Contextualizing adversity of ganglia findings can require a weight-of-evidence approach because morphologic changes of variable severity occur in ganglia but often are not accompanied by observable overt in-life functional alterations detectable by conventional behavioral and neurological testing techniques.

Prediction of photovoltaic power generation based on LSTM and transfer learning digital twin

This research offers a digital twin model for solar power production power prediction based on long short term memory network (LSTM), and then applies this model to other models with limited operational time and inadequate data through transfer learning. The prediction for the solar system’s electrical output. Due to the effect of sun irradiation, temperature, and other random elements, photovoltaic power output is very intermittent and fluctuating, making it impossible to anticipate photovoltaic power with precision. Synchronization and real-time updating of physical entities, thereby obtaining more accurate forecasting results than traditional forecasting methods, while utilizing knowledge learned from PV systems with sufficient historical data to assist PV systems with limited historical data in establishing a digital twin of power generation forecasting model, not only can obtain accurate prediction results but also save training time for the model. In this study, the PV historical data of three distinct sites from the open source websites of Queensland University and Shanxi Jinneng Clean Energy Company are used to validate the validity of the suggested technique.

Enhancing the Accuracy of Water-Level Forecasting with a New Parameter-Inversion Model for Estimating Bed Roughness in Hydrodynamic Models

The accurate and efficient estimation of bed roughness using limited historical observational data is well-established. This paper presents a new parameter-inversion model for estimating bed roughness in hydrodynamic models that constrains the roughness distribution between river sections. The impact of various factors on the accuracy of inversed roughness was analyzed through a numerical experiment with the number of measurement stations, observed data amount, initial bed roughness, observational noise, and the weight of the regularization term. The results indicate that increasing the number of measurement stations and the amount of observed data significantly improves the robustness of the model, with an optimal parameter setting of 3 stations and 30 observed data. The initial roughness had little impact on the model, and the model showed good noise resistance capacity, with the error significantly reduced by controlling the smoothness level of inversed roughness using a small weight of the regularization term (i.e., 100). An experiment conducted on a real river using the calibrated model parameters shows a forecasted water level RMSE of 0.041 m, 31% less than that from the Federal Emergency Management Agency. The proposed model provides a new approach to estimating bed roughness parameters in hydrodynamic models and can help in improving the accuracy of water-level forecasting.

Transit Arrival Time Prediction Using Interaction Networks

Accurate transit arrival time prediction is a critical factor for improving the quality of transit services. A significant factor that can affect transit arrival times is the other vehicles traveling on transit routes, as transit arrival time is significantly affected by traffic conditions. However, few previous studies considered traffic condition impacts in transit arrival time prediction due to a lack of real-time traffic data, reducing the accuracy in predictions under varying traffic conditions. To fill this research gap, crowdsourced speed data with wide coverage is utilized to indicate traffic conditions and to predict transit arrival time in conjunction with General Transit Feed Specification (GTFS) data. Interaction Networks (INs) are employed to model the interactions between transit speed, dwell time, and traffic speed for arrival time prediction. The proposed method only uses limited historical data and can predict arrival time at stops along a transit route. Ten days of data were collected from bus route #4 in Tucson, Arizona to evaluate the performance of the proposed method. The evaluation results show the average mean absolute percentage error (MAPE) of predicted arrival time on weekdays and weekends is 13.5% and 14%, respectively, indicating that the proposed method is promising for predicting transit arrival time while considering real-time traffic conditions. Furthermore, six traditional methods are compared with the proposed method, and the comparison results show the proposed method outperforms the other six methods.

Development of the framework for quantitative cyber risk assessment in nuclear facilities

Industrial control systems in nuclear facilities are facing increasing cyber threats due to the widespread use of information and communication equipment. To implement cyber security programs effectively through the RG 5.71, it is necessary to quantitatively assess cyber risks. However, this can be challenging due to limited historical data on threats and customized Critical Digital Assets (CDAs) in nuclear facilities. Previous works have focused on identifying data flows, the assets where the data is stored and processed, which means that the methods are heavily biased towards information security concerns. Additionally, in nuclear facilities, cyber threats need to be analyzed from a safety perspective. In this study, we use the system theoretic process analysis to identify system-level threat scenarios that could violate safety constraints. Instead of quantifying the likelihood of exploiting vulnerabilities, we quantify Security Control Measures (SCMs) against the identified threat scenarios. We classify the system and CDAs into four consequence-based classes, as presented in NEI 13–10, to analyze the adversary impact on CDAs. This allows for the ranking of identified threat scenarios according to the quantified SCMs. The proposed framework enables stakeholders to more effectively and accurately rank cyber risks, as well as establish security and response strategies.

Using Historical Data to Dynamically Route Post-Disaster Assessment Unmanned Aerial Vehicles in the Context of Responding to Tornadoes

Responding to tornado disasters resides at a unique intersection of search and rescue operations: it has attributes of wilderness and maritime search and rescue operations and search and rescue operations in the aftermath of earthquakes and hurricanes. This paper presents a method of attempting to leverage historical data to more efficiently identify the extent of the area damaged by a tornado. To assist in building and understanding the historical data, we also develop a method to generate tornado areas that react similarly to the limited historical data set. The paper successfully demonstrates the method of creating artificial tornado instances that can be used as a testing sandbox for the further development of tools when responding to tornado-type disasters. These artificial instances perform similarly in some important metrics to the historical database of tornado instances that we produced. This paper also shows that the use of historical tornado trends has an impact on the response method outlined in this article, typically reducing the standard deviation of the time it takes to fully identify the extent of the damage.

A new uncertain remanufacturing scheduling model with rework risk using hybrid optimization algorithm.

As a resource-conserving and environmentally friendly manufacturing paradigm, remanufacturing with the potential to realize sustainability in production has been extensively investigated. Scheduling plays a significant role in achieving the remanufacturing benefits. However, the remanufacturing process involves intricate uncertainties because it takes end-of-life products with different qualities as workblanks, which increases the risk of rework and complicates remanufacturing scheduling. Though the traditional stochastic optimization methods or fuzzy theory have been employed to address uncertainties in the remanufacturing scheduling problem, they are constrained with the limited historical data which renders it difficult to describe uncertainties accurately and intuitively. Therefore, a new uncertain remanufacturing scheduling model with rework risk is proposed, in which the interval grey numbers are applied to describe the uncertainty clearly and consider the rework risk in remanufacturing process. To solve this model, a hybrid optimization algorithm that combines differential evolution and particle swarm optimization algorithms through an efficient representation scheme is proposed. Besides, this algorithm integrates multiple improvements to maintain the diversity of the population and enhance its performance. Simulation experiments are conducted on 18 sets of instances with different scales, and the results demonstrated that the proposed algorithm obtains a better optimal solution than other baseline algorithms on 17 sets of instances. The main finding of this study is providing a new method for solving uncertain remanufacturing scheduling problem with rework risk practically and effectively.

Deep4Ener: Energy Demand forecasting for Unseen Consumers with Scarce Data Using a Single Deep Learning Model

Forecasting the energy demand of individual consumers is a vital component of future smart energy grids since it enables energy-saving mechanisms such as Demand Response, activity scheduling, and prosumer energy markets. However, training a separate model with each consumer's available smart meter data can raise significant cold-start and scalability issues, despite the fact that personalization can be achieved in cases where the respective training sets have adequate data. Namely, making accurate forecasts for new consumers with limited historical data is challenging since a machine learning model requires a significant volume of data to be trained adequately, while scalability becomes an issue when the number of consumers increases. Training a single model on multiple consumers can mitigate these issues, hence we propose a single-model RNN-based deep learning architecture named Deep4Ener, for consumer-level energy demand forecasting, trained on multiple users and capable of making predictions for unseen consumers with scarce historical data that were not included in the training phase. Deep4Ener learns common energy demand characteristics among different consumers, by utilizing a novel architecture for energy profiling, including clustering, and an encoder neural network for feature extraction. Experiments with data from two open datasets show that Deep4Ener achieves high predictive performance both for known and completely new consumers, while outperforming the current state-of-the-art, namely one-model-per-consumer, standalone RNN, and Amazon's DeepAR approaches. Finally, we demonstrate that Deep4Ener shines when combined with Transfer Learning to further improve its forecasting performance on different energy demand consumers with limited data available.

Prediction of meteorological drought and standardized precipitation index based on the random forest (RF), random tree (RT), and Gaussian process regression (GPR) models.

Agriculture, meteorological, and hydrological drought is a natural hazard which affects ecosystems in the central India of Maharashtra state. Due to limited historical data for drought monitoring and forecasting available in the central India of Maharashtra state, implementing machine learning (ML) algorithms could allow for the prediction of future drought events. In this paper, we have focused on the prediction accuracy of meteorological drought in the semi-arid region based on the standardized precipitation index (SPI) using the random forest (RF), random tree (RT), and Gaussian process regression (GPR-PUK kernel) models. A different combination of machine learning models and variables has been performed for the forecasting of metrological drought based on the SPI-6 and 12months. Models were developed using monthly rainfall data for the period of 2000-2019 at two meteorological stations, namely, Karanjali and Gangawdi, each representing a geographical region of Upper Godavari river basin area in the central India of Maharashtra state which frequently experiences droughts. Historical data from the SPI from 2000 to 2013 was processed to train the model into machine learning model, and the rest of the 2014 to 2019-year data were used for testing to forecast the SPI and metrological drought. The mean square error (MSE), root mean square error (RMSE), adjustedR2, Mallows' (Cp), Akaike's (AIC), Schwarz's (SBC), and Amemiya's PC were used to identify the best combination input model and best subregression analysis for both stations of SPI-6 and 12. The correlation coefficient ([Formula: see text]), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root relative squared error (RRSE) were used to perform evaluation for SPI-6 and 12months of both stations with RF, RT, and GPR-PUK kernel models during the training and testing scenarios. The results during testing phase revealed that the RF was found as the best model in forecasting droughts with values of [Formula: see text], MAE, RMSE, RAE (%), and RRSE (%) being 0.856, 0.551, 0.718, 74.778, and 54.019, respectively, for SPI-6 while 0.961, 0.361, 0.538, 34.926, and 28.262, respectively, for SPI-12 scales at Gangawdi station. Further, the respective values of evaluators at Karanjali station were 0.913 and 0.966, 0.541 and 0.386, 0.604 and 0.589, 52.592 and 36.959, and 42.315 and 31.394 for PUK kernel and RT models, respectively, during SPI-6 and SPI-12. Machine learning models are potential drought warning techniques because they take less time, have fewer inputs, and are less sophisticated than dynamic or scientific models.

Sales Volume Forecast of Typical Auto Parts Based on BiGRU: A Case Study

Inventory management is an important part of the auto parts supplier business. Accurate prediction of sales volume for different auto parts is the basis for staff to formulate marketing strategies and procurement plans. Based on the limited historical sales data of the South China, North China and East China branches of an auto parts company, some prediction models are trained and tested to determine the best model for predicting future production sales. An orthogonal experimental method is used to implement hyperparameter estimation for the prediction models on this basis. In addition, a posteriori test is used to verify the validity and accuracy of the Bi-GRU model in predicting the sales volume of typical auto parts. The results show that, compared with other models, the bidirectional gated recurrent unit (Bi-GRU) model has the highest accuracy in testing and is used to predict the future sales of typical auto parts. The posterior test proved that the validity and accuracy of the Bi-GRU model is verified. The orthogonal experiment method can effectively realize the hyperparameter estimation for each model. According to the prediction results, the sales volume of blind drive caps in South China, North China and East China will reach 18235, 17030 and 14949 pieces, respectively, after 90 days. Meanwhile, the corresponding sales volume of bolts will reach 13141, 15062 and 10253 pieces, respectively.

Reliable design of a congested disaster relief network: A two-stage stochastic-robust optimization approach

The preparedness of humanitarian relief networks can be enhanced by pre-positioning resources in strategic locations and using them when disasters strike, a strategy that gives rise to a two-stage planning problem. This paper presents a novel two-stage stochastic-robust optimization approach for integrated planning of pre- and post-disaster positioning and allocation of relief resources, while taking into consideration the uncertainty about demand for relief services and disruptions in the relief facilities and the transportation network. The proposed approach enables planners to effectively use limited historical data and imperfect experts’ opinions to obtain robust solutions while avoiding the over-conservatism of classical robust optimization methods. The objective sought is to minimize the expected total time victims need to receive assistance, including both access time to facilities and waiting/service time in them. Congestion in relief facilities is accounted for by modeling them as queuing systems and penalizing waiting time. A decomposition method based on column-and-constraint generation is implemented to solve the problem, whereas the nonlinear terms corresponding to queuing in the second-stage problem are handled using a direct search procedure. Applicability of the proposed approach is demonstrated through a real case study and the numerical results are analyzed to draw managerial insights.

Regional tree-ring oxygen isotope deduced summer monsoon drought variability for Kumaun-Gharwal Himalaya

The precipitation in the Kumaun-Gharwal (Uttarakhand) Himalaya (KGH) is predominantly regulated by the Indian summer monsoon (ISM) and has been declining over the last century. However, because of limited historical data, it is difficult to place this recent decreasing trend in the context of pre-anthropogenic influences and understand a fuller range of hydroclimate scenarios for the region. Thus, we developed a 508-year regional tree-ring stable oxygen isotope (δ18OTR) record for multiple coniferous taxa (Abies spectabilis, Cedrus deodara and Picea smithiana) for the KGH, which spanned 1508–2015 CE. The δ18OTR record explained 35.8% of instrumental June–August Palmer Drought Severity Index (JJAPDSI) variance modelled from a nearby meteorological station. The JJAPDSI reconstruction shows regional coherency with both instrumental and proxy-based independent hydroclimatic records providing confidence that it is a reliable proxy to assess the long term hydroclimatic variability of the region. We identified decreasing strength of JJAPDSI reconstruction in KGH during recent decades indicating intensified drought. This is in the context of pre-anthropogenic influences and understand a fuller range of hydroclimate scenarios for the region. The δ18OTR also has coherency with Pacific and Indian Ocean sea surface temperature variability illustrating the broader teleconnections that influence the regional hydroclimate.

Distributionally Robust Unit Commitment with N-k Security Criterion and Operational Flexibility of CSP

In order to reduce the conservatism of the robust optimization method and the complexity of the stochastic optimization method and to enhance the ability of power systems to deal with occasional line fault disturbance, this paper proposes a distributionally robust unit commitment (DRUC) model with concentrating solar power (CSP) operational flexibility and N-k safety criterion under distributed uncertainty. According to the limited historical sample data, under the condition of satisfying a certain confidence level, based on the imprecise Dirichlet model (IDM), an ambiguity set is constructed to describe the uncertainty of transmission line fault probability. Through the identification of the worst probability distribution in the ambiguity set, the adaptive robust optimal scheduling problem is transformed into a two-stage robust optimization decision model under the condition of deterministic probability distribution. The CSP flexibility column and constraint generation (C&CG) algorithm is used to process the model and the main problem and subproblem are solved by using the Big-M method, linearization technique, and duality principle. Then, a mixed integer linear programming problem (MILP) model is obtained, which effectively reduces the difficulty of solving the model. Finally, case studies on the IEEE 14 bus system and the IEEE 118 bus system demonstrate the efficiency of the proposed method, such as enhancing the ability of power systems to cope with occasional line fault disturbances and reducing the conservatism of the robust optimization method.

Reducing smearing effect in contribution plots and improving fault detection via polynomial approximated isomap embeddings

AbstractDimension reduction is an essential method used in multivariate statistical process monitoring for fault detection and diagnosis. Principal component analysis (PCA) and independent component analysis (ICA) are the most frequently used linear dimensional reduction tools, and the contribution plot is the most popular fault isolation method in the absence of any prior information on the faults. These methods, however, come with their shortcomings. The fault detection capability of linear methods may not be sufficient for non‐linear processes, and smearing effect is known to deteriorate the diagnostics obtained from contribution plots. While the fault detection rate may be increased by kernelized methods or deep artificial neural network models, tuning data‐dependent hyperparameter(s) and network structure with limited historical data is not an easy task. Furthermore, the resulting non‐linear models often do not directly possess fault isolation capability. In the current study, we aim to devise a novel method named ICApIso‐PCA, which offers non‐linear fault detection and isolation in a rather straightforward manner. The rationale of ICApIso‐PCA mainly involves building a non‐linear scores matrix, composed of principal component scores and high‐order polynomial approximated isomap embeddings, followed by implementation of the ICA‐PCA algorithm on this matrix. Applications on a toy dataset and the Tennessee Eastman plant show that the I2 index from ICApIso‐PCA yields a high fault detection rate and offers accurate contribution plots with diminished smearing effects compared to those from traditional monitoring methods. Easy implementation and the potential for future research are further advantages of the proposed method.

Characterization of Air Quality Monitoring Stations in North Region of Malaysia Using Chemometric Technique in Relation to Human Health Impacts

Air quality status plays a vital indicator towards environment, economy as well as human health impacts of a country. Therefore, characterizing the spatial air quality monitoring stations is critical as it can be grouped into clusters in order to minimize the numbers of stations. It could be more efficient towards human health monitoring by strengthening management and reducing costs. However, the assessment of air quality pattern requires multiple variables to be analysed. It becomes a multivariate problem that requires novel methodologies as agglomerative hierarchical cluster analysis (AHC) is used primarily to determine cluster pattern [1]. It becomes a multidimensional problem that necessitates unique approaches, known as hybrid cluster technique. Therefore, this research aimed to show the hybrid cluster framework in air quality monitoring stations in north region of Peninsular Malaysia in order to give a superior geographic cluster distribution with a distinct validation.
 
 The data set for all air quality monitoring stations in north region (14 stations) was obtained from the Department of Environment, Malaysia (DOE) for the years 2018 to 2019 (two years). Six air quality pollutants (PM10, PM2.5, SO2, NO2, O3 and CO) were involved in this study. Before clustering the data, chemometric techniques such as principal component analysis (PCA) was used to summarize the information content in huge data tables in order to gain a better understanding of the variables in order to reduce dimensionality. The AHC was then created using the PCA factor scores. The factor scores were employed in a discriminant analysis (DA) to verify the clusters [2].
 
 Results from PCA factor scores showed 12 out of 14 stations needed to be further investigated using AHC. High Polluted Region (HPR=three stations), Moderate Polluted Region (MPR= four stations) and Low Polluted Region (LPR=five stations) were established from AHC and have the same characteristics as shown in Figure 1. Each class was distinguished using discriminant analysis (DA) for verification. The researchers discovered that each class has its own set of variables. Based on the DA, the confusion matrix for the clusters was 87.66 % indicating a high percentage of correct classification obtained from the validated data set (Table 1).
 The framework presented here is a novel tool for identifying and categorising stations based on air quality pollutants. The hybrid cluster analysis technique used in this study can produce more precise pollutant distributions, which are useful in air pollution research. In addition, the study could help to improve the existing methodology for air quality assessment in a more simplified way and a better evaluation of the air quality status, and thus could become an alternative way for analysis of changes in air quality, especially in the absence or limited historical data, in response to a better and more sustainable indicator in air quality assessment and management.