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Review

Toward Enhanced Efficiency: Soft Sensing and Intelligent Modeling in Industrial Electrical Systems

by
Paul Arévalo
1,2,* and
Danny Ochoa-Correa
1
1
Department of Electrical Engineering, Electronics and Telecommunications (DEET), University of Cuenca, Balzay Campus, Cuenca 010107, Ecuador
2
Department of Electrical Engineering, University of Jaén, 23700 Linares, Spain
*
Author to whom correspondence should be addressed.
Processes 2024, 12(7), 1365; https://doi.org/10.3390/pr12071365
Submission received: 2 June 2024 / Revised: 28 June 2024 / Accepted: 28 June 2024 / Published: 30 June 2024
(This article belongs to the Special Issue Industrial Process Operation State Sensing and Performance Optimization)
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Abstract

:
This review article focuses on applying operation state detection and performance optimization techniques in industrial electrical systems. A comprehensive literature review was conducted using the preferred reporting items for systematic reviews and meta-analyses (PRISMA) methodology to ensure a rigorous and transparent selection of high-quality studies. The review examines in detail how soft sensing technologies, such as state estimation and Kalman filtering, along with hybrid intelligent modeling techniques, are being used to enhance efficiency and reliability in the electrical industry. Specific case studies are analyzed in areas such as electrical network monitoring, fault detection in high-voltage equipment, and energy consumption optimization in industrial plants. The PRISMA methodology facilitated the identification and synthesis of the most relevant studies, providing a robust foundation for this review. Additionally, the article explores the challenges and research opportunities in applying these techniques in specific industrial contexts, such as steel metallurgy and chemical engineering. By incorporating findings from meticulously selected studies, this work offers a detailed, engineering-oriented insight into how advanced technologies are transforming industrial processes to achieve greater efficiency and operational safety.

1. Introduction

The electrical industry is continuously evolving, driven by technological advancements to enhance the efficiency and reliability of industrial electrical systems. In this context, soft sensing and intelligent modeling have emerged as promising research areas. Soft sensing involves using virtual sensors and advanced algorithms to estimate electrical systems’ state and operating conditions [1,2,3]. Meanwhile, intelligent modeling entails the development of mathematical models and optimization techniques to improve the performance of these systems [2]. The motivation behind this work stems from the growing demand for more efficient and reliable electrical systems in the industry. Soft sensing and intelligent modeling offer an innovative approach to addressing these challenges by enabling better equipment condition monitoring, early fault detection, and operational performance optimization.
Moreover, with the rise of industry 4.0 and the digitization of industrial processes, there is an urgent need to adopt advanced technologies that enhance the efficiency and competitiveness of companies. By understanding the context and importance of soft sensing and intelligent modeling in the electrical industry, this study aims to analyze how these technologies can improve industrial electrical systems’ efficiency and reliability. Through a comprehensive analysis of case studies and current trends, we seek to provide a detailed, engineering-oriented perspective on how these innovations transform industrial processes and pave the way for greater operational efficiency and safety.
The electrical industry is undergoing a revolution driven by soft sensing, incorporating virtual sensors and advanced algorithms. For instance, in the biomedical field, algorithms such as nonlinear weighted total variation image reconstruction enhance the accuracy of electrical capacitance tomography [1,2]. Additionally, dynamic latent structures with time-varying parameters are being used to predict hard-to-measure variables in virtual sensing applications [3]. Soft tissue-based sensors are also being effectively employed in practical applications, such as assisted gloves [3]. In state estimation, various approaches are being applied to improve the efficiency and reliability of electrical systems. For example, the combination of electromagnetic flow tomography and electrical tomography through Bayesian estimation enables precise image reconstruction [4,5,6].
Furthermore, advanced models are being developed to estimate the state of charge of energy storage systems like supercapacitors [7] and the state of health (SOH) of lithium-ion batteries [8]. Operational state detection is crucial for the efficiency and safety of electrical systems. Methods such as the real-time monitoring of current consumption in industrial electrical equipment allow for proactive machine management and an early detection of deviations and faults [9,10,11]. Other innovative approaches include impedance measurement in superconducting circuits during the operation and remote detection of defects in insulating materials using optical thermography [12,13,14].
In the realm of industrial electrical system efficiency, performance optimization techniques play a crucial role. For example, electrical impedance tomography is used in medical and industrial applications to estimate the internal electrical properties of biological tissues through voltage and current measurements on their surface [15]. In the field of solar energy, artificial neural networks (ANN) are applied for maximum power point tracking and fault detection in partially shaded photovoltaic systems [16]. Electrical capacitance tomography visualizes multiphase systems in industrial applications [17]. For the control of brushless direct current motors, a system based on an adaptive neuro-fuzzy inference system (ANFIS) optimized by the bacterial foraging optimization algorithm has been developed [18]. In rotary ultrasonic machining, a dual compensation approach for frequency and impedance using a multi-objective genetic algorithm has significantly improved transmission efficiency and ultrasonic vibration stability [19]. In thermoelectric generation systems with non-uniform temperature distribution, an optimal control technique based on an equilibrium optimization algorithm has been proposed [20]. For frequency and voltage stabilization in hybrid energy systems, a second-order active disturbance rejection control strategy optimized with ANN has been developed [21]. In cogeneration plants integrated with photovoltaic energy, a modified firefly algorithm combined with machine learning techniques has been used to predict plant efficiency and optimize its operation [22].
In the field of industrial electrical systems, efficiency and reliability are critical for optimizing performance and reducing operational costs. Intelligent techniques like state estimation and Kalman filtering are pivotal in fault detection and condition monitoring [23]. Condition monitoring and fault detection and diagnosis are essential for preventing severe damage to rotating machinery, such as induction motors [24]. Electrical machines, which are widely used in industry, also require advanced techniques for condition monitoring and predictive fault diagnosis [25]. In the context of industry 4.0, disruptive technologies like the internet of things (IoT) and artificial intelligence (AI) are revolutionizing communication and control in smart industries [26]. Battery management in energy storage and electric propulsion applications is another area where efficiency and safety are paramount [27]. Battery management systems incorporate functional safety techniques to ensure battery cells’ safe and efficient operation [28]. Estimating batteries’ SOH is crucial for ensuring their safe operation and optimizing their lifecycle [29]. Despite significant advances in soft sensing and intelligent modeling in industrial electrical systems, several research gaps still need detailed attention. For instance, while condition monitoring and fault diagnosis have been active areas of interest, there remains a need for more robust and accurate techniques for early anomaly detection and real-time fault prediction.
Furthermore, although the application of disruptive technologies like IoT and AI has shown promise, further research is necessary to fully understand their effective integration into industrial environments and their impact on the efficiency and reliability of electrical systems. Another area requiring greater attention is battery management in energy storage applications, where optimizing the SOH of batteries continues to be a significant challenge. In summary, while considerable progress has been made, important research gaps must be addressed to advance efficiency and operational safety in the electrical industry.
This paper proposes a comprehensive literature review on using soft sensing and intelligent modeling in industrial electrical systems. The aim is to synthesize the latest advancements in this field, critically analyze the selected studies, identify emerging trends, and explore practical applications. The PRISMA method will be employed to ensure the rigor and transparency of the review, facilitating the effective identification of relevant studies and a coherent synthesis of their findings. This systematic and transparent approach will allow us to evaluate the quality of the research, identify potential knowledge gaps, and highlight areas needing further investigation. Consequently, this review will provide a detailed, engineering-oriented perspective on how these technologies transform industrial processes, leading to greater efficiency and operational safety.
The remainder of this paper is organized as follows: Section 2 presents a literature review and methodology, outlining the theoretical framework and research methods used. Section 3 provides a descriptive analysis of the literature, summarizing key findings from the reviewed studies. Section 4 details the results of our analysis. Section 5 discusses the implications of these findings, and finally, Section 6 concludes the paper, highlighting the main contributions and suggesting avenues for future research.

2. Literature Review Methodology

2.1. Study Selection Criteria

The bibliographic resources for this literature review were sourced from three prestigious databases relevant to the research area. Scopus, IEEE Xplore, and MDPI. These databases were chosen due to their extensive coverage of high-quality research articles in electrical and industrial systems, mainly focusing on innovative technologies such as soft sensing and intelligent modeling. The search terms were carefully selected to capture the most relevant literature. These terms include “soft sensing”, “intelligent modeling”, “industrial”, and “electrical”, among others. Combining these terms ensures that the search encompasses a broad yet targeted spectrum of research articles that align with the objectives of this review.
The years 2019–2024 were selected as the most appropriate period for mapping knowledge in this study’s thematic area. This period marks a significant phase of technological advancements and increased research activity in soft sensing and intelligent modeling. This timeframe captures the latest developments and emerging trends, providing a comprehensive overview of the current state of research and its practical applications in industrial electrical systems. Table 1 summarizes the search terms and queries defined for the literature review.
The search terms were derived from this study’s preliminary background and introduction, highlighting the electrical industry’s continuous evolution and the emergence of promising research areas such as soft sensing and intelligent modeling. These technologies leverage virtual sensors and advanced algorithms to estimate electrical systems’ state and operational conditions, thus enhancing monitoring, fault detection, and performance optimization. The growing demand for more efficient and reliable electrical systems in the industry, coupled with the advancement of industry 4.0 and digitalization, underscores the necessity of adopting these advanced technologies.

2.2. Search Process and Selection of Studies

The PRISMA approach ensures a rigorous and transparent review process, enabling the identification and synthesis of relevant studies while minimizing bias [30]. This methodology is well-suited for our research as it provides a structured framework for selecting high-quality studies, which is critical for understanding the advancements in soft sensing and intelligent modeling within industrial electrical systems. Figure 1 illustrates the flowchart of the literature review process. As depicted in the figure, the review begins by applying the search terms and queries in Table 1. This initial search yielded 279 items: 207 from Scopus, 62 from IEEE Xplore, and 10 from MDPI. With these raw results, the authors have assigned a coding system to the items to facilitate subsequent bibliometric processing. Articles from Scopus are coded as S-XX, those from IEEE Xplore as IEEE-XX, and those from MDPI as MDPI-XX.
The first review stage (R1) involves the removal of duplicate items. During this stage, 20 duplicate documents were identified and withdrawn. Next, the second review stage (R2) excludes items that are not journal articles, such as review papers, conference papers, book chapters, and books. While these documents are undoubtedly valuable and contribute significantly to the field, primary research articles published in peer-reviewed journals provide more direct and less biased information, essential for constructing a robust and unbiased literature review. This stage revealed that four items had bypassed the initial database filters and were subsequently rejected. The critical mass comprises 255 articles, which will undergo a preliminary bibliometric analysis.
Figure 2 illustrates the distribution of the preselected works across the different digital databases, revealing a predominance in Scopus, which accounts for 80.39% of the total. IEEE Xplore follows this with 15.69%, and MDPI with 3.92%. This distribution was expected, as Scopus encompasses a broader range of scientific publishers and journals than the other two databases under consideration. Scopus is known for its extensive indexing of diverse and high-impact journals, naturally resulting in more relevant articles being retrieved from this database.
The smaller proportion of MDPI’s works highlights the need to generate more scientific material related to the topic within this publishing house. This represents a niche the present work aims to address, contributing to expanding research in soft sensing and intelligent modeling within the MDPI database. Figure 2 also depicts the publication trend over the past five years, showing a clear and sustained increase in publications. The statistics indicate a notably high number of publications in 2024 despite the year not being halfway through. This trend suggests a continuous and growing scientific interest in the topic addressed by this research. The upward trajectory in publication numbers over the past five years indicates the increasing relevance and importance of research in soft sensing and intelligent modeling in industrial electrical systems. This sustained growth trend underscores the ongoing advancements and the expanding body of knowledge in this field, reflecting a robust and dynamic area of scientific inquiry that this literature review aims to cover comprehensively.
Moreover, Figure 3 shows the distribution of articles according to the journals hosted in the consulted databases. This distribution provides insights into which journals are most actively publishing research on soft sensing and intelligent modeling, helping to identify key publications and potential outlets for future research in this area.
Now, with the metadata of these 255 articles, the keywords from each article are extracted to cluster them and generate a word cloud map. This action helps to identify the frequency of terms used. Based on the most prevalent keywords in Figure 4, the following combinations of terms can be defined: soft sensing, state estimation, Kalman filtering, intelligent modeling, industrial electrical systems, fault detection, energy optimization, condition monitoring, predictive maintenance, machine learning in electrical systems, IoT in industry, electrical network monitoring, high-voltage equipment, battery health estimation, and energy consumption optimization.
In the following review step (R3), each item’s abstract was thoroughly reviewed for its relevance to the terms identified in the word cloud map. This exhaustive process resulted in the withdrawal of 186 articles, leaving only 69 whose abstracts are closely aligned with the identified terms to proceed to the next stage. Then, in the review step (R4), a full-text review of each work was conducted to determine the relevance of the topics concerning the identified terms and the main focus of this research. For this purpose, the research team defined a series of criteria to evaluate each of the 69 items using a five-level Likert scale for the evaluation metrics. The evaluation criteria and metrics devised for the conducted literature review are provided in Table 2.
A minimum threshold score of 36 out of 60 (60%) has been established to ensure the inclusion of relevant and high-quality studies in this literature review. This threshold ensures that selected articles closely align with the review’s focus on soft sensing, intelligent modeling, and related topics in industrial electrical systems. Each article is evaluated on criteria such as relevance, the quality of research, innovation, clarity, the depth of analysis, applicability, references, author expertise, impact, scope, case studies, technical accuracy, and future research directions. Setting the threshold at 60% guarantees that the included studies meet a sufficient methodological rigor and practical relevance standard while allowing for a comprehensive and inclusive review. This balanced approach ensures that the literature review incorporates valuable contributions without being overly restrictive, thus providing a robust and insightful analysis of the current state of research in the field.
Figure 5 shows the final scores achieved by each item at this stage. Based on the results, 29 articles meet the predefined minimum threshold; therefore, the remaining articles have been discarded.
Appendix A, Table A1, provides a comprehensive summary of the articles that successfully passed all stages of the literature review process and are the subject of analysis in the following section.

3. Descriptive Analysis of the Literature

Following the systematic selection process in the literature review, 29 items were identified as highly relevant to the research focus. These items were selected based on a thorough full-text review, ensuring their alignment with this study’s core themes and objectives. The comprehensive evaluation of these works is summarized in Table A1, which provides detailed information about each selected article, including their titles and core proposals.
To gain a deeper understanding of the current state of research and to facilitate a structured analysis, the selected literature was subsequently clustered into four main topics: intelligent modeling and optimization (IMO), soft sensing techniques, machine learning and neural networks, and process monitoring and optimization. This categorization was derived from carefully examining the articles’ titles and abstracts, identifying each work’s primary focus and contributions.
  • Intelligent Modeling and Optimization encompasses articles focusing on advanced modeling techniques and optimization strategies to enhance industrial processes’ efficiency and effectiveness. This cluster includes works that utilize innovative approaches such as Bayesian learning, just-in-time learning (JITL), and intelligent optimization frameworks to address various challenges in industrial systems.
  • Soft Sensing Techniques includes research that develops and applies soft sensing methods for industrial processes. These techniques involve indirect measurements and data-driven models to estimate process variables that are difficult or impossible to measure directly. The articles in this cluster explore various statistical and machine-learning methods to improve the accuracy and reliability of soft sensors.
  • Machine Learning and Neural Networks covers studies that leverage machine learning algorithms and neural network models to solve complex problems in industrial settings. This cluster includes works implementing deep learning, auto-encoders, and other neural network-based methods to enhance predictive accuracy and process control.
  • Process Monitoring and Optimization focuses on articles that aim to monitor and optimize industrial processes through data-driven and model-based approaches. This cluster includes research on state estimation, process monitoring, and dynamic optimization, utilizing techniques such as variational Bayesian learning and dynamic latent variable models.
The distribution of selected items across these four clusters is depicted in the Venn diagram in Figure 6. This figure illustrates the categorization of the selected literature, visually representing the research landscape and highlighting the areas of concentration within the field. By organizing the literature into these distinct topics, we can better understand the current trends and gaps in research, guiding future investigations and innovations in soft sensing and intelligent modeling in industrial electrical systems.

4. Results

After applying the PRISMA method, four main themes have been identified, representing significant research areas in IMO. These themes encompass a variety of approaches and applications within the field, including advanced modeling techniques, soft sensing, machine learning, and process optimization. In the following sections, we will detail each of these themes, examining key contributions from the literature and discussing the challenges and future trends in each area.

4.1. Intelligent Modeling and Optimization

4.1.1. Definition

IMO is an advanced approach that employs techniques in industrial electrical systems to enhance processes’ efficiency, productivity, and reliability [31]. It utilizes intelligent algorithms and machine learning methods to analyze complex data and make optimal real-time decisions. This approach finds application across various industrial sectors, including energy, manufacturing, chemistry, and automation, aiming to optimize the operation of electrical networks, improve product quality, and design safer and more efficient production processes [32,33]. Despite advancements, challenges persist regarding model interpretation and integration into real-time systems. However, the evolution of technologies such as cloud computing and the IoT is expected to continue driving the development and application of IMO in the future [33,34].

4.1.2. Applications

IMO has experienced significant growth in recent decades, with a wide range of applications across various industrial sectors. For instance, in the metallurgical sector, the study presented in article [31] proposes a semi-supervised online soft sensor model to predict silicon content in industrial blast furnaces. This approach leverages semi-supervised learning to absorb valuable information from unlabeled data, resulting in improved predictive performance compared to traditional soft sensors. Moreover, in the industrial process sector, article [35] introduces a β-variational autoencoder regression model for observing and measuring multimode industrial processes. This approach has been successfully applied in predicting variable quality for multimode industrial processes, demonstrating its efficacy and superiority in soft sensor modeling in complex industrial environments. In the field of chemical engineering, the study presented in [34] proposes an efficient (JITL) framework for soft sensing in industrial processes. This approach has been applied in ebullated bed hydrogenation and physical separation units, demonstrating higher predictive accuracy and operational efficiency compared to other methods. These current applications illustrate the versatility and effectiveness of IMO techniques in a variety of industrial contexts. From metallurgy to chemical engineering, IMO has shown its ability to enhance processes, optimize performance, and reduce operating costs across diverse industries.

4.1.3. Current Challenges

Despite significant advances achieved in the field of IMO, several important challenges persist that require attention and innovative solutions. For example, in the study on the soft sensing of liquefied petroleum gas (LPG) processes using deep learning [33], the challenge of the interpretability of AI and deep learning-based models is highlighted. While these models can offer high levels of predictive accuracy, their opacity regarding how they arrive at those predictions can be a barrier to adoption in industrial environments where a clear understanding of the model’s decision-making process is required. Additionally, in the IMO for a smart energy hub [31] article, the need to address the computational complexity associated with optimizing energy hub models is noted. As energy systems become more interconnected and diversified, there is a need to develop more efficient optimization methods to handle the vast data and complexity of modern energy systems.
Another significant challenge is highlighted in the study on Bayesian (JITL) [36], where the efficient selection of relevant samples and accurate base model construction are addressed. While JITL techniques offer the advantage of updating localized models in real-time, identifying relevant samples and constructing accurate base models remain areas of active research and development.

4.1.4. Future Trends

Future trends in the field of IMO point towards greater integration of advanced technologies and innovative approaches to address emerging challenges and leverage new opportunities in a variety of industrial applications. A significant trend is the increasing use of machine learning techniques and real-time predictive modeling in industrial environments, as highlighted in the study on the soft sensing of LPG processes using deep learning [33,37]. This trend is expected to continue, with more sophisticated AI models enabling more precise and efficient real-time decision-making across a variety of industrial processes.
Additionally, the optimization of energy systems, as discussed in the article on IMO for a smart energy hub [31], is expected to become increasingly important as companies seek to maximize the efficiency and profitability of their energy operations. This could involve the development of more advanced optimization algorithms and the implementation of more sophisticated automation technologies to manage and control complex energy systems. Another significant future trend is using Bayesian approaches and JITL methods in industrial applications, as mentioned in [36]. These approaches are expected to continue evolving and improving, focusing more on an efficient selection of relevant samples, accurate base model construction, and uncertainty management in industrial processes.

4.2. Soft Sensing Techniques

4.2.1. Definition

Soft sensing techniques use computational models to estimate difficult-to-measure variables in industrial processes, leveraging statistical methods and machine learning algorithms [38,39]. These methods predict quality parameters, enhancing process monitoring without expensive direct measurement instruments. By utilizing labeled and unlabeled data, they aim for accurate real-time predictions, which are crucial for operational efficiency and product quality [1]. For instance, the principal component-based semi-supervised extreme learning machine (PCSELM) model combines labeled and unlabeled data to enhance model accuracy, while a neural network approach optimizes input layers in dynamic batch processes, improving predictive performance [40,41].

4.2.2. Applications

Soft sensing techniques are crucial across various industries, enhancing process monitoring and product quality prediction. In metallurgy, they predict silicon content in blast furnaces, a hard-to-measure variable. The PCSELM model in [38] showcases superior predictive accuracy through semi-supervised learning, leveraging labeled and unlabeled data. Dynamic batch processes like penicillin fermentation and injection molding benefit from a neural network-based approach outlined in [40], optimizing information relevance layer by layer and outperforming existing methods.
JITL combines mutual information and partial least squares to improve soft sensor accuracy [42]. This method addresses non-linearity and collinearity, yielding more precise similarity measures and predictions. Additionally, a two-step statistical learning approach for batch process soft sensing [43] reduces data dimensionality. It constructs reliable soft sensors, enhancing accuracy in industrial applications such as personal care product manufacturing.

4.2.3. Current Challenges

Despite advancements in soft sensing techniques, challenges persist. Interpreting complex models, especially those based on deep learning, poses a significant hurdle due to their opaque nature, hindering trust and acceptance in industrial settings [38]. Computational complexity is another issue, as real-time data integration and processing, such as in JITL, demand efficient measures and strain resources [42]. Integrating domain-specific knowledge into data-driven models remains challenging despite promising results from methods like neural network-based representation learning [40]. Handling variability and complexity in industrial processes, such as non-linearity and multimodality, present further difficulties, exemplified by the challenge of managing multiple modes without prior information [44].

4.2.4. Future Trends

Future trends in soft sensing techniques involve integrating advanced machine learning and statistical methods to tackle current challenges and exploit new opportunities in industrial applications. One key trend is the growing adoption of sophisticated machine learning algorithms like deep learning and JITL to improve real-time predictive accuracy and decision-making. For instance, models like PCSELM demonstrate the potential for incorporating more advanced semi-supervised and unsupervised learning techniques to enhance model robustness and flexibility [38]. These models also focus on enhancing interpretability and transparency to facilitate industrial adoption. Techniques like the weighted autoregressive dynamic latent variable model aim to make predictions more understandable and trustworthy [45]. For most modern industrial processes with strong nonlinear and multimodal characteristics, the traditional linear PLS-based soft sensor may not work well. Meanwhile, the traditional global modeling approach has a high demand for data representation capability in the face of complex data distribution, which poses a challenge to soft sensing [46]. In addition, the unbalanced nature of data distribution exacerbates the model’s neglect of local information to some extent, which enhances the overall prediction difficulty of the model. To this end, based on the PLS, a novel quality-relevant feature clustering (QRFC) model is proposed for the first time in this article from the view of the local modeling of probabilistic fusion. In the QRFC, the PLS can give reasonable and explanatory guidance on the initial feature space for the modeling.
Another significant trend is optimizing energy systems using soft sensing techniques to maximize efficiency and profitability. Advanced optimization algorithms and automation technologies will improve the management and control of complex energy systems [38]. Bayesian approaches and JITL strategies will expand, providing more efficient real-time data processing and decision-making methods. Integrating multimodal data and cluster-based multiple models will further drive the evolution of soft sensing techniques [38,40]. Lastly, incorporating soft sensing models into real-time process control frameworks will be crucial for the adaptive and automated control of industrial processes. Advancements in model training, optimization, and classifier development will be necessary for optimal application timing [43]. These advancements will refine soft sensing techniques, making them more robust, interpretable, and capable of handling modern industrial complexities, enhancing process efficiency, product quality, and operational decision-making across various sectors.

4.3. Machine Learning and Neural Networks

4.3.1. Definition

Machine learning and neural networks represent significant advancements in AI, enabling the creation of models that can learn from data, make predictions, and support decision-making processes. Machine learning encompasses a broad range of algorithms that allow computers to learn patterns from data, improving their performance over time without being explicitly programmed. Neural networks, a specialized subset of machine learning, mimic the human brain’s structure and function, using interconnected layers of nodes (neurons) to process information and recognize patterns. These networks are particularly adept at handling large and complex datasets, making them invaluable for tasks that require high levels of pattern recognition, such as image and speech recognition, natural language processing, and predictive analytics [47].

4.3.2. Applications

Machine learning and neural networks find broad applications across industries, including industrial automation. ANFISs integrated with computer-aided design (CAD) data facilitate the precise control of robotic systems, enabling them to navigate obstacles and achieve desired positions with high accuracy [47]. In soft sensing, machine learning models, such as Echo State Networks (ESNs), estimate key variables in industrial processes. ESNs handle high-dimensional, nonlinear data and improve prediction accuracy by integrating auto-encoders to address dimension disaster problems [48]. The JITL strategy enhances the adaptability and accuracy of real-time process control models [42].
Data augmentation techniques, like DAWI-VSG shown in [49], expand datasets with virtual samples, which is crucial where real-world data is limited. Using methods like singular value decomposition to generate and refine virtual samples significantly boosts the predictive power of soft sensors [49]. Causal discovery algorithms, such as weight comparison causal mining (WCCM), uncover underlying relationships between process variables, enhancing feature selection for improved prediction accuracy and model interpretability [50]. Neural networks with upper and lower bound constraints handle missing values, ensuring prediction reliability even with incomplete or anomalous training data [51].

4.3.3. Current Challenges

Despite their widespread adoption, machine learning and neural networks encounter significant challenges. Handling high-dimensional data, leading to the “curse of dimensionality,” poses a significant hurdle for developing accurate and efficient models. Solutions like distributed ESNs with auto-encoders reduce input dimensionality and cluster input attributes using algorithms [48]. Modeling multimode processes, common in industrial settings, is another challenge. Traditional models struggle with their dynamic and multimode characteristics. Gaussian mixture models integrated with variational autoencoders (GM-GVAER) effectively capture dynamic features and handle multimode properties, improving soft sensor model accuracy [52].
Dealing with missing data persists as a challenge. Incomplete or abnormal data can lead to inaccurate predictions. Approaches like neural networks with upper and lower bound constraints for estimated missing values ensure robust predictions, preventing the overestimation of prediction errors and maintaining model reliability [51]. Utilizing unlabeled data efficiently is a limitation of traditional soft sensors. Semi-supervised models like the quality regularization-based semi-supervised adversarial transfer model (QR-SATM) leverage adversarial transfer learning to incorporate unlabeled data effectively. They enhance model performance by pretraining with unlabeled data and fine-tuning with labeled data [53].

4.3.4. Future Trends

The future of machine learning and neural networks in industrial applications is promising, with several key trends expected to drive advancements. Enhanced feature extraction capabilities will be crucial, with more sophisticated neural network structures, such as convolutional neural networks (CNNs) and recurrent neural networks, being integrated to extract complex features from industrial processes. This will likely improve model performance and prediction accuracy in various applications. Adaptive models that can dynamically adjust to changing process conditions and varying data sequences are also on the horizon. Such models will enhance the flexibility and applicability of neural networks in real-time industrial environments, allowing for more responsive and efficient process control [51].
Improving the interpretability of neural networks is another important trend. Mechanisms like attention layers can be added to models to highlight the importance of different variables and clarify causal relationships. This will improve the understanding of how models make predictions and enhance their utility in anomaly detection and process optimization. Combining domain-specific knowledge with data-driven approaches is expected to further enhance the robustness and reliability of machine learning models. Researchers can create more comprehensive models that better understand complex industrial processes by integrating limited prior knowledge into causal discovery algorithms and other data-driven methods.

4.4. Process Monitoring and Optimization

4.4.1. Definition

Soft sensing, a pivotal aspect of contemporary industrial operations, deviates from conventional sensor-based monitoring approaches. While traditional methods rely heavily on physical sensors for data acquisition, soft sensing leverages computational models to estimate crucial process variables, providing a cost-effective and scalable solution [54]. In industrial processes, soft sensing involves developing and deploying algorithms to infer process variables based on available data, often integrating machine learning and statistical techniques [33]. By employing these algorithms, industries can reduce reliance on physical sensors, which may be costly to install and maintain, while still obtaining accurate insights into process behavior.

4.4.2. Applications

Soft sensing applications span various industries, reflecting their versatility and utility in diverse operational contexts. For example, soft sensors integrated with advanced deep learning techniques have revolutionized monitoring capabilities in the oil refining sector, optimizing processes such as LPG purification with unprecedented accuracy and efficiency [33]. Similarly, in chemical manufacturing, data-driven modeling frameworks have empowered engineers to predict product yields and process dynamics with remarkable precision, driving improvements in operational efficiency and profitability [55].
Moreover, soft sensing is applicable in pharmaceutical sectors, where precise control over manufacturing processes is essential to ensure product quality and regulatory compliance [36]. By harnessing soft sensing techniques, pharmaceutical companies can monitor critical process parameters in real-time, facilitating timely interventions and quality assurance measures.

4.4.3. Current Challenges

Despite its transformative potential, soft sensing confronts several challenges that require ongoing research and innovation to address effectively. One significant challenge revolves around the dynamic nature of industrial processes, which often exhibit nonstationary behaviors and transient phenomena [56]. Adapting conventional modeling approaches to accommodate such dynamic environments necessitates the development of novel methodologies capable of capturing and responding to evolving process dynamics.
Additionally, data scarcity poses a significant obstacle, particularly in industries with limited access to large volumes of high-quality data [49]. Overcoming this challenge requires developing data augmentation and synthesis techniques, enabling the generation of representative datasets for training soft sensing models. Furthermore, ensuring the robustness and reliability of soft sensing algorithms in the face of noisy or incomplete data remains a critical area of research and development.

4.4.4. Future Trends

Several emerging trends are poised to shape the future of soft sensing in industrial applications. One such trend is the increasing integration of soft sensing with advanced analytics and AI techniques, including deep learning and reinforcement learning [44]. By leveraging these cutting-edge technologies, industries can unlock new capabilities in process monitoring, optimization, and control, paving the way for autonomous and adaptive manufacturing systems. Moreover, the advent of edge computing and IoT technologies holds promise for decentralized soft sensing solutions, enabling real-time monitoring and control at the device level [41]. This trend towards edge-based soft sensing architectures has the potential to enhance scalability, resilience, and responsiveness in industrial operations, particularly in sectors characterized by distributed and interconnected production systems.

5. Discussions

Figure 7 illustrates the key findings and future directions identified in the review of IMO techniques applied in industrial electrical systems. Four main themes emerge from the analysis, each represented by a distinct set of blocks in the diagram. The first block highlights the importance of IMO techniques, showcasing their growing applications across various industrial sectors. These techniques leverage advanced algorithms and machine learning methods to enhance efficiency, productivity, and process reliability. The second set of blocks focuses on soft sensing techniques, emphasizing their role in estimating difficult-to-measure variables in industrial processes. These techniques use statistical methods and machine learning algorithms to predict key quality parameters, enabling the improved monitoring and control of processes. Moving to the third set of blocks, machine learning and neural networks take center stage, demonstrating their versatility and utility in various industrial domains. These technologies enable the development of intelligent models for process control, predictive analysis, and anomaly detection, driving improvements in operational efficiency and product quality. Finally, the fourth set of blocks highlights process monitoring and optimization strategies, underscoring the shift towards autonomous and adaptive manufacturing systems. Integrating edge computing and IoT technologies promises real-time device-level monitoring and control, enhancing industrial operations’ scalability, resilience, and responsiveness.
In the optimization of intelligent manufacturing, challenges such as the interpretability of complex models and the management of incomplete data persist. Interpretability is crucial since complex models, although accurate, often function as “black boxes.” To enhance transparency, explanatory models like decision trees, post-hoc techniques such as local interpretable model-agnostic explanations (LIME) and shapley additive explanations (SHAP), and advanced visualization tools can be used. On the other hand, the management of incomplete data is a significant issue due to sensor failures and communication errors. To address this, data imputation techniques, the development of robust models, and semi-supervised learning algorithms can be employed. Additionally, error detection and correction can improve data quality in real-time. These combined strategies can increase the reliability and applicability of intelligent manufacturing technologies, allowing for more effective advancements in the field.
The review underscores the critical necessity of integrating domain-specific knowledge into learning models for industrial electrical systems. This integration is pivotal for enhancing the effectiveness and applicability of advanced algorithms in practical industrial environments. By infusing industry-specific insights into algorithmic frameworks, these models can achieve heightened predictive accuracy and operational efficiency. Achieving effective integration involves embedding practical industrial insights directly into algorithmic processes. For example, in fields like metallurgy and chemical engineering, understanding the intricacies of process dynamics and material behavior significantly bolsters the precision of predictive models. This alignment ensures that algorithmic outputs resonate more closely with real-world industrial conditions, thereby enhancing interpretability and fostering greater acceptance among industry stakeholders.
Furthermore, the integration of domain-specific knowledge facilitates the development of resilient models capable of adapting to dynamic operational challenges. While challenges such as model interpretability and adaptation to complex industrial environments persist, hybrid models that blend data-driven approaches with expert knowledge frameworks offer promising solutions. These methodologies not only optimize process efficiency and reduce operational costs but also pave the way for adaptive and sustainable industrial practices. Looking ahead, future research should focus on refining methodologies that seamlessly integrate domain-specific knowledge into learning models. This includes exploring advanced hybrid models and developing frameworks that effectively capture and formalize industry-specific knowledge into algorithmic solutions. By addressing these challenges, the potential of intelligent modeling and optimization in advancing industrial electrical systems towards greater efficiency, reliability, and sustainability can be fully realized.

6. Conclusions

This study used the PRISMA method to review literature using three prominent databases: Scopus, IEEE Xplore, and MDPI. It focused on soft sensing and intelligent modeling research in electrical and industrial systems. After applying selection criteria, 255 relevant articles were identified, with a significant predominance of publications obtained from Scopus, followed by IEEE Xplore and MDPI. The publication trend during the study period shows a sustained increase in scientific interest in these areas, reflecting the growing importance of research in soft sensing and intelligent modeling in industrial electrical systems. The method was filtered down to a total of 29 articles, which met the systematic literature review criteria defined by the authors.
Based on this, a review of the main contributions of these articles was carried out. In conclusion, this comprehensive review of IMO techniques in industrial electrical systems has identified key areas of application, current challenges, and future trends. Four main themes have been explored: IMO, soft sensing techniques, machine learning and neural networks, and process monitoring and optimization strategies. The applications of these techniques are diverse and encompass industrial sectors such as metallurgy, chemistry, and manufacturing. Examples have been highlighted, such as quality prediction in industrial furnaces, the monitoring of dynamic processes, and the control of industrial robots. However, significant challenges persist, such as the interpretability of complex models, managing incomplete data, and adapting to dynamic environments. Furthermore, greater integration of domain-specific knowledge into automatic learning models is required to improve their robustness and reliability.
Looking to the future, the integration of advanced technologies like deep learning and the IoT is poised to enhance real-time monitoring and control in industrial environments. Deep learning can process large datasets to improve predictive maintenance, fault detection, and quality control. For example, CNNs and RNNs can analyze sensor data to predict equipment failures, reducing downtime and maintenance costs. The IoT enables the interconnection of industrial devices for seamless data exchange and real-time monitoring. IoT sensors can continuously collect data from industrial processes, which deep learning algorithms can analyze to optimize operations and detect anomalies. This leads to smart factories where automated systems make real-time decisions, improving efficiency, reducing energy consumption, and enhancing safety. The continuous optimization of algorithms and interdisciplinary collaboration will be crucial to fully leveraging these technologies.

Author Contributions

Conceptualization, D.O.-C. and P.A.; methodology, D.O.-C.; software, P.A.; validation, D.O.-C. and P.A.; formal analysis, D.O.-C.; investigation, P.A.; resources, D.O.-C.; data curation, P.A.; writing—original draft preparation, D.O.-C.; writing—review and editing, P.A.; visualization, D.O.-C.; supervision, P.A.; project administration, D.O.-C.; funding acquisition, D.O.-C. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Acknowledgments

The authors thank the Universidad de Cuenca (UCUENCA), Ecuador, for easing access to the facilities of the Micro-Grid Laboratory of the Faculty of Engineering, for allowing the use of its equipment, and for authorizing members of its staff to provide the technical support necessary to carry out the experiments described in this article. The results of this research will serve as input for developing the project titled ≪Planeamiento conjunto de la expansion optima de los sistemas eléctricos de generación y transmisión≫, Proj. code: VIUC_XX_2024_3_TORRES_SANTIAGO, winner of the XX Concurso Universitario de Proyectos de Investigacion promoted by the Vicerrectorado de Investigacion of UCUENCA, a department to which the authors also wish to express their gratitude.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Table A1. Overall information on the selected studies for the literature review.
Table A1. Overall information on the selected studies for the literature review.
N°IDRef.Complete TitleArticle’s ProposalAuthors, Year
1S-180 [57]Soft sensing of silicon content via bagging local semi-supervised models Bagging local semi-supervised models (BLSM) improve the online prediction of silicon content in industrial blast furnaces, leveraging hidden information in process variables. He et al., 2019
2S-65 [35]Mode Information Separated β-VAE Regression for Multimode Industrial Process Soft Sensing An advanced regression model, SW-β-VAE and MA-SW-β-VAER, analyzes and measures multimode industrial processes using soft sensors. Shen et al., 2023
3S-41 [38]Principal Component-Based Semi-Supervised Extreme Learning Machine for Soft Sensing The PCSELM model enhances soft sensor performance by utilizing both labeled and unlabeled data. Shi et al., 2023
4S-11 [40]Data-Driven Soft Sensing for Batch Processes Using Neural Network-Based Deep Quality-Relevant Representation Learning A neural network-based deep quality-relevant representation learning approach improves soft sensing in dynamic batch processes by optimizing quality-relevant information. Jiang et al., 2023
5S-153 [42]A novel (JITL) strategy for soft sensing with improved similarity measure based on mutual information and PLS A new similarity measure method combining mutual information and partial least squares improves JITL-based soft sensor modeling for industrial processes. Song et al., 2020
6S-82 [32]Intelligent modeling and detailed analysis of drying hydration thermal and spectral characteristics for convective drying of chicken breast slices Convective drying characteristics of chicken breast slices at various temperatures are analyzed using ANN and semi-empirical models to optimize drying processes. Kumar et al., 2019
7S-32 [56]Probabilistic stationary subspace regression model for soft sensing of nonstationary industrial processes A probabilistic stationary subspace regression (PSSR) model enhances soft sensing for nonstationary industrial processes by capturing mathematical correlations between variables. Zhao et al., 2024
8S-112 [31]IMO for smart energy hub An IMO method for a smart energy hub model improves operation efficiency and reduces computational burden for multiple energy systems. Liu et al., 2019
9S-184 [36]Bayesian (JITL) and its Application to Industrial Soft Sensing Bayesian JITL (BJITL) improves soft sensor performance in industrial processes by enhancing relevant sample selection and base learner construction. Shao et al., 2020
10S-185 [47]Intelligent Modeling and Simulation of the Inverse Kinematics Redundant 3-DOD Cooperative Using Solidworks and MATLAB/Simmechanics Intelligent modeling with an ANFIS controller and CAD data enhances the inverse kinematics of redundant industrial manipulator robots. Bahani et al., 2022
11IEEE-014 [54]Intelligent State Estimation for Continuous Fermenters Using Variational Bayesian Learning Variational Bayesian learning algorithms accurately estimate states in continuous fermenters, focusing on improving estimation with a random transition probability matrix. S. Gao and S. Zhao and X. Luan and F. Liu et al., 2021
12S-12 [37]Robust Sparse Gaussian Process Regression for Soft Sensing in Industrial Big Data Under the Outlier Condition A robust sparse Gaussian process regression method addresses outliers in large datasets to improve model construction for industrial processes. Huang et al., 2024
13S-116 [43]A two-step multivariate statistical learning approach for batch process soft sensing A two-step approach using partial least squares and multiway partial least squares designs soft sensors for product quality prediction in industrial processes. Hicks et al., 2021
14S-170 [45]Soft Sensing Applications for Non-Stable Processes Based on a Weighted High-Order Dynamic Information Structure A novel weighted autoregressive dynamic latent variable (WARDLV) model addresses challenges of autocorrelation and non-stable features in industrial processes. Zhang et al., 2020
15S-110 [36]Powder composition monitoring in continuous pharmaceutical solid-dosage form manufacturing using state estimation—Proof of concept A model-based approach using a moving-horizon state estimator improves the monitoring of powder composition in continuous solid-dosage form manufacturing. Destro et al., 2021
16S-149 [34]Adaptive ensemble learning strategy for semi-supervised soft sensing An adaptive ensemble learning strategy for soft sensors enhances regression performance with limited labeled samples using semi-supervised learning. Shi et al., 2020
17S-21 [34]Efficient JITL framework for nonlinear industrial chemical engineering soft sensing based on adaptive multi-branch variable scale integrated CNNs. An efficient JITL framework (EJITL-AMVs-ICNN) enhances real-time updating of local models in chemical processes, improving prediction accuracy and reducing elapsed time. Chen et al., 2023
18S-02 [33]Soft Sensing of LPG Processes Using Deep Learning The integration of soft sensors and deep learning in oil-refinery processes enhances monitoring efficiency and predictive accuracy for de-ethanization and debutanization. Sifakis et al., 2023
19S-19 [46]Probabilistic Fusion Model for Industrial Soft Sensing Based on QRFC. A novel QRFC model based on PLS improves soft sensor performance in nonlinear and multimodal industrial processes. Yang et al., 2023
20S-25 [49]Novel virtual sample generation method based on data augmentation and weighted interpolation for soft sensing with small data A virtual sample generation method (DAWI-VSG) enhances soft sensing datasets with high-quality samples to improve prediction accuracy in industrial processes. Song et al., 2023
21S-31 [53]Quality Regularization-Based Semisupervised Adversarial Transfer Model With Unlabeled Data for Industrial Soft Sensing QR-SATM leverages unlabeled data for more accurate soft sensor predictions. He et al., 2024
22S-64 [50]Neural Network Weight Comparison for Industrial Causality Discovering and Its Soft Sensing Application WCCM algorithm discovers variable relationships to guide process modeling and control optimization in industrial processes. He et al., 2023
23S-10 [48]A New Distributed Echo State Network Integrated With an Auto-Encoder for Dynamic Soft Sensing A distributed ESN model integrated with an auto-encoder (AE-DESNm) handles high-dimensional data and improves dynamic soft sensor performance. He et al., 2023
24S-95 [52]Gaussian mixture deep dynamic latent variable model with application to soft sensing for multimode industrial processes A deep dynamic latent variable regression model (GM-GVAER) enhances soft sensing in multimode industrial processes by capturing dynamic features. Xu et al., 2022
25S-75 [51]Neural networks with upper and lower bound constraints and its application on industrial soft sensing modeling with missing values A neural network method with upper and lower bound constraints handles missing values in soft sensor data, improving prediction reliability. Lu et al., 2022
26IEEE-040 [39]A Data-Driven Soft Sensing Approach Using Modified Subspace Identification With Limited Iterative Expectation-Maximization An EM-SID algorithm improves predictive ability in data-driven soft sensor modeling by addressing biased system matrices estimation. W. Guo and T. Pan and Z. Li and S. Chen et al., 2020
27S-37 [55]Data-driven intelligent modeling framework for the steam cracking process A data-driven intelligent modeling framework (LARD-MARS) balances prediction accuracy and computational speed in the steam cracking process. Zhao et al., 2023
28S-178 [44]Soft Sensing of a Nonlinear Multimode Process Using a Self Organizing Model and Conditional Probability Density Analysis A self-organizing model and conditional probability density analysis handle nonlinear multimode processes for improved soft sensor performance. Wang et al., 2019
29S-48 [41]Weighted target feature regression neural networks based soft sensing for industrial processA weighted target feature regression neural network (WTFAER) was proposed to address the difficulties in measuring product quality online in industrial processes, demonstrating superior performance and generalization in simulations compared to other methods.Guo, X. and Wang, Q. and Li, Y., 2024.

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Figure 1. Flowchart of the literature review process.
Figure 1. Flowchart of the literature review process.
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Figure 2. Distribution of articles by digital database and year of publication.
Figure 2. Distribution of articles by digital database and year of publication.
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Figure 3. Distribution of articles by journal.
Figure 3. Distribution of articles by journal.
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Figure 4. Word cloud map of the keywords in the preselected articles.
Figure 4. Word cloud map of the keywords in the preselected articles.
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Figure 5. Final scores achieved by each item at the final stage of the review process.
Figure 5. Final scores achieved by each item at the final stage of the review process.
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Figure 6. Venn diagram showing the clustering of selected articles into four main topics.
Figure 6. Venn diagram showing the clustering of selected articles into four main topics.
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Figure 7. Trends and innovations in industrial electrical systems optimization.
Figure 7. Trends and innovations in industrial electrical systems optimization.
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Table 1. Search terms and queries utilized for the literature review.
Table 1. Search terms and queries utilized for the literature review.
DatabaseSearch TermsQuery String
ScopusJournal articles published between 2019 and 2024, written in English, that include either “Industrial” or “Electrical” along with either “Soft Sensing” or “Intelligent Modeling” in the title, abstract, or keywords.TITLE-ABS-KEY ((“Industrial” OR “Electrical”) AND (“Soft Sensing” OR “Intelligent Modeling”)) AND PUBYEAR > 2018 AND PUBYEAR < 2025 AND (LIMIT-TO (DOCTYPE, “ar”)) AND (LIMIT-TO (LANGUAGE, “English”))
IEEE XploreJournal articles published between 2019 and 2024, written in English, that include either “Industrial” or “Electrical” along with both “Soft Sensing” and “Intelligent Modeling” in all metadata.((“All Metadata”:Industrial) OR (“All Metadata”:Electrical)) AND ((“All Metadata”:Soft Sensing) AND (“All Metadata”:Intelligent Modeling))
MDPIJournal articles published between 2019 and 2024, written in English, that include either “Industrial” or “Electrical” along with both “Soft Sensing” and “Intelligent Modeling”.Industrial OR Electrical AND Soft Sensing AND Intelligent Modeling
Table 2. Evaluation criteria and metrics for full-text review.
Table 2. Evaluation criteria and metrics for full-text review.
CriterionDescriptionEvaluation Metrics
Relevance to ResearchHow closely does the paper align with the review’s focus on soft sensing, intelligent modeling, etc.1 = Not relevant, 2 = Slightly relevant, 3 = Moderately relevant, 4 = Highly relevant, 5 = Essential
Quality of ResearchThe rigor and reliability of the research methodology used.1 = Poor, 2 = Fair, 3 = Good, 4 = Very Good, 5 = Excellent
Innovation and OriginalityThe originality and contribution of the paper to the field.1 = Not original, 2 = Slightly original, 3 = Moderately original, 4 = Very original, 5 = Groundbreaking
Clarity and PresentationThe clarity of writing, structure, and presentation of the paper.1 = Poor, 2 = Fair, 3 = Good, 4 = Very Good, 5 = Excellent
Depth of AnalysisThe depth and thoroughness of the analysis provided in the paper.1 = Superficial, 2 = Basic, 3 = Adequate, 4 = In-depth, 5 = Comprehensive
ApplicabilityThe practical applicability of the research findings to industrial electrical systems.1 = Not applicable, 2 = Slightly applicable, 3 = Moderately applicable, 4 = Very applicable, 5 = Highly applicable
References and CitationsThe number and quality of references and citations used in the paper.1 = Poor, 2 = Fair, 3 = Good, 4 = Very Good, 5 = Excellent
Impact and InfluenceThe impact and influence of the paper within the research community.1 = Low, 2 = Fair, 3 = Good, 4 = Very Good, 5 = High
Scope and CoverageThe scope of the paper and the extent to which it covers relevant topics.1 = Narrow, 2 = Limited, 3 = Adequate, 4 = Broad, 5 = Comprehensive
Case Studies and ExamplesThe paper provides the inclusion and quality of case studies or practical examples.1 = None, 2 = Few/poor quality, 3 = Adequate, 4 = Several/good quality, 5 = Many/high quality
Technical AccuracyThe accuracy and reliability of the technical content presented.1 = Poor, 2 = Fair, 3 = Good, 4 = Very Good, 5 = Excellent
Future Research DirectionsThe paper discusses future research directions and potential advancements.1 = None, 2 = Limited, 3 = Adequate, 4 = Extensive, 5 = Comprehensive
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MDPI and ACS Style

Arévalo, P.; Ochoa-Correa, D. Toward Enhanced Efficiency: Soft Sensing and Intelligent Modeling in Industrial Electrical Systems. Processes 2024, 12, 1365. https://doi.org/10.3390/pr12071365

AMA Style

Arévalo P, Ochoa-Correa D. Toward Enhanced Efficiency: Soft Sensing and Intelligent Modeling in Industrial Electrical Systems. Processes. 2024; 12(7):1365. https://doi.org/10.3390/pr12071365

Chicago/Turabian Style

Arévalo, Paul, and Danny Ochoa-Correa. 2024. "Toward Enhanced Efficiency: Soft Sensing and Intelligent Modeling in Industrial Electrical Systems" Processes 12, no. 7: 1365. https://doi.org/10.3390/pr12071365

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