Neural Network Pattern Recognition Research Articles

An Automated Approach for Discriminating Hole Cleaning Efficiency While Predicting Penetration Rate in Egyptian Western Desert Wells

AbstractHigher rate of penetration (ROP) indicates successful drilling operation but is not the only drilling success measure. However, Conventional ROP prediction methods focus on increasing ROP and neglect the hole cleaning state, which can be altered by ROP changes. Higher ROP in vertical and deviated wells may increase cutting concentration, leading to hole cleaning problems such as overpulling and stuck pipe. With this problem in mind, this paper utilized geological, rheological, and drilling data of 31 vertical wells across four oil fields located in the Egyptian Western Desert, developed intelligent ROP prediction model through back propagation neural network (BPNN), and compared the proposed BPNN results with an empirical model. Finally, the pattern recognition algorithms including discriminant analysis, support vector machines, and neural network pattern recognition (NNPR) were implemented to discriminate hole cleaning efficiency following the ROP prediction process. Recognition models were developed based on predicted ROP, bit wear rate, specific energy, and drilling fluid carrying capacity index to evaluate hole cleaning. The accuracy of the multi-strategy classifier was evaluated using area under curve, confusion matrix, and receiver operating characteristic. The BPNN model outperformed the empirical model in terms of linear correlation coefficient (R = 98.6%) and average absolute error (AAE = 5.5%). Additionally, the best classification performance was achieved using the NNPR algorithm with 91% accuracy and a cross-validation error equal to zero. For validity, the proposed approach predicted ROP and classified hole cleaning efficiency for new vertical well in adjacent oil field, resulting in a 6% improvement in ROP.

Automated detection of stale beef from electronic nose data

AbstractAccurate detection of stale beef on the market is important for protecting the legitimate rights and interests of consumers. To this end, we combined electronic nose measurements with machine learning technology to classify beef samples. We used an electronic nose to collect information about the odor characteristics of different beef samples and used linear discriminant analysis to reduce data dimensionality. We then classified samples using the following algorithms: extreme gradient boosting, logistic regression, K‐nearest neighbor, random forest, support vector machine, and neural networks for pattern recognition. We assessed model performance using a 10‐fold cross‐validation technique. All these methods reached an accuracy of 95% or above, with F1 scores and AUC values above 0.96. The support vector machine algorithm outperformed all other models, achieving perfect recognition with 100% accuracy and F1/AUC scores of 1.0. Our study demonstrates that electronic nose data combined with support vector machine can be used to successfully discriminate between stale and fresh beef, paving the way for novel research directions in the detection of stale beef.

Efficient microplastic identification by hyperspectral imaging: A comparative study of spatial resolutions, spectral ranges and classification models to define an optimal analytical protocol

Microplastics (MPs) pollution is a global and challenging issue, necessitating the development of efficient analytical strategies for their detection to monitor their environmental impact.This study aims to define an optimal analytical protocol for characterizing MPs by hyperspectral imaging (HSI), comparing different setups based on spatial resolution, spectral range and classification models. The investigated MPs include polymers commonly found in the environment, such as polystyrene (PS), polypropylene (PP) and high-density polyethylene (HDPE), subdivided in three size classes (1000–2000 μm, 500–1000 μm, 250–500 μm). Furthermore, MP particles with diameters ranging from 30 to 250 μm were assessed to determine the limit of detection (LOD) in the different configurations. Hyperspectral images were acquired with two spatial resolutions, 150 and 30 μm/pixel, and two spectral ranges, 1000–1700 nm (NIR) and 1000–2500 nm (SWIR). Three classification models, Partial Least Square-Discriminant Analysis (PLS-DA), Error Correction Output Coding-Support Vector Machine (ECOC-SVM) and Neural Network Pattern Recognition (NNPR) were tested on the acquired images. The correctness of these models was evaluated by prediction maps and statistical parameters (Recall, Specificity and Accuracy). The results demonstrated that for MP particles larger than 250 μm, the optimal setup is a spatial resolution of 150 μm/pixel and a spectral range of 1000–1700 nm, utilizing a linear classification model like PLS-DA. This approach offers accurate predictions while being time- and cost-efficient. For MPs smaller than 250 μm, a higher spatial resolution of 30 μm/pixel with a spectral range of 1000–2500 nm and a non-linear classification method like ECOC-SVM is preferable. The LOD is 250 μm for the 150 μm/pixel resolution and ranges from 100 to 200 μm for the 30 μm/pixel resolution. These findings provide a valuable guide for selecting the appropriate HSI acquisition conditions and data processing methods to optimally characterize MPs of different sizes.

A robust myoelectric pattern recognition framework based on individual motor unit activities against electrode array shifts

Background and objectiveElectrode shift is always one of the critical factors to compromise the performance of myoelectric pattern recognition (MPR) based on surface electromyogram (SEMG). However, current studies focused on the global features of SEMG signals to mitigate this issue but it is just an oversimplified description of the human movements without incorporating microscopic neural drive information. The objective of this work is to develop a novel method for calibrating the electrode array shifts toward achieving robust MPR, leveraging individual motor unit (MU) activities obtained through advanced SEMG decomposition. MethodsAll of the MUs from decomposition of SEMG data recorded at the original electrode array position were first initialized to train a neural network for pattern recognition. A part of decomposed MUs could be tracked and paired with MUs obtained at the original position based on spatial distribution of their MUAP waveforms, so as to determine the shift vector (describing both the orientation and distance of the shift) implicated consistently by these multiple MU pairs. Given the known shift vector, the features of the after-shift decomposed MUs were corrected accordingly and then fed into the network to finalize the MPR task. The performance of the proposed method was evaluated with data recorded by a 16 × 8 electrode array placed over the finger extensor muscles of 8 subjects performing 10 finger movement patterns. ResultsThe proposed method achieved a shift detection accuracy of 100 % and a pattern recognition accuracy approximating to 100 %, significantly outperforming the conventional methods with lower shift detection accuracies and lower pattern recognition accuracies (p < 0.05). ConclusionsOur method demonstrated the feasibility of using decomposed MUAP waveforms’ spatial distributions to calibrate electrode shift. This study provides a new tool to enhance the robustness of myoelectric control systems via microscopic neural drive information at an individual MU level.

Predictive Maintenance in IoT-Monitored Systems for Fault Prevention

This paper focuses on predictive maintenance for simple machinery systems monitored by the Internet of Things (IoT). As these systems can be challenging to model due to their complexity, diverse typologies, and limited operational lifespans, traditional predictive maintenance approaches face obstacles due to the lack of extensive historical data. To address this issue, we propose a novel clustering-based process that identifies potential machinery faults. The proposed approach lies in empowering decision-makers to define predictive maintenance policies based on the reliability of the proposed fault classification. Through a case study involving real sensor data from the doors of a transportation vehicle, specifically a bus, we demonstrate the practical applicability and effectiveness of our method in preemptively preventing faults and enhancing maintenance practices. By leveraging IoT sensor data and employing clustering techniques, our approach offers a promising avenue for cost-effective predictive maintenance strategies in simple machinery systems. As part of the quality assurance, a comparison between the predictive maintenance model for a simple machinery system, pattern recognition neural network, and support vector machine approaches has been conducted. For the last two methods, the performance is lower than the first one proposed.

Evaluation of floatability characteristics of gastroretentive tablets using VIS imaging with artificial neural networks

Gastroretentive dosage forms are recommended for several active substances because it is often necessary for the drug to be released from the carrier system into the stomach over an extended period. Among gastroretentive dosage forms, floating tablets are a very popular pharmaceutical technology. In this study, it was investigated whether a rapid, nondestructive method can be used to characterize the floating properties of a tablet.To accomplish our objective, the same composition was compressed, and varied compression forces were applied to achieve the desired tablet. In addition to physical examinations, digital microscopic images of the tablets were captured and analyzed using image analysis techniques, allowing the investigation of the floatability of the dosage form. Image processing algorithms and artificial neural networks (ANNs) were utilized to classify the samples based on their strength and floatability. The input dataset consisted solely of the acquired images.It has been shown by our research that visible imaging coupled with pattern recognition neural networks is an efficient way to categorize these samples based on their floatability. Rapid and non-destructive digital imaging of tablet surfaces is facilitated by this method, offering insights into both crushing strength and floating properties.

Odor pattern recognition of olfactory neural network based on neural energy

Odor pattern recognition of olfactory neural network based on neural energy

Turbofan engine health status prediction with neural network pattern recognition and automated feature engineering

PurposeThis study aims to present the concept of aircraft turbofan engine health status prediction with artificial neural network (ANN) pattern recognition but augmented with automated features engineering (AFE).Design/methodology/approachThe main concept of engine health status prediction was based on three case studies and a validation process. The first two were performed on the engine health status parameters, namely, performance margin and specific fuel consumption margin. The third one was generated and created for the engine performance and safety data, specifically created for the final test. The final validation of the neural network pattern recognition was the validation of the proposed neural network architecture in comparison to the machine learning classification algorithms. All studies were conducted for ANN, which was a two-layer feedforward network architecture with pattern recognition. All case studies and tests were performed for both simple pattern recognition network and network augmented with automated feature engineering (AFE).FindingsThe greatest achievement of this elaboration is the presentation of how on the basis of the real-life engine operational data, the entire process of engine status prediction might be conducted with the application of the neural network pattern recognition process augmented with AFE.Practical implicationsThis research could be implemented into the engine maintenance strategy and planning. Engine health status prediction based on ANN augmented with AFE is an extremely strong tool in aircraft accident and incident prevention.Originality/valueAlthough turbofan engine health status prediction with ANN is not a novel approach, what is absolutely worth emphasizing is the fact that contrary to other publications this research was based on genuine, real engine performance operational data as well as AFE methodology, which makes the entire research very reliable. This is also the reason the prediction results reflect the effect of the real engine wear and deterioration process.

Determination of early breeder in goldfish (Carassius auratus Linn.) with learning vector quantization, probabilistic and pattern recognition neural networks

It is common practice to categorize growing fish according to quality in fish farming centers. For such an application, experienced and estimating people are needed. By pre-selecting the right fish for the ornamental fish industry, it gets ahead of the competitors. This study deals with the classification of early breeder determination in goldfish using three different Artificial Neural Network (ANN) techniques. This classification model can help the fish industry assess classification risks and make the right decision. The used dataset was derived from the results of the classification section of 120 goldfish. It consisted of 7 input parameters (day, live weight, body length, head height, head width, body height, and current class). During trial, all goldfish fed by a diet contained 360 g crude protein and 4449.85 kcal metabolizable energy (kg / dry matter). The important types of classification ANNs, namely Learning Vector Quantization Neural Network (LVQNN), Probabilistic Neural Network (PNN), and Pattern Recognition Neural Network (PRNN) were employed for the machine learning scheme. The training and test performances of the ANN models were compared with the correct prediction ratio. They showed that all of the proposed ANN techniques were well at classification. However, the PRNN model was better than the LVQNN and PNN as a classifier for the breeder selection of goldfish. Therefore, the results of PRNN model such as histogram, Receiver Operating Characteristic (ROC) curve, regression, confusion matrix, accuracy, sensitivity, precision, and F1 score were given and discussed. Furthermore, the classification of early breeder determination in goldfish were examined for days with the best PRNN.

Graph features based classification of bronchial and pleural rub sound signals: the potential of complex network unwrapped.

The study presents a novel technique for lung auscultation based on graph theory, emphasizing the potential of graph parameters in distinguishing lung sounds and supporting earlier detection of various respiratory pathologies. The frequency spread and the component magnitudes are revealed from the analysis of eighty-five bronchial (BS) and pleural rub (PS) lung sounds employing the power spectral density (PSD) plot and wavelet scalogram. The low-frequency spread, and persistence of the high-intensity frequency components are visible in BS sounds emanating from the uniform cross-sectional area of the trachea. The frictional rub between the pleurae causes a higher frequency spread of low-intensity intermittent frequency components in PS signals. From the complex networks of BS and PS, the extracted graph features are - graph density ([Formula: see text], transitivity ([Formula: see text], degree centrality ([Formula: see text]), betweenness centrality ([Formula: see text], eigenvector centrality ([Formula: see text]), and graph entropy (En). The high values of [Formula: see text] and [Formula: see text] show a strong correlation between distinct segments of the BS signal originating from a consistent cross-sectional tracheal diameter and, hence, the generation of high-intense low-spread frequency components. An intermittent low-intense and a relatively greater frequency spread in PS signal appear as high [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] values. With these complex network parameters as input attributes, the supervised machine learning techniques- discriminant analyses, support vector machines, k-nearest neighbors, and neural network pattern recognition (PRNN)- classify the signals with more than 90% accuracy, with PRNN having 25 neurons in the hidden layer achieving the highest (98.82%).

Fault Detection and Normal Operating Condition in Power Transformers via Pattern Recognition Artificial Neural Network

Aging, degradation, or damage to internal insulation materials often contribute to transformer failures. Furthermore, combustible gases can be produced when these insulation materials experience thermal or electrical stresses. This paper presents an artificial neural network for pattern recognition (PRN) to classify the operating conditions of power transformers (normal, thermal faults, and electrical faults) depending on the combustible gases present in them. Two network configurations were presented, one with five and the other with ten neurons in the hidden layer. The main advantage of applying this model through artificial neural networks is its ability to capture the nonlinear characteristics of the samples under study, thus avoiding the need for iterative procedures. The effectiveness and applicability of the proposed methodology were evaluated on 815 real data samples. Based on the results, the PRN performed well in both training and validation (for samples that were not part of the training), with a mean squared error (MSE) close to expected (0.001). The network was able to classify the samples with a 98% accuracy rate of the 815 samples presented and with 100% accuracy in validation, showing that the methodology developed is capable of acting as a tool for diagnosing the operability of power transformers.

#2534 Classification of patients with acute kidney damage on the base of blood pressure value as a risk factor using a neural network

Abstract Background and Aims In acute kidney damage, the monitoring of hemodynamic status is best achieved by determining the blood pressure value. It is considered that the values of diastolic blood pressure in young and healthy people are constant from the aorta to the periphery, and the values of systolic and pulse pressure increase from the periphery to the aorta. The frequency of hypertension correlates with the presence of a cardiovascular precipitating risk factor in acute kidney injury, hypertension is also a modifying risk factor in the second and third stages of acute kidney injury, while the presence of hypotension on admission can be a clinical indicator of its cause. In patients with acute kidney damage and in patients with sepsis, the mechanism of autoregulation of mean arterial pressure, which is affected by stroke volume and heart rate, is not effective. The aim of the paper is to examine the classification of hospitalized patients with acute kidney injury based on blood pressure as a risk factor. Method The study included 86 patients over 18 years of age of both sexes (39 men 45.3% and 47 women 54.7%) with an average age of 66.85 ± 15.30 years who were diagnosed with acute kidney injury on admission to hospital treatment. Patients were divided into groups according to the stages of renal insufficiency. The study was designed as a cross-sectional comparative study. The assessment of the existence of acute kidney damage, as well as the determination of the stage of the disease, was based on the diagnostic criteria proposed by the K/DIGO expert group for acute kidney damage. The study did not include patients who had disease progression after acute kidney failure and were treated with dialysis for more than three months. Basic clinical, biochemical and hemodynamic parameters were determined in all subjects at the beginning of treatment, except for the analysis of nitrogen status, which was determined both before and at the end of treatment. During the formation of the neural network (pattern recognition Mat Lab), the parameters of systolic arterial pressure, diastolic arterial pressure normalized by min-max normalization to values from 0 to 1 were included. The data were randomly distributed into three categories: 80% for training, 10% for test, 10% for validation, which means that the parameters of 68 patients were used for training, 9 patients for validation and another 9 patients for the test. The number of input parameters is 33 to 39, while the number of output parameters is 2 in relation to treatment. Formed neural networks with different included blood pressure parameters, structures of 25 neurons in the hidden layer, with 55 and 15 epochs and with accuracy of 97.7% and 90.7% of patient classification. Results Our results show that 40.3% of patients in the third stage of acute kidney injury have hypertension. The lowest average values of systolic (108.44 ± 22.81 mmHg) and diastolic (65.56 ± 15.29 mmHg) blood pressure were experienced by patients in the first stage of acute kidney damage, and the lowest values of mean arterial pressure existed in the second stage of acute kidney damage (68.20 ± 44.96 mmHg) .Statistically significant risk factors for the development of the third stage of acute kidney damage in the multivariate analysis were patients older than 65 years, and mean arterial pressure values less than 65 mmHg. The confusion matrices showed that the classifiers adapted to the minimum and maximum values of systolic, diastolic and mean arterial blood pressure are well adapted and achieve satisfactory accuracy with 97.7% and 90.7%. Conclusion By comparing blood pressure parameters in hospitalized patients in relation to the stage of acute kidney damage, no statistically significant deviations were found. Univariate logistic regression analysis showed that age over 65 was a significant independent risk factor for stage three acute kidney injury, while the multivariate model showed that risk factors for the development of stage three acute kidney injury were patients same age and middle arterial blood pressure less than 65 mmHg. Satisfactory accuracy of formed neural networks when classifying patients during validation training and test was also demonstrated.

Indoor Infrastructure Maintenance Framework Using Networked Sensors, Robots, and Augmented Reality Human Interface

Sensing and cognition by homeowners and technicians for home maintenance are prime examples of human–building interaction. Damage, decay, and pest infestation present signals that humans interpret and then act upon to remedy and mitigate. The maintenance cognition process has direct effects on sustainability and economic vitality, as well as the health and well-being of building occupants. While home maintenance practices date back to antiquity, they readily submit to augmentation and improvement with modern technologies. This paper describes the use of networked smart technologies embedded with machine learning (ML) and presented in electronic formats to better inform homeowners and occupants about safety and maintenance issues, as well as recommend courses of remedial action. The demonstrated technologies include robotic sensing in confined areas, LiDAR scans of structural shape and deformation, moisture and gas sensing, water leak detection, network embedded ML, and augmented reality interfaces with multi-user teaming capabilities. The sensor information passes through a private local dynamic network to processors with neural network pattern recognition capabilities to abstract the information, which then feeds to humans through augmented reality and conventional smart device interfaces. This networked sensor system serves as a testbed and demonstrator for home maintenance technologies, for what can be termed Home Maintenance 4.0.

Analysis of the Monitoring and Identification Effect of Cognitive Service Technology on Dc System in Power Grid

This study investigates the impact of cognitive service technology on the monitoring and identification capabilities within a direct current (DC) system in a power grid. This paper introduces a novel Pattern Recognition Neural Network (PRNN) by integrating a Pattern Recognition Algorithm (PRA) and Convolutional Neural Networks (CNN) to analyse patterns in the DC system's data. With the increasing complexity and interconnectivity of modern power systems, the need for advanced monitoring and identification solutions becomes crucial. Cognitive service technology, known for its adaptability and learning capabilities, offers a promising avenue for enhancing the performance and reliability of DC systems. The research employs a comprehensive approach, incorporating data analysis, modelling, and simulation to assess the effectiveness of cognitive service technology in monitoring and identifying critical parameters within the DC system. The study aims to contribute valuable insights into the application of cognitive services for improving the overall efficiency and resilience of power grids operating on direct current, thereby fostering advancements in smart grid technologies

Using machine learning to predict artistic styles: an analysis of trends and the research agenda

AbstractIn the field of art, machine learning models have been used to predict artistic styles in paintings. The foregoing is somewhat advantageous for analysts, as these tools can provide more valuable results and help reduce bias in the results and conclusions provided. Therefore, the objective of this research was to examine research trends in the use of machine learning to predict artistic styles from a bibliometric review based on the PRISMA methodology. From the search equations, 268 documents were found, out of which, following the application of inclusion and exclusion criteria, 128 documents were analyzed. Through quantitative analysis, a growing research interest in the subject is evident, progressing from user perception approaches to the utilization of tools like deep learning for art studies. Among the main results, it is possible to identify that one of the most used techniques in the field has been neural networks for pattern recognition. Also, a large part of the research focuses on the use of design software for image creation and manipulation. Finally, it is found that the number of studies focused on contemporary modern art is still limited, this is due to the fact that a large part of the investigations has focused on historical artistic styles.

Efficient water-related failure detection in PEM fuel cells: Combining a PEMFCs fractional order impedance model with FFT-PWM techniques and artificial neural network classification

Water management and early detection of faults in proton exchange membrane fuel cells (PEMFCs) are among the most critical constraints that limit the optimal spread of this type of energy. Consequently, it is necessary to enhance the reliability and durability of PEMFCs by developing an approach to diagnose and identify water failure modes. This paper proposes an effective and simple method to detect, diagnose, and classify various water failure modes in PEMFCs using a hybrid diagnostic approach. This approach combines the PEMFC fractional order impedance model (FOIM) with fast Fourier transform pulse width modulation (FFT-PWM) techniques and artificial neural network pattern recognition (ANN-PR) classification. The results show an accurate match between the electrochemical impedance spectroscopy (EIS) experimental data, the Nyquist impedance spectra of FOIM, and the FFT-PWM algorithm as a proposed alternative technique to EIS measurements. Learning of ANN-PR was performed using the frequency spectrum amplitude (FSA) database of the voltage and current signals produced by the PEMFCs FOIM DC/DC boost converter, which was generated using the FFT-PWM algorithm. The ANN-PR achieved low values for error accuracy, with the Low Square Error and Learning Error reaching 6.676 × 10−19 and 1.888 × 10−16, respectively. The elements inside the confusion matrix and the rest of the matrices confirm that the proposed model's accuracy, precision, recall, and high F1 score reached 100%. Furthermore, all predictions made by the ANN-PR model were consistently accurate across all areas of failure detection. Overall, the proposed method helps in analyzing, diagnosing, and classifying fuel cell failure modes such as flooding and drying, which may simplify the health assessment of PEMFC.

Neural Network-Based Classifier for Collision Classification and Identification for a 3-DOF Industrial Robot

In this paper, the aim is to classify torque signals that are received from a 3-DOF manipulator using a pattern recognition neural network (PR-NN). The output signals of the proposed PR-NN classifier model are classified into four indicators. The first predicts that no collisions occur. The other three indicators predict collisions on the three links of the manipulator. The input data to train the PR-NN model are the values of torque exerted by the joints. The output of the model predicts and identifies the link on which the collision occurs. In our previous work, the position data for a 3-DOF robot were used to estimate the external collision torques exerted by the joints when applying collisions on each link, based on a recurrent neural network (RNN). The estimated external torques were used to design the current PR-NN model. In this work, the PR-NN model, while training, could successfully classify 56,592 samples out of 56,619 samples. Thus, the model achieved overall effectiveness (accuracy) in classifying collisions on the robot of 99.95%, which is almost 100%. The sensitivity of the model in detecting collisions on the links “Link 1, Link 2, and Link 3” was 97.9%, 99.7%, and 99.9%, respectively. The overall effectiveness of the trained model is presented and compared with other previous entries from the literature.

Метод синтеза данных для повышения эффективности обучения нейронных сетей

The article is devoted to the formation of the initial data set for training neural networks. A proven method for creating synthetic data based on a graphics processor using a graphics pipeline is presented. A distinctive feature of this method is its modular architecture, which makes it easy to modify, delete or add individual stages to the synthetic image generation pipeline. A one-stage automatic detector based on a convolutional neural network of the Yolo type has been trained, the quality of the trained model and the operation of the recognition algorithm were also evaluated. Conclusions are drawn regarding the possibility of using this approach when creating representative samples of a large volume and their further use for training neural networks in pattern recognition.

Advanced Machine Learning Techniques in Gomoku: Strategy,Implementation, and Analysis

The strategic board game Gomoku has become a compelling domain for artificial intelligence (AI) research, particularly in developing and applying machine learning techniques. This paper comprehensively analyzes advanced machine learning strategies in Gomoku, focusing on logistic regression for board evaluation, neural networks for pattern recognition, and reinforcement learning for strategic gameplay. We discuss integrating these techniques in creating a sophisticated AI capable of high-level play and adaptability. Through this exploration, we highlight the potential of AI in strategic decision-making and its broader applications beyond board games.

Diagnostic Method for Hydropower Plant Condition-based Maintenance combining Autoencoder with Clustering Algorithms

The French company EDF uses supervisory control and data acquisition systems in conjunction with a data management platform to monitor hydropower plant, allowing engineers and technicians to analyse the time-series collected. Depending on the strategic importance of the monitored hydropower plant, the number of time-series collected can vary greatly making it difficult to generate valuable information from the extracted data. In an attempt to provide an answer to this particular problem, a condition detection and diagnosis method combining clustering algorithms and autoencoder neural networks for pattern recognition has been developed and is presented in this paper.First, a dimension reduction algorithm is used to create a 2- or 3-dimensional projection that allows the users to identify unsuspected relationships between datapoints.Then, a collection of clustering algorithms regroups the datapoints into clusters. For each identified cluster, an autoencoder neural network is trained on the corresponding dataset. The aim is to measure the reconstruction error between each autoencoder model and the measured values, thus creating a proximity index for each state discovered during the clustering stage.