The global positioning system (GPS) is an essential technology that provides positioning capabilities and is used in various applications such as navigation, surveying, mapping, robot simultaneous localization and mapping (SLAM), location-based service (LBS), etc. However, the GPS is known to be vulnerable to intentional attacks such as spoofing because of its simple signal structure. In this study, a direct method is proposed for GPS spoofing detection, using Attitude and Heading Reference System (AHRS) accelerometer and analyzing the detection performance with corresponding probability density functions (PDFs). The difference in the acceleration between the GPS receiver and the accelerometer is used to detect spoofing. The magnitude of the acceleration error may be used as a decision variable. Additionally, using the magnitude of the north (or east) component of the acceleration error as another decision variable is proposed, which shows better performance in some conditions. The performance of the two decision variables is compared by calculating the probability of spoofing detection and the detectable minimum spoofing acceleration (DMSA), given a pre-defined false alarm probability and a pre-defined detection probability. It turns out that both decision variables need to be used together to obtain the best spoofing detection performance. The global navigation satellite system (GNSS) is an essential technology for positioning and timing, and its application covers various areas such as navigation, surveying, mapping, robot simultaneous localization and mapping (SLAM), location-based service (LBS), etc. The global positioning system (GPS) is the original GNSS and its full operational capability (FOC) was declared in 1995 in the United States of America. The legacy L1 C/A code signal of GPS is very weak at the Earth’s surface and has a simple structure to implement . Thus, tExperiments have been conducted to understand the vulnerability of the GPS to spoofing ,5, whichmparison  and consmparison ,16,17,18Among the effective high complexity spoofing detection techniques mentioned in the prior study , the DOAIn this study, a direct GPS spoofing detection method is proposed which uses attitude and heading reference system (AHRS) and accelerometers via direct comparison of the acceleration estimated from the GPS receiver and the acceleration measured from IMU, which provides the acceleration error. The acceleration from the GPS receiver is estimated from the Kalman filter by including the acceleration as a state variable of the GPS dynamic system in this study, while the acceleration from the GPS receiver in Reference  is obtaiTwo performance measures are considered for spoofing detection. One is the probability of spoofing detection. The exact PDF for both decision variables is known and thus, for a given probability of false alarm, the detection threshold and the detection probability can be calculated. The other is the detectable minimum spoofing acceleration (DMSA), which is the magnitude of the minimum spoofing acceleration to obtain a pre-defined detection probability, given a pre-defined false alarm probability. The performances of the two decision variables for the two performance measures are compared and analyzed.The structure of the first-half of the proposed direct GPS spoofing detection method is given in b denotes the body frame and n denotes the navigation frame. The navigation frame uses the north(x)-east(y)-down(z) (NED) frame in this study. AHRS produces the transformation matrixIn this study, GPS spoofing detection is done by using the comparison of accelerations obtained from the GPS receiver and accelerometers. The block diagram of It is assumed that IMU calibration and initial alignment is performed in advance depending on the characteristics of various inertial sensors since there are many kinds of gyroscopes, such as ring laser gyro, fiber optic gyro, hemispherical resonator gyro, and low cost micro-electro-mechanical system (MEMS) gyro, and so on, and different gyroscope has different error sources, and accelerometer has also many types, such as pendulous type, vibrating type, silicon type, and MEMS type. Matrices use capital letters, and vectors, small letters. Matrices and vectors will use bold letters and scalars use plain letters.The GPS receiver usually provides position and velocity information. To obtain acceleration from the GPS receiver, the Kalman filter is used by including acceleration as a state variable. The dynamics of the GPS receiver can be described by the state-space model as in Equation (1), which has 11 state variables such as 3-dimensional position, velocity, acceleration, GPS receiver’s clock bias Pseudo range is the distance between the GPS satellite and the receiver. The difference between the measured pseudo range From the dynamic Equation (1) and the measurement (2), the accelerations n filter .AHRS provides the attitude and heading and thus, the direction cosine matrix for AHRS ,23,24,25In many cases, quaternion is used to avoid deadlock and to save time. Quaternion The direction cosine matrixThe quaternion The direction cosine matrix This section describes the acceleration error equation for the direct GPS spoofing detection and defines two decision variables to decide whether a spoofing signal exists or not. One decision variable is the magnitude of the horizontal acceleration error and the other is the magnitude of the north (or east) direction acceleration error. The probability density functions and the thresholds for spoofing detection are given for the two decision variables.The acceleration estimated from the GPS receiver is described as follows,The specific force measured from the accelerometers The acceleration error equation is described from the difference of Suppose that the hypothesisn will be omitted henceforth, for brevity.Only the In Equation (9), the random variables The variances The PDF of the Lemma 1.(Shim PDF) Consider the independent Gaussian random variablesandwith. Then, the magnitudehas the following PDF:where, andProof. X and Y is asThe variable change for the independent Gaussian random variables Defining s and b above comes from Hoyt’s paper [The idea of using ’s paper . ConsideDefining By algebraic manipulation of the above equation, From the relation between random variables From algebraic manipulation of Equation (13), Rayleigh PDF and Rice PDF are well-known PDFs as the relation to Gaussian, and those two PDFs are special cases of Equation (12), which becomes Rayleigh PDF with the condition of Defining The PDF ofCorollary 2.Consider the independent Gaussian random variablesandwith. Then the magnitudehas the following PDF:where,Proof. Equation (14) can be obtained easily from the PDF in Equation (12) with Equation (14) can be found in Reference  without In this study, the probability of false alarm is used to obtain the threshold for the detection of spoofing. The threshold Whether a spoofing signal exists or not is decided by the following decision rule:The variable Defining The PDF of Gaussian , since zThe threshold This subsection shows the structure of the proposed second-half of direct GPS spoofing detection method in In If any of the three decision variables Note that the threshold This section shows the performance of the proposed direct GPS spoofing detection method for the two decision variables Suppose that the probability of false alarm To see the detection performance result clearly, the vertical moving acceleration is supposed to be zero and the gravity is compensated before the acceleration error is obtained. Thus the following variances in Equation (23) are used in the simulation from now on.The detection thresholds This subsection analyzes the effects of moving acceleration on the performance of spoofing detection. The effects of moving acceleration, magnitude and direction are separately examined, for both decision variables The probability of detection The probability of detection Suppose that the probability of the false alarm is pre-defined as The reason the two black curves are the same in In this subsection, the effect of the direction of moving acceleration on the spoofing detection performance is presented. When the direction of This subsection analyzes the effects of spoofing acceleration on the performance of spoofing detection. The effects of the direction of the spoofing acceleration are examined for both decision variables This subsection analyzes the effects of sensor accuracy on the performance of spoofing detection. This section compares the performance of the proposed direct GPS spoofing detection method for the two decision variables The detection threshold This section defines the detectable minimum spoofing acceleration (DMSA) and compares the DMSA for the decision variables DMSA is the magnitude of the minimum spoofing acceleration to obtain a pre-defined detection probability For a given DMSA in This subsection shows the contour of DMSA for the decision variable When both decision variables In this study, a direct GPS spoofing detection method is proposed, with AHRS and accelerometers via the difference of the acceleration estimated from GPS receiver and the acceleration measured from IMU. From the acceleration error expressed in the navigation frame, two decision variables are defined for spoofing detection. One decision variable The spoofing detection performance can be evaluated using the detection probability, which can be calculated from the probability density function of both decision variables. The decision variable When detectable minimum spoofing acceleration (DMSA) is used, the decision variable The spoofing acceleration can happen to be any direction. Thus, given a pre-defined false alarm probability, the best algorithm to detect GPS spoofing is that the three decision variables The proposed GPS spoofing detection method in this paper depends on the acceleration error. If a ground vehicle runs across road irregularities such as potholes, bumps, and rubble, etc., then accelerometers may show large changes and deteriorate the GPS spoofing detection performance. Therefore, the flying or driving environment may have an effect on the GPS detection performance.


Whether the human visual system actually uses these perceptive cues for emotional processing remains to be investigated.Affective pictures are widely used in studies of human emotions. The objects or scenes shown in affective pictures play a pivotal role in eliciting particular emotions. However, affective processing can also be mediated by low-level perceptual features, such as local brightness contrast, color or the spatial frequency profile. In the present study, we asked whether image properties that reflect global image structure and image composition affect the rating of affective pictures. We focused on 13 global image properties that were previously associated with the esthetic evaluation of visual stimuli, and determined their predictive power for the ratings of five affective picture datasets . First, we used an SVM-RBF classifier to predict high and low ratings for valence and arousal, respectively, and achieved a classification accuracy of 58–76% in this binary decision task. Second, a multiple linear regression analysis revealed that the individual image properties account for between 6 and 20% of the variance in the subjective ratings for valence and arousal. The predictive power of the image properties varies for the different datasets and type of ratings. Ratings tend to share similar sets of predictors if they correlate positively with each other. In conclusion, we obtained evidence from non-linear and linear analyses that affective pictures evoke emotions not only by  Affective pictures have become increasingly popular in psychological, neuroscientific and clinical research on emotions over the last two decades . AccordiVisual material is particularly effective in eliciting emotions in human observers . It is gwhat they show, but also by how they show it.Less well investigated is the question of whether image properties of higher order, which reflect global image structure or image composition, may be involved in emotional processing of affective pictures. For example, a gun presented in a blurry, low-contrast and almost colorless photograph may evoke a higher aversive reaction than the same object presented in a attractive advertisement that is well balanced in brightness, color and image composition. By the same token, intrinsically pleasant scenes may be photographed in various ways that follow esthetic principles. As an example, erotic pictures, which are rated as positive and highly arousing, usually depict more or less symmetric bodies arranged in a stereotypically ordered manner. The influence of stimulus properties that are independent of specific content may be particularly relevant for studies demonstrating effects that arise as early as 100–200 ms during the neurophysiological processing of emotional stimuli . To summThe dichotomy between the processing of pictorial content and form has been an issue also in the field of experimental esthetics. On the one hand, it is clear that esthetic experience depends on image content, cultural context and the viewer’s familiarity and expertise, which are subject to cognitive processing to a large extent . For exaIn summary, global image properties have been linked to visual preference and/or esthetic experience in diverse types of natural, artificial and artistic visual material. In the present study, we show that these properties can be used to predict emotional responses to affective pictures from five published datasets. The details of the datasets are listed in International Affective Picture System . SAM is a non-verbal method that permits intercultural comparisons and the inclusion of participants at a very young age  constitute a dataset of 240 high-quality pictures that focus on disgust . The characteristics of the datasets are listed in The datasets were downloaded from the webpages mentioned in the original publications  diverge between the datasets . Second,For each image, we calculated thirteen image properties that covered diverse aspects of global image structure, as described in the following paragraphs. These properties were selected from an even larger set of image properties, which our group has studied previously in visual artworks and other visually pleasing images . From the original set, we omitted properties that correlated strongly with each other . OverallColor plays an important role in human preference for images , and in Scientists and artists have claimed that symmetry is a fundamental and universal principle of esthetics, to which the human brain is particularly sensitive  is indicative of the relative strength of high spatial frequencies (fine detail) versus low spatial frequencies (coarse structure) of luminance changes across an image. In general, this slope is around -2 for natural scenes as well as for large subsets of artworks and other visually pleasing images. Human observers thus prefer statistics that are similar to those of natural scenes . Despite this overall richness, the feature responses are relatively variable between the sections of an image (high to intermediate Pf) in traditional artworks. The two variances differ between artworks and several types of natural and man-made images. In the present study, we calculated the variances as described in The response characteristics of lower-layer CNN features resemble neuronal responses at low levels of the visual system, such as the primary visual cortex . The CNNectively . Richnes6.Code to calculate the above measures is available via the Open Science FrameworkTo find out whether the set of image properties contains any information that contributes to the prediction of the affective ratings, we carried out a classification experiment using a SVM with a radial basis function (RBF) kernel. SVM is a widely-used machine-learning algorithm, which partitions the feature space of the input data by using hyperplanes in a way that maximizes the generalization ability of the classifier. We used the Scikit-learn library  in PythoThe classifier was trained separately on each of the five datasets. The analysis was restricted to the two rating terms that were common to all five datasets . For each dataset and rating term, the affective pictures were ranked according to the rating. Rated images were binned into three equally-sized clusters, which represented the pictures with the lowest ratings, intermediate ratings, and the highest ratings. The intermediate cluster was not used in the classification experiment. The SVM-RBF classifier was trained to distinguish between the pictures of low ratings and high ratings. A 10-fold cross-validation paradigm was used with 90% of the low/high rated images used for the training and 10% for testing in each round. Ten rounds of cross-validation with different partitions were performed. The validation results were averaged for each dataset and rating term separately and provided an estimate of the mean accuracy rate.R2 values were calculated for each image property to estimate how much of the variability in the outcome is mediated by the predictors of each model. R2 values were adjusted to account for the number of predictors in each model (R2adj). As an index for the effect of the independent variables on the outcome, we calculated standardized regression coefficients βi, which provide an estimate of the number of standard deviations, by which the outcome will change as a result of a change of one standard deviation in the predictor, assuming that the effects of all other predictors are held constant. Values for βi were calculated with the lm.beta package of the R project.We used multiple linear regression to determine the dependence of the ratings on the thirteen independent variables for each dataset. For this task, we used the lm package in the R project . R2 valuAIC), which considers the fit of the model as well as the number of parameters, we identified image properties that shared a similar prediction quality as other variables in the model. By a stepwise elimination, these variables were dropped from the model, as long as the model improved . For the final models, R2adj and bi values were calculated again. The R2adj values of the original and reduced  models were of similar magnitude, indicating that the predictive power was comparable.Moreover, we aimed at reducing the number of independent variables in the multiple linear regression by excluding image properties that correlated highly. Using Akaike’s entropy-based Information Criterion  and the V-channel values (p < 0.0001). This result implies that the DIRTI pictures are less saturated and lighter than the NAPS-H pictures on average. There is also a prominent difference between the NAPS-H and GAPED datasets in the Fourier sigma values (p < 0.0001). The GAPED pictures deviate more strongly from a scale-invariant Fourier spectrum than the NAPS-H pictures. Note that the image properties are not independent of each other and correlate to varying degrees, as revealed for the entire dataset of images in The values for the global image properties of each image analyzed in the present study can be accessed at the Open Science FrameworkThe ratings were taken from the five previous studies. They were obtained separately for each dataset using different scales . TherefoMean values for the affective ratings are listed in high) and the one third with the lowest ratings (low), respectively. Ratings for valence and arousal were considered separately. In this binary task, the mean accuracy is 50% for a random assignment of the labels high and low. Results from a 10-fold cross-validation experiment  and for arousal .As a first step toward assessing whether the statistical image properties can predict emotional ratings of the affective pictures, we used a classification approach. An SVM-RBF classifier was trained to recognize images that belong to the one third of images with the highest ratings . Values range from 0.017 to 0.195. Moreover, standardized regression coefficients βi were calculated. In the tables, bold letters indicate the variables that have a significant effect on the ratings when the other variables are controlled for. Not all independent variables have the same predictive power in the full models. Therefore, to eliminate less influential variables from the models by stepwise iterations, we calculated the Akaike Information Criterion (AIC), which allows us to compare the relative quality of the fit for different original and reduced models, when applied to the same set of data  for each dataset and rating. To simplify the description, we will explore the restricted models only in the following sections.To begin with, full models with all thirteen image properties were studied. Results are listed in  of data . ResultsAdditionally, in view of the correlations between some of the independent variables , we askeWe observe a high variability in the image properties that predict the ratings in the different datasets in the following respects: First, the datasets differ in the image properties that predict their ratings. Second, image properties differ in which of the individual ratings they predict within a given dataset. All variables predict ratings for some of the datasets, but some variables, such as the color parameters , 1st-order entropy, the symmetry measures (left/right symmetry and up/down symmetry), and the CNN variances (Pa and Pf) serve as predictors in all datasets, albeit for different ratings. None of the image properties is a significant predictor for all ratings over all five datasets.i values in Interestingly, the independent variables contribute to the ratings of valence and arousal with opposite algebraic signs for three of the datasets  for the GAPED-A  subset, the GAPED-Sn (snakes) subset and the GAPED-Sp (spiders) subset. Predictive power is higher for the GAPED-H (scenes violating human rights) subset . For the GAPED-A and GAPED-H datasets, ratings of acceptability with respect to internal  and external  norms (The GAPED database  containsl) norms  were anal) norms .We studied to what extent global image properties predict emotional responses to stimuli from five affective picture datasets . The datasets were analyzed separately because they differ in important respects . Nevertheless, the datasets share some features, as outlined below.i of opposite algebraic signs. With a positive correlation, the regression coefficients βi tend to have the same algebraic sign. For the IAPS and OASIS datasets, such systematic relations are not observed, as correlations between the ratings are weaker or absent (The present study confirms previous findings that some of the ratings are correlated with each other in a given database . In partr absent .The image properties studied by us have been associated with preference judgments in previous studies (see section “Introduction”). We therefore speculated that they might predict emotional responses, such as valence and arousal, as well. The results from the present study confirm this notion in general.R2adj) ranges from 2 to 20%. Again, the predictive power differs between datasets. For example, it is relatively low for the ratings of the IAPS dataset consciously choose pictures that are congruent at the perceptual and semantic levels. For example, someone might take a photograph of a pleasing landscape by carefully selecting a well-balanced and appealing detail of the scene while a photograph of vomit in a dirty sink might be less esthetically motivated and composed. In a similar vein, The magnitude of the present results can be compared to ratings in the field of visual esthetics. Here, sets of objective image properties similar to the ones used in the present study have been used to predict diverse esthetic ratings, such as linking, beauty or visual preference. As in the present study, results depend on the datasets analyzed. For example, in the study by Evidence for a direct role of low-level image properties in affective evaluations of images has been obtained, for example, by Studies regarding scene perception reached similar conclusions. Short and masked presentations of 100 ms and less are sufficient for viewers to comprehend and describe complex scenes such as line drawings, but also naturalistic scenes . This fiSimilarly, low-level image properties were shown to play a role in esthetic judgments. A particularly well-studied example is the preference of curved over angular objects or line patterns . This prBesides general effects on esthetic preference, there are also indications that individual taste for low-level features plays a role in esthetic judgments. R2adj values of 0.02–0.09) is associated with many different variables. By contrast, only 4 out of the 13 properties are predictive for the DIRTI dataset . The relatively large R2adj values for the DIRTI dataset (0.17–0.20) are thus mediated by a few image properties only.We also noted that the datasets differ widely in how many and which of the image properties are predictive for the ratings, when the other image properties are accounted for . Similarly, the provided values could be used across databases to generate picture sets  that are matched for the image properties with a prominent effect on the ratings. This way, a bias for particular image properties can be avoided when subsets of images are selected from a database.An alternative approach would be to use the established values of individual pictures as covariates for statistical analyses. To foster such an approach, we are making the values available to the scientific community via the Open Science Framework . Last but not least, the effect of image properties on affective ratings might be more prominent if the idiosyncratic style of one or a few photographers predominates in a given affective dataset. Presumably, such stylistic particularities can be avoided by collecting images from a wide range of sources and photographers.In conclusion, the interplay between low-level image properties and their interaction with higher cognitive functions is a key issue in understanding emotional and esthetic perception. Here, we stress the impact of global image properties on emotional ratings and that this should be regarded in future research by selecting appropriate images from datasets. Additionally, we show how insights from empirical esthetics may shed light on basic visual and emotional perception.https://osf.io/r7wpz). For availability of code to calculate the properties, see text footnote 6.The values for the global image properties of all five afffective image datasets can be accessed at the Open Science Framework (CR, AK, and CD conceived the experiments. CR, MG, MM, and AK collected and analyzed the data. CR and CD wrote the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


F-score, are employed to evaluate the performance of the proposed system. Furthermore, evaluation and comparison of the proposed system with the existing machine learning algorithms are presented. Finally, the proposed system has enhanced the performance of machine learning algorithms.Chronic diseases represent a serious threat to public health across the world. It is estimated at about 60% of all deaths worldwide and approximately 43% of the global burden of chronic diseases. Thus, the analysis of the healthcare data has helped health officials, patients, and healthcare communities to perform early detection for those diseases. Extracting the patterns from healthcare data has helped the healthcare communities to obtain complete medical data for the purpose of diagnosis. The objective of the present research work is presented to improve the surveillance detection system for chronic diseases, which is used for the protection of people's lives. For this purpose, the proposed system has been developed to enhance the detection of chronic disease by using machine learning algorithms. The standard data related to chronic diseases have been collected from various worldwide resources. In healthcare data, special chronic diseases include ambiguous objects of the class. Therefore, the presence of ambiguous objects shows the availability of traits involving two or more classes, which reduces the accuracy of the machine learning algorithms. The novelty of the current research work lies in the assumption that demonstrates the noncrisp Rough K-means (RKM) clustering for figuring out the ambiguity in chronic disease dataset to improve the performance of the system. The RKM algorithm has clustered data into two sets, namely, the upper approximation and lower approximation. The objects belonging to the upper approximation are favourable objects, whereas the ones belonging to the lower approximation are excluded and identified as ambiguous. These ambiguous objects have been excluded to improve the machine learning algorithms. The machine learning algorithms, namely, naïve Bayes (NB), support vector machine (SVM), K-nearest neighbors (KNN), and random forest tree, are presented and compared. The chronic disease data are obtained from the machine learning repository and Kaggle to test and evaluate the proposed model. The experimental results demonstrate that the proposed system is successfully employed for the diagnosis of chronic diseases. The proposed model achieved the best results with naive Bayes with RKM for the classification of diabetic disease (80.55%), whereas SVM with RKM for the classification of kidney disease achieved 100% and SVM with RKM for the classification of cancer disease achieved 97.53 with respect to accuracy metric. The performance measures, such as accuracy, sensitivity, specificity, precision, and  Chronic diseases are serious diseases because they pose a serious threat to people's lives and persist over long periods. They can impede the freedom and health of people who have physical disabilities. Thus, they further cause frustration of people who suffer from various health disabilities. The available vaccines and medicine cannot completely prevent chronic diseases because they show no indications in any case. With aging changes, chronic diseases continue to become a more common phenomenon. Hence, there is a need to identify factors causing them and to take the required corrective measures accordingly. Factors such as smoking, physical inactivity, food diet, and insufficient or excessive alcohol consumption could largely contribute to chronic diseases. Previous studies have identified chronic diseases as the seventh cause of death among other causes. In the United States, they resulted in 65.8% of deaths among US males and 67.2% of deaths among US females in 2010 [The machine learning algorithms increase the level of individual prediction, and therefore diagnosis will ultimately strengthen anticipation efforts. The availability of well prevention measures will not only enhance or provide good health for persons but also reduce healthcare spending. Machine learning techniques have been used widely in the healthcare domain. They have now become crucial tools for healthcare management. They have also assisted in improving health care by using the prediction measures for epidemic diseases faced by people around the world. The World Health Organization (WHO) has significantly benefited from the employment of machine learning applications that improve the quality of health care.Machine learning algorithms are considered to be classification, clustering, and prediction for the sake of solving various issues in real-time applications. They provide an assurance of the classification and prediction solutions for stability and reliability in performance. Based on machine learning algorithms, a few researchers have developed successful healthcare systems. Algorithms include statistics, SVM, decision trees, clustering, and optimization algorithms and others. Machine learning applications rely largely on datasets that analyze and discover the patterns that are used to solve specific tasks. The healthcare system has the potential promotion in the health domain to extract and discover the hidden patterns in the database . Thus, tThe remaining parts of the article are organized into sections. Introduction is discussed in There is a considerable number of research works that have been done in relation to the classification and the prediction of healthcare data. Solanki  proposedIn this research, the training dataset consists of 3000 values with 13 different features. From the experimental results, it is shown that the regression algorithm performs better than other algorithms. Kim et al.  have proIn the current research article, traditional machine learning algorithms are employed for predicting chronic diseases. Therefore, the result of the existing classification algorithms is needed to make the healthcare system more reliable. Subsequently, the soft clustering algorithm is applied to increase the accuracy of classification algorithms.The proposed model is designed explicitly to classify chronic diseases using machine learning algorithms. The chronic disease datasets have been collected from the different resources as follows:The diabetes data collected from the machine learning repository contained nine attributes, eight features, and one class. This dataset has been gathered from an automatic electronic recording device and paper records .  Table The cancer data collected from the Kaggle contained nine attributes, 30 features, and 1 class. These features are obtained from digitized images of breast cancer .  Table The collected kidney data from the Kaggle contained 26 attributes, 24 features, and 1 class .  Table Machine learning algorithms have succeeded in a number of real-time applications such as image processing recognition, video recognition, marketing prediction, weather forecasting, and network security. The conventional machine learning algorithms are used to identify the objects belonging to exactly one class. In data analysis, it may be possible that an object shows the characteristics of different classes . In thatIn   (P1) An object   (P2)   (P3) An object  ⇕ The proposed RKM clustering approach is based on a simple K-means clustering –42. Petewlower and wupper. For each object vector, d , support vector machine (SVM), K-nearest neighbor (KNN), and random forest tree, are presented to predict chronic diseases for enhancing healthcare systems.n-dimensional space where there are a number of features of data, and the values of features are the values of a specific coordinate. The classification of data is achieved by finding the best difference between the classes of data using hyperplane. A support vector machine algorithm classifies data by separating the hyperactive plane of label training data. The SVM obtains lower error when the margin is large. In the present research work, two classes of chronic diseases are used. All types of kernel functions are applied to classify the chronic disease datasets in which radial basis function (RBF), along with kernel function, obtain high accuracy. The kernel function is applied and observed that the RBF function and kernel function are appropriate with the RKM algorithm to obtain good accuracy.σ is a parameter.The support vector machine is used to analyze data as classification and regression. In the SVM algorithm, the data point is considered as A = A1, A2, A3,…, An is regarded as the feature vector of chronic disease features, and the values of the features are A1, A2, A3,…, An and are considered as a number of features in the dataset. C indicates a class of chronic data as normal and abnormal. The Bayes equation is shown as follows:  Conditional probability:Naive Bayes algorithm is defined as a probabilistic method used to classify the dataset based on the well-known Bayes theorem of probability. The naïve Bayes classification algorithm works as prior probability, posterior probability, likelihood probability, and evidence probability. It normally uses probability distributions. The working Bayesian algorithm is as follows: Assume A on the given class c is independent of the values of other predictors, and it is known as conditional class independence. P(C|A) is the posterior probability of class c, given predictor (feature).  Theorem is as follows:It is assumed that the predictor A K-nearest neighbors algorithm is a simple machine learning algorithm, which uses the entire dataset in its training phase. KNN algorithm has low complexity in programming and implementation. The basic idea can be presented in a sample space when its nearest neighboring features belong to a category, and then the features belong to the same category. The KNN classification algorithm can be used with either a single or a multidimensional feature dataset and can find the closest features. It employs the Euclidean distance method for finding the closest point among the features.D is the dataset.D is the dataset, i = 1, 2,…, m is the class of dataset D, and the probability is piA decision tree algorithm is one of the powerful decisions. It is used to build the block of a random forest. It works to select the best split of an object from the dataset in each step. To reduce the high harnessed of variance, we can create multiple trees with various samples of datasets and combine this operation with bootstrap aggregation or bagging. The disadvantage of the bootstrap aggregation method is used to spill the values of each tree, which creates a problem in decision-making. Furthermore, it makes predictions of training data similar and mitigates the variance originally sought. Thus, the random forest algorithm can be further used for the classification and regression problems and for the overfitting of data as well. The selected attributes are measured by employing the information gain method to discover the value or the information from the entire dataset. The information gain method is calculated for each splitting attribute with selecting high gain attributes. It is assumed that B be an attribute in dataset D and {b1, b2, b3,…, bn} are values of the attributes in B. Attributes are a partition for generating the amount of information from attributes.Let The attributes show the highest information as follows:F-score evaluation matrices have been employed to test the proposed model. The evaluation matrices are computed by using the equations  as  as F-scoP + N):Accuracy is the number of correct predictions made by the model over all kinds of predictions made. It is calculated as the total number of correct labels (TP + TN) divided by the total number of chronic disease datasets  is a measure that tells us about the percentage of patients who do not suffer from chronic diseases, which are predicted by the model as not chronic diseases:Sensitivity  is the measure that tells about the percentage of patients who actually suffer from chronic diseases, which are diagnosed by the classification algorithms on chronic diseases:Precision is a measure that tells about the proportion of patients that we diagnosed as having chronic diseases, actually had chronic diseases. It is known as positive predictive value (PPV):F1-score  is the harmonic mean (average) of the precision and recall:F-score have been presented to test the proposed system against the existing machine learning techniques. Moreover, for validating the proposed system, the datasets are divided into 70% train and 30% test. Numerous experiments have attempted to evaluate the proposed system. The results of machine learning algorithms and enhanced model to the various datasets are presented as follows:Therefore, the rough K-means algorithm is applied for improving the classification of chronic diseases. It is used to determine the ambiguous objects that have obstructed the classification algorithms. It has further experimented with various standard chronic datasets. It is aimed here to improve the diagnosis of chronic diseases. In the beginning, the conventional classification algorithms are applied to predict chronic diseases. However, it is observed that the obtained results were not appropriate. From the obtained results, it is noted that there are ambiguous objects that decrease the accuracy of machine learning algorithms. One of the biggest challenges that we have faced within the implementation of the proposed system is the ambiguity embedded in the variable of the standard dataset. For this reason, the RKM algorithm is considered to handle these ambiguous objects so that the accuracy of the classification algorithms can be improved. The RKM algorithm is appropriately designed for detecting the ambiguity in the chronic disease datasets. The experimental results have shown that the performance of the proposed system is better than that of the conventional models. For measuring and evaluating the performance of the proposed system, the performance measures are applied. The standard evaluation matrices, namely, accuracy, specificity, sensitivity, precision, and In this section, different experiments of classification algorithms with the enhanced proposed system have been conducted. The soft computing rough K-means algorithm is used to handle ambiguous objects. The ambiguous objects in chronic disease datasets have reduced the performance of machine learning algorithms. When applying the classification algorithm on the original diabetics data, it is observed that the results are not favourable. From the data, it is investigated that there are ambiguous objects that hinder the classification algorithms. The diabetes data contain seven instances and two classes. These ambiguous objects are examined by RKM clustering to assist in determining the exact class of ambiguous diseases or the closest one. The dataset has been clustered for two clusters corresponding into two classes that are labelled variables in datasets. The RKM algorithm has clustered the ambiguous objects into upper approximation and lower approximation. Those objects that belong to upper approximation, which belongs to one or more cluster numbers, are excluded. Among 768 instances, 718 instances are clustered as a lower approximation. Moreover, the remaining objects are clustered as an upper approximation and are considered as ambiguous objects as well. The ambiguous objects have been denied from the data. The classification algorithm is applied to process the data in a lower approximation for diagnosing the diseases. F-score, in that order. The results of random forest with RKM are 77.20, 56.09, 69.05, and 62.0. Furthermore, the obtained results by using KNN with RKM are 71.30%, 79.29%, 56.58%, 77.08%, 77.08%, and 78.70%. Finally, from the obtained data, it is investigated that the classification algorithm is improved by using the RKM algorithm. Figures 4This section demonstrates the classification of kidney diseases with the help of machine learning algorithms and the enhanced proposed system. 8This section shows the classification of cancer disease using the existing machine learning algorithms and the proposed system using the RKM algorithm. The cancer data contain 569 instances that are classified into two classes such as benign and malignant. The soft computing RKM clustering algorithm is used to handle ambiguous objects. It clusters data into two clusters according to the class label of data. The RKM technique has clustered data into lower approximation and upper approximation. The objects belonged to the lower approximation are appropriate objects, and are processed by using a machine learning algorithm. However, the objects that have been clustered into upper approximation are considered as ambiguous ones. The RKM is clustered into 539 objects in the lower approximation, and the remaining objects are in the upper approximation. 12In this section, a comparative analysis between the proposed model and some of the other state-of-the-art work is used in the same datasets. The comparison is very important because it examines the results of the proposed model. The accuracy metric is used to compare the proposed model with the existing classification algorithms. The performance of the existing machine learning is thwarted from diagnosing chronic diseases because of the availability of ambiguous objects. These ambiguous objects show traits in more than one class. To identify and process the ambiguous objects explicitly, we have demonstrated the noncrisp RKM clustering that can handle these ambiguous objects to improve the accuracy of classification algorithms. The framework of the proposed system lies in its use of a soft clustering algorithm, namely, rough K-means that can be employed for modelling ambiguity. The rough K-means clustering can assist in determining the exact class of the ambiguous objects or the approximate ones. It is observed that the RKM algorithm has increased the performance of the conventional machine algorithms to predict chronic diseases. The ambiguous objects are excluded from chronic dataset. Therefore, the RKM algorithm clustered the data into lower and upper approximation. The objects clustered in lower approximation are considered as appropriate objects. Additionally, the objects that belong to the upper approximation are denied and considered as ambiguous objects. The objects that belong to the lower approximation are proposed by using machine learning algorithms to predict chronic diseases. The experimental results demonstrate that the proposed system is successfully employed for the diagnosis of chronic diseases. Comparative analysis results between existing machine learning algorithms and the proposed system are presented. Moreover, it is observed that the results of the proposed system are superior in terms of accuracy, specificity, sensitivity, precision, recall, and F-score performance measures. Identifying common web search activity behaviour is regarded as a proxy for chronic disease risk factors using machine learning algorithms can be considered in future work.


A high-order polynomial fitting method is proposed to accelerate the computation of double-Gaussian fitting in the retrieval of the Brillouin frequency shifts (BFS) in optical fibers showing two local Brillouin peaks. The method is experimentally validated in a distributed Brillouin sensor under different signal-to noise ratios and realistic spectral scenarios. Results verify that a sixth-order polynomial fitting can provide a reliable initial estimation of the dual local BFS values, which can be subsequently used as initial parameters of a nonlinear double-Gaussian fitting. The method demonstrates a 4.9-fold reduction in the number of iterations required by double-Gaussian fitting and a 3.4-fold improvement in processing time. For about three decades, Brillouin scattering has been widely used in the development of distributed optical fiber sensors. Exploiting the Brillouin acousto-optic interaction between optical signals and the optical fiber material, a distributed temperature or strain profile along an optical fiber can be obtained for sensing purposes ,2. The eAlthough several signal processing approaches have been proposed to estimate the BFS ,4,5,6,7,In this paper, we propose and validate the use of a high-order polynomial fitting to obtain an initial estimation of the frequencies of the two Brillouin peaks, with the aim of reducing the computation time of nonlinear double-Gaussian fitting methods. Compared to the conventional approach, which in the best situation uses the intrinsic BFS of the non-perturbed fiber as an initial parameter, our method reduces the numbers of iterations and the computation time of double-Gaussian fitting based on NLS regression using the Levenberg–Marquardt algorithm . ExperimTo test the proposed fitting procedure, a standard layout of a Brillouin optical time-domain analysis (BOTDA) system is used, as shown in To evaluate the proposed high-order polynomial fitting method, we induce a local double Brillouin spectral peak by applying a sharp longitudinal strain variation at the end of a 50-km-long sensing fiber. As shown in Note that BGS measurements exhibit different spectral behavior depending on the applied strain. Thus, for small weights  two overlapping BGS can be observed; while for larger weights , the two spectral peaks are clearly separated. Polynomial curves of different orders have been fitted to each of the measured spectra. While the conventional second-order curve only fits one resonance peak , polynomTo extract an estimation of each peak frequency in local BGS measurements, the first three derivatives of the fitted curve must be calculated. This procedure is shown in It is worth noting that the large degree of freedom given by the seven coefficients of the sixth-order polynomial curve and the presence of noise lead to uncertainties in the initial estimation of the BFS values. These uncertainties are essentially due to the influence of noise on the spectral overfitting that may result from the high-order polynomial curve. To reduce uncertainty in the initial estimated BFS values, it is possible to use the histogram of the peaks found at the local position, which could be calculated within a window moving along the fiber. The histogram allows us to find the most-commonly repeated BFS values and take them as more precise BFS estimations compared to the values directly obtained from fitting. To increase the number of measured data points and obtain reliable histograms, longitudinal oversampling along the traces could be used. If the spatial resolution and noise bandwidth do not lead to a relevant number of independent points, another (or complementary) approach could be the use of consecutive measurements to make the histogram with enough relevant data points. In this case, The estimated BFS values are then used as initial parameters of a double-Gaussian fitting algorithm based on a nonlinear least-square regression using Levenberg–Marquardt algorithm . SimilarBefore evaluating the computation times, we compare the BFS values retrieved by the conventional double-Gaussian fitting  and the ones estimated directly from sixth-order polynomial fitting. Note that the proposed fitting method could be applied to the entire optical fiber, regardless the number of local BGS peaks existing along it. This means that the method does not require a previous knowledge of the BFS distribution, so that the existence of a single or dual BFS values can be obtained automatically by applying process described in Results in Then, the impact of the proposed approach is evaluated in terms of the number of iterations and processing time. Fitting is first performed using the local BFS of the unperturbed fiber as initial parameter. The number of iterations and processing time are compared to the ones obtained with the same algorithm but starting from the BFS values estimated by the sixth-order polynomial fitting.In conclusion, in this paper we have proposed and experimentally validated the use of high-order polynomial fitting to accelerate the processing time of double-Gaussian fitting in distributed Brillouin sensors being affected by existing or artificially induced double Brillouin spectral peaks. Experimental results verify a 4.9-fold reduction in the number of iterations and a 3.4-fold reduction in the processing time of double Gaussian-fitting based on NLS regression using the Levenberg–Marquardt algorithm. A future analysis of reliability and uncertainty of the proposed method is still required to assess the feasibility of using high-order polynomial fitting alone, without the need of Gaussian fitting, to obtain the dual BFS peak values. This must also be compared with an analysis of the BFS uncertainty provided by the double-Gaussian fitting, which, to the best to our knowledge, does not exist today in the literature.


Global optimization is an algorithmic need that is ubiquitous throughout the natural sciences, engineering, and other technical spheres. It is a non-trivial task, particularly when the function to be optimized has many local minima and the optimization algorithm may get trapped in the local minima of the function to be optimized. For that reason, many competing approaches have been proposed for global optimization, especially those inspired by nature. The goal of the library proposed here is to develop a user-friendly framework in C++11 (with wrappers for Python) that can be used to successfully and efficiently carry out global optimization of challenging cost functions with minimum expertise required.CEGO  is a C++11-based optimization library that minimizes an arbitrary cost function. In C++, the cost function to be minimized is of type std::function<double>, where CEGO::AbstractIndividual is the base class for an individual in the population of candidate solutions. The independent variables to be optimized are of type std::vector<CEGO::numberish>, where the datatype CEGO::numberish can accept both discrete (integer) and continuous values.The implementation of the ALPS algorithm , 2009 foLatin hypercube sampling to generate the initial population of individuals in the population.A generic architecture for evolving the layered population(s). In the current version, differential evolution  is the dUse of native C++11 threads (with a thread pool) to parallelize the evaluation of the cost function, allowing for a nearly-linear speedup as more computational cores are made available.Ability to log all inputs and outputs  for further analysis of the progress of the optimization.1 and is used to demonstrate the functionality of the library, though it cannot fully leverage the parallelism available in CEGO at the C++ level.A single-threaded Python wrapper (PyCEGO) is written with pybind11A brief summary of the functionality of CEGO includes:optimization of cost functions of two- and ten-dimensional continuous variables.the mixed-integer nonlinear optimization problems of the constrained optimization of a pressure vessel mass and dimensionally-constrained spring inverse modeling of Gaussian bumps.A few Jupyter notebooks  are provAll global optimization problems successfully obtain the minimum value from the literature, or better. Furthermore, a binder  environmAn example is given here of the global optimization of the modified hundred-digit optimization problem (


Position estimation techniques for solenoid actuators are successfully used in a wide field of applications requiring monitoring functionality without the need for additional sensors. Most techniques, which also include standstill condition, are based on the identification of the differential inductance, a parameter that exhibits high sensitivity towards position variations. The differential inductance of some actuators shows a non-monotonic dependency over the position. This leads to ambiguities in position estimation. Nevertheless, a unique position estimation in standstill condition without prior knowledge of the actuator state is highly desired. In this work, the eddy current losses inside the actuator are identified in terms of a parallel resistor and are exploited in order to solve the ambiguities in position estimation. Compared to other state-of-the-art techniques, the differential inductance and the parallel resistance are estimated online by approaches requiring low implementation and computation effort. Furthermore, a data fusion algorithm for position estimation based on a neural network is proposed. Experimental results involving a use case scenario of an end-position detection for a switching solenoid actuator prove the uniqueness, the precision and the high signal-to-noise ratio of the obtained position estimate. The proposed approach therefore allows the unique estimation of the actuator position including standstill condition suitable for low-cost applications demanding low implementation effort. Solenoid actuators have proven to be a simple and robust actuation principle for various applications such as valves and electromechanical switches. Being based on the reluctance principle, they offer linear motion with large strokes and high forces. Due to their simplicity, such actuators are produced in high quantities for low prices. With the recent tendencies towards condition monitoring and predictive maintenance, mainly under the concept of Industry 4.0, also monitoring of the state and the condition of such actuators gains interest. In particular, a knowledge of the actuator position is required in order to detect if the solenoid actuates correctly under varying external loads. Usually, position information is obtained by additional position sensors such as linear variable differential transformers (LVDTs) or encoders, which increase the size and the cost of the actuation system significantly. The usage of additional sensors can be avoided by applying position estimation techniques for actuator monitoring and control ,2,3,4,5,State-of-the-art techniques for sensorless position detection of solenoid actuators can be divided into three categories: observer based on the back-induced electromotive force (back-EMF) ,8, identThe differential inductance of a solenoid actuator shows a significant dependence on the actuator position and is exploited in various techniques that allow the estimation even at standstill condition. It can only be identified when the actuator is persistently excited, which can be achieved by approaches injecting an additional excitation signal into the actuator ,6,9,10. The state-of-the-art works ,27,28 moAs mentioned above, the preferred parameter used for position estimation is the differential inductance, which has the demerit of an ambiguous position estimate. Such ambiguity can be resolved by the identification of a lumped parallel resistor that represents eddy current losses. While some works based on the differential inductance are especially optimized for low computational and sampling effort, similar approaches for the parallel resistance do not exist. Therefore, the synthesis of an estimator for the parallel resistor with low demands on computational power and sampling rate is desired, especially for solenoid actuators that are placed in the low-cost segment. Moreover, the parallel resistance suffers from a large variance in identification, making data fusion with another parameter like the differential inductance necessary for a successful implementation of a position estimator. State-of-the-art works apply a binary decision-making algorithm for this, hence a more sophisticated approach with an internal weighting of the parameter values seems to promise more accurate results with higher SNR.In this work, a position estimator based on the identification of the differential inductance and the parallel resistor is proposed with the focus lying on a resource-efficient identification of those parameters. Before introducing the methods used for identification, a detailed electromagnetic model of a solenoid actuator is derived, and the current ripple induced in such an actuator is analyzed by taking into account the presence of eddy currents. The response of the current ripple during a PWM switching voltage transient is exploited for deriving a resistance estimator. For a resource-efficient identification of the differential inductance, the Integrator-Based Direct Inductance Measurement (IDIM) technique, known from prior works ,26, is pIn the following, current ripples inside solenoid actuators are analyzed under the consideration of eddy currents. A magnetic circuit model including eddy currents is proposed and its interaction with the electrical model of a solenoid is examined. Finally, an investigation of the response of the electromagnetic model to a PWM voltage is made with the particular focus lying on the switching time instants, where the effect of the eddy currents is significant.x, the air gap reluctance is position-dependent and can be described as ([The magnetic flux path of actuators can be modeled by means of magnetic reluctances ( p. 15):(ibed as ( p. 69):.The plunger of solenoid actuators represents a voluminous piece of soft magnetic material, where the creation of eddy currents is delayed between the outer parts and the inner parts of the plunger. In particular, this phenomena resembles the skin effect, where the eddy currents in the inner parts are delayed since they not only are affected by the original magnetic field, but also from the field that is induced by the eddy currents in the outer parts ( p. 51). u and current v as well as a total flux N magnetic reluctances and inductances [x. For a better comprehension and modeling, the following calculations will take place in the Laplace domain with the Laplace value denoted as s. By applying the Kirchhoff rules, the total flux V can be obtained:The equivalent circuit is divided into an electrical subsystem, consisting of an electrical voltage uctances , which aFor each single RL element inside the cascade, it can be calculated:W of the coil can be considered in the calculations. Equation  Equation  allows tFor the case of one RL element (Applying Equations  and 9)  9) yieldBy means of algebraic manipulation, the transfer function of the magnetic circuit can be obtained:Thus, the transfer function of the magnetic circuit with one eddy current element has no zeros and one pole. The electrical system can be modeled by applying the Kirchhoff rules as:By defining the electrical transfer function:It is visible that the resulting transfer function of the electrical circuit has one pole and one zero. For sake of generalization, the polynomial of the nominator is denoted as By using Equation , the traEquation , the traSimilarly to the case N of eddy current elements. In the following, an experimental measurement of the current ripple of the actuator under test ITS-LZ 1949 from Red Magnetics is shown and compared to the discussed models. This experimental result is already anticipated for this discussion, while the solenoid actuator itself, its parameters and the test-bench are described in detail in In order to simplify the mathematical treatment of the eddy currents and reduce the number of parameters in this model, it is desired to reduce the number Equation , is consEquation , is showthe work  also useThe reluctances in the model can be summarized into one reluctance denoted as The calculations made above are conducted in the Laplace domain for sake of comprehension. Nevertheless, the parameters By means of algebraic manipulation, Equations –21) can can21) cThe term Reformulating this equation leads to a classical differential equation with the input In common solenoid actuators, the parallel resistance Equation  resembleElectromagnetic actuators are usually driven by PWM-based switching power electronics. In this work, a bipolar edge-aligned PWM is considered that can be formulated asEquation , becauseThe rising edge of the PWM voltage can be formulated as:Solving the differential Equation  for the N of RL elements smooths that current jump. Nevertheless, the height of that cusp can be modeled appropriately even with a number This result considers the parameters to be constant over one PWM period, which simplifies the analytical solution. Due to the fact that the mechanical time constant of the actuator is considerable larger than the PWM period, this assumption can be applied. In the following, position estimation techniques are presented and an approach for data fusion of different position estimates in terms of a multilayer perceptron neural network is discussed. The first estimator is based on the identification of the differential inductance In the following section, the Integrator-Based Direct Inductance Measurement (IDIM) technique is described briefly, which is based on the analog integration of the current ripple in order to estimate the differential inductance of a solenoid actuator. The technique is explained, derived and validated thoroughly in ,26 and, The reset trigger signal hosen as :(33)r(t)The trigger signal is designed in such a way that PWM switching instants are avoided during integration. In particular, the waiting time rocedure ,21,22. TThe behavior of the analog signal-processing circuit shown in Inserting Equation  into theThe integral can be solved for the PWM input Equation  and can sistance . For mossistance :(37)QQUDC( A being :(40)A=QLd≈−N of RL elements also increases the accuracy of the model, while increasing the modeling and computational effort. As mentioned in In order to solve the ambiguities that occur when using approaches based on the differential inductance, another parameter needs to be determined which allows a unique estimation of the actuator position. As seen in From Equation , it can The height of the cusp can be calculated with Equation  as:(44)ΔBy considering the measurements time instants Therefore, the height of the cusp can be approximated as:Finally, an estimate of the position-dependent parallel resistance can be obtained:It has to be highlighted that the estimation of the parallel resistance depends on the difference between two current samples, which are very close to each other. Measurement noise as well as limited bandwidth and slew rate of the current sensor have a significant influence of the obtained estimate. It is therefore desired to use a high bandwidth current sensor with anti-aliasing filter in front of the AD converter. Additionally, in order to increase the SNR, the estimate of the resistance needs to be low pass filtered digitally with a cut-off frequency that is higher than the mechanical frequency of the actuator.In position ,27,28.Despite the problem of ambiguities, the position estimation through the differential inductance variance . Given tance [Rp . This siInstead, this work uses a multilayer perceptron (MLP) neural network for data fusion. Such an MLP can train its input weights based on experimental data, that allows the MLP to give more weight on the input pability , thus alpability . The impIn the following section, experimental results of the proposed position estimator based on the identified differential inductance The experiments were obtained by means of the test-bench shown in The linear positioning table M403.4DG from Physics Instruments was operated under position control with 200 nm resolution and was able to block the position with forces up to 50 N . The tabThe PWM frequency of the actuator was chosen to be 1 kHz in order to avoid a decrease of the differential inductance present at higher frequencies. In order to estimate the position based on the determined values of turation  and a cuion from , where aEquation . Thus, sThis work evaluated the position estimation on a use case scenario involving end-position detection for a switching solenoid actuator. In such a use case, only two current conditions, in particular zero mean current and full mean current (timation . In partThe proposed position estimator was validated in the use case scenario of an end-position detection for switching solenoid actuators. During this experiment, the actuator was either in zero mean current condition or in full mean current condition. The positioning table was able to move the plunger in a quasi-static condition over the entire position range and the position measured by the positioning table was compared to the position estimated by the discussed approach. The experiments were conducted in a short time so that the effect of temperature rise due to self-heating of the actuator could be considered small given the large thermal time constant of the system.In this work, the problem of ambiguities in position estimation for solenoid actuators based on the differential inductance has been addressed. In order to achieve a uniqueness of the position estimate, the eddy current losses inside the actuator are evaluated when a PWM voltage is applied. In particular, at the PWM switching instants, the current shows considerable cusps, which can be modeled by a lumped parameter model involving a resistor in parallel to the main inductor. This resistor exhibits a monotonous dependency on the position, thus allowing a unique position estimate.The discussed approaches for the identification of the differential inductance as well as the parallel resistance are computationally lightweight and require a reduced sampling effort. In particular, the Integrator-Based Direct Inductance Measurement technique, used for estimation of the differential inductance, requires seven samples per PWM period while the proposed parallel resistance estimator requires three samples per each PWM period. Thus, AD converters with low sampling rate and low performance microcontrollers can be used, thereby allowing the implementation of sensorless position estimation on solenoids used in cost-critical systems. In contrast to state-of-the-art works, the position is estimated by means of a small neural network, that weights and merges the different position-dependent parameter information. Therefore, the position estimator benefits from high accuracy and high SNR due to the identified value of the differential inductance and exhibits no ambiguities due to the identified value of the parallel resistor.Experimental validation involving a use case scenario for sensorless end-position detection proves the uniqueness, accuracy as well as high SNR of the approach. Nevertheless, the estimate still shows an error that is related to the negligence of hysteresis in the obtained characteristics. Therefore, identifying and compensating the hysteresis is a promising research aspect for further increase of accuracy. Moreover, the effect of temperature dependency has been neglected during the experiments. In industrial applications, the actuators are usually exposed to environments with large temperature variation, influencing the magnetic permeability and electrical conductivity of the used materials. Thus, further investigations on the temperature dependency of the position estimation need to be conducted.The IDIM method has been submitted for patenting and reference can be found in .


Car body parts are sometimes responsible for irritating noise caused by assembly defects. Typically, various types of noise are known to originate from within the interior trim panels of car doors. This noise is considered to be an important factor that degrades the emotional satisfaction of the driver of the car. This research suggests an in-process inspection system consisting of an inspection workstation and a noise detection method. The inspection workstation presses down the car door trim panel by using a pneumatic pusher while microphones record the acoustic signals directly above the door trim panel and on the four sides of the workstation. The collected signals are analyzed by the proposed noise detection method after applying noise reduction. The noise detection method determines the presence of irritating noise by using noise source localization in combination with the time difference of arrival method and the relative signal strengths. The performance of the in-process noise detection system was evaluated by conducting experiments on faulty and healthy car door trim panels. The powertrain, drivetrain, tire contact with the road surface, and climate-control system are considered to be major sources of annoying noise audible in the interior of a car. This noise can adversely affect the driver’s ability to concentrate . Recent The increasing attention paid to BSR noise has led a number of researchers to investigate and study the mechanical reason(s) for the noise. Broadly speaking, BSR noise is defined as noise that varies in the low-frequency band and is caused by movements between loosening or tightening assemblies while driving on the road ,7. More Increasing concerns about BSR noise have prompted automakers to pay attention to reduce this type of noise. Thus, another approach, namely conducting sampling inspection in the laboratory, has been suggested. These inspections are generally conducted by reproducing the bumpy road environment with artificial vibration generators containing shaker-fixtures . Most reIn this regard, the easiest way to remove the background noise is to filter the collected signal by applying a high-pass filter, which assumes the background noise to be primarily distributed in the low-frequency bands. However, the possibility of making an erroneous decision when removing all the low-frequency bands exists because the frequency components of the actual background noise are usually non-stationary. Thus, considering the non-stationary nature of background noise, methods based on time-frequency characterization such as wavelet transform, were suggested to reduce the accidental elimination of BSR noise .However, laboratory inspection is limited to representative vehicles to shorten the development cycle. Apart from this, sampling inspection methods pose the risk of affecting the quality of products, and therefore it is necessary to develop an efficient in-process inspection system ,16. In fTherefore, the necessity of developing inspection systems capable of conducting an inspection regarding the state of parts during the manufacturing process without affecting the cycle time has increased. This paper presents an in-process BSR noise detection system for car door trim panels. An inspection workstation is designed to reproduce situations in which an inspection engineer presses against the car door trim panel, and acoustic data are collected by two groups of microphones during the inspection. The presence of BSR noise is determined by applying the time difference of arrival and the relative signal strengths of the signals. The results of a practical test involving real car door trim panels provide empirical support for the detection performance of the developed system.The in-process BSR noise detection system consists of an inspection workstation and a noise detection method. The system is designed based on the assumptions about the acoustic signals shown in The conventional approach of noise detection using microphones is represented as in Therefore, we suggest the in-process BSR noise detection system depicted in Details of the constructed inspection station and the signal-processing procedure are introduced in subsequent sections.2. The acoustic signals are simultaneously captured by the two groups of microphones consisting of the microphone array and the parabolic microphones. The data acquisition system collects the acoustic signals at a sampling rate of 44,100 Hz, which is similar to that used by typical acoustic signal-processing methods. Each group of microphones is designed to concentrate on the respective different types of acoustic signals. The microphones of the microphone array are assumed to collect a mixture of abnormal noise, process noise, and background noise, whereas the parabolic microphones are assumed to intensively collect background noise only.We assumed that the inspection process is conducted at the end of the process in which the car door trim panels are manufactured. The fully assembled car door trim panel is transferred into the workstation and fixed to jigs installed at the bottom. Then, the car door trim panel is slowly pressed down for two seconds by the pneumatic pusher with a pressure of 10 kgf/cmThe microphone array is positioned 50 mm above the car door trim panel to enable it to more effectively capture the acoustic signals of the three different types of nose originating from the panel. The microphones are mounted at each vertex and corner of the acrylic rectangular plate, the size of which is sufficient to cover the car door trim panel. Surplus space between the microphones of the array is removed to allow the pneumatic pusher to operate. Because the number of microphones and the processing time of the noise detection method are proportionally related, it is necessary to determine the appropriate number of microphones. We conducted a simple test to compare the accuracy of noise source localization and processing time because the localization process is the most time-consuming step of the noise detection method.The space between the microphones is divided into uniform rectangles according to the arrangement of microphones. The precision of localization is determined by estimating the position at which noise is generated 10 times and by using 6, 9, and 12 microphones. As expected, the processing time increased sharply with the number of microphones, with the detection precision of 9 and 12 microphones being similar, whereas that obtained with 6 microphones was relatively low. Thus, 9 microphones were selected and installed as the microphone array.On the other hand, four parabolic microphones were installed in parallel at the center and pointing outward to the four corners of the system to capture the shop-floor background noise more effectively, while being insensitive to the sounds emitted inside the workstation during the inspection process. Each parabola is designed to have a holder to which to attach the microphone at its focus. Note that a parabolic microphone is useful to attenuate the noise originating from the back of the parabola .The proposed in-process BSR detection procedure consists of four phases as shown in ith microphone in the microphone array are defined as anarrayi[n], prarrayi[n], and bnarrayi[n], respectively, where i = 1, 2, …, 9 and n = 1, 2…, 200. The noise collected by the jth parabolic microphone is defined as anparaj[n], bnparaj[n], and prparaj[n], respectively. The signal collected by the ith microphone in the microphone array is defined as isi[n], and the signal collected by the jth parabolic microphone is defined as esj[n]. Assuming that the three types of noise are statistically independent, isi[n] and esi[n] can be represented as below:As mentioned before, the signals recorded by the microphones are categorized as originating from abnormal, process, and background noise. Specifically, the abnormal, process, and background noise collected by the n] and prparaj[n] are considered to be negligibly small in esj[n]. Then, we can rewrite (2) as below:Based on the nature of omnidirectional recording of parabolic microphones described in the previous section, the magnitudes of anparaj[arrayi[n], is defined as the noise generated during operation of the pneumatic pusher and the actuators for inspection and prarrayi[n] is the average of the signals collected by repeating the inspection 150 times with healthy car door trim panels. Because the collected signals are considered to contain both process noise and background noise, prarrayi[n] is obtained by applying noise reduction to the collected signal.The process noise, prarrayi[n] from isi[n] by removing prarrayi[n] and esj[n] as shown in i[n] and esj[n] are represented in the time-frequency domain by applying short time Fourier transform (STFT), ISi and ESj, where the window size w is determined as 172 and the size of the frequency bin m as 258. The time-frequency information of esj[n] is removed from ISi by applying a spectral subtraction method , which yields the spectrum of the remaining signal RSesi:i is obtained by removing the time-frequency information of prarrayi[n] from RSesi.The objective of the noise reduction step is to highlight ann method ,22,23, nj = 1, 2, …, 4. The remaining signal RSesi computed by using (4) is assumed to contain the abnormal noise and process noise. Subsequently, spectral subtraction is applied to RSesi to remove the spectrum of the process noise, PRarrayi. To do this, the attenuation factor for the spectral subtraction of The attenuation factor is generally obtained by averaging the time-frequency components of trained background noise. Some variants of spectral subtraction methods proposed over-estimation of the noise spectrum and spectral flooring for non-stationary noises ,24. Here factors ,26; henci[n] is obtained by applying inverse STFT to RSi.Finally, the spectrum of the remaining signal, RSi, is obtained as follows:i[n]. After applying noise reduction, the remaining signal, rsi[n] is assumed to contain abnormal noise only when the car door trim panel is faulty. Alternatively, rsi[n] is assumed to be null when the car door trim panel is healthy. The existence of any abnormal noise in rsi[n] is determined by comparing a measure of the signal in the form of the energy of the signal with the predefined threshold . If the energy of any rsi[n] is significantly larger than the reference energy, it leads to conclude that abnormal noise may exist.The reference energy as a threshold is obtained by averaging the energy of the noise-reduced signals that were recorded by repeating the inspections 150 times with healthy car door trim panels. In other words, the reference energies are assumed to have no significant power because the background noise and the process noise are removed. The reference energy of the nine microphones is compared with the energy of rsi[n] exceeds that of the threshold, then the remaining noise may contain background noise that has not been perfectly removed because of the limitation of the noise reduction method. Thus, determining the existence of abnormal noise in the remaining signal by only comparing the energy could lead to an ambiguous result. This problem was solved by considering the estimated location of the dominant signal in rsi[n] as supplementary information. If the dominant signal is estimated to exist inside the inspection workstation, abnormal noise is assumed to exist in rsi[n]. In the opposite case, rsi[n] is assumed to predominantly comprise residual background noise  is conducted by applying the hyperbolic time difference of arrivals (TDOA) method , is defined as the cross correlation between a signal of a fixed microphone and the ith microphone, rs1[n] and rsi[n], respectively, where i = 2, 3, …, 9. Specifically, gcci[n] is obtained by applying inverse fast Fourier transform (IFFT) to the multiplication of the weighting function and the cross-spectral density between rs1[n], and rsi[n] as follows  exceeds the predefined threshold, and further it is estimated that the noise is coming from inside the workstation. As a result, we can conclude that the panel is generating noise. Second, in cases of a healthy door trim panel as shown in i[n] can exceed the predefined threshold due to irregular background noise. However, by noise source localization, we can estimate that the noise is coming only from outside the workstation, and consequently we can conclude that the panel is healthy. Last, if the energy of rsi[n] does not exceed the predefined threshold as shown in We compared the performance of the proposed method with a popular noise reduction method using the high-pass filter. Note that the high-pass filter, by its nature, removed the pre-specified low-frequency components, assuming them as the background noise. The pass band of the filter was determined with empirical experiments and was set to be 500 Hz. As summarized in As mentioned earlier, the performance of the spectral subtraction highly depends on the parameters, and cannot process situations in which the spectrum of the background noise overlaps with the spectrum of abnormal noise. This problem could be solved by applying a machine-learning technique to spectral subtraction to reduce the musical noise. Alternatively, it would be necessary to develop a novel noise reduction method that assumes statistical dependence between the different types of noise.Regarding the errors generated during the noise source localization step, the arrival times may not be obtained accurately due to errors in the noise reduction. A problem would also arise when only a few of the microphones detected a signal that is not shared with all the others, in which case it could also reduce the accuracy of localization.In addition, abnormal detection utilizes only the energy of a signal, which does not consider the time-varying characteristics of the acoustic signals. A new detection method based on the pattern recognition technique would enable the types of BSR noise to be distinguished. The detection precision would also be increased because the patterns would be able to consider various characteristics of signals. This would not only improve the effectiveness of the algorithms, but also the configuration of the workstation.The acoustic signals are highly affected by the data collection environment, such as the direction of each microphone, and the presence of obstacles that generally cause signals to reverberate. The proposed methods could be used to assess the arrangement of the microphones and different shapes of the microphone array. We aim to implement these improvements in future studies by using empirical experiments.This study presented an in-process BSR noise detection system for car door trims. The system was developed for overcoming the limitations of the conventional BSR noise detection methods, such as model based pre-evaluation inspection, test-drive based pre-evaluation, and sampling inspection. To do so, the system installed the two groups of microphones and applied the noise reduction method.A signal analysis method that performs noise reduction, abnormal noise detection, and noise localization was applied to determine whether abnormal noise is present. In particular, the method utilizes a spectral subtraction method, hyperbolic TDOA approach, and compares the energy of signals. A total of 200 BSR inspection results with real car door trim panels demonstrated 99% accuracy for faulty car door trim panels, and 96% for healthy car door trim panels. The performance comparison with the high-pass filter-based method showed that the proposed method efficiently reduced the background noise while preserving the signal of interest.For further study, it is necessary to consider the spectral overlap between the signal of interest and the background noise. In other words, various sound sources must be efficiently separated to extract the frequency components of the signal of interest. Moreover, signal energy evaluation for noise detection decision can be further improved by applying pattern recognition techniques.