Virtual Reality (VR) technology uses computers to simulate the real world comprehensively. VR has been widely used in college teaching and has a huge application prospect. To better apply computer-aided instruction technology in music teaching, a music teaching system based on VR technology is proposed. First, a virtual piano is developed using the HTC Vive kit and the Leap Motion sensor fixed on the helmet as the hardware platform, and using Unity3D, related SteamVR plug-ins, and Leap Motion plug-ins as software platforms. Then, a gesture recognition algorithm is proposed and implemented. Specifically, the Dual Channel Convolutional Neural Network (DCCNN) is adopted to collect the user’s gesture command data. The dual-size convolution kernel is applied to extract the feature information in the image and the gesture command in the video, and then the DCCNN recognizes it. After the spatial and temporal information is extracted, Red-Green-Blue (RGB) color pattern images and optical flow images are input into the DCCNN. The prediction results are merged to obtain the final recognition result. The experimental results reveal that the recognition accuracy of DCCNN for the Curwen gesture is as high as 96%, and the recognition accuracy varies with different convolution kernels. By comparison, it is found that the recognition effect of DCCNN is affected by the size of the convolution kernel. Combining convolution kernels of size 5×5 and 7×7 can improve the recognition accuracy to 98%. The research results of this study can be used for music teaching piano and other VR products, with extensive popularization and application value. With the rapid growth of science and lifestyle change, the way of education and learning is also facing the challenge and opportunity of significant transformation and development. The coronavirus disease 2019 (COVID-19) outbreak has provided a broad space for the development of online music education, but there are many problems with online music teaching ,4. VirtuAt present, there are still many deficiencies in the music teaching system in schools, which can be divided into the following two aspects. 1. The use of modern teaching equipment and the corresponding teaching tools. Music classroom teaching enables students to understand music and through the audiovisual combination to learn music through sound. With the progress of technology and the country’s emphasis on education, multimedia devices have gradually entered the classroom of every school. Although multimedia facilities are available in some schools, they are not used to their fullest extent. Teachers need to use multimedia equipment to promote the classroom teaching of music and stimulate students’ interest in learning music by projecting pictures, videos, and recordings on multimedia. Students can learn about some performers’ classic works and so on. At the same time, to enable students to get closer to and understand music, the school also needs to be equipped with corresponding teaching tools, such as piano, electronic keyboard, cucurbit flute, flute, and other musical instruments. The purpose is to enable students to learn musical instruments in music lessons, learn music theory knowledge, and improve their musical literacy. 2. Innovation of teaching mode and teaching concept. Nowadays, to effectively improve the quality of music teaching in school and make students have good music literacy through music teaching, firstly, the traditional teaching mode and teaching concept should be completely changed. Combining with the requirements of the new curriculum standards, the quality education goal is taken as the guiding direction of students’ music teaching mode and concept. The "indoctrination" teaching method in the traditional teaching mode should be transformed, highlighting the main position of students in learning, actively communicating with students, and guiding them to fully realize the importance of music learning to their healthy growth.In this context, this study developed a virtual piano with an HTC Vive kit and Leap Motion sensor fixed on the helmet as the hardware platform, and Unity3D and related SteamVR plug-in and Leap Motion plug-in as the software platform. The virtual piano is composed of a virtual keyboard with Cube components. The script response function of being approached and pressed or released by Cube components is compiled to record the performance events of the virtual piano keyboard. The sound of the virtual piano is further realized with the help of the Musical Instrument Digital Interface (MIDI). To enhance the performance, a gesture recognition algorithm is proposed and implemented using machine learning (ML) theory. Specifically, Dual Channel Convolutional Neural Network (DCCNN) is used to collect the user’s gesture command data. The dual-size convolution kernel is employed to extract the feature information in the image and the gesture instruction in the video. Then the DCCNN recognizes it. After the spatial and temporal information is extracted, color pattern images and optical flow images of the Red-Green-Blue (RGB) are fed into the DCCNN, and the prediction results are merged to get the final recognition result. The gesture recognition algorithm implemented in this study can be used not only for the property setting of virtual piano but also for other VR products, which have a wide range of promotion and application value.In optimizing the music teaching system, many researchers have conducted in-depth explorations. Loveridge (2020)  pointed It can be seen that with the development of digital image technology, the gradual popularization of three-dimensional (3D) panorama is the breakthrough point, and image-based VR technology gradually stands out. 3D panorama has attracted more and more attention due to its low development cost, strong realism, and convenient and quick panorama generation. However, the independent panorama technology lacks audio, so the teaching materials combined with Unity3D will make students feel the real audio-visual world.In this study, the HTC Vive VR kit is adopted as the hardware platform of the virtual piano. A complete set of HTC Vive VR devices is displayed in The Vive uses Lighting House indoor location technology. Two rows of Light Emitting Diodes (LEDs) inside the locator emit a scanning beam six times per second that alternately scans a location space with 15*15 feet in horizontal and vertical directions. The HTC Vive has over 70 photosensitive sensors on the helmet and handles ,15. As tUnity3D is a professional game engine developed by Unity Technologies, which enables game developers to easily complete various game creativity and 3D interactive development ,18. UnitThe piano comprises 88 black and white keys, black and white keys separated by half a note, from left to right in the bass, middle and high registers. For simplicity, seven notes, do, re, mi, fa, so, la, and si, are set respectively in the bass, middle, and high registers of the developed virtual piano, with 21 white keys and 15 black chromatic keys. Canvas  is used During the performance, the MIDI keyboard sends the information by pressing the key to the computer in real-time, and the computer records the info individually. After the music is played, the MIDI format document is kept –26. DuriIn Each key-playing event of the virtual piano and its property-changing event are recorded in the programmed array. The data recorded in the array is saved to a hard disk file. A MIDI file header is added to the file according to the MIDI specification, which can realize the MIDI file archive of the music played by the virtual piano. MIDI files usually start with a header block followed by one or more track blocks, with header blocks marked by ASCII code MThd and track blocks marked by ASCII code MTrk. The specific composition of the header block of a MIDI file contains information such as header type, header length, and data section. The header length is a variable constant, and the highest bit of each byte is the flag bit. The data section involves format, track number, partition, and a total of 3 16-bit bytes, which need to store high; The track block consists of a series of data streams made up of MIDI messages that are actually repositories of file song content data.Syntax and format for header blocks:<Header type><Header length><Format><Number of tracks><Partition><4d546864><00000006><ffff><nnnn><dddd>The ID of the header block and track block is 0x4D546864 and 0x4D54726B; "00000006" is the number of bytes describing the length information of the header block. Currently, in MIDI protocol, this value is fixed at 6. "ffff" indicates a track format, which is generally a synchronous multi-track format; "dddd" specifies the basic time format type, which can be of two types. Type 1 defines the tick number of a quarter note, the tick being the smallest unit of time in MIDI. Type 2 defines the number of Simple Mail Transfer Protocol (SMTPE) frames per second and the tick of each SMTPE frame.Solfeggio is the skill of reading music scores using visual, auditory, and other perceptual methods. Solfeggio is helpful for students to quickly master the melody of music, enhance their perception and understanding of music, and improve their performance level. Rapid reflexes from vision to singing are required in this process, which requires intensive training. Some researchers use Convolutional Neural Networks (CNNs) combined with video tracking technology to identify the object. However, how to show the dynamic rhythm of singing and make the teaching process more straightforward and effective remains an open question. Curwen gesture by Hungarian music educator John. Curwen was created and used in music teaching. Thus, applying Curwen gesture to music perception teaching can increase learning interest, improve intonation, and enrich learning content. The main research content of this study is how to use the computer to recognize gestures in music teaching and establish the HCI music perception teaching method. The Curwen gesture is demonstrated in CNN is a feedforward neural network that includes convolution computation. It can perform supervised and unsupervised learning by mimicking the visual mechanism of the human eye. The convolution kernel parameters in the hidden layer have the characteristics of weight sharing and interlayer connection, which makes it possible to learn the features of grid-like topology with reduced computation. As a result, CNN is often used to process images and speech. The structure of CNN consists of input, hidden, and output layers. The input layer can handle multidimensional data and must standardize input characteristics. The output layer can use logical or normalized functions to output the category tags. The hidden layer usually contains three common layers: convolutional layer, pooling layer, and fully connected (FC) layer, among which the convolutional and pooling layers are the unique structure of CNN. The convolutional layer contains the weight coefficient, while the pooling layer does not. The specific CNN structure is shown in DCCNN is employed to recognize static gestures and extract advanced features to realize advanced recognition of multiple gestures, avoiding the preprocessing of traditional gesture recognition. DCCNN can obtain advanced features of different granularity and enhance gesture recognition.CNN can extract the required features after training. In general, CNN has multiple convolutional and pooling layers. There are many convolution kernels in the convolutional layer to extract local features, and each convolution kernel can map a featured image. Under the same conditions, a small convolution kernel can increase the feature information, reduce the number of parameters, and improve the recognition effect. Therefore, the recognition effect of multiple small convolution kernels is higher than that of large convolution kernels. If the convolution kernels are too small, image features may not be extracted. Traditional CNN uses a fixed-size convolution kernel, so the image granularity is also fixed. Thereby, some features will be lost during the learning process, thus reducing the accuracy of network recognition. DCCNN with dual size convolution kernel has two convolution layers, two pooling layers, and one FC layer, as plotted in Dynamic gestures contain more information about motion than static gestures. Therefore, how to recognize the gesture is the focus of this section. The optical flow characteristics of the video are analyzed, and the motion information of the video is identified by DCCNN. Video information is divided into spatial information and temporal information. Spatial information refers to the surface information of video frames, while temporal information refers to the optical flow between frames. Thus, spatial and temporal information is extracted from RGB and optical flow images, and DCCNN is applied to identify motion information. The two images are input into the network, respectively, and the predicted results of each network are combined to form the final recognition result. DCCNN consists of two dimensions, space and time, respectively processing spatial and temporal information. One is single-frame CNN, where videos are input via single-frame RGB images to describe the spatial characteristics of the images; Another CNN inputs the video through dense optical streams of multiple frames to describe the temporal properties of the video, combining the two networks to identify the video. DCCNN can acquire motion information of video data effectively. CNN is used to convolve, merge and fully connect spatial feature images and temporal images, and recognize video by combining spatial and temporal features.The constructed DCCNN structure uses a convolution kernel in the convolutional layer to convolve single-frame images and multi-frame optical flow images. Its structure is portrayed in To verify the influence of the size of the DCCNN kernel on the recognition effect, two parallel experiments are conducted using convolution kernels of different sizes, and the results are denoted in The learning curve of the neural network is suggested in The learning curve is to display the performance of the network against new data by calculating the accuracy and cross-validation of the training set under different training set sizes, to determine whether the variance or deviation of the network is too high and whether increasing the training set can reduce the overfitting phenomenon of CNN. The three types of cellular neural networks involved were tested using training from scratch, pre-training spatial network, and cross-input pre-training strategies, and the results are illustrated in According to the actual demand, the constructed music teaching system based on the VR system has been subjected to two stress tests, and the test results are exhibited in As can be seen from the experimental results of the system pressure test in The results of the system comparison test are outlined in In This study uses two data sets from ChaLearn Gesture Dataset (CGD)2011 and Jester for training. The recognition accuracy of the two-stream CNN proposed by Solanki and Pandey (2019) , the twoWith the popularity of modern computers, smartphones, and other smart terminals, VR technology will be widely used and further challenge the traditional music teaching mode. Therefore, the application of VR technology in music teaching will be more extensive, such as rhythm skills training. VR technology can simulate related music equipment and construct related equipment simulation training. This study studies the music teaching system based on a virtual simulation system. A virtual piano is developed with Unity3D and related SteamVR plug-in and Leap Motion plug-in as the software platform and HTC Vive kit and Leap Motion sensor fixed on the helmet as the hardware platform. Based on ML theory, a gesture recognition algorithm is proposed and implemented. Specifically, DCCNN is adopted to collect gesture command data of users, and a dual-size convolution kernel is applied to extract feature information in images and gesture commands in videos. The DCCNN then recognizes it. Future work will focus on the above two aspects. (1) The model’s compatibility is further improved, and the code is optimized. (2) Relevant data will be further collected to construct reasonable datasets to understand the actual situation and optimize the model.S1 Data(ZIP)Click here for additional data file.


Genome-wide association studies have proven their ability to improve human health outcomes by identifying genotypes associated with phenotypes. Various works have attempted to predict the risk of diseases for individuals based on genotype data. This prediction can either be considered as an analysis model that can lead to a better understanding of gene functions that underlie human disease or as a black box in order to be used in decision support systems and in early disease detection. Deep learning techniques have gained more popularity recently. In this work, we propose a deep-learning framework for disease risk prediction. The proposed framework employs a multilayer perceptron (MLP) in order to predict individuals’ disease status. The proposed framework was applied to the Wellcome Trust Case-Control Consortium (WTCCC), the UK National Blood Service (NBS) Control Group, and the 1958 British Birth Cohort (58C) datasets. The performance comparison of the proposed framework showed that the proposed approach outperformed the other methods in predicting disease risk, achieving an area under the curve (AUC) up to 0.94. The human genome is the whole set of deoxyribonucleic acid (DNA) sequences in humans, which consists of approximately three billion base pairs ,2. HumanGenome-wide association studies (GWASs) have proven their ability to unveil susceptibility variants in human diseases ,4. TheseMany machine learning algorithms have been applied to SNP data analysis in order to build a model that is able to predict disease risk for unseen samples. However, the process of developing a risk prediction system using genomic data is computationally expensive due to the extremely high dimensionality number of features. Consequently, it has become essential to provide the classifier with a manageable number of discriminative SNPs. Moreover, selecting the most convenient classification algorithm for building the prediction model is also a crucial step for achieving high model performance. Traditional machine learning techniques have been successfully employed in GWASs for risk prediction ,20. HoweMachine learning techniques have been effectively used in a variety of disease risk prediction systems based on human genomic variations . The autThe authors in  comparedp-value of their association with the phenotype of interest to control the number of selected SNPs and use the top associated SNPs as input to a prediction algorithm [p-value could limit the opportunity to identify inter-SNP correlations [p-value thresholds. Moreover, in [Risk prediction methods typically apply different techniques in order to select a manageable number of SNPs. Most studies rank SNPs based on the lgorithm . Howeverelations ,44. Moreelations , it was In this work, an accurate deep-learning framework for complex disease risk prediction has been proposed. An adequate subset of SNPs that are highly correlated and non-redundant has been selected using the Joint Mutual Information (JMI) method . Then, tp-value Genotype data were obtained from the WTCCC  for sevete of 5% ,50,51,52Mutation exists in the gene copy that is inherited from both parents. The allele frequencies are represented by A and B for the major allele frequency and minor allele frequency, respectively. Any given SNP could have the value of AA or BB to indicate that it is a homozygous SNP and the value of AB for a heterozygous SNP. In this proposed work, we used the additive model to encode SNPs. The encoding technique counts the minor allele appearance. Consequently, the coding value 0 represents AA, 1 represents AB, and 2 represents BB. Finally, after implementing the aforementioned coding technique, the dataset is represented in numerical format.n samples and q SNPs, which can be represented by a j for the sample i. Let If a dataset consists of The proposed framework predicts the risk of an examined disease using SNP data. An MLP-based binary classifier has been developed to predict the disease risk status. A mutual information feature selection technique has been applied to decrease the feature space dimensionality and select the most discriminative SNPs. The dataset was split into (70%) training and (30%) testing sets, keeping the class ratio of each group similar to that of the whole dataset, and the testing data were only used for analysing the predictive power of the proposed system as illustrated in The extremely large number of SNPs in the genome makes the application of machine learning techniques on SNP data computationally impossible. Consequently, the application of feature selection techniques is necessary for the selection of a significantly smaller subset of SNPs. Statistical and machine learning-based feature selection methods have demonstrated their ability to select an optimal SNP subset out of the whole genome ,53. In tMutual information feature selection methods have been widely applied in the biomedical field . Mutual Y. JMI uses mutual Information to measure the amount of relevancy and redundancy between features. JMI calculates not only mutual information between features and the class label but also takes into consideration the correlation between the new feature and already selected features D, thus ensuring a good trade-off between relevancy and redundancy [Y and is highly complementary to the already picked features j in D. The JMI for a feature JMI is a popular feature selection technique that selects a subset of features to maintain a high feature association and maximum correlation with the class of interest . This medundancy . A higheD. F-fold cross-validation has been applied in order to create a matrix q being the number of SNPs of each sample and In this work, JMI was applied over the training set to select a subset of SNPs, W for a given SNP j is calculated as presented in Equation  are modelling tools inspired by the function of neurons in the human brain. These networks offer an alternative way to handle complex problems and are able to perform predictions for linear/nonlinear problems. Multi-Layer Perceptron (MLP) is one of the popular feed-forward neural networks that consists of an input, hidden, and output layer. In this work, the feedforward MLP consisting of one input layer and one output layer along with five hidden layers has been employed, as conceptualised in L, the input is the sum of the weights for each neuron with a bias after applying an activation function in layer The input feature vectors are passed through the multiple hidden layers downstream to the output layer . The feay can be gained by Equation y=f. The proposed models’ hyperparameters have been optimised using a grid search of the k-fold cross-validation technique with k = 3. This technique can ensure how accurately the model would perform in practice and avoid overfitting. Since we are implementing our model on different diseases, a modular model consisting of multiple modules is used. While similarities between models are possible, training the models separately means that all the architectures are optimised using various hyperparameters. After implementing a grid-based search, all possible hyperparameter value combinations have been examined. The best performances have been achieved with five hidden layers and 512 neurons in each hidden layer for all dataset models. Different activation functions for the hidden layers were evaluated: the tanh function performed the best out of the examined activation functions in three datasets, namely RA, T1D, and T2D, while the relu function performed better in CAD and IBD. The best performance of the HT dataset has been achieved using the sigmoid function. The softmax function was used in the output layer for all models. The softmax activation function used in our model is presented in Equation softDifferent optimizers were used as a learning algorithm. The Adam optimizer outperforms the compared optimisation functions in most models. For BD and HT datasets, the best optimizers were NADAM and rmsprop activation functions, respectively. However, for the other parameters, all models achieved their best performance using the same values. In order to avoid model overfitting, a dropout technique that drops neurons randomly along with their connections has been used with a probability of 0.6. The best performance was achieved using 200 epochs for all models. Finally, the best learning rate was achieved using a 0.001 learning rate. The proposed models can be validated using test data in order to demonstrate their high-performance ability. Possible hyperparameter values are given in After building the networks and optimising the parameters on the seven aforementioned complex disease datasets, we came up with more than one model: the first one uses the same hyperparameters for three datasets , and the model uses the Adam optimizer and tanh activation function. A slight difference was implemented by using the relu activation function in the CAD and T1D datasets. On the other hand, two more models were implemented using NADAM, tanh and rmsprop, sigmoid as optimiser and activation functions, respectively. Finally, the proposed models can be validated using test data in order to demonstrate their high-performance ability.N data points, where ith data point.The cross-entropy cost function, which is explained in Equation , has beeDifferent experiments were conducted to evaluate the performance of the examined deep learning prediction architecture in terms of accuracy (Equation ), sensitEach dataset was split into two main parts: 70% for training the system and 30% for testing the system. Furthermore, in order to identify the optimum features subset, a five-fold cross-validation technique was implemented to train data during the feature selection process. To this end, the training samples were shuffled and split into five groups. The splitting kept the ratio of the classes similar in each group to that of the original dataset. Then, the experiment of selecting features was repeated five times, and at each fold we used one group for testing the model and the remaining four groups as a training set. The final classification performance results were computed using the 30% of the original dataset that was unseen by the feature selection and training phases.a were selected for the final feature vector.At the end of the fifth fold of the feature selection process, each SNP had a weight value, depending on how many times the SNP has been selected. SNPs with weights larger than the threshold value The threshold value was selected experimentally, by evaluating different values and selecting the optimal value, as shown in The performance of the examined prediction deep neural network approach for each dataset in terms of accuracy, sensitivity, precision, F1 score, and MCC is presented in The proposed MLP was compared with other state-of-the-art machine learning techniques. The best performance with the compared techniques was achieved using SVM and linear discriminant analysis (LDA). A comparison of SVM, LDA, and the proposed MLP performance in terms of F1 score is shown in Finally, we compared our proposed system prediction performance against other studies conducted on the WTCCC datasets as presented in Applying deep learning techniques to complex disease genomic datasets is not a trivial task, and the pre-processing of the data can be highly affected by many factors leading to a severe impact on the final conclusions. The proposed framework was able to select a subset of high discriminative SNPs that contributed to improving the prediction ability. A number of SNPs that have been identified with high discriminative values in our proposed system have been previously identified to be associated with diseases in other published works. Out of the selected SNPs, 75 SNPs were identified to be highly correlated with different diseases in the original dataset , 23 SNPsIn this work, a deep learning approach using MLP has been proposed to predict the risk of complex diseases based on genomic variations. The proposed approach exploits the JMI filter feature selection method in order to select a subset of SNPs with high discriminative power. The selected features are then fed to an MLP-based prediction algorithm to distinguish between healthy and affected samples. The proposed model has been evaluated on seven state-of-the-art datasets from WTCCC, UKNBS, and 58C. The experiment results demonstrate the superiority of the proposed model as compared to the traditional machine learning techniques, achieving an F1-score of 0.94. Moreover, the obtained results have been compared with state-of-the-art methods that were applied on the same datasets. An improvement in terms of an AUC of up to 22% compared to previous methods was achieved using the proposed approach. The proposed framework was also able to identify a number of SNPs that have high discriminative value and were previously identified to be linked with diseases in other published work. Taking into consideration the obtained prediction performance, as well as the performance of other methods proposed in the literature, it is evident that the proposed approach is applicable and efficient for complex disease risk prediction from SNP data.


Demand of Power electronics converter is increased due to the rapid increase of green re-sources. The distributed nature of uncontrolled renewable energy resources are connected with the grid via power electronics converter. DC-DC converters are high-frequency current conversion circuits that use transformers, inductors, and capacitors to smooth switching noise into regulated DC voltages. In this study, a comparative performance analysis of Proportional integral Derivative (PID) and fuzzy logic controller (FLC) for DC-DC Boost Converter is presented. PID-based controller for dynamic boosting of DC-DC boost converter was replaced by Fuzzy Inference system (FIS) to study the system behavior. Five different membership functions were performed to observe the response of the system for DC -DC boost converter with FIS controller. The performances of FIS-based controller and PID-based controller for DC-DC boost converter were compared in detail. Also, the proposed techniques for the switching mode of DC-DC converter have been applied. The performance analysis of both PID and fuzzy controller was simulated using MAT LAB. The results of FIS based approach are better than PID based controller in terms of transient responses. Demand of Power electronics converter is increased due to the rapid increase of green re-sources. The distributed nature of uncontrolled renewable energy resources are connected with the grid via power electronics converter . DependiThe new three-port converter that merge Buck-Boost and dual-active bridge converters has been suggested by author in reference  and concFuzzy logic resembles a human decision methodology for vague and inaccurate information. This makes the real-world problems considerably simpler and is based on truth rather than the usual truth or falseness or 1/0 as Boolean logic. The fuzzy logic approach of control encourages people to learn, without requiring effort, the unpredictability of machines, since it lets them assume the correct points without a clear idea of the path to reach. By utilizing the fuzzy logic control concept, qualitative and heuristic considerations that cannot be handled by conventional control theory can be used for control function in a systematic form. In references , 19 FLC Despite its numerous advantages, FLC is not without its drawbacks. The most significant of these is that when developing a fuzzy controller, the trial and error method is typically required. In order to develop a fuzzy controller, no systematic procedure has been established in –24. TypiIn literature fuzzy logic controllers have been applied for the proposed problem, however, the various structure of FLC controller has not been addressed.The literature also revealed that said problem with varying voltage levels and loads have not been incorporated properly.Heuristic knowledge based rules can be incorporated into the controller’s fuzzy logic implementation.Five different membership functions were carried out to observe the response of the system for DC-DC boost converter using FIS controller.The parameters of the proposed controllers are optimized by a Ziegler-Nichols (ZN) based closed loop strategy to enhance the stability of the system.Further, the proposed techniques have been assessed on different modes of the converter.The boost converter, also called a step-up converter, is a DC-to-DC converter that increases voltage and decreases current from a given input (supply) to the desired output (load). Double semiconductors (transistor and diode) and an energy storage component make up this variety of switched-mode power supply . It is common practice to add capacitor-based filters to the converter’s output (load-side filter) and input to smooth out the voltage (supply-side filter). The basic structure of the boost converter is depicted in Because Ve is less than Vs in a boost converter, hence the output current is smaller than input current and can be states as:The primary driving principle of a boost converter is the inductor’s tendency to produce and reverse polarity when the magnetic field is rapidly fluctuated. When the switch is turned off, current flows in the direction of the winding and a small magnetic field is induced, thereby allowing energy to be accumulated in the inductor. When the switch is opened, a higher impedance will decrease the current. During the on-site conversion, the inductor current will decrease until the current persists to the load. Therefore, the capacitor is charged by the diode (D) from two sources in series which cause higher voltages , 31. The1) Continuous mode: For the inductor current to remain constant between cycles, the DC voltage across the inductor must be at zero in the steady state. Because the inductor’s voltage drop is directly proportional to the inductor’s current rise. So average value of Vs isIf we consider a diode with no voltage drop and a capacitor large enough to keep its voltage constant and can be represented as:Variation of IL through the Off-period can be represented as:Considering that the entire system is in a constant state, the quantity of energy utilized at the start and conclusion of a communication cycle must be identical. The inductor’s stored energy can be expressed as:Therefore, the current required at the start and at the end of the commutation cycle must be equal and overall, the current has remained constant2) Discontinuous mode: The inductor current value drops to zero in this mode, which is typical of DC-DC converters. However, in continuous conduction mode, the inductor current is constantly flowing and never stops. For this reason, in discontinuous conduction mode, the inductor current does not remain constant throughout the cycle but rather decays to zero well before the end of the period. The inductance mode of continuous conduction is greater than the inductance mode of discontinuous conduction. If the diode current is greater than the ripple current, the diode will always be turned on, regardless of the polarity of the applied to the switch. When the current through the DC leg of the inductor is less than through the RL, the overall current through the diode is zero. Until the diode is opened, the diode will cease to conduct, and its voltage will be at zero. To generate a higher output voltage, the DCM circuit’s duty cycle ratio is based on both the input and output voltages and the switching frequency. Discontinuous inductance for the boost converter as:Duty cycle for DCM isThe proportional gain in PID controller increased the control signal and overshoot of the system and also it does not eliminate the steady-state error. By including an integral component in the controller, the rising time is decreased, the overshoot and settling times are increased, and the steady-state error is decreased . The resThe primary disadvantage of PID controllers is their inability to adapt with nonlinear systems and approach the improved performance. It will have a dynamic response, produce overshoot, have a long settling time, and long rise time, all of which will affect the boost converter’s output voltage (step-up). The basic structure of FIS is given in FIS based controller, has been design and implemented for DC-DC boost converter by employing the same parameters of the PID controller. The performance of the system has been assessed for three different cases depicted in Different scenarios have also been validate using Fuzzy logic based PID controller. For case 1 the simulation was run for 0.05 seconds using Matlab/Simulink tool. Here in this case single 15 ohms resistor are used. The reference voltage increases from 200V to 300V. FLC is used to simulate a DC-DC converter with the same parameters as those listed in In this paper, PID and FLC controllers are designed to control the output voltage of the inverter. The results of the output voltage of the inverter reveals that the FLC based controller has minimum overshoot and produces high gain in the output voltage compared to the PID controller. Moreover, five different reminiscence functions have been performed to observe the response of the system for the DC-DC boost converter using FIS, which gives a lower settling time for the FLC compared to the PID controller. Moreover, the fuzzy controller shows good stabilization characteristics while it does not need to know the mathematical model of the boost converter in the controller design process compared to the PID controller. Therefore, it can be concluded that the FLC provides better performance in terms of overshoot limitation and sensitivity to parameter changes compared to PID controller. The FLC also shows significant reduction in noise and settling time during switching operation compared to PID controller. Therefore, this study shows that the FLC is an intelligent controller with good transient response for the proposed problem compared to the PID controller. The experimental results will be considered in future studies to evaluate the performance of the same system as well as more complex system incorporating with fuel cell in distributed power system.S1 File(TXT)Click here for additional data file.


This paper presents a novel analytical solution for journal-bearing viscoelastic lubrication using the perturbation method. The nonlinear Giesekus model was used for the constitutive equations to study the effects of fluid elasticity, shear-thinning viscometric functions, and strain-hardening elongational viscosity of viscoelastic lubrication. The investigation focuses on the impact of characteristic parameters such as mobility factor, eccentricity ratio, and Weissenberg number on the fluid film pressure distribution, load capacity, and shear stress. Although distinguishing between the normal stress differences and extensional viscosity in mixed viscoelastic flows is complicated, we investigated the role and contribution of these two factors. By increasing the elasticity of the fluid, the portion of both mentioned parameters increases consequently. Furthermore, analyses and comparisons show the contributions of the first normal stress and elongational viscosity to the load capacity of the bearing through the stress ratio and flow type parameter for the first time. The research findings indicate that fluid elasticity enhances the load capacity of the bearing compared to a Newtonian lubricant with the same effective viscosity. Moreover, the bearing load capacity is divided into two regions. In the linear region, the mobility factor and Weissenberg numbers have minimal effects leading to a linear increase in the load distribution, and in the exponential region, the load capacity changes are considerable. This research provides valuable insights into the behavior of viscoelastic lubrication in journal-bearing systems. This ultimately led to the development of hydrodynamic lubrication, the foundation of modern lubrication theory. He also calculated the pressure distribution of the fluid film and reported the results.Despite decades of research, finding an exact analytical solution for the Reynolds equation governing journal-bearing lubrication remains a challenging problem. The primary objectives of lubrication include reducing friction, preventing heat generation, and minimizing wear on rotating components. To achieve these objectives, a thin film of lubricant separates the shaft from the bearing. Tower4 used the brief forms of Navier–Stokes and continuity equations to obtain a second-order differential equation for the pressure distribution of lubrication film. Sommerfeld5 was the first to introduce a series of dimensionless numbers relevant to bearings, among which the Sommerfeld number stands out as particularly important. Solving the lubrication equation is a complex problem that has captured the interest of numerous researchers. Dowson6 studied the generalized Reynolds equation for the lubricant layer. Raimondi and Boyd9 used an iterative method to solve the Reynolds equation numerically. And in 1958, they presented three papers on the numerical solution of the Reynolds equation for journal bearings. A large volume of data was available for designers for the first time.Reynolds10 investigated the problem of hydrodynamic lubrication of journal bearings for compressible lubricants. The results of Raimondi’s numerical solution were very accurate and had an acceptable agreement with the experimental results. Reddi11 solved the problem of lubrication for the incompressible lubricant using the finite element numerical method. He described the advantages of finite element methods over other numerical methods. Reddi and Chu12 then generalized the solutions for the compressible lubricant using the finite element method.Using the finite difference method, Raimondi13 used the finite element method to investigate gas-bearing lubrication. He applied a slip condition to the surfaces and examined the different parameters of the bearing. Dinariev14 extended the Reynolds theory for the hydrodynamic lubrication problem in the presence of a viscoelastic lubricant. Based on his qualitative and numerical analysis, the relaxation time effect expanded the pressure distribution and reduced the bearing capacity of a lubricating layer. Urreta et al.15 summarize the work developing hydrodynamic lubricated journal bearings with magnetic fluids. Sfyris and Chasalevris16 obtained an exact solution for the Reynolds equation while assuming a Newtonian fluid and considering time dependency. They implemented this solution for a finite journal bearing. They used their exact solution results and examined the characteristics of journal bearing while assuming a Newtonian fluid17. Rao et al.18 analytically solved the Reynolds equation for sliding and journal bearings while considering slip boundary conditions. Vignolo et al.19 solved the Reynolds equation for a finite-length bearing. They used the perturbation method and regarded the term .20 continued Gustavo’s solution and solved the unsteady Reynolds equation.Malik21 studied the misaligned journal bearing and investigated the effect of the deviation on the static and dynamic characteristics of the bearing. Most studies dealing with bearing lubrication start with the well-known Reynolds equation. This equation is known as the classic lubrication theory of fluid film and is based on the Newtonian fluid. However, in many applications of lubricants in different industries, the approximation of the Newtonian fluid model cannot be used for the lubricants.Another common subject in bearing studies is misalignment. Jang and Khonsari22. A decade of studies has determined the effects of lubricants on polymer structures. In most cases, polymeric lubricants perform better than Newtonian ones23. One of the early investigations on finite-width journal bearing using non-Newtonian fluid was done by Tayal et al.24. They used the Prandtl model to study the shear thinning and shear thickening of lubricant in cylindrical coordinates. Horowitz and Steidler25 examined the effect of non-Newtonian oil on finite bearing characteristics by employing a logarithmic function for viscosity alternations. Tanner26 focused on a power-law fluid for a short journal bearing.Based on the literature, using a few long-chain polymeric additives could improve the lubrication with much higher efficiency. In the mid-1950s, converting Newtonian lubricants to non-Newtonian lubricants by adding mineral oils became an accepted method28 investigated the necessary parameters of a journal bearing for a pseudo-plastic fluid assuming a finite width. Swamy29 computed the load capacity of non-Newtonian lubricants in limited-length journal bearings and showed that using non-Newtonian lubricants increases the load capacity. They examined the damping properties of non-Newtonian lubricants in journal bearings besides the effect of non-Newtonian lubricants on fluid instability. They reported that non-Newtonian lubricants are more stable than Newtonian ones30. Raghunandana et al.31 employed the non-Newtonian model developed by Dien and Elrod to find the stability margin for different support parameters of non-Newtonian lubricants.Wada and Hayashi.33 examined the performance of a hydrodynamic journal bearing under a micropolar lubricant. Abdel-Rahman34 studied the flow of non-Newtonian lubricant through a conical bearing in an external magnetic field. Elsharkawy35 used a finite difference scheme to solve a modified form of the Reynolds equation to investigate the effect of geometry, pressure distribution, load carrying capacity, side leakage flow, and friction factor. The results demonstrated that additives increase the load-carrying capacity but decrease friction and side leakage coefficient. Tian et al.36 simulated the non-Newtonian fluid between eccentric cylinders with the finite element method. In their study, the flow in the annular gap between the eccentric rotating cylinders was a shear-extensional controllable flow. Sakim et al.37 showed that couple stresses improve the load capacity and reduce friction, while permeability and deformation of a porous elastic journal bearing have reverse trends. Chetti and Zouggar38 presented a numerical study of the effect of elastic deformation on the static characteristics of a circular journal bearing operating with non-Newtonian fluids obeying the power law model. Li et al.39 numerically solved the generalized Reynolds equation, heat conduction, and energy equations to study variations in bearing performance due to misalignment. They also showed that thermal effect and surface roughness considerably influence lubrication performance. Gwynllyw and Phillips40 investigated the effect of relaxation time and gap size considering the PTT and the Oldroyd-B constitutive equation. Gertzos et al.41 simulated a bearing with Bingham fluid as the lubricant using the commercial software Fluent. Lin42 examined the non-Newtonian effect of couple stresses of short journal bearing. The Study showed that decreasing values of the system parameter for constant couple stress parameters can shift sub-critical bifurcation into super-critical bifurcation. Wierzcholski43 used the Rivlin-Ericksen constitutive equation to model and solve the lubrication problem for a micro-bearing. Guemmadi and Ouibrahim44 investigated the behavior of the generalized Maxwell viscoelastic fluid for lubrication of a journal bearing by applying a finite volume method.Das et al45 used Maxwell's convective equation to study the effect of the Deborah number on the pressure distribution. He solved the problem concerning the perturbation theory, and the Deborah number was considered as perturbation parameter. Huang et al.46 calculated the pressure distribution for sliding and journal bearings, using a second-order fluid model. By varying the thickness of the fluid film, they discovered that the normal stress distribution was strictly dependent on the thickness. When it decreased, the normal stresses for a second-order fluid increased. Akyildiz and Bellout47 investigated the pressure distribution of a slider bearing for a PTT lubricant. They focused on the effect of the Deborah number on the pressure field. Kumar and Sharma48 evaluated a conical hybrid journal bearing with micro-grooves while considering the shear-thinning and piezo-viscous behaviors of the lubricant. Chetti et al.49 presented a theoretical study of the effects of elastic deformation and viscosity variation with pressure on the performance characteristics of a circular journal bearing lubricated with non-Newtonian fluids, considering the Barus law and the power law model. Mokhtari et al.50 looked into the Deborah number's impact on the pressure distribution and other characteristics using a FENE-P lubricant. Ahmed and Biancofiore51 proposed a new modeling technique based on lubrication theory, considering the viscoelastic effects. As a result, they obtained a modified equation for the pressure, i.e., the viscoelastic Reynolds (VR) equation. They also52 extended the VR approach to the non-linear finitely extensible non-linear elastic (FENE) type constitutive relations that account for the finite extension of the polymer chains and shear thinning. Soni53 investigated the numerical solution to predict the dynamic performance of finite bearing considering the combined influence of turbulence regime and non-Newtonian flow. Agrawal and Sharma54 examined the performance of micro-grooved hole-entry hybrid spherical thrust bearing (HSTB), considering the non-Newtonian behavior of the lubricant. Hashemabadi and Mirnajafizadeh55 solved the lubrication problem analytically by considering the SPTT model as representing fluid. They investigated the effects of some variables on velocity and pressure distribution. They also examined the impacts of changing the slope of the slider bearing.Tichy.56 considered the upper-convected Maxwell model (UCM) to study the lubrication problem. In addition to the Deborah number, they also took interest in eccentricity (ε) effects. They showed that the viscoelastic property of the fluid causes increase of the lubricant’s pressure distribution and positively affects the lubrication procedure. Nessil et al.57 analyzed various aspects of lubrication theory, including heat transfer for a power-law fluid, and discussed the hydrodynamic parameters of the bearing. They concluded that the power-law index (n) plays a significant role in temperature distribution. Further, they examined the load capacity, pressure distribution, temperature distribution, and frictional force. Li58 conducted a study on non-Newtonian lubrication. The PTT constitutive equation represented the lubricant fluid, and they considered the Deborah number as the perturbation parameter. Soni and Vakharia59 studied turbulence effects in addition to the non-Newtonian influence of lubricants in cylindrical coordinates for a finite journal bearing. Ng and Pan's linear turbulence model was applied in the finite element method to analyze the problem. Abbaspur et al.60 analyzed the viscoelastic lubrication of a thrust bearing using the Giesekus constitutive equation. In their work, Cartesian coordinates were employed, while the present investigation necessitated the use of polar coordinates due to the journal bearing geometry. They used perturbation theory and considered the mobility factor as the perturbation parameter. From the geometry perspective, it is worth mentioning that the current study focused on the journal bearing , whereas in the Abbaspur et al.60 the geometry was sliding bearing with reciprocating motion. in the current study for the first time, the role of two parameters for journal bearings: the elongational viscosity and the first normal stress difference compared.Li et al61, and Phan-Thein-Tanner (PTT) model62 are better choices. Viscoelasticity is the property of a material to demonstrates both viscous and elastic properties under the same conditions when it undergoes deformation. Broadly speaking, viscoelasticity is divided into two major fields: linear and nonlinear. Linear viscoelasticity is the field of rheology devoted to the study of viscoelastic materials under very small strain or deformation where the displacement gradients are very small, and a linear relationship between stress and rate of strain for linear materials can describe the flow regime. In principle, the strain has to be sufficiently small so that the material's structure remains unperturbed by the flow history64. The linear viscoelastic models have several limitations. For example, they cannot describe strain rate dependence of viscosity or normal stress difference phenomena since they are nonlinear effects. Due to the restriction to infinitesimal deformations, the linear models may be more appropriate for describing viscoelastic solids rather than viscoelastic fluids. Despite the limitations of the linear viscoelastic models and despite being of less interest to the study of flow where the material is usually subject to large deformation, they are very important in the study of viscoelasticity for several reasons66.They are used to characterize the behavior of viscoelastic materials at small deformations.They serve as a motivation and starting point for developing nonlinear models since the latter are generally extensions to the linear.They are used for analyzing experimental data obtained in small deformation experiments and for interpreting important viscoelastic phenomena, at least qualitatively.Most models used to investigate the lubrication problem for a non-Newtonian fluid were simple and linear models. They could not predict the behavior of these fluids precisely. For more reliable results, nonlinear and complex models such as the Giesekus, FENE-POn the other hand, in reality many of fluids are nonlinear, with large deformations, and with nonlinear response in the presence of such deformations. Nonlinear viscoelastic behavior is usually exhibited when the deformation is large and most of the time when the material changes its properties under . It is worth mentioning that they can describe strain rate dependence of viscosity or normal stress phenomena since these are nonlinear effects. For these reasons, nonlinear viscoelastic mathematical models are needed. Among the nonlinear models, the Giesekus model obtained the most precise outcome due to its generality for the lubrication problem. The Giesekus viscoelastic model is based on a molecular configuration and describes non-linear viscoelastic properties. Also, this model describes many parameters such as linear regions (power-law) of viscosity, the first and second normal stress coefficients, the continuous strain-hardening elongational viscosity with a finite asymptote, the complex viscosity, and start-up curves.This Study presents an analytical solution for hydrodynamic lubrication of a journal bearing with variable film thickness using Giesekus fluid for the first time. The equations were solved using the perturbation method, and the mobility factor was employed as the perturbation parameter. The effects of the mobility factor, the Weissenberg number, eccentricity of pressure distribution, the first and second normal stress differences, and load capacity are discussed. In this paper, the contribution of each normal force via stress ratio (SR) analysis  distinguish which can be considered the main innovative aspect of the present study. Also the flow type parameter to distinguish the flow type from kinematic point of view is used. It is a term that can be used to describe certain characteristics or properties related to the flow behavior of fluids, particularly in the field of fluid dynamics and rheology. This parameter provides information about how a fluid flows or behaves under different conditions. Depending on the context, various flow type parameters may be relevant. It helps determine flow regimes, predict flow patterns, and design efficient systems.A new analytical solution for nonlinear viscoelastic lubrication in journal bearings is presented.The role and contribution of the first normal stress difference and the elongational viscosity on the load capacity are investigated via the stress ratio and flow type parameter.The effects of mobility factor, fluid elasticity, and geometrical properties on journal-bearing lubrication via viscoelastic fluids are studied in detail.The main innovative aspects of the present study can be summarized as follows:The governing equations for incompressible viscoelastic fluids are the continuity and momentum.67:equations, given by64:where T” is the transpose operator, and The superscript “61. It should be noted that the values of 56 and physically acceptable mobility factor   \documenConsidering the exhibited geometry, the velocity boundary conditions can be written as69:The dimensionless Reynolds equations in a polar coordinate system where Zero-order Reynolds equation:The first-order Reynolds equation:The second-order Reynolds equation:69 are considered:In order to solve Reynolds equations using the change of variables, the following assumptions proposed by SomerfieldThe pressure boundary conditions for the present problem are written as:An unwrapped schematic of the film shape is shown in Fig. Finally, after solving Reynolds equations, by considering Sommerfeld's assumption and pressure boundary conditions, the final form of Eq.  can be eDue to the large size of the solution of pressure distribution, Load bearing capacity is the maximum ability of a journal bearing to take loading before failure occurs. Once the pressure distribution is determined, the load capacity can be calculated. The radial and tangential nondimensional load capacity obtained by the integration of nondimensional pressure along and perpendicular to the line of centers are expressed in Eq. :25\documAfter integration and simplification, the different orders of load-carrying capacity are written as follows:64:The first and second normal stress differences are two important rheological properties of viscoelastic liquids. The shear flow of polymeric solutions is not isotropic due to the alignment of polymeric chains along the streamlines, and it causes an imbalance between the normal forces:where The viscoelastic liquids exhibit a strain-hardening resistance against elongational deformations. The elongational viscosity of the Giesekus model in the steady uniaxial extensional deformation can be obtained from the following relationship:The flow type parameter, ξ, is another useful dimensionless factor to identify the contribution of different types of deformations in a mixed flow:Unlike the stress ratio, ξ is a kinematic parameter and may vary within the range , in which ξ = − 1 characterizes a solid-like rotational flow, ξ = 1 characterizes a pure extensional flow, and ξ = 0 characterizes a simple shear flow.70 was used to validate the present solution. They employed the UCM model for viscoelastic fluid within a journal bearing. The UCM model is a differential generalization of the Maxwell model for the case of large deformations based on the upper-convected time derivative. According to the UCM the shear viscosity and the first normal stress difference are independent of shear rate and hence the model fails to describe the behavior of most viscoelastic fluids. Furthermore, it predicts a steady-state elongational viscosity that becomes infinite at a finite elongation rate, which is obviously far from physical reality. A major limitation of the UCM is that it do not allow for strain dependency and second normal stress difference. To account for strain dependent viscosity and non-zero second normal stress difference among other phenomena, more sophisticated models such as Giesekus which introduce additional parameters should be considered. This equation, Giesekus model, however, has rarely been used because of the theoretical and experimental complications it introduce.The work of Liu and GrecovThe model can be written as:71. In the study by Kai Liu and Dana Grecov, two parameters are available for validation along the cylinder: pressure distribution and shear stress. Given the relevance of these parameters to the context of journal bearings, the pressure distribution have chosen. This selection is based on the crucial role pressure distribution plays in journal bearings, as it directly influences their load-carrying capacity, friction reduction, lubrication efficiency, stability, wear and tear, and overall performance.To verify the precision of the perturbation method, a comparison was made with the UCM model’s results. There are resemblances between the behaviors of the Giesekus model Eq.  and the 70 are consistent with a perturbation method. Another point to note is that as the Weissenberg number decreases , so the total amount of normal stress difference resulting from shear and elongation is considered as the apparent first normal stress difference. Figures For all three influential parameters , the apparent first normal stress difference first has a descending trend followed by an increasing trend. At first glance, augmenting each of the three parameters magnifies the amount of apparent first normal stress difference. Moreover, the apparent first normal stress difference profiles are almost flat for low relaxation times. Changes to the stress profiles due to changes in influential parameters are clearly nonlinear and display significant viscoelastic effects.According to Figs. mentclasspt{minimaFigures 10. According to the Fig. Consequently, this makes the journal bearing work more efficiently and safely since high load capacity maintains a minimum thickness of lubricant that is necessary between two relatively moving surfaces. This is a beneficial impact of viscoelasticity on journal-bearing performance. An increase in eccentricity enhances the load capacity. This is consistent with the experimental observations of higher load capacity load for higher eccentricityAs mentioned before, the stress ratio (SR) is defined as the ratio of stress resulting from the elongational viscosity to the first normal stress difference. A diagram of SR along the angular coordinate θ is shown in Figs. 64:According to Fig. g to Eq. , there iAs a result, the magnitude of the elongational viscosity, which characterizes a fluid's resistance to elongational deformation, is higher than the first normal stress difference in the present problem. Moreover, because of their long chain molecules, polymers exhibit stiff resistance to any elongational deformation; therefore, the elongational viscosity of a polymer is generally quite high.Figure The present study looked at the effect of viscoelastic fluid lubrication on the performance of journal bearings by employing the Giesekus model. The major variables of the Giesekus fluid flow in a journal bearing were developed by applying the perturbation theory.As the eccentricity ratio increases, the pressure distribution of the fluid increases, while with the increase of the mobility factor and the Weissenberg number, the pressure distribution decreases.Mobility factor variations have no significant effects on the bearing pressure distribution.The first normal stress difference for variation of all three effective parameters  initially shows a downward trend and then an upward trend while by increasing all three parameters, the first normal stress difference also increases.The second normal stress difference alternations for the mobility factor, the Weissenberg number, and the eccentricity ratio are similar. For large values of independent variants, the dependent quantity fluctuates more evidently. The extreme amounts are near the narrowest region of a journal bearing.The bearing load capacity can be divided into two parts: a linear region where the mobility factor and Weissenberg numbers have little effect and the bearing load distribution increases linearly, and a second area where load capacity changes are exponential.When the Weissenberg number is zero, it implies that elastic effects are negligible, and the fluid can be treated as a simpler, Newtonian fluid. As a result, you can observe that increasing the Weissenberg number significantly affects bearing load capacity when using a viscoelastic fluid compared to a Newtonian fluid.When a viscoelastic fluid experiences deformation or shear, the polymer chain within the fluid have the capacity to elongate and retain elastic energy. This elastic energy can help support and distribute the load, increasing the load carrying capacity and a feature not observed in conventional Newtonian lubricants.Increasing the mobility factor in the Giesekus model leads to an increase in shear stress than Newtonian lubricants because it enhances the material's elastic response and its ability to resist deformation, store energy, and generate shear stress as a result.Greater eccentricity ratios can lead to the formation of elevated shear stress areas within the bearing. While these regions are vital for supporting loads, it's imperative to effectively control them to avoid excessive wear and overheating.Polymers exhibit a stiff resistance to any elongational deformation due to their long chain molecules; hence, the elongational viscosity of a polymer is naturally high. Therefore, this subject can be monitored particularly where the flow has higher viscoelasticity, such as Generally, the fluid flow is similar to a simple shear flow except around The main conclusions drawn from the present study are:Supplementary Information.


The cement industry includes energy-intensive processes, e.g., clinker rotary kilns and clinker grate coolers. Clinker is obtained through chemical and physical reactions in a rotary kiln from raw meal; these reactions also involve combustion processes. The grate cooler is located downstream of the clinker rotary kiln with the purpose of suitably cooling the clinker. The clinker is cooled through the action of multiple cold air fan units as it is transported within the grate cooler. The present work describes a project where Advanced Process Control techniques are applied to a clinker rotary kiln and a clinker grate cooler. Model Predictive Control was selected as the main control strategy. Linear models with delays are obtained through ad hoc plant experiments and suitably included in the controllers’ formulation. A cooperation and coordination policy is introduced between the kiln and the cooler controllers. The main objectives of the controllers are to control the rotary kiln and grate cooler critical process variables while minimizing the fuel/coal specific consumption of the kiln and the electric energy consumption of the cold air fan units within the cooler. The overall control system was installed on the real plant, obtaining significant results in terms of service factor and control and energy-saving performances. Clinker is the fundamental component of the cement, which is produced through a baking process in a kiln and a subsequent cooling process in a cooler, and large amounts of thermal and electric energy are required . In manyrocesses ,4. Clinkrocesses .2) emissions and plant conduction costs, Advanced Process Control (APC) systems can be considered [Data selection, acquisition, storage and analysis retain a primary role in the design of decision support systems and expert systems  able to nsidered . APC sysnsidered , can be nsidered  and are nsidered . In addix) control problem is tackled. A data-driven model for the NOx process variable is achieved and a real-time optimization problem is formulated and solved through a particle swarm optimization algorithm. In [Different approaches for the monitoring, high-level optimization and APC of cement industry clinker rotary kilns and grate coolers have been proposed by researchers, engineers and practitioners. Monitoring and high-level optimization solutions are proposed in ,14,15,16The monitoring and high-level optimization algorithms reported in the previous paragraph are not in charge of the management of the real-time operation of the plants. In this context, APC systems can play a key role in rotary kiln and grate cooler control and optimization. APC system solutions for cement kilns are proposed in ,26,27,28With regard to kilns, in , mathemaWith regard to clinker coolers, an optimization method for the performance of PID controllers is proposed in . A proceIn , a multiThe procedural steps for qualified plant survey and data selection, acquisition, storage and analysis phases play a fundamental role before beginning an APC project for cement plants. These phases have not been thoroughly detailed in the literature;An overall assessment of the Key Performance Indicators (KPIs) to be computed and exploited for the evaluation of the performance provided by an APC system on a grate cooler has not been thoroughly detailed in the literature.The present paper proposes the design and the field implementation of APC systems for the clinker rotary kiln and grate cooler of the cement industry. The paper aims to provide holistic knobs and solutions for the assessment of APC methods in the cement industry. The present paper extends the contents reported in , providiA procedure for the inclusion of the kiln filling degree in the control matrix of an APC system while maintaining a linear formulation for the process variables’ constraints;An architecture that allows the cooperation between different APC systems;An APC system scheme capable of taking into account bad data detection and local control loop malfunctions;A two-layer MPC scheme with a cooperation policy between the layers that can be characterized by LP or QP formulations. This feature allows the adaptation of an APC scheme to subprocesses with different control specifications;A method for the exploitation of sensor/analyzer redundancy in an APC system. This feature allows us to ensure a reliable control in all operating conditions, including tailored plant operations ;The definition of different priority rankings for controlled variable constraint relaxations based on the current operating conditions.In addition to the mentioned technical merits, the following innovative scientific contributions, not present in the literature, characterize the proposed paper:The control and energy-saving results achieved with the field implementation confirmed the validity of the proposed approach. To the best of the authors’ knowledge, projects that include implementation in the real process and are designed as lasting control applications and not as temporary tests are not widespread. The field application of an APC system designed and tested through virtual environment simulations requires significant reliability and robustness features in order to bridge the gap between simulations and field application.The paper is organized as follows: Raw meal is suitably preheated in a suspension preheater composed of a cyclone tower  and nitrogen oxides (NOx) levels near the ID fan  and unexpected events .Before the installation of the proposed APC systems, the control of the clinker rotary kiln and grate cooler was managed by plant operators manually and/or through standard control logics. Plant operators manually adjusted the setpoints of the ID fan speed, meal flow rate, precalciner coal, solid secondary fuel, kiln speed and kiln coal; in addition to manual control, standard control logics could intervene on grate speed and on cold air fan unit flow rates.Thanks to an accurate plant survey and to an accurate data analysis see , some coThanks to the nature of the considered processes, two APC systems were designed and a cooperation policy between them was established see . The firThe list of the Manipulated Variables (MVs), Controlled Variables (CVs) and measured Disturbance Variables (DVs)  of each The plant survey was a fundamental step for the APC project. Thanks to the plant survey, tailored interviews were performed with plant operators, technologists and engineers.The selection of the process variables to be acquired and stored (reported in the previous section), together with the definition of the hardware and software architecture to be exploited in real-time, was a key phase that required special effort. In addition, free lime analysis was selected together with the variables responsible for energy consumption measurement, e.g., electric energy.PC Server (SCADA and Database)). A Supervisory Control And Data Acquisition (SCADA) system was installed, and a database was created on the PC server. The PC server acquired data from a SCADA system, from a database already present in the plant (Plant SCADA and Database), and from plant Programmable Logic Controllers (PLCs). In particular, free lime analysis results are entered by plant operators on the plant SCADA system and stored in the plant database.Process variables and setpoints analysis and processing;Local control loops performance evaluation;Detection, reporting and analysis of particular process conditions;KPI definition.Subsequent to the plant survey and to data selection, acquisition and storage, described in the previous section, a tailored data analysis procedure was designed and implemented . The datThe process variables and setpoints analysis and processing subphase involved the process variables being measured by sensors/analyzers, free lime laboratory analysis and the setpoints commanded to the local controllers. First, measurement/acquisition errors/malfunctions were investigated, together with PLCs communications issues. Suitable data preprocessing techniques  were applied in order to detect the bad data to be discarded/replaced. In addition, suitable exponential filters were used to improve the robustness of selected measurements. The applied filters have the form:The local control loops performance evaluation subphase consisted of an assessment of the performances of the local controllers of MVs and DVs. Experimental tests were performed, consisting of suitable step moves on the setpoints, evaluating the rise time, overshoot and settling time. Furthermore, deviation conditions between setpoints and process variables were investigated .Through data analysis, particular known process conditions were examined; one particular condition was cyclone cleaning, which is a standard procedure that is periodically executed on the suspension preheater. Bad detection logics were developed so to automatically detect sensor unreliability. Sensor unreliability can be automatically detected through the bad detection logics; in addition, plant operators, through the SCADA interface see , could sBad Detection, Data Conditioning, Decoupling Selector and Model Selector. An overall data analysis reliability flag results from the data analysis checks for the kiln and for the cooler. In addition, checks are suitably grouped to obtain critical conditions, for example, the unavailability of all oxygen measurements. This flag is exploited by the APC systems ;Cooler electric energy consumption;Service factor, i.e., the percentage of time the APC system is fully in service.The kiln fuel/coal average specific consumption is computed, taking into account different terms, e.g., the meal flow rate, the kiln coal, the precalciner coal and the solid secondary fuel. With regard to the grate cooler, the following KPIs were selected:It was not possible to use as a KPI the height of the clinker bed because the sensor was installed after the commissioning of the APC system see .The definition of the KPIs allows us to compare the system performances pre and post commissioning the APC system, providing some metrics to prove robustness and reliability as well.To the best of the authors’ knowledge, the proposed methods for plant surveying, data selection, acquisition, storage and analysis represent a technical innovation for APC systems on cement plants, with a specific focus on clinker rotary kilns and grate coolers. In addition, to the best of the authors’ knowledge, the grate cooler control KPI represented by the counter on the second sub-chamber pressure represents an additional technical innovation in the literature of APC systems on cement-industry clinker grate coolers. Not executing an in-depth plant survey and/or not using accurate methods of data selection, acquisition, storage and analysis may mean missing a key prerequisite for designing robust and lasting APC systems. In addition, a non-accurate choice of the KPIs to be observed for the evaluation of the installation of an APC system could cause an incomplete assessment of the overall benefits provided.In order to design an MPC solution for the processes under consideration, the modelization is a fundamental requirement because MPC techniques strictly depend on the obtained process model . A lineaA data-based modeling approach was adopted for the related relationships of all MVs-CVs and DVs-CVs pairs see , the secFor exploiting the step test data for each input-output pair , a First Order Plus Dead Time (FOPDT) model  was adopted, and suitable parameters’ values were identified . ConsideAs previously mentioned, the input–output relationships related to kiln filling degree , To the best of the authors’ knowledge, the formulated Equation (3) represents a scientific contribution to the literature of clinker rotary kilns APC systems.As schematized in APCs Supervisor) was designed in order to implement a cooperation policy between the kiln APC system (Kiln APC System) and the cooler APC system (Cooler APC System). This module runs with the cooler APC system sampling time (30 s) and carries out two tasks:Definition of a supervised APC status value for the both the kiln and cooler APC system;Definition of the meal flow rate data to be used in the cooler APC system.The supervised APC status values for the kiln/cooler APC system take into account the APCs status value (see in the following) and a criticality matrix, which defines whether an APC system can be active while the other APC system is not active. In addition, the APCs supervisor module defines the meal flow rate data to be used in the cooler APC system. Meal flow rate is a measured DV for the cooler APC system see , while iHu) . These dTo the best of the authors’ knowledge, the proposed cooperation architecture of SCADA and Database module  to the APCs Supervisor module. This flag defines if the considered APC system can conduct the plant. For example, if a watchdog communication error is detected in the communication between the SCADA and the PLCs , computes the MVs value to be applied to the plant  and Dynamic Optimizer (DO). The Predictions Calculator block, based on the current linear process model, computes the CVs free response [MPC module is used to compute the MVs value to be sent to the plant.The stem see  is comporesponse  over theMPC module implement a two-layer optimization strategy: the TOCS module represents the upper layer, while the DO module constitutes the lower layer. The MVs sequence is computed by DO module through a QP problem, while TOCS module computes feasible and consistent constraints and targets steady-state configuration for the DO module (see in the following) based on a LP [The other two blocks of the  on a LP  or QP prDO module QP formulation minimizes the following quadratic cost function:The generic TOCS module QP (or LP) formulation minimizes the following quadratic (or linear) cost function:The generic In Equations (4) and (6), lgorithm .DO and TOCS modules, as stated before, take into account process variables predictions over the DO module (TOCS formulation (DO MVs future control moves (assumed here in the first consecutive TOCS MVs move in Equations (6) and (7a).dels see . Δu^k+i|on steps ), while DO and TOCS modules include process variables constraints (Equation (5a–e) and Equations (7a–e)); MVs constraints  and ) are considered as inviolable (hard) constraints, while CVs constraints  and ) are set as soft constraints [MPC module, suitable logics for the preprocessing of modified MVs magnitude constraints were implemented in order to always preserve the feasibility of the optimization problems to be solved.Both the straints ,53. All soft constraints can be relaxed, if needed, through the action of suitable nonnegative slack variables included in CVs DO module are the TOCS module are the For the solution of the optimization problems reported in (4)–(7e), the decision variables of the TOCS formulation through the DO formulation through TOCS formulation includes the option of penalizing the magnitude of the MVs move in Equation (6), through suitable coefficients contained in the SCADA and Database module  was selected for the kiln APC system. Furthermore, a prediction horizon equal to 150 prediction instants (150 min) was set in order to capture the significant part of the behavior of all CVs based on the two obtained process models see ; the conAs discussed in x variable; this variable must be replaced by chimney ammonia flow rate during cyclone cleaning. In addition, if a malfunction of the kiln nitrogen oxides analyzer occurs during normal production, fan nitrogen oxides is controlled instead.Examples of defined rules resulting from the data analysis regard oxygen  are not present for this controller. The remaining terms allow us to search the minimization directions for the fuel/coal specific consumption of the kiln while respecting process constraints; for this purpose, the element of the vector The DO module of the kiln APC system, a trade-off between the minimization of the magnitude of the control moves and the minimization of the tracking error with respect to the defined MVs targets was ensured in the quadratic cost function (see Equation (4)), through the suitable tuning of the positive definite matrices soft constraints satisfaction ) by suitably tuning the positive definite matrix Within the DO module, in order to limit the computational effort required for the solution of the optimization problem. All the CVs of the same group  represents a scientific contribution to the literature of clinker rotary kilns APC systems. This feature makes it possible to ensure the best control actions in all operating conditions and to also use the APC system in the case of tailored plant operations  and unexpected events . In addition, to the best of the authors’ knowledge, the proposed priority rankings for CVs constraints relaxations represent a further scientific contribution to the literature of clinker rotary kilns APC systems; a fixed tuning could not ensure the desired performance in all operating conditions, and for this reason switching between different tuning settings represents an important feature.With regard to the cooler APC system, the suitable customization of the modules described in the previous section see  was condSCADA and Database module to the MPC module as external targets (see TOCS block (see TOCS and DO blocks (see TOCS and DO formulations). In Equations (4) and (6), the tuning parameters were set to prefer a deviation of the fans more distant from the kiln exit, in order to decrease the air flow rate in the case of a violation of the lower constraint of the clinker exit temperature. In order to allow a decrease in the cold air fan flow rates in this case, a fixed offset was established between the upper and the lower constraints of each fan. The clinker exit temperature  represents a scientific contribution to the literature of grate cooler APC systems. This feature allows us to ensure the best control actions in all operating conditions and also to allow the use of the APC system in the case of unexpected events . In addition, to the best of authors’ knowledge, the overall proposed control method for grate coolers is a scientific contribution to the literature of grate cooler APC systems.The computational framework exploited for all the project phases, excluding the commissioning phase, was represented by a laptop computer with the following specifications: Intel(R) Core(TM) i8-3840QM CPU with 3 GHz HDD. A MATLAB environment was used for data analysis, modelization and virtual environment simulations. The MATLAB Identification Toolbox, MATLAB Control System Toolbox and MATLAB Optimization Toolbox were exploited for process identification and controller synthesis. Furthermore, a MATLAB environment was also used for the project maintenance in order to analyze APC system performance and KPIs . For theThe project phases reported in MPC module  are avoided, which could cause dangerous disturbances in the combustion of the kiln. For example, the risk of raising dust from the grate cooler (thus causing problems of occlusion of the air ducts) and of lowering the clinker exit temperature are conditions that compromise the quality of the final product. In fact, the air recovered from the grate cooler—strongly influenced by the clinker distribution in it—is used as the secondary air and tertiary air of the kiln see .As reported in With regard to the rotary kiln, different procedures were performed for the KPI evaluation see . A compaWith regard to the grate cooler, different procedures were performed for the KPI evaluation see . First, Finally, the reported qualitative and quantitative analysis of the KPIs proves the robustness and reliability of the proposed APC systems.The procedural steps for a qualified plant survey;An in-depth customization of the data selection, acquisition, storage and analysis phases;An overall assessment of the KPIs to be computed and exploited for the evaluation of the performance, provided by an APC system on a grate cooler;The definition of the control matrix;The MPC problem formulation and tuning;A feature to take into account bad data detection and local control loops malfunctions in the APC systems architecture;The exploitation of the sensor/analyzer redundancy in an APC system;A cooperation policy between the rotary kiln and the grate cooler APC systems.In this paper, the design and the field implementation of APC systems for the clinker rotary kiln and grate cooler of a cement industry were proposed. MPC was exploited as a control strategy; in particular, a tailored two-layer MPC scheme was proposed. Different technical and methodological novelties were provided with regard to the literature of APC systems for clinker rotary kilns and grate coolers. The innovative methods concerned:Virtual environment simulations allowed us to test and check all the designed features within the APC systems. The overall control system was installed on the real plant, obtaining significant results in terms of service factor and control and energy-saving performance. With regard to the rotary kiln, significant improvements in the control of the critical process variables, e.g., oxygens and nitrogen oxides level, were observed after the installation on the real plant. The consequent reduction in their standard deviation allowed for a safe approach to process operating limits, leading to fuel/coal specific consumption reduction and the achievement of energy efficiency certificates. With regard to the grate cooler, the APC system increased the average tertiary air temperature and synergistically contributed to the combustion efficiency in the kiln. This improvement was possible due to the optimization of the conduction of the grate cooler, based on the grate speed regulation and on the automation of the regulation of the fans in the sub-chambers, which takes into account the raw meal flow rate. In addition, a decrease in the electrical energy consumption of the cold air fan units was obtained while ensuring the recovery of the needed heat to the kiln and to the preheater.Future work will be focused on the extension of the developed control systems to other significant subprocesses of the cement industry, e.g., the mill. In addition, further theoretical and practical improvements for the developed methods will be investigated.