Convenient and fast fault diagnosis is the key to improving the service safety and maintenance efficiency of gearboxes. However, the environment and working conditions under complex service conditions are variable, and there is a lack of fault samples in engineering applications. These factors lead to difficulties in intelligent diagnosis methods based on machine learning, while traditional mechanism-based fault diagnosis requires high expertise and long time periods for the manual analysis of data. For the requirements of diagnostic convenience, an automatic fault diagnosis method for gearboxes is proposed in this paper. The method achieves accurate acquisition of rotational speed by constructing a rotational frequency search algorithm. The self-referencing characteristic frequency identification method is proposed to avoid manual signal analysis. On this basis, a framework of anti-interference automatic diagnosis is constructed to realize automatic diagnosis of gear faults. Finally, a gear fault experiment is carried out based on a high-fidelity experimental bench of bogie to verify the effectiveness of the proposed method. The proposed automatic diagnosis method does not rely on a large number of fault samples and avoids the need for diagnosis through professional knowledge, thus saving time for data analysis and promoting the application of fault diagnosis methods. Gearboxes have many advantages such as a constant transmission ratio, high dynamic torque, and compact structure, and they have been widely used in mechanical transmission systems in wind power generation, aviation, shipping, rail transport, and other industries . MechaniThe vibration-based fault diagnosis method has been widely used in condition monitoring systems for machines and equipment because of its convenience in obtaining extensive information related to the health status of gearboxes . Yin et To overcome the reliance on user expertise, intelligent methods such as machine learning and deep learning have been introduced into fault diagnosis with the continuous development of computer technology. Singh et al.  proposedThe promotion of diagnosis technology must avoid over-reliance on the user’s knowledge, the user’s experience, and manual signal analysis, while it should not be limited by the demand and constraint of a large number of fault samples. In this paper, based on the vibration response mechanism of gearbox faults, a piece of interference-resistant automatic fault diagnosis technology is constructed. The rest of this paper consists of the following sections. The automatic diagnosis method of gear faults is proposed in The proposed automatic diagnosis method of gear faults aims to improve the diagnostic convenience. The method is based on the mechanism of gearbox faults and achieves accurate acquisition of rotational frequency by constructing the rotational frequency search algorithm to overcome the inconsistency between control speed and actual speed. Furthermore, the self-referencing characteristic frequency identification method is proposed, and a framework of anti-interference automatic diagnosis is constructed.X is the relative displacement of the gear along the line of action; K(t) is the gear mesh stiffness; M is the equivalent mass of the gear pair; E1 is the average net elastic deformation of the gear after being loaded; E2 is the additional displacement caused by gear errors and failures.A pair of meshing gears can be regarded as a vibrating system with mass, spring, and damping, whose mechanical model is shown in K(t) of the meshing pair changes periodically with time due to the repeated process of periodically entering and exiting meshing during gear operation. Its frequency domain is the meshing frequency of the gears. If the rotational frequency of the driving wheel is rf, the number of teeth is Z1, the rotational frequency of the driven wheel is rf2, the number of teeth is Z2, the meshing frequency mf, and its higher harmonics can be expressed as:The meshing stiffness The vibration response component due to the meshing stiffness excitation can be expressed as:r is the amplitude modulation factor. Expanding the above equation, it can be seen that the vibration response of the faulty gear includes the frequency components of Taking the driving wheel gear failure as an example, the vibration response of the failed gear can be expressed as:requency , as showThe basis of automatic diagnosis is the automatic extraction of gear characteristic frequency components, which depends on the accurate acquisition of speed signals. Considering the economy and system complexity, many machines often do not have an additional speed test system but obtain the speed signal directly from the motor control system. Due to the transmission lag and data reading priority problems, the data acquisition system has difficulty in synchronizing the vibration signal with the speed signal, resulting in a mismatch between the acquired speed signal and the tested vibration data. The rotational frequency search algorithm is proposed for the problem of inaccurate rotational frequency. It takes advantage of the inter-constrained relationship among the frequency components such as the rotational frequency component, the meshing frequency component and its higher harmonics in the gear rotor system. The flow of the algorithm is shown in (1)The maximum time lag ((2)Spectrums of the acquired vibration signal are calculated and the upper envelope curve on the spectrum in the range of the concerned higher order harmonics is extracted.(3)The frequencies of all envelope peaks are extracted and compared with the frequency bands of rotational frequencies and each higher order harmonics. The frequencies of peaks within the frequency band are recorded as rotational frequencies or their higher harmonics.(4)The extracted higher order harmonics are used to extrapolate the predicted rotational frequency.(5)Based on the predicted rotational frequency, the frequency band of the gear-mesh is calculated and the meshing frequency is extracted as a corroboration frequency.(6)The rotational frequency inferred from the meshing frequencies is finally used as the searched rotational frequency.Using the rotational frequency search algorithm, the accurate rotational frequency can be obtained, and the synchronization problem between the displayed speed and true speed corresponding to the collected vibration signal can be overcome.The traditional mechanism-based fault diagnosis needs manual analysis of vibration signals to observe whether there are obvious fault characteristics in the signal waveform or spectrum. However, manual observation of features such as waveforms and spectra rely heavily on the experience and expertise of the user and requires significant data analysis time. This section constructs a self-referencing feature frequency identification method based on the gear fault response mechanism to realize automatic identification of fault feature frequency components in gear vibration signals.PI) and spectral peak saliency morphology index (SI) are constructed from two visual attention elements to replace the manual signal analysis. The main principle of the method is shown in In the manual analysis of the signal, the user can accurately and quickly determine whether there is a feature frequency component of the fault by observing the significance of the spectral peak at the feature frequency in the spectrum. Inspired by the intuition of visual senses in the manual signal analysis, the peak outlier index Calculate the gear ratio using structural parameters such as the gear pair meshing relationship and the number of teeth.(2)Obtain the displayed rotational speed signal  and the sampling frequency and determine the exact rotational speed and frequency of the input axis using the rotational frequency search algorithm.(3)Combining the gear ratio and the obtained rotational frequency of the input shaft, the rotational frequency of each gear shaft and the meshing frequency of each meshing pair are calculated.(4)Eight fault characteristic frequencies such as first-order and second-order side frequencies of the first- and second-order mesh frequencies on the left and right (as shown in (5)The above eight fault characteristic frequency components are identified using the self-referencing feature frequency identification method to determine whether there is a fault component at the corresponding frequency.(6)The identification results of fault characteristic frequency components are analyzed, and fault diagnosis decisions are made by using the logic shown in the framework of anti-interference automatic diagnosis.If there is no characteristic frequency, the diagnosis results is “no fault”.If the counts of fault characteristic frequency components in one channel exceed the threshold at a certain speed, the diagnosis results is “fault indication”.If the counts of fault characteristic frequency components in one channel at different speeds or in multiple channels all exceed the threshold, the diagnosis results is “gear fault location”, and the faulty gear is located based on the characteristic frequency and the fault mechanism.Engineering users can obtain the diagnosis results of gears directly using this diagnostic framework and method without manually analyzing the vibration signals. This method saves a certain amount of analysis and diagnostic time and it does not depend on the user’s experience and expertise in data analysis and does not require various types of fault samples.A high-fidelity fault simulation experimental bench of bogie is used to validate the proposed automatic fault diagnosis method of the gear. The following section will introduce the experimental setup and experimental process.According to the real structure of the bogie, a high-fidelity fault simulation experimental bench of bogie was designed and established. The combined units of the experimental bench are shown in The control system realizes the integrated control of the experimental bench, including motor speed control, load torque control, etc., which can realize the simulation of multi-speed and variable torque load. The speed range of the test stand motor is 300–3600 r/min. It can make the axle reach a speed of 125–1500 r/min, which is consistent with the actual bogie speed range. The magnetic powder brakes on both ends of the spindle can apply a braking torque from 0 to 50 N m. Bearings and drive gears can be quickly disassembled to enable simulation studies of each typical fault. In summary, the experimental bench has similar composition, similar transmission structure, similar boundary, and consistent load characteristics to the real bogie, which can effectively realize the verification of the diagnosis method.The acquisition system of vibration data is shown in Based on the bogie gearbox experiment system, gear fault experiments are carried out to obtain vibration data of different gear faults and to verify the proposed fault diagnosis method. It mainly includes fault parts preparation and measurement point arrangement.Pinion gears of gear meshing pairs in engineering are more prone to failure than large gears due to frequent load alternations. In this experiment, the pinion gear is used as the test object to produce typical gear damage, including normal, scratch, tip broken, and root crack, as shown in The vibration acceleration sensors are arranged at three locations, as shown in In this paper, a degradation stage recognition method of bearings is proposed based on outlier cleaning. The outlier detection method combining global abnormal segments detection and accurate location of abnormal impulses is constructed, realizing the accurate and quick removal of impulse-types outliers which have significant interference with the identification of degradation points. The main conclusions of this paper are as follows:The mechanism-based manual diagnosis method and the proposed mechanism-based automatic diagnosis method are compared to verify the feasibility and superiority of the automatic diagnosis method.Manual diagnosis means that the presence or absence of a fault is determined by observing at the characteristic frequency whether there exists a significant fault frequency component.fr) is about 16.6 Hz and the gear meshing frequency (fm) is about 348 Hz. According to the mechanism analysis, the pinion fault is characterized by the side frequency components of the pinion shaft rotational frequency on both sides of the meshing frequency.In the experiment, the motor speed was set to 1000 RPM by the controller, but there was an error between the actual output speed of the motor and the control speed. The number of pinion teeth for the drive gear is 21 and the number of teeth for the large gear is 75. Therefore, the rotational frequency of the pinion shaft  of normal gears is low and there are no significant side frequencies on either side of the meshing frequency, i.e., fm + fr, fm + 2fr, fm − fr, fm − 2fr. On the contrary, for the three states of the faulty gears, it can be seen that there are significant components at meshing frequencies and there are intuitive and significant frequency components at the faulty characteristic frequencies  of the pinion. Therefore, the status determination of normal or faulty gears can be realized by using the vibration data of normal gears as a reference and manually featuring the frequency amplitude comparison.As shown in In order to avoid the manual spectrum analysis in the above diagnosis process, the proposed automatic diagnosis method is conducted to realize the automatic diagnosis of faults.Firstly, the rotational frequency search method is verified. In this case, the controller shows the rotational speed as 1000 RPM, and there is an error between the actual speed of the motor and the speed set by the controller. Assuming that there is ±40 RPM error in the measured speed, the minimum speed obtained is 960 RPM and the maximum speed is 1040 RPM. The estimated rotational frequency range is from 16.0 Hz–17.3 Hz.The results of the rotational frequency search are given in In order to avoid the fluctuation of rotational speed and the frequency calculation error in the low frequency band, the higher mesh frequency is used as the corroboration frequency to finally infer the rotational frequency. The average rotational frequency calculated by the three searched frequencies is 16.4 Hz. The mesh frequency was then inferred to be 344.4 Hz by the mesh relationship. The mesh frequency extracted in the frequency band range around the inferred mesh frequency (344.4 Hz) is 343.11 Hz, as shown in The search process of the rotational frequency is automatically executed by the diagnostic program, without manual participation in data analysis.PI and SI for frequency component identification can be extracted at the four fault characteristic frequency components  on both sides of the meshing frequency, which are Fre1, Fre2, Fre3, and Fre4 in After the rotational frequency is obtained, the characteristic indexes PI and SI are calculated for the drive end of normal gear and the scratch gear. Then, we kept adjusting their weight parameters to make the difference between the normal and faulty feature frequencies greater and further selected the threshold lambda accordingly. In this example, after a certain amount of parameter combinations, we eventually selected the parameters alpha and beta as 0.8 and 0.2 which makes the difference the most significant. We took According to the self-referencing characteristic frequency identification method in By comparing Based on the thresholds and fusion coefficients calibrated by the normal and scuffed samples at the drive end, the vibration acceleration signals of the gears in four states of normal, scratch, tip broken, and root crack in two measurement points can be discriminated.There are eight characteristic frequencies in total in the signals from two measuring points of each faulty gear. When a fault characteristic frequency component is determined to exist at a certain frequency (included in the eight characteristic frequencies), the count increases by one. The cumulative results of each measuring point are shown in According to the fault diagnosis technology framework in In this case, the characteristic frequency counts of the two measurement points for the normal gear are less than two, so there is no “abnormal” state in the “measurement point warning” and the final fault identification status is “normal pinion”. For the three fault states of the pinion , the characteristic frequency counts of both measurement points are greater than two. Therefore, both measurement points are “abnormal”. According to the technical framework of fault diagnosis, it can be determined that there is a gear fault. The counts of fault characteristic frequency components correspond to the pinion, so the fault can be localized to the pinion gear.In this example, the proposed automatic fault diagnosis method is validated with gears of four states. The comparison and verification of the results show that:The proposed rotational frequency search algorithm can accurately extract the actual rotational speed of the gear shaft in the case of inaccurately measured rotational speed, which provides the basis for characteristic frequency identification.The proposed self-referencing characteristic frequency identification method can accurately determine whether there is a significant frequency component at a certain frequency to achieve automatic discrimination of fault frequency components.Faults are accurately identified and located based on the framework of anti-interference automatic diagnosis technology, which is constructed by frequency component identification, frequency component counting, measurement point warning, and fault identification.Therefore, the above validation results show that the proposed method can achieve automatic diagnosis of gear faults without the need for extensive manual data analysis and without relying on a large amount of sample data.To improve the convenience of gear diagnosis, an automatic gearbox fault diagnosis method is proposed in this paper. The effectiveness of the proposed method is verified via a bogie experiment with faulty gears. The main conclusions are as follows.(1)The rotational frequency search algorithm, which is constructed to overcome the problem of inconsistency between the control speed/feedback speed and the real-time speed of sampled vibration data, realizes the accurate calculation of rotational frequency and provides a basis for the automatic characteristic frequency identification.(2)PI and SI) are constructed to simulate the manual spectrogram identification process. It avoids the problem that the way of discriminating frequency components is by an absolute threshold, which is vulnerable to noise and working conditions’ interference.A self-referencing characteristic frequency identification method is proposed, and the fault characteristic frequency components are identified automatically. The indicators ((3)The framework of anti-interference automatic diagnosis is constructed to realize automatic extraction of fault features based on a rotational frequency search algorithm and a self-referencing characteristic frequency identification method. The diagnostic interference caused by a single frequency component, calculation errors, or individual channel abnormality can be avoided by a multi-channel and multi-frequency joint diagnosis mechanism.


In December 2017, a decomposed unidentified body was found near the river Tronto in Teramo, Italy. The corpse was found without any identifying documents or specific personal belongings, except for a packet of cigarettes. The medical examiner determined a gastric perforation from the intake of hydrochloric acid to be the cause of death. A jar of muriatic acid found near the body led to suicide being considered the manner of death. The Penal Court in Teramo appointed two forensic odontologists to complete the postmortem assessment and collect dental data for personal identification. The corpse was found wearing a complete set of upper and lower dentures. The dental autopsy and 42 periapical X-ray images helped generate a biological profile of a man totally edentulous with upper and lower dentures, as well as an osteosynthesis with two plates and screws in the left ascending ramus of the mandible. In March 2018, the sister of a missing person reported the disappearance of her brother, and a presumptive identification was performed through visual recognition of the decomposed body. The sister confirmed the presence of two dentures and the location of the maxillo-facial surgery for the treatment of the fractured mandible. A complete dental autopsy was able to establish his identity without any DNA comparison needed. This case highlights the importance of performing a complete dental autopsy inclusive of dental radiographs, and its value in the identification of all unknown human remains even when totally edentulous.Despite a corpse being edentulous, a complete dental autopsy can still be useful.Dental radiographs, such as bitewings, periapical images, panoramic radiographs, and CT scans, are recommended in all identification autopsies.A complete dental autopsy should be performed in all cases of human identification. The scientific literature in the human identification field of forensic science highlights the importance of a multidisciplinary approach when performing this process, through the collection of primary identifiers  and secondary identifiers . The ideDespite these caveats, here we report a successful identification of an edentulous unidentified body. In this case, a satisfactory complete dental autopsy narrowed the search of reported missing persons in that specific geographical area and then helped establish the body’s identity.https://rncni.clio.it).In Abruzzo, one of the 20 regions of Italy with over 1.3 million inhabitants, there are currently 3 961 reported missing persons  and seveIn December 2017, a decomposed unidentified body was found near the river Tronto in Teramo, Italy. The corpse was found without any identifying documents or specific personal belongings, except for a packet of cigarettes. The medical examiner determined the cause of death to be a gastric perforation following the ingestion of hydrochloric acid. A jar of muriatic acid was found near the body, which led the manner of death to be considered suicide. After the judicial autopsy performed by the medical examiner, the Penal Court in Teramo decided to appoint two forensic odontologists to collect the postmortem dental data for personal identification. The deceased individual was found wearing a complete set of upper and lower dentures.In March 2018, 3 months after the body was found, a woman reported that her brother, who lived alone, had gone missing. A presumptive identification was performed through a visual recognition of the partially decomposed corpse. The woman confirmed that her brother was wearing dentures and provided authorities with the name of the dentist. She also revealed that he had previous face trauma, as well as maxillo-facial surgery to treat the fractured mandible. The odontological assessment resulted in a preliminary generic biological profile, which then helped establish the identity of the corpse through comparisons of the radiological postmortem data with the antemortem panoramic X-ray and dental data received from the dentist and hospital. No DNA comparison was required in this case.A dental autopsy was performed, which included an intra-oral examination with photographic images, denture images, and full dental radiography of the jaws. A portable X-ray device coupled with a digital sensor was used, and a total of 42 periapical X-Ray images were recorded . Dental This profile was circulated by the Carabinieri Police Agency, then also sent to the regional association of missing persons, called “Penelope Abruzzo”, and to the editorial board of a national TV programme on missing persons, named “Chi l’ha Visto?” (“Have you seen this person?”).The initial search for compatible reported missing persons did not offer any positive feedback, until the woman mentioned above reported her brother as missing after not hearing from him for several months. This was approximately 3 months after the body was found. An initial visual recognition of the partially decomposed corpse was performed with consideration given to sex and age compatibility. Further antemortem medical and dental data obtained from the sister revealed the name of her brother’s dentist, that he was wearing both upper and lower dentures, and that he had been hospitalized for face trauma that resulted in a fractured mandible. By knowing the name of the hospital he was a patient in, the police was able to obtain his medical records. The records revealed that he was diagnosed with a complete fracture of the left angle of the mandible, which was treated by the maxillo-facial surgery unit. An antemortem radiograph highlighted an osteosynthesis of two plates and screws on the left angle of the mandible and a wide cystic pathology . FollowiThe compatibility of the preliminary biological profile and the comparisons with the antemortem and postmortem radiological dental data helped establish the identity of the corpse without having to collect a DNA sample.The requirement to perform a dental autopsy in each case of human identification where teeth and jaws are present incorporates best standards in human identification  and INTE


Conclusion: Compared with the existing methods for predicting pulmonary function parameters, the present algorithm can achieve a higher accuracy rate. At the same time, this algorithm uses specific processing structures for different features, and the interpretability of the algorithm is ensured while mining the feature depth information.Objective: Pulmonary function parameters play a pivotal role in the assessment of respiratory diseases. However, the accuracy of the existing methods for the prediction of pulmonary function parameters is low. This study proposes a combination algorithm to improve the accuracy of pulmonary function parameter prediction. Methods: We first established a system to collect volumetric capnography and then processed the data with a combination algorithm to predict pulmonary function parameters. The algorithm consists of three main parts: a medical feature regression structure consisting of support vector machines (SVM) and extreme gradient boosting (XGBoost) algorithms, a sequence feature regression structure consisting of one-dimensional convolutional neural network (1D-CNN), and an error correction structure using improved K-nearest neighbor (KNN) algorithm. Results: The root mean square error (RMSE) of the pulmonary function parameters predicted by the combination algorithm was less than 0.39L and the R In recent years, artificial intelligence (AI) and machine learning (ML) have rapidly evolved in various fields, including healthcare. These methods can help detect diseases, improve pathological classification, and predict disease patterns and epidemiology, a prime example of which is ML-based algorithms developed during the COVID-19 pandemic . In addiThe above studies are all able to achieve good results in their corresponding fields, but not in the field of chronic respiratory diseases.At the same time, chronic respiratory diseases, including chronic obstructive pulmonary disease (COPD) and asthma, are significantly increasing in regard to morbidity and mortality worldwide. They can affect individuals of all age groups and cause over 3 million deaths each year according to World Health Organization data ,8. ThereThe assessment of the patient’s pulmonary function parameters is a prerequisite for the prevention and treatment of chronic respiratory diseases. Today, spirometry is one of the most widely-used techniques to assess pulmonary function . Unfortu2 exchange  in volumetric capnography and tested the hypothesis that EFFi may be used for the diagnostics and grading of COPD [Meanwhile, volumetric capnography has emerged as a technique for pulmonary function assessment that helps to solve the problem of inaccurate prediction of pulmonary function parameters and has wide application prospects . Jarenbä of COPD . Kellere of COPD . AlthougTherefore, in this paper, a combination algorithm based on volumetric capnography data is proposed for the first time to solve the problem of the accuracy of pulmonary function parameters prediction, thus improving the accuracy of pulmonary function parameter prediction. The novelty and contributions of this study are as follows.(1)This paper is the first to propose the use of volumetric capnography data for the prediction of pulmonary function parameters, which is more accessible and less demanding for testers than other studies.(2)The algorithm proposed in this paper combines the advantages of traditional machine learning algorithms for processing high-dimensional medical features and deep learning for learning low-dimensional sequence features, to improve the accuracy of pulmonary function parameter prediction.(3)This paper provides a reference paradigm for other medical data processing by handling high-dimensional features and low-dimensional features in medical data.In the subsequent sections, we first establish the signal acquisition system and compensate the system signal using an adaptive control algorithm. Then, the proposed combination algorithm is described in detail and the performance of different algorithms is compared. The experimental results show that the combination algorithm proposed in this paper has high accuracy in the prediction of pulmonary function parameters and can significantly improve the quality of pulmonary function assessment.To enable better volumetric capnography data acquisition, we built a homemade signal acquisition system. We tested the performance of the system with a PWG-33 pulmonary waveform generator and a carbon dioxide concentration verification platform, and the system’s measurement error was within 5%. The signal acquisition system is shown in The embedded system of the handheld device is shown in The microprocessor module is used to perform adaptive control algorithm and data processing, the power management module is responsible for the power supply of the entire device, the 4G communication module is responsible for signal transmission, the display module and the keyboard control module are used to interact with the user, and the sensor acquisition module is used for data acquisition.The user interface mainly includes a personal information window, a control information window, a time information window, and a result display window. Firstly, the user fills in the contents of the personal information window as prompted. Then, different buttons are selected for interaction in the control information window. When the start button is clicked, the user interface plays a guided breathing tone and collects the user’s breathing information. At the same time, the time information window displays and records the breath time information. After breathing, the user can click the show button to display the results. The respiratory flow rate, the respiratory carbon dioxide concentration, and the volumetric capnography will be displayed in the result display window. Finally, the user can click the save results button to save the collected information in CSV format locally for subsequent processing and analysis.During respiration, the flow rate will always change. As a result, inconsistencies in the characteristic parameters of volumetric capnography can occur under different respiratory conditions. Therefore, the signal acquisition system uses an adaptive adjustment algorithm based on minimum prediction error to ensure the accuracy of volumetric capnography measurements. The algorithm can ensure the consistency of the characteristic parameters of volumetric capnography, and control the flow in advance to reduce the lag in the flow control due to the ability to predict the flow according to the actual flow. The algorithm is similar to the idea of minimizing the local structure error ,20,21.The adaptive adjustment algorithm is mainly divided into three stages, the prediction of respiratory flow at the next moment, the calculation of forecast error, and the adaptive adjustment of smoothing parameters.Prediction of respiratory flow at the next moment.Set the initial sampling flow Calculation of forecast error.Get the actual respiratory flow Set the error calculation window size Adaptive adjustment of smoothing parameters.According to Control the sampling flow Algorithm 1: Adaptive Adjustment Algorithm.Input:initial sampling flow error calculation window size Output:smoothing parameters while obtaining the actual respiratory dofor len very well and provide good explanations, but the accuracy needs to be improved . Deep leInspired by the combinatorial structure , we propWe constructed a two-layer medical feature regression structure using support vector machines (SVM) and extreme gradient boosting (XGBoost) algorithms to take full advantage of the medical data in the volumetric capnography and also based on the a priori knowledge of the airflow limitation cutoffs of GOLD2020 .For the prior medical knowledge of the airflow limitation cutoff point in GOLD2020, we first need to build a first-level classification task to determine whether a patient has airflow limitation or not. For this classification task, the input features are high-dimensional data such as medical features and demographic features, for which the support vector machine (SVM) algorithm has a good processing effect. SVM is an optimal margin-based classification technique in machine learning .Since the SVM algorithm is used for the binary classification task, the results obtained are too sparse with only two possibilities. Therefore, to provide more information for the secondary prediction, we used the sigmoid function to make the output result of SVM probabilistic, which contains more information and is denser. The Sigmoid function is calculated as:We combined the output probability values of the SVM with the original features as the input features for the second-level prediction to perform the regression prediction of the FEV1 and FVC parameters. For the regression prediction task, we chose the XGBoost algorithm for secondary regression in order to show the importance and interpretability of each feature on the regression results.XGBoost was recently proposed by Chen and Guestrinis . It is bTo learn the set of functions used in the model, we minimized the following regularized objective.The training loss function In addition, XGBoost includes two key techniques: shrinkage and column subsampling. At each stage of boosting, the shrinkage algorithm scales the newly supplied weights, reducing the effect of each tree and overfitting. To speed up the training process, column subsampling only selects a random subset of input characteristics while creating a tree .The medical feature regression structure is shown in First, the first-level prediction structure was constructed using SVM with FEV1/FVC = 0.7 as the threshold to classify and predict the airway obstruction condition and obtain the corresponding probability values . SubsequTo be able to make full use of the volumetric capnography data, we want to mine information from the low-dimensional raw sequence signals, in addition to using traditional machine learning algorithms for the high-dimensional medical and demographic features.2 sequence data, deep learning networks have better learning abilities. When choosing the deep learning network structure, we considered that the original sequence information is only one-dimensional in depth; therefore, if we use network structures such as long short-term memory (LSTM) and gated recurrent units (GRU), it will increase the computational effort when performing the data processing with no effective improvement. Therefore, we chose the simpler one-dimensional convolutional neural network (1D-CNN), which is widely used in medical sequence signals [For the original low-dimensional CO signals ,33,34.2, Given a sequence of COThe convolution filter is applied to each window, resulting in scalar values In practice, one typically applies more filters, The network structure is shown in The network parameters are shown in When building the network, we followed the general structure including a convolution layer, pooling layer and a dropout layer . The conAfter processing high-dimensional information by traditional machine learning algorithms and low-dimensional information by deep learning algorithms, we need to combine the results of both algorithms organically to combine the respective advantages of both algorithms. To ensure the operability and interpretability of the synthesis results, we chose the improved K-nearest neighbor (KNN) regression algorithm as the output of the final results ,39.The traditional KNN algorithm is mainly used for classification problems. For two points Here, we used the spatial distance when The traditional KNN algorithm divides the test samples into classes of the k-nearest samples in the n-dimensional space. We made certain improvements to the KNN algorithm to fit the regression problem here.For any training sample, with the medical feature regression structure and the sequences feature regression structure, we get the output of a four-dimensional vectorThe true output of that sample isFor the test sample, the same four-dimensional output can be obtained with the two structures mentioned above.In the four-dimensional space, we calculated the distance between the test sample and all training samples. We chose the With the improved KNN algorithm, we fully consider the output predicted by each traditional machine learning algorithm and deep learning algorithm, then integrate the results to arrive at the final prediction result. The improved KNN algorithm has advantages such as simple computation and strong interpretation.Algorithm 2: Combination Algorithm.Input:Test set Output:for doMedical Feature Regression Structure  Fusion of features from  Sequence feature regression structure Error correction structure By splicing the vectors  endThe details of the combination algorithm flowchart are shown in Algorithm 2.Given the sensitivity of medical data to maximum error, we propose a comprehensive error evaluation index comprehensive percentage error (CPE), which integrates the maximum percentage error, mean absolute percentage error, and root mean square percentage error and is more suitable for the prediction evaluation of medical data .The maximum percentage error (MPE) computes the maximum residual error percentage, a metric that captures the worst-case error between the predicted value and the true value. The mean absolute percentage error (MAPE) is an evaluation metric for regression problems. This metric is sensitive to relative errors. It is for example not changed by a global scaling of the target variable. The root mean square percentage error (RMSPE) is a measure of the deviation between the predicted value and the true value. They are defined as follows:The comprehensive percentage error (CPE), which is a combination of the maximum percentage error, mean absolute percentage error, and relative standard deviation, reflects the overall error of the regression results. The smaller the comprehensive error percentage, the better the regression results.Therefore, the accuracy rate (ACC) considering the combined comprehensive percentage error is2 acquisition was greater than 4000 sampling points. Pulmonary function experiments were performed to obtain the pulmonary function parameters, FEV1 and FVC. A total of more than 1007 subjects were obtained with three types of characteristic data. The volumetric capnography features are described in We performed volumetric capnography experiments and spirometry experiments on 1007 subjects . The sampling frequency of the volumetric capnography was 200 Hz, the sampling time of the data was greater than 20 s, and the length of the sequence of COTo improve contrast and produce a balanced database, a 10-fold cross-validation strategy was applied 10 times to decrease generalization error in the training set. The dataset is first divided into 10 equally-sized, mutually-exclusive subsets: In this study, cross-validation was performed ten times, with the results of the ten cross-validations being averaged as the final result to assess the algorithm’s performance.To further assess the performance of our proposed combined algorithm, we compared single-structure machine learning and deep learning algorithms for pulmonary function prediction.We used a single-structure conventional machine learning algorithm for pulmonary function prediction. Demographic and medical features were processed by SVM and XGBoost algorithms, and the results were evaluated using the relevant regression evaluation metrics.2 and ACC metrics. This is consistent with the medical phenomenon whereby FEV1 measurements are dependent on the effort of the tester and have poor predictive accuracy. In the RMSE index, FVC is 0.48 L greater than FEV1’s 0.43 L, and since it is an absolute value, FVC is greater than FEV1, making the absolute value of RMSE of FVC greater than FEV1. Overall, the traditional machine learning algorithm was able to do a better job of processing the medical features and getting the expected results. The maximum in the R2 metric was 0.79 and the maximum ACC was up to 79%. The result, however, still has room for improvement.The results of the conventional machine learning algorithm are shown in The features’ importance is shown in The fitting curves and error percentages of conventional machine learning algorithms are shown in 2 sequences are processed by a one-dimensional convolutional neural network and the results are evaluated using relevant evaluation metrics.We used a single-structured deep learning algorithm for pulmonary function prediction. The COThe results of the deep learning algorithm are shown in 2 of 0.57. The fitting curves and error percentages of the deep learning algorithm results are shown in We used combination algorithms to regress medical features using traditional machine learning algorithms and sequence features using deep learning algorithms, and finally, we combined the results through an error correction structure to perform a quadratic regression.2 index, both FEV1 and FVC reached 0.85 and above. This indicates a good fit of the results. On the RMSE metric, the FVC prediction result of 0.39 is greater than that of 0.35 for FEV1, which may be because the combined algorithm combines the output of traditional machine learning algorithms and includes prior medical knowledge in the execution process.The fitting curves and error percentage of the combination algorithm’s results are shown in Comparison of experimental resultsTo further demonstrate the superiority of this combination algorithm, we compared the results of the single-structure algorithm with the combination algorithm on the same data set, as shown in 2 metrics are greater than 0.85, indicating that the predicted values are strongly correlated with the actual values. The combined learning algorithm incorporates medical feature information and sequence feature information to a certain extent, which can reduce the MAPE and MPE metrics of the predicted values and means that the prediction results have a greater application range.In Comparison with state-of-the-art performance2 index, this study obtained results greater than 0.85, which exceeds the results in the literature [As shown in terature ,13,14. Iterature ,14. In s2 series to fully explore the deep features in the sequence, and then the improved KNN algorithm is used to combine the results both simply and effectively to improve the accuracy of pulmonary function parameters. This algorithm can significantly improve the accuracy of pulmonary function parameter prediction in the assessment stage of respiratory diseases.In this paper, an algorithm combining traditional machine learning and deep learning was proposed to address the problem of the low accuracy of pulmonary function parameters in assessing respiratory diseases. The algorithm processes medical features by SVM and XGBoost algorithms to ensure the interpretability of the algorithm. The one-dimensional convolutional network is also used to analyze the CO2 was determined to be greater than 0.85 through a ten-fold cross-validation experiment. The algorithm was compared with other algorithms for pulmonary function parameter prediction, and the method was able to better utilize medical and serial features to achieve significant results. In addition, unlike most methods, the method proposed in this paper utilizes carbon dioxide volume data, which can be a better alternative to spirometry.The proposed combined algorithm was compared with the single-structure algorithm and showed improvement in all regression metrics. The root mean square error (RMSE) of the pulmonary function parameters predicted by the combination algorithm was less than 0.39 L and the RHowever, the algorithm proposed in this paper also has some limitations. The performance of the proposed algorithm needs to be improved when extracting information on sequence features. Additionally, this paper mainly focuses on the field of pulmonary function parameter prediction, and further research is needed to apply the algorithm to other fields. There are still some problems that need to be overcome in the course of further research. For example, the number of testers in this dataset is limited, so more samples are needed to validate the performance of the algorithm. Additionally, multidimensional test data can be incorporated for a more accurate prediction of pulmonary function parameters from multimodal data.


To prevent the frequent occurrence of transmission line galloping accidents, many scholars have carried out studies. However, there are still many difficulties that have not been solved. To address the issues that have arisen during the installation of the monitoring system, a new installation technique for the galloping monitoring terminal structure has been developed, and structural design and transmission line impact have been taken into account. A method combining Kalman and Mahony complementary filtering has been shown to solve the problem of wire twisting when galloping is taken into account. The displacement is derived by double-integrating the acceleration, although the trend term has a significant impact on the integration result. To handle the trend term issue and other error effects, a method combining the least-squares method, the adaptive smoothing method, and the time-frequency domain hybrid integration approach is used. Finally, the monitoring terminal’s structural design is simulated and evaluated, and the measured amplitude is assessed on a galloping standard test bench. The difference between the measured amplitude and the laboratory standard value is less than 10%, meeting the engineering design criteria. And the galloping trajectory is identical to the test bench trajectory, which is critical for user end monitoring. With the state’s development of transmission line building size, the region covered by the power grid has grown in recent years, and the terrain traversed has become more complicated. Furthermore, because of the frequent occurrence of adverse weather, transmission line galloping accidents  are wideScholars in the United States and overseas have conducted extensive experimental and theoretical studies on transmission line galloping amplitude monitoring. Simultaneously, related researchers have presented their wire galloping amplitude monitoring systems and monitoring methods.Huang et al.  proposedBjerkan et al.  proposedHuang et al.  proposedTo eliminate the signal trend item, low-pass filtering, polynomial fitting, and mean value methods are used. Only high-frequency noise can be filtered out using the low-pass filtering approach. Although the polynomial fitting method is straightforward, the type of trend item must be specified ahead of time. The mean approach is straightforward, but it needs a significant amount of computation. Zhang et al.  proposedTo summarize the issues with the wire galloping monitoring system, they are as follows: No consideration was given to the installation of monitoring systems and the impact on the original transmission line in the design of the wire galloping monitoring system. The torsion phenomena generated by the wire galloping was ignored when the galloping amplitude algorithm was built. Although acceleration integration yields a bigger trend term, it is unable to effectively eliminate the trend term.This paper’s contribution to the above issues is as follows: (1) Aiming at the problematic installation of the sensor monitoring system, combining the spacer bar with the galloping monitoring system was proposed to design the three-dimensional structure of the four-split spacer bar. The improved three-dimensional structure was subjected to a two-way fluid-structure coupling analysis, and the effect of the improved structure on wire galloping amplitude was assessed; (2) Given the problem that the twisting of the wire itself is not considered in the algorithm design, this paper proposes to use the Kalman filter and the Mahony complementary filtering algorithm to solve the galloping posture of the wire. The attitude calculation solves the problem of inaccurate acceleration measurement caused by the twist of the wire itself when the wire is galloping; and (3) To address the significant trend term induced by the double integration in the time domain, an improved smoothing filtering technique and the time-frequency domain hybrid integration approach are proposed.x-axis attitude sensor is presented as a terminal sensor for wire galloping amplitude monitoring. The basic principle of wire galloping is that the three-axis acceleration sensor in the six-axis attitude sensor monitors the acceleration signals in the x, y, and z axes. The acceleration is double-integrated in the time domain to generate the displacement signal. Take, for example, the y-axis direction.A siVelocity and displacement are calculated with the following formula:t (m/s2); t (m/s); and t (m).Formula: x-axis attitude sensor, an MCU, a wireless communication module, and a power management system make up the on-line galloping monitoring system. x-axis attitude sensor in the galloping monitoring system monitors the wire’s galloping acceleration in three dimensions and the torsion angle in three directions. The wire galloping acceleration data may be gathered in real-time by conducting attitude calculations on the acceleration and angular velocity using Mahony complementary filtering. We can acquire the wire’s galloping amplitude data by processing the acceleration data, and the wire’s galloping trajectory curve may be fitted using the galloping amplitude data.The structural properties of high-voltage transmission lines are used to design a wire gallop amplitude monitoring system. A siThe descriptions of each device in The terminal of the galloping monitoring system needs to be fixed on the high-voltage transmission line to minimize the size and weight of the system. Because the terminal node must fulfill long-term operational requirements, the power management system is built with solar photovoltaic panels, large-capacity lithium batteries, and lithium battery charging management modules. The block diagram and physical map of the power management system are shown in The descriptions of each device in The galloping amplitude monitoring system’s terminal must be mounted directly on the transmission line. The structural design of the galloping monitoring terminal in this article takes into account the monitoring system’s climatic characteristics, the terminal node’s post-maintenance, and the limitations of the traditional terminal node installation technique. The terminal nodes of a conventional transmission line galloping monitoring system are installed directly on the transmission lines. The galloping monitoring system’s terminal is situated on a high-voltage transmission line, and improvements to the spacer bar construction will influence wire galloping. After a large number of simulated trials, the influence of the improved spacer bar structure and the original spacer bar structure in the wind field was investigated. The influence of the improved spacer bar on the original transmission line is intuitively measured using the galloping displacement simulation data.The spacer bar and wire are then formed into a structure. In the wind field, a two-way fluid-structure  interactUnder the same wind field circumstances, the maximum galloping displacements of the improved spacer bar construction and the original spacer bar structure are 4.5329 mm and 4.2212 mm, respectively, according to the wire galloping displacement data in The monitoring terminal of this intelligent galloping on-line monitoring system collects three-axis acceleration and three-axis gyroscope data from each galloping monitoring location using 3-axis acceleration and 3-axis gyroscope sensors, respectively. In principle, integrating the acceleration yields the velocity and displacement data of galloping. The straight double integration of the acceleration data will generate a more significant trend item, which can entirely drown the original galloping displacement data. At the same time, as the wire gallops, the component of gravity acceleration merges with the component of body acceleration, resulting in erroneous acceleration measurement. A novel solution is offered to the problems that exist in the current galloping monitoring system.The torsion ,27 of thThe design principle of the galloping attitude calculation algorithm is as follows: First, the raw data from the three-axis acceleration and gyroscope sensors are subjected to Kalman filtering to reduce noise interference. Second, the Mahony complementary filtering technique is used to process the acceleration and gyroscope data. The galloping attitude angle of the wire can be obtained by data fusion of the acceleration data and the gyroscope data. Filtering off the component of gravitational acceleration via the galloping attitude angle yields accurate acceleration data. Finally, the newest acceleration is preprocessed, and the galloping amplitude is calculated using time-frequency domain hybrid integration. The whole algorithm design flow chart is shown in The Kalman filter is an efficient recursive filter that can estimate the state of a dynamic system from incomplete and noisy measurements. The Kalman filter just needs to know the estimated value of the previous instant to calculate the estimated value of the present state. Kalman is presented to anticipate the future state of the system and output acceleration and angular velocity data based on the signal characteristics of the data in this architecture.x-axis attitude sensor. Noise and a slowly changing bias term frequently disrupt sensor results. The three-axis accelerometer measures the acceleration as: A 3-axis acceleration and a 3-axis gyroscope make up the siIn the formula: The angular velocity measured by the three-axis gyroscope isIn the formula: The data measured by the acceleration sensor is selected as the input, and the state variable equation is derived by the Kalman filter as follows:In the formula: Assuming that the mean values of noise The state update equation isAfter Kalman filtering, the acceleration data is The following is the design idea of Mahony’s complementary filtering algorithm: the sensor’s measured acceleration is cross-multiplicated with the theoretical acceleration derived from the quaternion ,32, and Galloping will cause the wire to twist, resulting in an angle between the coordinate system where the sensor is located and the geographic coordinate system. Therefore, the two coordinate systems need to be unified. The transformation of two coordinate systems requires a coordinate rotation matrix to achieve the unification between the two coordinate systems. The coordinate rotation matrix is:It can be seen from the coordinate rotation matrix that the Euler method has a large amount of calculation, and the conversion between quaternions and Euler angles is used to reduce the amount of calculation. When Euler angles are represented by quaternions, the direction cosine matrix may be calculated as follows:The gravitational acceleration in the geographic coordinate system is After Kalman filtering, the acceleration data become The error correction amount of the gyroscope may be calculated by multiplying the theoretical acceleration vector by the measured acceleration vector.Gyroscope total error compensation For gyroscope compensation, error compensation using PI control is as follows:The angular velocities after error compensation are respectively Using the quaternion to solve the attitude angle of the wire galloping is:The combined algorithm of Kalman filtering and Mahony complementary filtering is compared with the attitude angle measured by the quaternion attitude solution alone. The galloping amplitude monitoring system’s attitude sensor is mounted on the turntable. The turntable is rotated at a set angle each time to compare the inaccuracies between the measured values of the two methods and the actual input values. It is more accurate to evaluate which algorithm is based on the error angle. The three coordinate axes of the attitude sensor are given 0°, 30°, 60°, and 90° inputs, respectively, on the turntable, and the accuracy of the system is evaluated by the measured values of the attitude angle. The above steps are repeated to process the attitude angles monitored by the two algorithms. The test results are shown in The combination of the Kalman filter and the Mahony complementary filter is closer to the actual input value than the attitude angle measured by the quaternion algorithm alone according to the experimental findings in the table. The results of the experiments demonstrate that the attitude angle method proposed in this research has a tiny inaccuracy with the real input value. A more precise attitude angle can reduce the influence of gravitational acceleration.The impact of gravitational acceleration must be filtered out since the wire galloping causes gravity to create the gravitational acceleration component on the carrier coordinate system. Subtract the gravitational acceleration component on each axis from the sensor’s measured acceleration. The problem of erroneous acceleration measurement caused by wire twisting can be solved by this method.The components of gravitational acceleration on each axis may be computed using the coordinate rotation matrix. Euler angles are used to describe the gravitational acceleration component of each axis:More accurate acceleration data can be produced by subtracting the gravitational acceleration component from the acceleration processed by the Kalman filter. The latest acceleration calculation formula is derived as follows:Noise interference will inevitably be introduced in the functioning of the galloping monitoring system sensor due to the sensor’s complicated operating environment. If additional interfering signals are present in the acceleration data acquired by the accelerometer, the double integration in the time domain produces bigger trend components. The true signal will be fully drowned as a result of these trend elements. The least-squares approach, adaptive smoothing filtering algorithm, and time-frequency domain hybrid integration are used to tackle this problem.k = 1, 2, 3, …, n). An m-th order polynomial is used to fit the acceleration signal, and the polynomial is as follows:The time between any two consecutive data points may be estimated using the characteristics of the galloping amplitude monitoring system, assuming the digital signal captured by the galloping amplitude monitoring system is m-th order polynomial to the acceleration signal, the following polynomial conditions must be met:To better fit the m + 1 undetermined coefficients From the conditions of the above formula, Periodic errors will inevitably arise during data integration, resulting in spikes and burrs on the integral data curve. Smoothing filtering is essential for processing to eliminate these mistakes from the data curve. When smoothing filters are used, the smoothing order is an important indicator in the smoothing filtering process. The following circumstances will arise due to the smoothing order difference: The data is severely deformed when the smoothing order is large. At the same time, the smoothing effect on the data curve is poor when the smoothing order is low. As a result, to acquire more accurate galloping amplitude data, the appropriate smoothing order must be determined. When the wire’s cross-section is the same, taking into account the correlation between wind speed and galloping acceleration has a substantial influence on the accuracy of the final galloping amplitude. The following is the best smoothing order correlation expression:n is the number of sampling points.The formula: r is the Pearson correlation coefficient ; vi is tThe integral data curve after smoothing and the integral data curve without smoothing is shown in The error caused by single integration in the time domain is minor due to the significant accumulated error in the process of double integration in the time domain. The error will be reduced by using time-domain single integration, the least-squares approach to eliminate the trend component, and smooth filtering. The low-frequency signal has a greater impact on the double integral in the frequency domain, but the low-frequency signal has a lesser influence on the single integral in the frequency domain. As a result, the time-frequency domain hybrid integration algorithm is proposed, which combines the benefits of time-domain and frequency-domain integration. The velocity is obtained by first integrating the processed acceleration data in the time domain and removing the trend term. Then, using the Fourier transform, the speed is transferred to the frequency domain and one integration in the frequency domain is undertaken. Lastly, inverse Fourier transform is used to obtain the galloping amplitude in the time domain.The data curves of the double integration in the time domain and the time-frequency domain hybrid integration algorithm are shown in The conductor galloping experiment was conducted on the transmission line galloping test bench provided by the State Grid Transmission Line Galloping Prevention and Control Laboratory. The experimental platform serves as a base for assessing if any galloping monitoring system is accurate. The wire galloping is produced by the mechanical vibration of the galloping test bench. Change the galloping amplitude of the wire by a given input signal.The prototype of the galloping monitoring system was mounted on the wire to test the accuracy of the designed galloping monitoring system’s amplitude measurement. The light curtain sensor measures the test bench’s galloping amplitude. When the wire begins to gallop, the light curtain sensor checks the wire’s position in real-time using the light emitted to get the test bench’s galloping amplitude data. Give the test bench specific input values during the experiment. Allow the galloping monitoring system to begin collecting the galloping acceleration when the test bench’s monitoring terminal detects that the galloping amplitude has reached the goal amplitude and there is galloping with the same amplitude. When the galloping acceleration is processed using the galloping amplitude monitoring method suggested in this study, the monitoring system’s galloping amplitude may be calculated. The galloping amplitude of the monitoring system is then compared to a laboratory-measured standard amplitude to determine the accuracy of the proposed galloping monitoring system algorithm. The experimental equipment for wire galloping is shown in z-axis in the direction parallel to the wire is not apparent, wire galloping focuses on the galloping displacement of the x and y axes in the direction of the wire cross-section. Next, we mainly analyze the galloping displacement in the x and y-axis directions.The designed gallop monitoring system’s amplitude measuring accuracy is assessed on the test mentioned. Let the proposed gallop monitoring system collect 1000 acceleration data points in the directions of the x, y, and z axes, respectively. The galloping amplitude data may be acquired by using the galloping amplitude algorithm proposed in this work to process acceleration data. The amplitude monitored by the monitoring system is compared to the galloping amplitude of the test rig to determine the accuracy of the amplitude measurement of the monitoring system. Because the influence of the The x and y axes acceleration data curves are collected by the galloping monitoring system using Matlab software. The acceleration curve recorded by the galloping monitoring system is presented in x-axis and y-axis integration procedures are identical, the galloping algorithms are compared using the x-axis as an example. The curve shown in Because the x-axis and y-axis oscillate up and down at 0.24 m and 0.12 m, respectively, and the motion is roughly equal-amplitude motion, and the maximum amplitude point error is within 10 percent. Through the amplitude error, it can be seen that the galloping amplitude of the wire can be better monitored.The motion of the galloping test rig is equal to amplitude motion, and the galloping amplitudes of the x and y axes monitored by the test rig are 0.24 m and 0.12 m, respectively. The gallop amplitude curves of the x and y axes tracked by the gallop amplitude monitoring system described in this research are displayed in The monitored wire’s movement can be better described using the spatial galloping trajectory. In MATLAB software, the galloping amplitude of the x, y, and z axes is obtained using a galloping algorithm, and the spatial galloping trajectory of the wire is drawn. The galloping amplitude monitoring system calculates the difference between 1000 displacement data points acquired on the x and y axes and the standard displacement. The x and y axes deviation graph was drawn by using MATLAB software. Based on an examination of existing transmission line galloping monitoring system demands, this paper proposes an intelligent transmission line galloping monitoring system. In order to address the challenges that exist in the installation of the monitoring terminal equipment of the current gallop monitoring system, this research proposes that a new device be installed on the original spacer bar device to solve the monitoring terminal installation problem. The impact on the original spacer bar is assessed in the structural design, and the effects of the improved spacer bar and the original spacer bar on the transmission line are compared and investigated. According to the simulation results, the error of the galloping displacement of the installed improved spacer bar is within 7.38 percent of that of the original spacer bar under the same wind field conditions. The improved spacer bar structure’s galloping displacement error may fulfill the original transmission line’s technical standards.In the algorithm design of the galloping monitoring system, the problem of the fusion of gravity acceleration and measurement acceleration generated by the twisting phenomena of the wire galloping is not considered. It is proposed that the Kalman filter and the Mahony complementary filter be used to tackle the problem of erroneous acceleration measurement caused by wire twisting. The calculated attitude angle is used to remove the gravitational acceleration component caused by the wire twist from the measured acceleration. The comparison data for attitude angle computation shows that the algorithm proposed in this study can produce a more accurate attitude angle.The least-square approach, adaptive smoothing method, and time-frequency domain hybrid integration algorithm are offered to tackle the effect of the vast trend term caused by the double integral in the time domain. Adaptive smoothing filtering is presented to better compute the smoothing order and remove the amplitude error caused by large or small smoothing filtering orders. The benefits of fewer trend terms generated by time-domain one-integral and less effect of low-frequency in frequency-domain one-integral are combined in a hybrid integration in the time-frequency domain to lessen the effects of other faults. When compared to the amplitude of the standard test bench, the amplitude measured by the monitoring system has an error of less than 10%. The monitoring system has restored a galloping trajectory that is nearly identical to that of the test bench. The galloping amplitude monitoring system proposed in this study satisfies actual engineering requirements.According to the experimental results, the monitoring and standard amplitudes have a small error. In future research, potential error sources will be investigated in order to lessen the influence of errors on experimental outcomes.


This work demonstrates that PIB has better residual convergence in large gradient surface processing. It is expected to realize ion beam machining with a higher convergence ratio.The continuous phase plate (CPP) provides excellent beam smoothing and shaping impacts in the inertial confinement fusion application. However, due to the features of its dispersion, its surface gradient is frequently too large (>2 μm/cm) to process. When machining a large gradient surface with continuous ion beam figuring (IBF), the acceleration of the machine motion axis cannot fulfill the appropriate requirements, and the machining efficiency is further influenced by the unavoidable extra removal layer. The pulsed ion beam (PIB) discretizes the ion beam by incorporating frequency-domain parameters, resulting in a pulsed beam with a controlled pulse width and frequency and avoiding the extra removal layer. This research evaluates the processing convergence ability of IBF and PIB for the large gradient surface using simulation and experiment. The findings reveal that PIB offers obvious advantages under the same beam diameter. Compared with the convergence ratio ( The focus radiation of an inertial confinement fusion device must be highly homogenous ,2. The iThe processing method represented by magnetorheological finishing (MRF) technology has achieved good results in the processing of large-diameter CPP components . HoweverIon beam figuring (IBF) realizes the change of material removal amount in different processing regions by controlling the dwell time of the ion beam on the surface of the component. By changing the aperture of the ion beam, the accurate machining of small characteristic sizes can be achieved ,9,10.However, when there is a large gradient surface error, the corresponding dwell time changes greatly, and it is difficult to match the speed change in finite time only by the acceleration of the moving axis of the machine tool . There iBased on the current status of ion beam processing, we used pulse power to discretize the continuous ion beam of IBF. The controllable pulse width and frequency were realized by introducing frequency-domain parameters. The parameters that control the amount of material removed are transformed from dwell time to duty cycle. As a result, by adjusting the duty cycle in real time, the amount of material removed from each scanning grid can be precisely regulated .This material removal method based on duty cycle adjustment enables the motion axis to move uniformly during the processing ,15,16, cIn The continuous ion beam figuring method subtracts the target surface from the initial surface to obtain the expected removal and then grids the data. By inverse convolution, the removal function and removal amount of each grid point, the dwell time of each grid point is determined. By changing the speed of the machine tool motion axis, the dwell time of each grid point can be adjusted to realize the change of the corresponding point processing removal ,21,22.In this way, the corresponding dwell time obtained by inverse convolution is zero for regions that need not be removed—that is, the speed of the machine tool axis is infinite at this time, which is impossible to achieve. Therefore, there will be an extra removal layer with this calculation method, which means that the area where the component does not need to be removed will still be sputtered by the ion beam. As a result, the efficiency of machining error convergence is affected, and the modification ability of ion beam machining is reduced.The PIB solves this problem by changing the principle of material removal. The key parameter matrix that controls the variation of the resection is the duty cycle (DC) matrix, which can contain zero values . After tn continuous one-dimensional errors.To solve the duty cycle from Assume that there is now a sinusoidal error with wavelength Assuming that the machine moves at a uniform speed B is the removal rate of the function volume, and Since the duty cycle cannot be negative, Equation (4) is modified to:n non-negative corrected one-dimensional duty cycle vectors to obtain the matrix and convoluting the function matrix to obtain the total processing removal at this time, the removal amount corresponds to a non-negative duty cycle matrix, which is usually not completely consistent with the actual processing removal amount. Therefore, the relaxation factor Combining Set the duty cycle matrix correction The fitting residuals are given by:k = k + 1 continue to iterate until the fitting residual If In this section, we verify the convergence effect of machining residuals for actual workpieces. To increase the efficiency, we processed fused quartz samples with a diameter of 100 mm using MRF. f < 0.1 mm−1 as shown in f = 0.13 mm−1, which fulfills the requirements of modification. We use the simulation algorithm to calculate the residuals of IBF and PIB. The final duty cycle matrix and relaxation factor  had a higher convergence ratio than IBF (γ = 2.02); thus, PIB is a superior processing method to achieve a higher convergence ratio of the optical components. The PIB has the potential to become the next generation of ion beam modifying tools with its “spot removal” characteristics and lower dynamic requirements of the machine tool, and this is important for the further development of ultra-precision machining.Through the comparison of the actual CPP surface modification, the residuals also show that PIB (


The analysis of experimental data of the solar irradiance, collected on the marine surface, clearly highlights the intrinsic stochasticity of such an environmental parameter. Given this result, effects of randomly fluctuating irradiance on the population dynamics of a marine ecosystem are studied on the basis of the stochastic 0-dimensional biogeochemical flux model. The noisy fluctuations of the irradiance are formally described as a multiplicative Ornstein-Uhlenbeck process, that is a self-correlated Gaussian noise. Nonmonotonic behaviours of the variance of the marine populations’ biomass are found with respect to the intensity and the autocorrelation time of the noise source, manifesting a noise-induced transition of the ecosystem to an out-of-equilibrium steady state. Moreover, evidence of noise-induced effects on the organic carbon cycling processes underlying the food web dynamics are highlighted. The reported results clearly show the profound impact the stochastic environmental variables can have on both the populations and the biogeochemistry at the basis of a marine trophic network. One of the most prominent aspects which characterize oceans and seas consists in their capability of absorbing atmospheric In the political management of current scientific and social issues such as climate change and ecosystem health5, ERSEM6, PISCES7, ERGOM8, and DARWIN9. In our study we adopt a stochastic version of the BFM, where random fluctuating processes affecting the environmental variables are taken into account. The BFM is exploited in several fields of application, ranging from short-term forecasting11, ocean acidification12 and climate change14, to process studies17, biogeochemical cycling18 and carbon sequestration19.Physical, biogeochemical, and ecological properties of marine ecosystems can be investigated through multi-nutrient and multi-plankton biogeochemical models, like BFM21 to macroscopic ecological systems22. Noise can induce intriguing and counterintuitive dynamical effects in living systems such as stochastic resonance26, noise enhanced stability28, and noise delayed extinction29, otherwise absent in deterministic dynamics. Moreover, several examples in climate science30 population dynamics32, ecology33, epidemiology35, bioinformatics37, neuroscience and biology39, indicate that noise acts not only as a source of disorder, but also as an essential feature of the dynamics of natural systems.The need of considering noise sources in the modeling of natural systems stems from their unavoidable interaction with the surrounding environment, which acts on the systems through not only deterministic but also stochastic “forces”. Random fluctuations are often responsible for the emergence of ordered phenomena from disordered dynamics. Such subtle mechanisms thus turn out to be fundamental in determining dynamic properties of chaotic systems belonging to all length scales, from microscopic physical systems like glasses40 as well as by both deterministic forcings 42 and random fluctuations of physical variables44 such as temperature46. The combination of the two factors can alter the net growth rate of the phytoplankton biomass production mechanism47 and drive a phytoplankton system from a stability condition to another and vice-versa49.The key-ingredient of these unpredictable effects is the simultaneous presence of nonlinear interactions and random fluctuations, which characterizes natural complex systems. Marine ecosystems indeed are characterized by nonlinear interactions52. In this sense, the separation of the deterministic signal  from the noise (the short-range changes in the weather) has been at the basis of methods developed for identifying particular features of human-induced effects in the analysed experimental data53.Such examples demonstrate that, to correctly and exhaustively grasp experimental features of natural systems, the mathematical description cannot neglect the environmental random perturbations. Stochastic models can represent a powerful tool to reproduce the spatio-temporal evolution of marine ecosystems in a better agreement with field data, shedding a new light on the hidden mechanisms which govern the dynamics of natural ecosystems, suggesting strategies and indicating possible solutions about urgent climatic issues. Stochastic models for the climate, for example, provided a means of proving that human emissions of carbon dioxide cause the increase of atmospheric temperature56. However, in ecological systems also light plays a fundamental role in driving their dynamics. To the best of our knowledge, what is reported in this paper is the first attempt to analyse the dynamic aspects related to the randomicity of the solar irradiance. This idea finds its root in the examination of experimental time series of the irradiance parameter which account for the intrinsic stochastic character of light.As for biogeochemical and ecological models, until now the attention has been mainly focused on the effects stemming from random temperature fluctuations60, the stochastic character of light is taken into account by modeling the solar irradiance dynamics as a Brownian particle subject to a multiplicative self-correlated Gaussian noise. The zero-dimensional stochastic biogeochemical flux model (SBFM)54, then, simulates a planktonic food web made of nine populations under the influence of a randomly fluctuating irradiance. Moreover, it accounts for biogeochemical cycles of carbon, phosphorus, nitrogen and silicate as well as the evolution of dissolved and particulate organic matter.In the present work, basing on previous studiesThe paper aims at showing that irradiance parameter does have an intrinsic stochastic component, and that such a stochasticity has a significant impact on the dynamics of plankton community and the resulting structure. Our results demonstrate that the coefficient of variation  in the stochastic process reaches a maximum in correspondence to critical values of  the random fluctuations' intensity for all the bio-variables. Irradiance random fluctuations mainly affect bio-physical processes related to plankton dynamics  but such ‘localized’ noisy perturbations on the lowest trophic levels can be reverberated, and indirectly affect the highest levels too. The analysis of the probability density functions reveals the ergodic character of the network dynamics, as well as the noise-induced generation of an out-of-equilibrium steady state, i.e. of a dissipative state sustained by the existence of a continuous series of perturbations, filtered by the nonlinear dynamics describing the plankton response to light intensity. This last aspect particularly shows how the interplay between random and deterministic fluctuations of the environmental parameters is fundamental in determining the basic dynamic features of complex systems like a marine ecosystem.This section is devoted to show results and to highlight eventual effects of the interplay between the nonlinearity characterizing the system dynamics and the presence of noisy fluctuations for the irradiance variable.61 (yellow points). The latter is a multispectral atmospheric radiative transfer model that is in turn forced by experimental-model data based on ECMWF ERAINTERIM reanalyses which provide, for example, cloud cover data. The radiative model is partly stochastic since it considers the effects stemming from the presence of clouds, averaged along a single day (this explains why the yellow points are slightly less scattered). We see that the OASIM model accurately reproduces the profile which emerges from the experimental data. Further, we stress that the experimental data are only used in this initial analysis. In the biogeochemical simulations the irradiance signal is fully reconstructed starting from a realistic seasonal cycle combined with a range of different random fluctuations, and the information from OASIM is not used. In the second panel (b) the daily (black points) as well as the three-month (red points) running mean of the experimental series are plotted. Figure The need of taking into account noisy fluctuations of such an environmental variable is well demonstrated in Fig. On the basis of such experimental results, we postulate the hypothesis that random fluctuations of light cannot be neglected, most of all in the study of ecological systems where light profoundly determines the system dynamics, governing fundamental processes at the basis of of the food web.D and The solar irradiance forcing is derived considering a deterministic seasonal oscillation combined with an Ornstein-Uhlenbeck process. The coefficient of variation (CV) of simulated light forcing, Fig. entclass1pt{minimaD). As it is clear the values of D have been chosen in order to obtain a relative standard deviation ranging from D and Each pixel represents the mean value on time of CV calculated with respect to 1000 different stochastic realizations. from Eq.  by puttiversus the time correlation parameter are shown for different fixed values of D.In this section the noise-induced effects on the population dynamics are examined. The nine planktonic populations present a different qualitative behaviour of the CV, compared to that of the irradiance. In this case, the CV is characterized by a strong non-monotonic dependence on the parameter D-dependent range is D. Therefore, these two species, in particular, and the whole system, in general, are extremely sensitive to the auto-correlation time which characterizes the noise.The existence of a maximum value for CV can be appreciated for each species. Although the qualitative behaviour is the same for all strains, particular attention has to be payed on diatoms and nanoflagellates. All the other species, indeed, present a percent variation of standard deviation between D approach the horizontal axis, tending asymptotically to vanish as D, that is, just an intense noise is not enough to generate a greater response of the ecosystem. In particular, experimental data are characterized by a CV approximately equal to 0.361, which corresponds to values of D and D, indeed, can generate slight effects when the correlation time We note that the different curves related to the different selected values of entclass1pt{minima56. There, the authors analyse a simpler, less realistic model of two interacting populations, whose dynamics is affected by a randomly fluctuating temperature. In that case, moreover, the deterministic oscillations of the temperature are suppressed, and the system exhibits intrinsic Lotka-Volterra oscillations whose frequency match with the characteristic one(s) of the noise. On the contrary, here, the observed maximum response . In this scenario indeed, besides dinoflagellates, diatoms and nanoflagellates are practically extinct as well, exhibiting thus a constant vanishing variance. All the other strains, instead, present qualitatively the same nonmonotonicity with only slight differences , probably due to the extinction of diatoms and nanoflagellates which causes relevant differences in the system dynamics. More specifically, the system’s response seems to depend on both the noise intensity and the correlation time , the non monotonic behaviour of CV with respect to both see Fig. .D and D.In this scenario  we have studied the dependence on both parameters We see that the mean value and the variance of these populations are strongly affected by the presence of random fluctuations in the irradiance. Specifically, as the noise intensity increases the mean values of picophytoplankton and bacteria concentrations exhibit a shift. In particular, the results indicate that picophytoplankton is disavantaged by the presence of a noisy component in the irradiance, which indeed tends to inhibit its ability to absorbe the solar light, slowing down its growth. As a consequence, since phytoplankton and bacteria compete for the same resources, as the former declines the latter are favoured, with a compensation mechanism which allows their predators (zooplankton populations) to be almost not affected by the noisy behaviour of the irradiance. Further, we note that for intermediate values of the noise intensity  is present. It is easy to observe that also in this instance the major noise-induced effect appears in nanoflagellates and diatoms with a percent standard deviation of 50D decreases, is due to the fact that for D remarkable differences arise and clear peaks of CV appear in the considered range of variation.Figure These plots show that, for a fixed value of D and D corresponding to the maximum value of CV, indeed, basically depends on the specific value of Also in this case, the interplay between the two parameters D-D-Finally, we point out that the different dynamic scenarios identified by the mentclass2pt{minim62. The different curves, related to different values of D, approach the same (vanishing) value for large D lead to significant differences of the variance. In particular, detritus, L-DOC and SL-DOC exhibit a clear non-monotonic behaviour whose maximum value depends on the combined values of D-In this subsection the effects of the irradiance noise on the biogechemistry are analysed. In Fig. entclass1pt{minimaD occurring at small D  which simulates the dynamics of a marine ecosystem composed of nine populations, considering several biological and chemical processes at the base of such a network system, like respiration and excretion By examining the nine-year temporal series of the irradiance, collected by the Boussole buoy on the Gulf of Lion, we extracted information about the main features which characterize the random fluctuations of the light intensity. On this basis, we modeled the noise affecting the irradiance with a zero-mean multiplicative Ornstein-Uhlenbeck process, imposing the limited range D) and their correlation time : primary producers (phytoplankton), predators (zooplankton), and decomposers (bacteria). Within these functional classes more specific functional subgroups can be identified to better define the planktonic food web. Diatoms (P1), flagellates (P2), picophytoplankton (P3) and dinoflagellates (P4) constitute the class of primary producers. The class of predators consists of: i) microzooplankton, composed of heterotrophic nanoflagellates (Z6) and microzooplankton (Z5); ii) Mesozooplankton, distinguishable in omnivorous (Z4) and carnivorous (Z3). Bacteria (B1) are responsible for the basic aspect of recycling organic compounds in inorganic constituents such as nitrates, phosphates and silicates. The BFM provides a much more realistic description of the microbial food-web trophic interactions than the remarkably simpler Lotka-Volterra type models65. It accounts, indeed, also for the major biogeochemical processes that form the basis of the dynamics of a pelagic marine ecosystem. The BFM simulates, for example, the cycles of nitrogen, phosphorus, silica, carbon, and oxygen in water due to plankton activity. A sketch of the trophic network is shown in Fig. The deterministic biomass-based BFM includes a conspicuous number of studies and applications, namely66, although carbon is the fundamental “currency” of life, that is, the leading element in the BFM framework.The state of each plankton functional group is formalised as a vector whose components are given by the primary constituent concentrations. The physiological condition of bacteria, for example, is defined by the set of intracellular concentration of carbon, nitrogen, phosphorus, silicon and chlorophyll. The health of the cell is of course defined by the intracellular quota of all elements54. The deterministic oscillations, at the steady state, are related to the seasonally periodic behaviour of solar irradiance and environmental temperature. The former oscillates with a seasonal period between a lower value during winter (T(t)) deterministically varies over one-year period  dominates among the primary producers, winning the competition for nutrients (in particular nitrates) . For more specific details and the full list of equations and processes included in the BFM, Ref.D is the intensity of a white Gaussian noise source (expressed in second), and Considering the solar irradiance as a stochastic process leads to the stochastic version of the Biogeochemical Flux Model (SBFM). In this work the irradiance is considered to be influenced by a multiplicative self-correlated Gaussian noise. The choice of a multiplicative noise is simply due to the fact that the light signal vanishes during the night and then the noise intensity must necessarily vanish as well. The random fluctuating light can be formally described by the following Langevin equationIt is important to underline that mentclass2pt{minim69, namely:69, through the stationary correlation functionThe stochastic process we consider in Eq.  correspoIt is worth noticing that the damping term in Eq.  is needeD and the correlation time parameter The model equations were integrated within a time-window of nine years. In order to neglect the transient dynamics and to focus only on the oscillating steady state (which characterizes the long-time system behaviour), in the multi-panel figures only the last five years have been considered. The mathematical complexity of the model requires that we numerically integrate the equations and average the results over a set of realizations. We chose the Ito scheme to numerically solve the Fokker-Planck equations and to perform 1000 realizations for each dynamical scenario identified by a precise couple of values for the noise intensity Due to the nonlinear character of the BFM, averaging over different realizations does not rule out the effects stemming from random environmental fluctuations. In a linear model, indeed, the mean value of a generic variable is not affected by stochastic perturbations. Conversely, in the presence of nonlinearities, intriguing counterintuitive changes may be observed both for the variance and the mean value of the state variables.