The update processes of the two sets are combined to form a joint feature update mechanism, and multiple features of k categories are jointly updated. Using this method, data of all categories of retail stores can be linked so that historical data of different categories of goods can provide support for the prediction of each category of goods and solve the problem of insufficient product data and features. The method is verified on the retail sales data obtained from the Kaggle platform, and the mean absolute error and weighted mean absolute percentage error are adopted to analyze the performance of the model. The results reveal that the forecasting method can provide a useful reference to decision-makers.To solve the problems of high prediction costs and difficult practices in multi-category product classification in the retail industry, optimize the inventory, and improve resilience, this work introduces a forecasting method for multi-category product sales. The forecasting method divides the data into a category set and a numerical set, uses the stacking strategy, and combines it with catboost, decision tree, and extreme gradient boosting. During the feature engineering process, the ratio and classification features are added to the category feature set; the sales at  Over the past few decades, various industries have adopted digital technologies to strengthen data-based applications. Intelligent forecasting in retail sales based on cheap and accurate machine learning (ML) not only provides more accurate inventory management but also decreases inventory losses and reduces goods detention costs. It also reduces economic losses caused by the shortage of goods during peak sales, thus improving sales controllability. Under the adverse circumstances of macroeconomic slowdown, e-commerce impact, and public health emergencies, accurate sales forecast is an effective way to solve inventory loss, goods retention, and other challenges of a single product based on digital technology. However, a single total number of sales does not provide suitable information for practical applications. This is because sales data with time series characteristics tend to be stable and periodic after summarizing, and the data structure is simple. Consequently, enterprises cannot accurately stock goods based on the total number of sales. Therefore, managers require detailed short-term product forecasting. In addition, it is fundamental in the retail industry to control costs, provide quality services, and assess market competition.Research on sales forecasting originated from the autoregressive model proposed by Yule . Later, Since 2020, the COVID-19 pandemic has further raised the demand for short-term multi-category sales forecasting. However, the computational cost of classification and prediction of multi-category products in the retail industry is high, and the implementation is challenging. First, due to the non-stability of the sales cycle, sales data for specific categories of goods may be distributed at different stages throughout the time series, and data in the early and late sales period can cause errors in multi-category sales forecasting. Second, the time series analysis of all products may lead to the loss of original data characteristics after category segmentation (Zhao and Li t + 1) by the prediction results at t, multiple features of k categories are jointly updated. Then, the historical data of different categories of goods can provide support for the prediction of each category of goods, solve the separation problem of product features, and provide a useful reference to decision-makers.To solve this problem and provide a useful reference for retail sales forecasting, this study comprehensively combines the hybrid-decision tree, hybrid-XGboost, and hybrid-catboost algorithms and proposes a nonlinear, multi-category, and joint feature updating algorithm that associates all data types in retail stores. The ratio and classification features are added to the category feature set, and a feature updater helps to generate the feature for the next predicting step. As the feature updater can generate the features used in the prediction at time , and The feature set M is continuous data prediction, which helps improve the applicability of subsequent modeling.There is a certain correlation between The date in the time feature is transformed into a datetime format, and the sales category and sales volume are converted to the floating-point format. Samples that do not contain the date and category feature are considered invalid and removed from the training set. In addition, a week in which the sales data are missing is regarded as non-sales, and this feature is treated with a zero-fill method.For category features, an encoding method is used to convert string data to numerical data. The label coding method is used for the store and department features, which are sorted numerically in ascending order, starting from one. In addition, to make full use of the aggregate help model for continuous data prediction and improve accuracy, the data reflecting the trend of the sales curve are updated with the corresponding numerical characteristics based on the moving average method  is obtained based on the prediction results at time t; features used in the prediction at time (t + 1) are also generated by the prediction results at t, which poses a great challenge to the effectiveness of the multi-category product sales forecasting analysis method . The sales at t are used for training to obtain the prediction at (t + 1). Regarding the moving average of two steps, MA2 at (t + 1) is generated by the average value of sales at time t and the predicting sales at (t + 1). Other features are generated by their own equations.In this study, the joint feature update uses an iterative prediction method. An example of the method is depicted in Fig. In sales forecasting, forecasting the future sales based on time series for each category separately has more practical economic value and significance than forecasting the total sales of all categories jointly. Traditionally, the multi-category time series prediction is performed by considering each category separately—a model is developed for each category, and each model uses its own loss function to determine appropriate model parameters, which increases the computational cost significantly. In this study, the integrated characteristics of data are added to the dataset used for model training, and only a single loss function is used to obtain the parameters k represents the categories based on the time series ; t represents time with the length of n moments; k; kth category at time t; kth category at time t.In the proposed multi-category joint feature update prediction optimization algorithm presented, a dataset is expressed as follows:N and C are feature categories in feature set M; data are updated based on M.The multi-category hybrid prediction model ; and the total monthly predicted value MAE) is obtained by summarizing all category errors and dividing the final sum by the total number of categories, which is expressed as follows:In this work, the catboost, decision tree, and XGboost models are used to predict the Tv_ sales data by using traditional methods and mixed models. The period of Tv_sales data is three months; the predicted value of The specific situation is depicted in Fig. As presented in Fig. For time-series data, the same model may not be valid on different datasets. Therefore, it is necessary to test and select appropriate models according to different datasets. This has been a common challenge in the ML field. The comprehensive results indicate that adopting a hybrid-decision tree algorithm can greatly improve the accuracy of multi-category product sales prediction for all datasets. The XGboost model achieved a significant improvement after the adoption of the multi-category method. Generally, the proposed multi-category retail sales forecasting method has a more stable forecasting effect than the single-category method. This is because the proposed method can avoid the phenomenon of ill-conditioned forecasting caused by a small number of data points.MAE results to evaluate the improvement effect of the models. Therefore, a weighted mean absolute percentage error (WMAPE) is adopted as an evaluation index. It provides a solution to situations where actual sales are zero at t. The calculation method is the sum of  is called traditional WMAPE. The WMAPE of the corresponding multi-category hybrid prediction method is called hybrid WMAPE. The error reduction rate in Table WMAPE and traditional WMAPE. The specific WMAPE results are presented in Table The WMAPE and traditional WMAPE data, the error rate of the three models is reduced. After the catboost model used a multi-category hybrid prediction method, its WMAPE decreased by an average of 3.218% over the three months. The WMAPE of the mixed multi-category decision tree prediction model is reduced by 4.501% in three months. The error reduction rate of the XGboost regression prediction algorithm is reduced by 4.779% in three months. The results indicated that on the Tv_sales dataset of the retail industry, the prediction performance of the multi-category combined feature update hybrid prediction method performed better than the three traditional methods.By comparing the result of hybrid Among the three multi-category joint feature hybrid algorithms, the decision tree and XGboost regression algorithms showed significant improvement, while the catboost algorithm achieved only slight improvement. As the weighted average percentage error of prediction of the catboost algorithm is the lowest among the three models, it can be concluded that the catboost has a good performance. Catboost uses combinatorial category features to leverage relationships between features, thereby greatly enriching the feature dimension. It can improve the accuracy rate even when it is very close to the maximum accuracy. This indicates that using the hybrid method can help the model determine the nature of the relationship between the time-series data of different categories of products. Generally, the multi-category product sales forecasting prediction method based on joint feature update achieved better prediction accuracy than the traditional single-category method, so it can provide more detailed data support to decision-makers.Accurate category sales forecasting has always been an important part of the retail industry, especially in the context of attaining normalization during the pandemic. The proposed hybrid model can effectively improve the rate of stocking, saving costs, and reducing inventory wastage. According to the empirical analysis results, the multi-category sales forecast of the retail industry can be optimized in the two following aspects: digital age retail enterprises can combine a variety of factors influencing sales, which can make the positive category sales forecast more accurately; increase the ratio feature, making it more scientific and reasonable by using historical data mining information; provide better data samples and data relationship characteristics; improve the accuracy of a sales forecasting model; and provide an effective path for retail inventory optimization.The proposed hybrid sales forecasting method based on joint feature updating has higher accuracy and smaller error than the traditional methods. The proposed method can be used for multi-category sales forecasting in the retail industry to balance the contradictions between the efficiency and accuracy of the forecasting model effectively, providing valuable decision-making information to decision-makers.k models that are required for k categories, the proposed hybrid algorithm has a better simulation effect, greatly saves computing and storage resources, and has a faster training speed.Compared with traditional methods, the multi-category forecasting method can solve the problem of insufficient product data and features. The ratio and classification features are added to the category feature set, and the historical data of different categories of goods can provide support for the prediction of each category of goods. Compared with MAE and WMAPE analyses, the prediction results of multi-category mixed sales obtained by the fusion of multiple algorithms are closer to the real data than the result of a single model. The MAE results of the proposed method are lower than those of the traditional model, and the WMAPE has a lower error rate. The proposed hybrid method can achieve an average performance improvement of approximately 4% compared with the three traditional methods. Further, compared with a single model, the multi-category sales forecasting method processing is performed based on the total number of products and the correlation between features and category attributes, and multiple features of k categories are jointly updated. The multi-category hybrid model uses default parameters to improve the training speed and save computing and storage resources. Compared with the existing methods, the proposed method has a lower computational cost and a better model-fitting effect.Based on the Effective multi-category sales forecasting can provide good data support to the retail industry, which can appropriately devise the inventory plan and improve the anti-risk ability. The proposed hybrid forecasting method based on joint feature updating can not only serve as a reference in the retail industry but can also be applied to other similar sales forecasting industries.


Magnetic nanoparticles (MNPs) with various shapes and special  properties are promising for magnetic hyperthermia. The efficiency of this therapy depends mainly on the MNPs’ physical characteristics: types, sizes and shapes. This paper presents the hyperthermic temperature values induced by cubic/sphere-shaped MNPs injected within a concentric tissue configuration  when an external time-dependent magnetic field was applied. The space-time distribution of the nanoparticles as a result of their injection within a tumoral  tissue was simulated with the bioheat transport equation (Pennes equation). A complex thermo-fluid model that considers the space-time MNP transport and its heating was developed in Comsol Multiphysics. The cubic-shaped MNPs give a larger spatial distribution of the therapeutic temperature in the tumoral volume compared to the spherical-shaped ones. MNP doses that induce the therapeutic (hyperthermic) values of the temperature (40 ÷ 45 °C) in smaller volumes from the tumoral region were analyzed. The size of these regions  was computed for different magnetite cubic/sphere-shaped MNP doses. Lower doses of the cubic-shaped MNPs give the hyperthermic values of the temperature in a larger volume from the tumoral region compared with the spheric-shaped MNPs. The MNP doses were expressed as a ratio between mass concentration and the maximum clinical accepted doses. This thermo-fluid analysis is an important computational instrument that allows the computations of the MNP doses that give therapeutic temperature values within tissues. Magnetic hyperthermia is a promising therapy for the treatment of oncological diseases ,2. This The goal of this paper is to analyze the capability of cubic/spherical-shaped MNPs to generate and transfer therapeutic heat within tumoral tissues when the alternating magnetic field is applied. The temperature distribution developed by these nanoparticles with various shapes (but the same volume) within a tumor–healthy-tissue configuration was studied. Considering their mass transport as a result of the ferrofluid insertion in the abnormal  tissue, the bioheat transfer equation (Pennes equation) was solved using a finite element method (FEM) in the Comsol Multiphysics software 5.6. The MNP doses that determine the hyperthermic values of the temperature were analyzed. The efficiency of these MNPs to destroy the tumoral tissues was discussed. The cubic MNPs have a larger heating rate in a unit time and unit volume than the spherical nanoparticles, ensuring a better heating process and implicitly efficient thermal damage of the abnormal  tissues. This comparative study describes the thermal response of the tumoral tissues heated by the cubic and spherical magnetite MNPs.This section describes the temperature model that considers the transport of MNPs and their bioheat transfer within tissues in an applied electromagnetic high-frequency field. In this approach, the intravascular structure of the tumoral  region was considered ,18. i = 1) and normal (i = 2) tissues  is the frequency factor, and  . The temperature values within a configuration of the liver tissues were determined in the following range for frequency f: 100–650 kHz and amplitude 1. First, the temperature generated by a magnetite nanoparticle with a cubic shape was compared with the one with a spherical shape when a magnetic field was applied. In this idealized model, both magnetite nanoparticles with the same volumes were inserted within a concentric abnormal–normal cell configuration a,b. In tIn this analysis, the spherical magnetic nanoparticles have the radius R = 8 ÷ 10 nm, and the length of the cubic magnetic nanoparticles (with the same volumes) is As the size of the spherical nanoparticle decreases, the anisotropy energy associated with aligning the magnetic moment perpendicular to the surface of the nanoparticle increases. This can lead to a higher magnetic anisotropy in smaller nanoparticles. Furthermore, smaller nanoparticles can exhibit single-domain magnetic behavior, which means that all of the magnetic moments in the nanoparticle are aligned in the same direction. This can result in a higher magnetic anisotropy due to the absence of domain walls. In cubic nanoparticles, the anisotropy arises from the shape anisotropy and the crystallographic anisotropy, which results from the difference in energy associated with aligning the magnetic moment along different crystallographic directions. As the size of the cubic nanoparticle decreases, the shape anisotropy energy associated with aligning the magnetic moment perpendicular to the surface of the nanoparticle increases, similar to what happens in spherical nanoparticles. In addition, the magnetocrystalline anisotropy energy can also change with the nanoparticle size due to the quantization of electronic energy levels, which can result in different electronic structures for different sizes. Overall, the combination of shape and magnetocrystalline anisotropies can lead to a complex dependence of magnetic anisotropy on nanoparticle size, and the optimal size for magnetic hyperthermia may depend on the specific material and crystalline structure. In general, smaller cubic nanoparticles can exhibit higher anisotropy, which can make them more efficient in magnetic hyperthermia.2. Second, the spatial distribution of the temperature generated by the  nanoparticles with the same values of the specific loss power P in a concentric abnormal–normal  cell was analyzed. s and anisotropy constant K were considered from published experimental data [s and anisotropy constant K; and (ii) the different sizes of the nanoparticles with the same volumes used in these simulations.In magnetic hyperthermia, the surface area and the gap between the magnetic nanoparticles (MNPs) and the surrounding tissue have a significant impact on the heating efficiency and effectiveness of the treatment. The surface area is an important factor, as it determines the amount of energy that can be absorbed by the MNPs when subjected to an external alternating magnetic field. MNPs with a larger surface area have a greater number of magnetic moments exposed to the magnetic field, which leads to greater heat generation. Thus, MNPs with a larger surface area, like cubic magnetic nanoparticles, are generally more effective for hyperthermia treatment. Also, the gap between the MNPs and the tissue is also an important factor to consider in magnetic hyperthermia. The distance between the MNPs and the target tissue can affect the heating efficiency, as it determines the amount of heat that can be transferred from the MNPs to the surrounding tissue. A smaller gap between the MNPs and the tissue can result in more efficient heating, as the heat generated by the MNPs is more readily transferred to the tissue. 3. The values of the specific loss power density developed by the cubic- and sphere-shaped nanoparticle with the frequency and amplitude of the magnetic field were studied. The values of saturation magnetization Mtal data ,10. The Cubic-shaped magnetic nanoparticles release more energy per unit volume compared to spherical ones. From the magnetic point of view, a simple explanation of this observation is given next. The release of energy in magnetic nanoparticles depends on their magnetic properties, specifically the process of magnetization and demagnetization. The energy released during this process is known as hysteresis loss or magnetic energy loss. Considering the difference in shape between cubic and spherical magnetic nanoparticles, a cubic shape has more edges and corners compared to a sphere. These edges and corners introduce discontinuities in the crystal lattice structure of the nanoparticle. Such irregularities can enhance the energy loss during magnetization and demagnetization processes. During magnetization, when an external magnetic field is applied, the magnetic moments of the nanoparticles align with the field. This alignment requires energy. The energy required to align the magnetic moments is stored in the form of magnetic potential energy within the nanoparticles. However, when the external magnetic field is removed, the nanoparticles return to their original state, and this demagnetization process also releases energy. The energy release is due to the relaxation of the magnetic moments and the conversion of magnetic potential energy back into other forms . Regarding the differences between cubic and spherical nanoparticles, the edges and corners in cubic nanoparticles act as regions with higher magnetic field gradients compared to the smooth surface of spherical nanoparticles. These gradient variations create additional strain and increase the energy required for magnetization. During the demagnetization process, the irregularities in the cubic nanoparticles lead to a higher probability of domain wall motion and nucleation, resulting in more energy release compared to spherical nanoparticles. The shape of cubic nanoparticles provides more favorable sites for domain wall movement and facilitates the relaxation of magnetic moments, thereby increasing the energy release. In summary, the cubic shape of magnetic nanoparticles, with its edges and corners, introduces crystal lattice irregularities that enhance the energy loss during magnetization and demagnetization processes. This results in a higher energy release per unit volume compared to spherical nanoparticles. This explanation provides a simplified understanding of the phenomenon, and the actual behavior of magnetic nanoparticles is more complex, involving factors such as material composition, particle size and surface effects. Particle size influences the effect of energy release in magnetic nanoparticles. The size of the nanoparticles can significantly influence their magnetic properties, including the energy release during magnetization and demagnetization processes. As the size of the nanoparticles decreases, several size-dependent effects become active. One important effect is the increase in the surface-to-volume ratio. When nanoparticles are smaller, a larger proportion of their atoms or ions are located at the surface compared to the bulk. The surface atoms have different characteristics and can exhibit enhanced reactivity and altered magnetic behavior compared to the interior atoms. In the case of energy release, the surface effects can affect the magnetization and demagnetization processes. Smaller nanoparticles have a higher proportion of atoms located at the surface, which can result in higher surface energy and increased magnetic anisotropy. Magnetic anisotropy refers to the preferred orientation of the magnetic moments within the nanoparticles. The increased magnetic anisotropy in smaller nanoparticles can lead to more stable magnetic configurations and a higher energy barrier for magnetization. As a result, smaller nanoparticles may require more energy to achieve magnetization, and consequently, they can release more energy during the demagnetization process. Furthermore, the size-dependent effects also influence the dynamics of domain wall motion and nucleation. In smaller nanoparticles, the domain walls have to traverse a shorter distance, making their movement easier and more energetically favorable. This can lead to a higher probability of domain wall motion and nucleation, enhancing the energy release. It is worth noting that while smaller nanoparticles tend to exhibit enhanced energy release, there is a limit to this effect. At extremely small sizes, quantum confinement effects become dominant, and the behavior of the nanoparticles deviates from the classical understanding. In such cases, additional factors such as quantum tunneling and spin-crossover phenomena come into play, leading to more complex magnetic behavior. In summary, particle size plays a crucial role in the energy release of magnetic nanoparticles. Smaller nanoparticles with an increased surface-to-volume ratio can exhibit enhanced magnetic anisotropy, more favorable domain wall dynamics and higher energy release during magnetization and demagnetization processes. However, it is important to consider the interplay of various factors, including shape, composition and surface effects, to fully understand the behavior of magnetic nanoparticles.In the following sections, one shows the temperature analysis for two concentric domains (tissues)  .max = 10 mg/cm3. 3. In the following simulations, the space-time temperature values generated by the same magnetite MNP doses that had the cubic and spherical shapes in a magnetic field  were computed from Equations (1), (6) and (8) for a malignant tissue that had a 40 mm diameter. At the center of the tumor–healthy-tissue configuration, the maximum clinical accepted concentration was CThe thermal damage of the tumoral tissue was studied in the same magnetic field conditions for both types of MNP shapes. Cubic-shaped MNPs have a larger spatial distribution which determines a larger volume covered by the hyperthermic temperature values compared to the spherical ones a. In thical ones . The shape of MNPs is very important for the efficiency of the magnetic hyperthermia method. Cubic-shaped magnetic nanoparticles release larger energy in unit volume per unit time compared with the spherical ones. A similar trend of heating efficiency in cubic magnetic nanoparticles was observed in the experimental work published . Low con


Facing the challenges of motorised traffic, many cities around the globe started implementing measures to transform their urban transport systems. One of the major challenges for the success of adequate policies is not only their effectiveness but also whether they are accepted by city residents. With a quantitative case study in four neighbourhoods in Frankfurt am Main (N = 821), this article investigates the acceptability of three measures: (i) parking management, (ii) the conversion of car lanes into cycle lanes and (iii) the closure of an inner city arterial road to car traffic. The results show a surprisingly high acceptability for all measures if the benefits for local residents are tangible. Thus, successful policy packages may combine push measures with either pull measures, as suggested frequently in the literature, or with improvements for other land uses . Furthermore, the perceived effectiveness, daily travel practices and intentions to reduce car use, the built environment and, to a lesser degree, socio-demographics explain differences in acceptability by population group. Many policymakers and researchers emphasise the need to transform the current car-dominated mobility system to accommodate both the needs of today’s and future generations, to mitigate climate change, land degradation and the exploitation of fossil fuel resources and to improve urban quality of life UNFCCC . This trHowever, daily travel practices as well as planning and policy decisions by local authorities remain dominated by the prevalence of the private car. Despite well-known successes in other ‘best practice’ cities, policymakers often hesitate to implement effective strategies to reduce car dependence, since they are afraid that local residents and other stakeholders will not accept them Bratzel .This gap between the effectiveness and acceptability of transport-related policies is a challenge for policymakers and researchers. For example, Steg  and HarmSo far, many case studies have focused on monetary transport measures. Our study, in contrast, examines measures that focus more on the redistribution of public space. It is the objective of this article to analyse the public acceptability of transport-related policy measures in an urban setting. All investigated measures aim to improve the quality of life in urban neighbourhoods, but also contribute to modal shifts by promoting non-motorised, public and shared modes, by reducing the space allocated to the private car and by simultaneously redistributing public space for other transport or non-transport uses. We focus on three urban transport policy measures combining ‘push’ and ‘pull’ elements to reduce the use of private cars and increase the use of alternative modes: (i) the expansion of parking management with increased prices and the redistribution of on-street parking space for other purposes, (ii) the conversion of car lanes into cycle lanes and (iii) the closure of an inner-city, four-lane road section to car traffic and its conversion for non-motorised transport and other non-transport uses.The selection of these measures in the case study was inspired by ongoing public discussions, media coverage and efforts in the city of Frankfurt am Main for a transformation of the urban transport system. The local government implemented all three measures at least temporarily in some small areas in Frankfurt am Main between 2020 and the end of 2021 when we conducted a quantitative survey to assess the residents’ support for these. However, it was not the aim of this study to evaluate the acceptance of these particular early implementations. Instead, we wanted to assess, more generally, how the local population perceived the potential expansion of these measures either to their own residential neighbourhood (for parking management and lane conversions) or permanently (in the case of the inner city road closure).For each of the three measures, we will not only assess their acceptability by the population, but also develop a framework for explaining the differences in the levels of acceptability using four factors: (i) the perceived effectiveness of the different measures, (ii) travel practices and intention to reduce car use, (iii) the built environment and (iv) socio-demographics. It should be noted that the three measures took place within the same time period and within the same city, but were not part of a consistent strategy by the local government or other stakeholders . In the last two decades, the city introduced stepwise schemes to strengthen alternatives to the car, mainly cycling and public transport. The modal share of cycling increased from 9% to 2003 to 20% in 2018 , almost all the political parties in the city of Frankfurt am Main and the local government agreed to support the cycling movement’s demands. As a result, the local government adopted an ambitious plan ‘Bicycle City Frankfurt am Main’ in 2019 shifting policy objectives further away from the private car and strengthening non-motorised modes. Among the actions being taken, the conversion of car lanes into cycle lanes on different arterial roads was expected to be highly controversial in the local media. However, after the implementation of one of the first lanes in 2020, controversy was limited. Instead, local residents appreciated the improvements to their quality of life  to achieve an urban transport transformation. Despite many synergies between the measures and an overlapping of many stakeholders involved, each of the measures followed its own rationalities, objectives and time horizons. Thus, with our study we did not aim for an assessment of a  cohesive strategy, but limited our survey to the assessment of each measure on its own.We conducted a quantitative, written survey in four Frankfurt am Main residential neighbourhoods in November and December 2020. Our rationale for the neighbourhood selection was as follows: (i) for all three measures, trials were located in inner city areas (approximately a radius of 3 km from the city centre); (ii) earlier work suggested relatively high acceptability of parking management policies in inner city neighbourhoods  we did not aim for a representative sample of Frankfurt residents but for different degrees of being affected by the urban transformation process that, as yet, mainly focus on inner city areas and where a high share of well-educated people live; and (ii) the underrepresentation of lower income and less educated people in quantitative surveys is a well-known methodological bias Lepper . Only BoWe assessed the perceived effectiveness of the three measures discussed using 19 items: five for parking, seven for the conversion of car lanes into cycle lanes and seven for the road closure of the Mainkai table . It is rWe conducted a principal component analysis (PCA) with all 19 items. With the Meyer-Olkin criterion, we derived three factors explaining 70.1% of the variance of these items: (i) perceived effectiveness of parking policies, (ii) perceived effectiveness of a road closure to car traffic and (iii) perceived effectiveness of a conversion of car lanes into cycle lanes table . It shouRegarding daily travel practices, respondents were asked about the frequency of their car, public transport, bicycle and walking mode use respectively. Individuals are considered a regular user of a particular mode if they use it at least once a week table . In addiTo measure the acceptability of policy measures table , we emplConsidering the controversies in the local media regarding some of the measures being investigated, as well as the reluctance of local politicians to implement such measures and their concerns about facing opposition, the acceptability of all three groups of measures is surprisingly high table . HoweverThis positive attitude towards non-motorised modes is also reflected, among other things, in the acceptability of the Mainkai road closure to car traffic. 71% of the respondents support the idea of converting the inner-city, four-lane road in the future. 60% believe this measure to be necessary, but there is a strong polarisation of opinions regarding its closure to cars: 45% approve this but almost the same amount of respondents disapprove. We understand this polarisation as a result of the ongoing and at times polemic public discussions between the supporters and opponents of the measure during the experimental closure. Though some of these different opinions may be attributed to the residential location and how it was affected by the Mainkai closure , despite the high conflict potential of parking in urban policymaking. However, it should be noted that only one fifth of respondents agrees to an introduction of parking fees alone in their own residential neighbourhood. This is not surprising, noting that in Frankfurt am Main, as in most German cities, parking has been free for a long time with the exception of the inner city section . AlthougThe support for converting on-street parking spaces to other uses depends strongly on the alternatives. The highest agreements for conversions of parking spaces are to cycle lanes (59%) and urban green spaces (52%), to a lesser degree to bicycle parking (43%), wider pavements (41%), seating areas (37%), outdoor areas for gastronomy (36%), carsharing parking (34%), playgrounds (31%) and delivery services (23%).In order to investigate which factors influence the acceptability of different measures, we calculated regression models for each of the following three measures: (i) the package of parking management measures with increased parking fees and the redistribution of on-street parking spaces for other purposes, (ii) the conversion of car lanes into cycle lanes and (iii) the acceptability of the closure of the inner-city, four-lane Mainkai road to car traffic table .By testing the assumptions of linear regression models, we found that multicollinearity was met but not the normality of residuals. Since the models’ sample size is relatively large, the small deviation of the residuals from a normal distribution does not necessarily lead to biased results, but should be acknowledged (Schmidt and Finan All three regression models show significant results with relatively high explanatory powers (adjusted R² between 0.40 and 0.61). The constant is significant in all models, indicating the relatively high acceptability of all measures, in particular for the conversion of car lanes into cycle lanes.In each of the models, the perceived effectiveness of the specific measure is the strongest predictor of variances in acceptability. In the model for parking measures, furthermore, regular bicycle users support the measures more than others and residents with permanent car availability less so. Those not intending to reduce their car use and thus being in the predecision stage also are less inclined to support the potential parking measures. Also, the built environment has a significant effect. Residents living further away from the city centre (Bonames/Nieder-Eschbach) agree with the measures to a lesser degree than those of the more centrally located residential neighbourhoods . Finally, most sociodemographic factors are not significant. However, older people are less likely to support the parking measures than younger people.In the model for the conversion of car lanes into cycle lanes, the effects of regular bicycle use and car availability are similar to the parking measures model. Thus, regular cyclists support the idea of lane conversions to a higher degree than others and residents with permanent car availability to a lesser degree. Furthermore, being in the predecision stage of the SSBC model reduces the acceptability of the lane conversion. Surprisingly, for the built environment, the acceptability pattern does not follow the model for parking measures. For lane conversions, the inner city residents (Altstadt/Sachsenhausen-Nord) agree with the measure to a lesser degree than residents in the other neighbourhoods . Socio-demographics are not relevant for this model.Finally, the regression model for the Mainkai road closure to cars reveals an effect of daily travel practices. Regular car use, unsurprisingly, reduces the acceptability of a road closure to car traffic. Additionally, as in the other two models, regular cyclists are more likely to support this measure. In contrast, the residential neighbourhoods show no effect in the model. Compared to the other neighbourhoods, residents in Altstadt/Sachsenhausen-Nord do not show a higher or lower support for the road closure. This, at first glance, surprising result can only be understood by a more detailed look at the local residents. By dividing the residents in the neighbourhood into those living in the immediate vicinity of the closure on the north bank of the river Main (Altstadt) and those who live on the south side of the river Main (Sachsenhausen-Nord), we find that 64% of the residents in the Altstadt but only 32% in Sachsenhausen-Nord approve the measure. Of the sociodemographic factors, only age is significant. Similar to the parking management model, older people support the road closure less than younger people.Our results indicate a surprisingly high acceptability of the proposed measures by the local residents. However, the level of agreement differs between the measures studied. More than two thirds of the respondents support the car lane to cycle lane conversions, 56% the parking management package and 45% the Mainkai closure. Furthermore, and similar to previous studies Steg , combinaIn each model, the perceived effectiveness of the specific measure assessed (e.g. effectiveness of parking measures in the parking model) is the strongest predictor of acceptability which is similar to findings reported in earlier studies  parking management, (ii) the conversion of car lanes into cycle lanes and (iii) the closure of an inner city arterial road to car traffic.To assess the local residents’ acceptability of measures for an urban transformation, we developed an integrated theoretical framework. This combines psychological (perceived effectiveness and intention to reduce car use), sociological , spatial (built environment) and transport related  factors to improve our understanding of acceptability. Further, the model does not focus on the acceptability of national, regional or city-wide policy measures but on the neighbourhood level.The results show that all factors of the model contribute to the explanation of acceptability, but perceived effectiveness is the strongest factor in all models. However, this may be due to a reversed causality, meaning that a low perceived effectiveness is not the reason but the consequence of a low acceptability of the measure in question . For example, the ‘push’ measures of parking management can be combined with the conversion of parking spaces to other land uses  or for non-motorised transport (e.g. a cycle lane). Thus, urban transport transformation is not a task for transport planners alone but also for integrative urban and transport planning.Urban transport transformations are always complex tasks which are difficult to implement. In the case of Frankfurt am Main, the context has been very supportive for urban transformation policies in the last five years. The international movements for mitigating climate change  as well as the local ‘Radentscheid Frankfurt’ campaign were strongly supported by the public. Additionally, the administrative law court decisions regarding the need to reduce car emissions section  and the But even if a majority of residents supports specific measures for an urban transport transformation, its implementation may still become difficult if a local group of people vehemently opposes a measure  and succeeds in forming an alliance with other urban initiatives and stakeholders . The example of the Frankfurt Mainkai closure shows that a strong polarisation of residents’ opinions in two adjacent neighbourhoods caused a standstill in political decision making and consensus finding. Possibly the support of local residents for this measure might have increased considerably with better involvement of the public in the planning process (Odeck and Bråthen


This study presents a novel method that combines a computational fluid-structure interaction model with an interpretable deep-learning model to explore the fundamental mechanisms of seal whisker sensing. By establishing connections between crucial signal patterns, flow characteristics, and attributes of upstream obstacles, the method has the potential to enhance our understanding of the intricate sensing mechanisms. The effectiveness of the method is demonstrated through its accurate prediction of the location and orientation of a circular plate placed in front of seal whisker arrays. The model also generates temporal and spatial importance values of the signals, enabling the identification of significant temporal-spatial signal patterns crucial for the network’s predictions. These signal patterns are further correlated with flow structures, allowing for the identification of important flow features relevant for accurate prediction. The study provides insights into seal whiskers’ perception of complex underwater environments, inspiring advancements in underwater sensing technologies. Given the limitations of the current underwater navigation systems, there has been a growing interest in advancing underwater sensing capabilities. The increasing scientific, military, and commercial demands, along with the exploration of the uncharted underwater world, have been the driving force behind these developments. Underwater robots employ various navigation systems, including inertial, geophysical, and acoustic systems, to estimate their position, velocity, and acceleration . HoweverTo address these challenges, different types of sensors are utilized on underwater robots . Camera-In recent years, there has been significant research on exploring the sensing abilities of phocid seals to address challenges in underwater sensing. These seals possess remarkable whisker arrays that enable them to detect and distinguish hydrodynamic disturbances caused by potential prey. Studies have shown that seals can detect disturbances with speeds as low as 245 μm/s and frequencies ranging from 10 to 100 Hz . BehavioPrevious studies on the fundamental mechanism of seal whisker sensing have mostly focused on the geometric effects, revealing that the whisker’s unique undulated shape can suppress self-induced vibrations by disrupting the Kármán vortex street in the wake . Our recWhile these findings confirm the high sensitivity of seal whisker sensing, the fundamental mechanism of wake identification and tracking remains largely unknown. Seal whiskers are arranged in a stereotyped grid pattern known as the vibrissa array, and the resulting bend moments at the root of the whiskers collectively form sensory inputs. Recent studies have suggested that seals may correlate temporal-spatial patterns of whisker array signals with surrounding flow patterns for intelligent perception. Various flow features, such as highest velocities, velocity gradients, and wake spatial extension, have been proposed as potential cues for object perception . ArtificIn this study, we aim to develop a novel method that combines a computational fluid-structure interaction (FSI) model with an interpretable deep-learning model to investigate the fundamental mechanisms underlying seal whisker sensing. The novelty of the method lies in its ability to establish connections between crucial signal patterns, flow characteristics, and attributes of upstream obstacles, thereby enhancing our understanding of the intricate sensing mechanisms. The effectiveness of the method is demonstrated through its ability to accurately predict the location and orientation of a circular plate positioned in front of seal whisker arrays. To achieve this, we placed a circular plate within a free stream, located upstream of the seal’s head. Two whisker arrays were integrated onto the seal’s head, replicating the realistic location, structure, geometry, and orientation observed in reported data. A one-way FSI model was employed to compute the plate-induced wake and subsequent dynamics and signals of the whiskers, represented by the root bending moment. By systematically varying the plate’s location and orientation, we generated diverse wake characteristics and whisker signals.We further developed and trained an interpretable neural network model to learn and accurately predict the location and orientation of the upstream plate based on the whisker signals. Importantly, the model produces temporal and spatial importance values, allowing for the identification of crucial temporal-spatial signal patterns contributing to the network’s predictions. We then correlated these patterns with flow structures, enabling the identification of important flow features for prediction. The outcomes of this study provide novel insights into seal whiskers’ ability of perceiving and interpreting complex underwater environments, which have the potential to advance the development of underwater sensing technologies.The rest of the paper is organized as follows: C. The presence of the whiskers in the flow field is ignored in this study.The flow field is modeled using unsteady incompressible Navier-Stokes equations:The current study employs an in-house immersed boundary method based incompressible flow solver, as described by  sensing . DetailsEach whisker is modeled as elastic structure and dynamics of whisker is governed by the Navier equation:Upon solving the dynamic equation at each time step, the hydrodynamic loadings along each whisker are estimated based on the local flow speeds using a simplified drag-lift model. To achieve this, each individual whisker is discretized into a series of whisker segments, each one spanning one segment. The hydrodynamic force acting on each segment is computed using The seal whisker array model, depicted in x, y, and z directions, respectively. The highest grid density is concentrated near the circular disk, its wake region as well as the whisker arrays, with minimum grid cell sizes of The whiskers are discretized using ten-node tetrahedral cells, resulting in a range of 9,700–34,100 cells depending on the length of the whiskers. The whiskers are fixed at the base, preventing any movement or rotation. The solid simulations are performed on the same XSEDE Expanse cluster, with one processor allocated for each whisker. Thus, for each parametric case that includes 88 whiskers, the average computational cost for the solid simulation is 184 CPU hours.A group of parametric simulations were conducted by systematically varying the location  and orientation  of the circular plate, as defined in Vision Transformer (ViT)  has demoM non-overlapping image patches, M is determined by G is defined in ViT across all network layers, projecting the flattened 1D token G-dimensional vector using a trainable linear projection. The output of this projection is considered as token embeddings. Similar to BERT’s token  and Pacinian corpuscles (PC mechanoreceptors), specialized in detecting static and dynamic changes . Merkel The subsequent step involves a data transformation process aimed at consolidating the inputs from individual whiskers to generate a signal map, as depicted in G = 96.The network training process involves regression training for 1,000 epochs using the Adam optimizer. A batch size of 25 and an initial learning rate of 0.001 are used, along with a multi-step learning rate scheduler. The input samples are divided into train and validation groups using the 5-fold method, with 500 samples for training and 125 samples for validation. Each video sample has a size of The implementation of the method utilizes PyTorch 1.12.1 and Skorch 0.11.0  frameworThis section begins with a comprehensive examination of the influence of the plate’s location and orientation on both the flow field and whisker signals. Subsequently, the outcomes of the interpretable deep learning network are presented, including accuracy measurements and importance value maps of the signals. Lastly, the correlation between the importance value maps, whisker signals, and flow field is analyzed, while also investigating the underlying mechanisms. To facilitate the discussion, five exemplary cases are selected for a detailed investigation, which are summarized in The vortex shedding frequency also changes with the orientation of the plate. To illustrate the relationship, We partition the whisker arrays into four regions: LT (left top), LB (left bottom), RT (right top), and RB (right bottom) whiskers, and calculated the average signals, Overall, the signals at the root of the whisker arrays exhibit temporal and spatial patterns that align with the dynamics of the vortices. There is a clear correlation between the arrival of the vortices and the temporal variation in the signals. The regions where the vortices directly impact the whiskers tend to exhibit stronger signal amplitudes. The distinct vortex dynamics in each case result in different temporal and spatial patterns of the signals, providing an explanation for the discernible differences among the cases.The neural network was trained successfully to predict the location and orientation of the upstream plate. An essential capability of the interpretable network is its ability to generate temporal and spatial importance of the signals within the trained network, allowing for the identification of significant temporal-spatial signal patterns that contribute to the network’s predictions. In our study, as outlined in In The variation in temporal importance patterns highlights the importance of considering the temporal dynamics and their specific correlations with the underlying flow structures when interpreting the prediction process. To illustrate this relationship, we present the vortex structures determined by the In the In the In the case of In the case of The current interpretable deep learning network also provides the importance of each whisker through spatial importance (SI) maps at individual time patch. To gain a deeper understanding of the signals used for prediction, In this study, we developed a novel method that combines a computational fluid-structure interaction (FSI) model with interpretable deep-learning models to investigate the fundamental mechanisms of seal whisker sensing. We demonstrate that the method is able to accurately predict the location and orientation of a circular plate upstream of a seal’s head by using the bending moment signals at the root of whisker arrays. The algorithm also reveals crucial temporal-spatial signal patterns utilized in the prediction process, enabling establishing correlations between important signal patterns, flow features, and characteristics of upstream obstacles for enhanced understanding.The FSI model couples an incompressible flow solver and structural dynamics solver in a one-way coupling manner. We generated diverse wake characteristics and corresponding whisker dynamics by placing a circular plate upstream of a seal’s head and systematically varying the location and orientation of the plate. Two types of wake patterns were observed. For most of the cases, the wake is characterized by two vortex rings shed from two edges of the plate with a phase difference. The translation of the upstream plate solely affects the position of the wake, without altering its structures. However, when the orientation of the plate is changed, it induces an inclination in the wake’s trajectory, a shift in the orientation of the vortices, and an increase of the vortex shedding frequency. Furthermore, the side farther from the inflow corresponds to the location of the stronger vortex, while the side closer to the inflow is associated with the weaker vortex. In contrast, for the cases where one of the orientation angles is the largest while the other is non-zero, no vortex shedding occurs in the wake. Instead, the wake is characterized by two streamwise vortex legs attached to the side of the plate. The whisker signals are represented by the bending moments at the root of each whisker. The signals exhibit temporal and spatial patterns that align with the dynamics of the vortices. There is a clear correlation between the arrival of the vortices and the temporal variation in the signals. The regions where the vortices directly impact the whiskers tend to exhibit stronger signal amplitudes.We train the network model to learn the location and orientation of the upstream plate based on the whisker signals. The results show that the model is able to predict the location of the plate with the accuracy of 90%–92.0% and the orientation of the plate with the accuracy between 86% and 89%. The analysis on the temporal importance of the signals reveals that the prediction process primarily relies on the time instances when the wake vortices actively interact with the whiskers. When the vortices are at varying distances from the whiskers, such as when the upstream plate is translated, interactions with the vortices in close proximity to the whiskers have a more significant impact, while interactions with the distant vortex ring have minimal influence. In the context of predicting the orientation of the upstream plate, interactions with all vortices can be important. However, interactions involving the vortices that carry more orientation information tend to hold greater significance, even if these vortices do not cause the strongest disturbance and signals. It suggests that the vortices that provide crucial orientation cues play a crucial role in the prediction process, even if their influence on the overall flow disturbance and signal strength is not the most pronounced. Spatially, the whiskers in stronger flow disturbance areas are more important in the prediction. The spatial arrangement of the important whiskers not only captures the vortex ring structure in the wake, but also provides valuable information about the location and size of the rings. In the context of the signals used for prediction, our results suggest that the bending moment generated by the lift force plays a crucial role in the prediction process. The direction of the moment may also be important as important whiskers are all associated with the bending moment in one direction.Taken together, we demonstrate that the developed interpretable neural network is able to accurately predict the location and orientation of the upstream object of seal whisker arrays. More importantly, it allows for the identification of significant temporal-spatial signal patterns that contribute to the network’s predictions, which can then be further correlated with flow structures, enabling the identification of the crucial flow features that are sensed for accurate prediction. These insights are crucial for the development of intelligent flow sensors capable of accurately perceiving and interpreting complex underwater environments.We would like to acknowledge that our study utilized a simplified drag-lift model in our one-way coupling approach to estimate the hydrodynamic loadings along each whisker. This simplified model does not take into account the feedback effect of the whiskers on the surrounding flow. In reality, the presence of the whiskers would influence the surrounding flow, resulting in different drag and lift values that could potentially affect the outcomes of our research. However, we believe that the impact of the whiskers on the surrounding flow would be small due to the small diameter of the whiskers (with a mean diameter of 0.66 mm). This diameter is approximately 1-2 orders of magnitude smaller than the scale of the vortices in the wakes, which range from 20 mm to 120 mm. Considering this scale difference, we believe that the one-way coupling approach still provides valuable insights while significantly reducing the computational cost associated with conducting full FSI simulations. It is important to note that future investigations could explore the implications of the two-way coupling between the whiskers and the surrounding flow for a more comprehensive understanding of the hydrodynamic interactions.In all the simulation cases, we observed that the frequency of the bending moments consistently matched the shedding frequency of the wake vortices. This behavior is a direct consequence of the one-way coupling approach, where the feedback effect of whisker dynamics on the flow was disregarded. It is worth noting, however, that in our previous research , we discFinally, seal whisker arrays display distinct spatial grid patterns combined with variations in whisker length and orientation. These patterns are believed to play crucial functional roles in enhancing the seals’ sensing capabilities. For instance, it is believed that longer whiskers located on the caudal side of the array can provide a larger detection area, extending the reach and sensitivity to water movements. Moreover, the variation in whisker length and orientation may allow for high sensitivity in wide frequency range and flow direction. Further studies are needed to fully investigate these effects, particularly by comparing the sensing capabilities between different whisker arrangements. The current findings are limited to a single configuration, and more research is necessary to gain a comprehensive understanding.


The fault diagnosis of rolling bearings is critical for the reliability assurance of mechanical systems. The operating speeds of the rolling bearings in industrial applications are usually time-varying, and the monitoring data available are difficult to cover all the speeds. Though deep learning techniques have been well developed, the generalization capacity under different working speeds is still challenging. In this paper, a sound and vibration fusion method, named the fusion multiscale convolutional neural network (F-MSCNN), was developed with strong adaptation performance under speed-varying conditions. The F-MSCNN works directly on raw sound and vibration signals. A fusion layer and a multiscale convolutional layer were added at the beginning of the model. With comprehensive information, such as the input, multiscale features are learned for subsequent classification. An experiment on the rolling bearing test bed was carried out, and six datasets under various working speeds were constructed. The results show that the proposed F-MSCNN can achieve high accuracy with stable performance when the speeds of the testing set are the same as or different from the training set. A comparison with other methods on the same datasets also proves the superiority of F-MSCNN in speed generalization. The diagnosis accuracy improves by sound and vibration fusion and multiscale feature learning. The rolling bearing is a critical component of rotating machinery such as the wind turbine, the hydraulic turbine, and the aero-engine. Rolling bearing faults are the leading cause of the failure of rotating machinery, bringing economic losses and even unplanned downtime. The fault diagnosis of rolling bearings before catastrophic failure is one of the main concerns of these industries  and is eThe traditional fault diagnosis of rolling bearings is constructed by extracting fault characteristic frequencies (FCFs) from monitoring signals ,3. FCFs Although these methods have proved effective under speed-varying conditions, prior knowledge is necessary to calculate the FCFs or FCOs. Deep learning (DL) algorithms have recently gained increasing interest and have proved their ability to diagnose faults more automatically and intelligently ,12. As aStudies on the fault diagnosis of rolling bearings under variable speed conditions using CNN represent a growing field. Huang et al.  construcSome examples in the literature attempt to deal with the cross-domain problem by transfer learning algorithms, but the transfer of the model is relatively complicated, and data from the target domain are essential for training a model ,24. A CNOne of the outstanding advantages of CNN is its capability to process multidimensional data so that the input of a CNN model can contain heterogeneous information . CNN witIn addition, convolutional kernels of different sizes were adopted in the proposed model. The concept of multiscale convolution comes from the CNN model codenamed Inception . ConvincThis paper primarily includes the following contributions:(1) The data fusion, feature extraction, and fault classification processes are combined into an end-to-end automated procedure. The proposed model works directly on the raw signals of sound and vibration.(2) The proposed method has a strong generalization capacity. In model validation, different speed-varying situations are taken into consideration. Datasets are constructed by samples at multiple constant speeds or speeds changing with time. The speeds of the testing samples are the same as or are unknown to the training sample. The proposed method can achieve high and stable accuracy under various datasets, especially fault diagnosis when crossing different speed domains.(3) The F-MSCNN method adds a fusion layer and a multiscale convolutional layer to enhance the model performance under speed-varying conditions. The adaptive fusion of the sound and vibration data is realized at the beginning of the network to input comprehensive information to the model. The multiscale convolution operators could increase the depth and width of the network to learn more comprehensive features.(4) The feature maps learned by F-MSCNN are visualized to reveal the inner feature learning mechanism.The layout of this paper consists of five sections. jth output feature matrix of the lth convolutional layer ith input feature matrix of the layer l − 1. Φ is added to enhance the nonlinear expression ability. A rectified linear unit (ReLU) and sigmoid are commonly used as activation functions.A convolutional neural network is a specialized kind of neural network that uses the convolution operation in at least one layer in place of a general matrix multiplication . A typicw, the jth max-pooling output of the layer l + 1 is presented as:jth output feature map of layer l. t denotes the tth pooling region and The pooling layer is used to reduce the spatial size of the feature map. The pooling operation helps to reduce computational complexity and avoid over-fitting. The pooling layer does not learn features. It performs downsampling by dividing each of the input feature maps into rectangular pooling regions. Max-pooling is the most widely used pooling type. For the one-dimensional max-pooling, given the size of the pooling region l, and the corresponding output is After several rounds of the convolutional and pooling layer, the fully connected layer is added to generate the high-level feature vector. The fully connected layer multiplies the inputs by a weight matrix and then adds a bias vector. Each neuron of the previous layer is connected to this layer.This paper proposes a novel CNN-based deep learning approach that is aimed at the fault diagnosis of rolling bearings under speed-varying conditions. The proposed F-MSCNN provides an end-to-end automated procedure to perform more accurate fault classification when the operating speed changes with time. A fusion layer and a multiscale convolution layer were added to better fuse and extract the characteristic information from the raw vibration and sound signals. The structure of F-MSCNN is shown in m × 2 as the input of the model, where m is the length of one sample. The fusion process was realized by a two-dimension convolution operation with k convolutional kernels of size n × 2. Fusion by convolution is also a feature extraction process that can fully obtain the common and distinctive information of sound and vibration signals.Signal fusion has been proven as an effective way to enhance diagnosis accuracy. A fusion layer was constructed at the beginning of the F-MSCNN model to enrich the condition information and obtain a comprehensive description of the diagnostic object. The sound and vibration signals are two commonly used signals for condition monitoring and the fault diagnosis of rolling bearings. Usually, an accelerometer for collecting vibration signals is installed near the faulty rolling bearing so the abnormality can be captured in a timely manner. The mounting position should be carefully arranged for the accelerometer, and it is better installed on the vibration propagation path not far away from the monitored object to avoid interferences from other vibration sources. The sound signal is homologous to the vibration signal. A microphone was used for sound acquisition, which generally had a wider effective bandwidth to capture more information . AdditioThe conventional CNN structure used in fault diagnosis adopts only one kernel in the convolution layer. However, under speed-varying conditions, the inherent characteristics of the signals are diverse at multiple speed scales. A multiscale layer with convolutional kernels of different scales was added in an F-MSCNN model to better extract the features and enhance the diversity and performance of the model. The multiscale layer is illustrated in p(x) is the target distribution while q(x) denotes the estimated distribution of the soft-max layer.The training process of the proposed F-MSCNN is detailed in this section. The cross-entropy between the predicted soft-max output probability distribution and the target label probability distribution is defined as the lost function of the model:β is the momentum and α is the learning rate. The momentum stochastic gradient descent algorithm was applied to minimize the cost function during the training process to optimize the parameters. The use of momentum can reduce the oscillations of the stochastic gradient descent. The momentum update rule for the weight and bias parameters is: jth input and output of BN, and the operation of BN is denoted by:Batch normalization (BN) was used to accelerate the training process and reduce the internal covariate shift of the model . Xj and The process of the fault diagnosis of rolling bearings under speed-varying conditions using F-MSCNN is illustrated in Step1: Sound and vibration signals from varying speeds of the rolling bearings were collected synchronously. Both of the signals were sliced without overlap into small segments for the following model training, validation, and testing. The two segments of the sound and vibration signals at the same period of time were combined together as an input map. The input was directly put into the model without expert experience or signal processing technologies. Step 2: The data map, including sound and vibration data, was used as the input of the F-MSCNN model to establish an end-to-end automated fault diagnosis framework. The output of the model was fault labeled. Information fusion, multi-scale feature extraction, and classification were realized by training the model. The training samples were mixed with multiple speeds but did not need to cover all the operating speeds.Step 3: The trained model was put into use for fault diagnosis under speed-varying conditions. The testing samples could be in the same working condition as the training samples, which is the common treatment. The testing samples could be in other speed conditions different from the training samples due to the speed generalization ability of the model.The proposed approach was verified by an experiment with rolling bearings on the machinery fault simulator, as shown in For each condition of the bearing, the data were collected at different rotating speeds from 600 to 2400 rpm with an equal interval of 300 rpm, so there were seven working conditions with different speeds. For each constant speed, the sampling time was 30 s. Additionally, another three working conditions with speed decreasing from 2400 to 600 rpm at the rate of 1 Hz/s and 0.5 Hz/s were considered. The sampling time was 30 s and 60 s, respectively. The same health condition under different speeds was treated as one class, and there were four classes in all for classification. The sound and vibration signals were divided by a sliding window to form sub-samples, and there was no overlap between each sample. The length of each sample was 1024. All the samples were grouped into seven datasets to test the performance of the proposed approach under different speed conditions. The vibration and sound signals in each sample were first combined together as an input matrix with a size of 1024 × 2 according to the proposed method. An F-MSCNN model was built and trained using the input matrices obtained from the training samples. The architecture parameters of the proposed F-MSCNN are displayed in The diagnosis accuracies on six datasets are listed in The parameters of F-MSCNN were decided by trial and error to obtain a relatively better diagnosis performance for all the datasets. When adjusting the parameters, some training and validation samples were used to optimize the parameters. Once the parameters were optimized and selected, they were fixed to evaluate the model performance by the testing samples. The influence of the training samples on the diagnosis results was carried out in this paper. The mean testing accuracy and standard deviation of different datasets with respect to different numbers of training samples are shown in The proposed F-MSCNN model was able to work directly on the raw signals and learn the features automatically. However, CNN is generally regarded as a black box. The ability to explain the inner feature learning mechanism of the network is worth noticing with further study.The activations of the convolutional layers are visualized in The feature distribution of the test samples was visualized by t-SNE to understand the inner feature learning process qualitatively. The proposed F-MSCNN method was compared with other deep learning methods to further demonstrate its effectiveness in signal fusion and multiscale convolutions. The same six datasets are used for comparison, and the results are represented in The average computational time and the number of trainable parameters for different methods are listed in The proposed F-MSCNN was also compared with the long short-term memory method (LSTM)  and the This paper proposed an improved model named F-MSCNN for the fault diagnosis of rolling bearings under speed-varying conditions using sound and vibration signals. The aim was to classify different types of faults accurately when the speeds of the testing samples were nonstationary and unknown to the trained model. F-MSCNN added a fusion layer and a multiscale convolutional layer to the original CNN to enhance the generalization ability by combining health conditions and working conditions information from different sensors and integrating multiscale features. F-MSCNN provided a simple end-to-end fault diagnosis framework that worked directly on raw sound and vibration signals without hand-crafted feature extraction. The sound and vibration signals were firstly fused by a two-dimension convolution to extract the common and distinctive features. The fused signals are then convolved by multiscale kernels to represent the features of various speeds.The proposed method was tested by the sound and vibration data from a rolling bearing test bed. Six datasets are constructed to test the effectiveness of the model under different speed-varying conditions. Not only multiple speeds were considered, but speeds fluctuating with time were also studied. The speeds of the testing samples could be the same as the training samples or more strictly restricted to new working conditions unknown to the trained model. The results show that the proposed method had a strong adaptation ability for different speed domains and could achieve a high and stable diagnosis accuracy under different working speeds. The proposed method was also compared with other CNN-based methods and other machine learning methods with higher accuracy, better stability, and strong robustness to the change in speeds. In addition, to display the inner feature leaning mechanism of the network, visualization analysis was performed, including visualizing the activations of all the convolutional layers and feature distribution.Further work will consider other changeable working conditions, such as the working loads, and conduct experiments on other objects, including the gearbox, to expand the scope of application of the model. The performance of the proposed model could be further explored under compound faults using a blind dataset. An example of a blind test is shown in Reference . Additio


Distributed Dynamic Strain Sensing (DDSS), also known as Distributed Acoustic Sensing (DAS), is becoming a popular tool in array seismology. A new generation of engineered fibers is being developed to improve sensitivity and reduce the noise floor in comparison to standard fibers, which are conventionally used in telecommunication networks. Nevertheless, standard fibers already have extensive coverage around the Earth’s surface, so it motivates the use of the existing infrastructure in DDSS surveys to avoid costs and logistics. In this study, we compare DDSS data from stack instances of standard multi-fiber cable with DDSS data from a co-located single-fiber engineered cable. Both cables were buried in an area located 2.5 km NE from the craters of Mt. Etna. We analyze how stacking can improve signal quality. Our findings indicate that the stack of DDSS records from five standard fiber instances, each 1.5 km long, can reduce optical noise of up to 20%. We also present an algorithm to correct artifacts in the time series that stem from dynamic range saturation. Although stacking is able to reduce optical noise, it is not sufficient for restoring the strain-rate amplitude from saturated signals in standard fiber DDSS. Nevertheless, the algorithm can restore the strain-rate amplitude from saturated DDSS signals of the engineered fiber, allowing us to exceed the dynamic range of the record. We present measurement strategies to increase the dynamic range and avoid saturation. Optical fibers are able to carry light and propagate it over long distances with minimum attenuation, and so is a preferred medium for broad-band transmission systems around the world. When using the scattering properties of the glass fibers, the fiber can be turned into a distributed sensing system that provides substantial advantages over conventional electronic sensors ,2,3,4. ODistributed Dynamic Strain Sensing (DDSS), also known as Distributed Acoustic Sensing (DAS), takes place when the Rayleigh scattering is used aside with optical time-domain reflectometry OTDR; ,10) in a in a10])Measurements in DDSS are carried out conventionally by using standard fibers. Light pulses are sent along the fiber, and the measurements depend on the phase of the back-scattered signals produced by random imperfections within the glass fibers. Phases in consecutive time intervals are compared in the extremes of a defined length, named gauge length, to receive a phase-shift measurement. The phase shift is an expression of the strain rate within the defined gauge length.Proper phase readings depend on the intensity of the back-scattered signal, and so does the signal-to-noise ratio (SNR). However, some of the imperfections in the glass do not guarantee a uniform high-intensity scattering of the light, so it affects the dynamic range and introduces noise ,19. In cThere is a noticeable improvement in the DDSS methods with the use of engineered fibers in terms of SNR and sensitivity ,18,20,23Conventional telecom cables often have several fibers (12 to 80), but distributed fiber optic sensing methods only use one dedicated fiber. Using two or more fiber instances of the same cable may allow an increase in the SNR, e.g., by stacking each fiber’s instance measurements . While tWe first explain our setup in the field, then explore our proposed technique to spatially match the different standard fibers, and expand this method to match the standard fibers with the engineered fiber. Following, we introduce and characterize saturations found within the DDSS data and a proposed method to assess them. In the end, this leads to a performance analysis between the use of multiple standard fibers and single engineered fibers.We deployed two fiber optic cables  at a 2.5 km distance from the active craters of Mt. Etna volcano in Sicily and buried them beneath the ground in non-consolidated scoria. The first cable is 1.5 km long, contains 12 individual telecom fibers (standard), and was buried 30 cm beneath the surface (July 2019). The second cable is 0.5 km long, contains an engineered fiber (Constellation), and was buried at 15 cm depth in another trench following the same path as the standard cable (September 2019). For simplicity of the fieldwork, we connected the engineered fiber to one of the 12 fibers within the standard cable see  and recoThe used engineered fiber is composed of the same glass material as the standard one but with scattering centers. Each scattering center works as a mirror that reflects around 0.01% of the transmitted light, increasing the back-scattered light intensity by 100 times more the one of the standard fibers ,30. The Each type of fiber was recorded with a different interrogator  Silixa . HoweverIn order to locate each channel (trace) within the known path of the cable, we performed tap tests at specific points along the cable ,15,24 wiTo compare the signals recorded in the standard fibers, we need to make sure that the channels from the different fiber instances match spatially as best as possible . As showx of one fiber instance. For the same x, but where the channels of the fibers share the same location, they should be the same spatial function. Therefore, the two spatial signals are cross-correlated to produce a CC function To find the best channels correspondence, we cross-correlate (CC) with each other the windows corresponding to each individual fiber instance along the spatial dimension . Since tT is the total number of time samples in a given time window. The lag where the stacked CC function reaches its maximum value is used to shift the positions of the channels and establish a channel-to-channel correspondence between the two fiber instances.The spatial CC is repeated for all time samples, so then all CC functions can be stacked and produce a final spatial cross-correlation function N as the consecutive stack of fiber instances; from 1 to N.We use the first fiber as a base against the other instances, compute the spatial CC to find the best channel equivalences, and stack the signals (dependent on time) by summing per channel and averaging them. The stacks have instances in the same way as the fiber instances. We define a stack instance When comparing the standard and engineered fibers, the channel correspondence must be addressed similarly. We applied the same routine of spatial CC to have channel equivalences between both types of fibers. For this purpose, we used the standard fiber instance one and the engineered one . The comAs mentioned before, both types of fibers were interrogated with different channel spacing; 2 m for standard and 1 m for engineered. To compare signals from both cables, we explore two methods: (1) by introducing artificial channels with linear interpolation between the existing ones in the standard DDSS data and (2) by removing intermediate channels in the engineered DDSS data. The two methods differ by a shift of one channel, which then assures that the spatial CC works properly. We decided to adopt the alignment obtained by the second method since this one depends exclusively on real DDSS data.To analyze the relation between standard fiber instances, stack instances, and engineered fibers, we performed a Principal Component Analysis (PCA) on the amplitudes of each of the stack instances at the standard fiber in relation to the amplitudes of the engineered fiber. This method constructs a covariance matrix using a set of variables. The retrieved eigenvalues and eigenvectors are used to analyze multi-variable relationships for a subsequent variable reduction to re-describe the relationship in lower dimensions ,34. In oDDSS signals could be saturated due to strong motion events, such as tap tests. Signal saturation in DDSS is not as similar as in Broad-Band (BB) seismic instruments . In BB instruments, the saturation is shown as ℑ of H and take the derivative signal to have the angle change in time:We attempt to correct the saturated signals by first computing the Hilbert Transform To restrict the values of H and the maximum In this work, we focus on correcting for saturation due to phase jump since they can distort the real amplitude signal, and so any pre-processing, such as filtering, would not give the correct waveform , the comparison between the standard stack instances and the engineered fiber amplitudes shows a starting ratio of 1.641 and a For the noise frequency (highpass), the slopes between stack instances and engineered signal are three orders of magnitudes lower than the ones registered with the lowpass filtered signal. Further, the slope is indirectly proportional to Based on the results of We apply the suggested algorithm for signal saturation correction to three different types of traces: (1) stack instance four, (2) fiber instance one (stack 1), and (3) engineered fiber. We expected that a noise reduction due to stacking could facilitate the signal saturation corrections on standard fiber data. However, the correction performed for stack five and fiber instance one a,b have Regarding the CF, there is a clear difference between the one produced by the stacked DDSS data d and theTheoretically, two fibers deployed at the same location following the same path should measure the same strain rate. Nevertheless, we noticed a discrepancy of 66% in amplitudes for equivalent channels between the standard and engineered fibers a. The glOptical noise is random across the length of the interconnected fiber instances, and so we expected to have a reduction during the stacking process, where the engineered fiber acts as a reference to evaluate the noise reduction during stacking. Effectively, from stack instance one to two there is a significant reduction in optical noise compared to other stack instances based on lues see a, also slues see .An increase in noise can be noticed in stack instance four. We attribute this to possible constructive interference of the optical noise between stack three and fiber instance four.  reduced e.We achieved, at stack instance five, a maximum reduction in the initial noise presented in the lowpass filter scenario see . The calThe best stack instance (No. 5) shows smoother signals, where wave phases can be recognized easier than by only using one fiber see ; howevernstances c. The laWe derived a mathematical expression for estimating the best stack instance to use based on the total interrogated fiber length and the length of the fiber instances see . TheoretThe PCA method was able to establish a relationship between the two fibers and describe the noise level. The example used to study the relationship is non-saturated in either of them, as they correspond to a weak tremor. However, in saturated signals, the relationship would pass from a linear to a non-linear regime, and so PCA becomes unreliable for establishing a relationship. In such a scenario, other methods should be explored to avoid non-linear regimes due to saturations.Signal saturation in DDSS is an effect due to the limitation of unwrapping for phase-shifts in the range raw data . Our phaWhen assessing correction for saturated signals, the engineered DDSS signal was properly reconstructed, while the standard signals from stack instance five and fiber instance one were not see b,c. DespA phase jump described with few time samples  located in the upper and lower limits of the dynamic range produces a clear peak in the characteristic function (CF), as in the case of the engineered DDSS signal e. We notN is the increment ratio of the laser rate. Additionally, to avoid the saturation effects, the sampling frequency should also be increased. The dynamic range is dependent on the sampling frequency and the gauge length; higher sampling rate and lower gauge length would increase the dynamic range, and so avoid signal saturation. However, this would reduce the strain-rate sensitivity [Due to the limitations of saturation correction, there are some variables to consider in order to avoid this phenomenon or facilitate the correction in standard DDSS data in the future. The initial laser rate should be increased as it can lower the noise floor to a factor of 1/N , where Nsitivity ,27. Strositivity .The conversion factor from counts to strain rate provided with the unit obeys the following equation:Based on the strain-rate conversion factor equation, a sampling frequency of no less than 3054 Hz would have avoided signal saturation for the engineered fiber without changing the gauge length. This calculation takes into consideration a limit of 90% of the dynamic range and the maximum integer value of an int16 number type as a precaution near the real limit.We demonstrated that optical noise could be reduced significantly by stacking the first two fiber instances of a standard multi-fiber cable. In our setup, a stack of five fibers achieves the maximum noise reduction of 20.04% within the main frequency content of the signal. As a result, the wavefield is smoothed, and wave phases can be easily followed. A stack of four fibers would achieve the best improvement for a sampling frequency of 1 kHz if the total interrogated fiber length has been equivalent to four spliced fiber instances of 1.5 km each. Stacking improvement depends on the cable length, which has an effect on the maximum laser rate for use. Therefore, for future multi-fiber surveys, we recommend taking these variables into consideration to establish which instance  the fiber must be interrogated to achieve the best stack improvement.Here we characterized for the first time two types of distortions in DDSS signal: quasi-phase jumps and phase jumps. The phase jumps are DDSS saturation that occur due to exceeding the dynamic range of measurement. These are characterized by phase jumps that can be corrected if SNR is large enough. We developed an algorithm that is able to correct signal saturation and restore the true values from distorted signals with some limitations, such as noise level. It is recommended to increase the laser rate as much as the total fiber length can handle to reduce the noise floor. However, this might bring limitations toward maximum time decimation that determines the output sampling frequency and, therefore, the output volume of the data.If the optical noise is low enough, we suggest including a saturation correction scheme as part of fundamental pre-processing when working with strong motion events for DDSS measurements. Otherwise, depending on the conversion factor from counts to strain rate handled by the unit, it is advisable to estimate the range of strain or strain rate to select which final sampling frequency after time decimation and gauge length is convenient for the survey. The correct parameters would set the ideal dynamic range and sensitivity to capture the desired events and so signal saturation can be avoided for the desired events to record.The PCA method is suitable for evaluating the relation between two signals only when the relation is mostly linear. The method also has problems when it involves saturated regimes as it becomes non-linear. Both types of fiber saturation present a non-linear regime within the record, and so machine learning approaches may help to overcome this and could also correct the quasi-phase jumps at the same time.Despite engineered fibers having a lower noise level due to scattered points uniformly distributed along the fiber, the stacking of DDSS data on standard fibers can be a cheap option for measuring the strain rate in volcano-tectonic environments; with a noise reduction that facilitates the continuity in wave phases. Stacking DDSS data routines can be a step further and motivates the exploitation of the existing coverage of standard multi-fiber telecom cables in cities and out of urban areas.