The-growing influence of urbanisation on green areas can greatly benefit from passive acoustic monitoring (PAM) across spatiotemporal continua to provide biodiversity estimation and useful information for conservation planning and development decisions. The capability of eco-acoustic indices to capture different sound features has been harnessed to identify areas within the Parco Nord of Milan, Italy, characterised by different degrees of anthropic disturbance and biophonic activity. For this purpose, we used a network of very low-cost sensors distributed over an area of approximately 20 hectares to highlight areas with different acoustic properties. The audio files analysed in this study were recorded at 16 sites on four sessions during the period 25–29 May (2015), from 06:30 a.m. to 10:00 a.m. Seven eco-acoustic indices, namely Acoustic Complexity Index (ACI), Acoustic Diversity Index (ADI), Acoustic Evenness Index (AEI), Bio-Acoustic Index (BI), Acoustic Entropy Index (H), Normalized Difference Soundscape Index (NSDI), and Dynamic Spectral Centroid (DSC) were computed at 1 s integration time and the resulting time series were described by seven statistical descriptors. A dimensionality reduction of the indices carrying similar sound information was obtained by performing principal component analysis (PCA). Over the retained dimensions, describing a large (∼80%) variance of the original variables, a cluster analysis allowed discriminating among sites characterized by different combination of eco-acoustic indices (dimensions). The results show that the obtained groups are well correlated with the results of an aural survey aimed at determining the sound components at the sixteen sites . This outcome highlights the capability of this analysis of discriminating sites with different environmental sounds, thus allowing to create a map of the acoustic environment over an extended area. Changes in the natural landscape are generally prompted by induced modifications of encroaching urbanisation. Such modifications may impact the environment at different levels: from the growth of urban heat islands , to greeThe study of environmental sounds has grown in importance as non-invasive techniques for ecological monitoring and have been recognised to convey important information on ecological status, such as species presence, environmental conditions and habitat quality . This emClimate change and habitat degradation due to chemical pollution and technophonic noise sources may affect natural animal populations. Anthropogenic noises are always regarded as a pollutant for the environment as animal communication could be hampered, thus potentially causing changes in their distribution. For this reason, mapping biophonic activities on medium–large areas may help monitor the consequences of the spread of urbanisation.The diffusion of the eco-acoustic approach among researchers has been favoured by the possibility of analysing acoustic recordings and converting them from a temporal domain to a frequency domain . Several indices implemented on a matrix of frequency intensities have been published in recent years . They aThe need for cost-effective soundscape assessment tools is not limited to traffic noise mapping in urban areas, but it is a requisite across all fields of eco-acoustics and bioacoustics. The increasing memory storage and decreasing cost of hardware makes acoustic surveys comparable to satellite monitoring in terms of scalability in space and time, but has the potential benefit of providing a real picture of local population dynamics.Although sounds are environmental components quite known at the level of individual species, they have not yet been implemented to monitor ecological dynamics on a large scale. In particular, sounds may play a primary role to describe the composition, diversity and dynamics of communities , and to Recently, cost-effective soundscape assessment tools have successfully been applied to traffic noise mapping in urban areas, examples of which can be found for the cities of Madrid , Rome 22, Paris The outline of this paper is as follows: in In this section, we describe the Parco Nord area under study, the instrumentation used, and the data acquisition scheme. We also include the analysis methodology used for the analysis of the recorded signals based on the calculation of the eco-acoustic indices and the statistical process of obtaining a spatial map of different sound activities in the area. In the last part, we describe the adopted sound-truthing with all the categories of sounds considered for the validation of the results.The Parco Nord of Milan expands over an area of approximately 790 hectares all the way up to its northern border and is encircled by a highly urbanised area. About 45% of the surface is devoted to green spaces and vegetation: wooded areas (over 100 ha), meadows, shrubs, hedges, and ponds. The remaining is dedicated to agricultural activities and infrastructures. More than 100 species of trees, shrubs and ornamental plants grow in the area.The chosen area of study consists of a tree-covered parcel of approximately 20 hectares. It is an area dating back to 1983, one of the first reforestations implemented to restore the area intended to become a park. This parcel of wood has been thinned out over time to favour the regeneration of the wood itself. Nowadays, it has a semi-natural structure, with herbaceous layers of nemoral flora, shrub layers and the presence of dead woods. There is a small body of water   was calcorted in . This inAs for the acoustic characterisation of the area, many sources which may bring to a partial masking of the singing activity of the avian community are present. We can identify them as: noise generated by park users, vehicular traffic, road works, and occasional overflights of the nearby Bresso airport. The birds detected in recent surveys in all the park belong to 39 different species.As highlighted in the Introduction, the main purpose of this work was to investigate the sound environment within a homogeneous plot of land (a wooded parcel) with the aim of quantifying the spatial variations at an increasing distance from technophonic sound sources. Creating maps of environmental sounds over a large area may require important financial commitment that could benefit from the availability on the market of very low-cost recorders (VLCRs). We used SMT security digital audio recorders with a 48 kHz sampling rate and a power bank lifetime of two weeks.Computation of the ACI index for white noise source.Behaviour of each VLCR at different frequencies.One of the disadvantages of using very low-cost recorders is the possible different microphone sensitivities they may have, causing a different response to a sound exposure. For this reason, an initial set of 46 VLCRs (numbered R01–R46) was preliminarily tested in the laboratory to select sensors with similar behaviour. In fact, the use of very low-cost sensors occasionally implicates the presence of anomalies in the responses, both in the range of frequencies and in signal intensity. The mounting position of the sensor in the sound field can also lead to response differences. According to a testing procedure implemented ad hoc, all recorders were individually mounted on a stand and exposed to white noise generated by a calibrated flat loudspeaker placed at a fixed distance. All responses were recorded with the same directivity . The response of each VLCR was evaluated in terms of:We opted for this procedure because the ACI index provides an overall evidence of any anomalies in the frequency response. The process of the ACI index calculation  was useseewave”  in the fseewave” . A dedicAcoustic Entropy Index (H), which highlights the evenness of a signal’s amplitude over time and across the available range of frequencies ;Acoustic Complexity Index (ACI), which determines the modulation in intensity of a signal over changing frequencies ;Normalised Difference Soundscape Index (NDSI), which accounts for the anthropogenic disturbance by computing the ratio between technophonies and biological acoustic signals ;The Bio-Acoustic Index (BI), which is calculated as the area under the mean frequency spectrum above a threshold characteristic of the biophonic activity ;Dynamic Spectral Centroid (DSC), which indicates the centre of mass of the spectrum .Acoustic Diversity Index (ADI), which provides a measure of the local biodiversity at the community level without any species identification .Acoustic Evenness Index (AEI), which provides reverse information of ADI with high values identifying recordings with dominance of a narrow frequency band .In general, eco-acoustic indices were grouped into categories aiming to quantify the sound amplitude, its level of complexity, and weight the importance of geophonies, biophonies, and technophonies (soundscape). In this work, we focused on the following set of eco-acoustic indices:For each site, the eco-acoustic indices were computed at 1 s integration time. The information in each time series was extracted using the most representative statistical metrics. For this purpose, seven descriptors were considered: the mean value, median, mode, standard deviation (SD), interquartile range (IQR), skewness, and kurtosis.In this subsection, we will present methodologies used for the analysis of the recorded signals.Principal component analysis (PCA) is a multivariate technique that analyses a dataset in which observations are described by several inter-correlated quantitative dependent variables, thus acting as a dimensionality-reduction method to reduce the number of variables or the dimensionality of large datasets . The priCluster analysis is a set of techniques aiming to find patterns in a set of objects in such a way that objects in the same group or cluster are more “similar” to each other than to those in other clusters. It is used as an approach to summarise the main characteristics of a dataset and is a common technique for statistical data analysis such as pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics, and machine learning .Hence, searching for spatial patterns of different bio/anthropic activities in the area of study has been addressed by applying an unsupervised clustering analysis to group together the information carried by the selected principal components (PCs). Here, we employed the following clustering algorithms: ‘hierarchical’ agglomeration using Ward algorithm ; k-MeansIn this section, we describe the scheme adopted for the aural analysis of audio files in order to quantify distinct sound features. A single expert carefully listened to each recording according to the following scheme: one-minute listening to every two minutes of continuous recording, for a total of 70 min-listening per site. In particular, this activity was focused on determining biophonic activities , technophonic sources , human voices and steps and rain and wind sounds, as reported in Each recording was labelled according to the categories illustrated in Corvus cornix), the wood pigeon , and the cuckoo (Cuculus canorus) produced sounds in the interval considered to be restricted to technophonies. Actually, the carrion crow’s call spectrum, which is the most active, is centred at approximately (1.3–1.4) kHz, as illustrated in The results presented in this section refer to the audio files recorded on 25 May 2015, from 06:30 a.m. to 10:00 a.m. The choice of eco-acoustic indices and their settings for the analysis requested an initial tuning due to the specific environment under investigation. We started with the seven eco-acoustic indices described in However, adjusting the interval bounds for human-generated and biological sounds  was not sufficient to obtain satisfactory results in terms of groups of sites with similar sound features. Considering the spectrogram of two recordings taken simultaneously at Site 2 and Site 17 see , we can As reported above, PCA was performed in order to reduce the number of clustering variables and obtain an insight into the variable relevance. Here, we illustrate the results obtained for the statistical metrics describing the distribution of the indices.V, given by In keeping with the largest possible variance of the original variables, we selected the first 3 dimensions out of 35 original variables . Dimensions %= 78.2% a. The co. In our case, Site 18 is separated from the other sites. On the contrary, k-means operates the other way round, as an agglomerative algorithm (bottom–up process). As such, the two clusters are almost equally occupied (cluster 1 with seven observations and cluster 2 with eight observations). We also tested the solution at three and four clusters to possibly highlight more complex patterns in the acoustic data. In this case, both DIANA and k-means algorithms provide the same outcome with Site 18 to form a single cluster for both the two options (three and four clusters).Actually, as a divisive hierarchical clustering algorithm, DIANA starts with one large cluster containing all For a straightforward interpretation, we considered the distribution of mean values of each index into the obtained clusters. As can be clearly seen, the statistical analysis based on a reduced number of dimensions is able to quite efficiently separate the mean-index values based on the k-means algorithm. This result reflects the robustness of the clustering after the substantial dimension reduction.In order to evaluate whether these differences are significant, we applied the Wilcoxon–Mann–Whitney test (WMW)  to the tThe spatial distribution of the different acoustic descriptors representative of Dimensions 1, 2 and 3 see  is illusIn this section, we present the results on the NDVI index computed for the period 17–19 May 2015. The NDVI index is usually employed to analyse remote sensing measurements and assess whether the observed area contains live green vegetation, as described in In this section, we will combine the results of the statistical analysis performed on the eco-acoustic indices in order to determine a spatial map of environmental sound in the area of study.In Similarly, the acoustic entropy index, H, is related to frequency homogeneity over the spectrum and its variation over time. This means that high values of H are correlated with higher frequency occupation of the spectrum and time. In our specific case, cluster 1 is characterised by a value of H = 0.76, while H = 0.82 for cluster 2. Cluster 1 is also characterised by a <DSC> median value of 0.48 kHz lower than for cluster 2 with <DSC> median values of about 0.52 kHz see . In bothThe three-cluster solution highlights Site 18 which contains distinctive eco-acoustic indices from the previous cluster 2. This can be clearly observed by looking at As it is apparent from We also analysed the potential effect of the nearby airport traffic. During the measurement period, 20 airplanes taking off were counted. Their effects on the eco-acoustic indices were evaluated with reference to Site 17 which sits at a distance of approximately 700 m from the runway. This result is confirmed by calculating the indices’ value over a one-minute interval before, during (at 01:41), and after take-off, as shown in In order to provide a more solid interpretation of the results emerging from the cluster analysis, we checked for all the aural characteristics highlighted by an expert operator. In The perceived singing abundance in the two clusters, shown in In order to determine the potential influence of the vegetation coverage as a biophonic activity driver, in As a final remark, the analysis on the remaining time slots, namely from 26 May 2015 to 29 May 2015, confirms the results presented above in terms of sites membership in the different clusters. This fact underlines the robustness of the analysis and the stationarity of the sound environment during the analysed period.Urban parks are often exposed to road traffic noise produced by the surrounding roads and other anthropogenic sounds due to the presence of people and noises from construction sites. Such sounds alter the natural soundscape, reducing the overall sound quality of a park, thus interfering with the presence of biophonic activity either due to the partial overlapping of frequencies or high background noise levels. For this reason, assessing the health of urban ecosystems and extending the concept of the soundscape, previously limited to residential urban areas, also to urban green areas using an eco-acoustic analysis approach, would help monitor biodiversity estimation and obtain useful information for conservation and development planning.The availability of very low-cost sound recorders allowed drawing a real picture of the sound environment over an extended area with a cost-effective solution. In particular, we focused on studying the sound characteristics collected at 16 sites at the Parco Nord located in the city area of Milan, Italy, using very low-cost sensors distributed over an area of nearly 20 hectares. Statistics, PCA and cluster analysis, applied to five eco-acoustic indices, allowed identifying areas (clusters) with different sound characteristics.What drives the cluster formation is essentially Dimension 1 of the PCA with 54.1% of explained variance and represented by the correlated indices ADI, AEI, and H. The spatial distribution of ADI see a retraceIn general, two main areas emerge from the statistical analysis. The first (cluster 1) is characterised by less frequency modulation, frequency richness, and with an overall lower spectral centroid, typical of areas with less biophonic activity and higher anthropophonic disturbances (traffic noise and construction site). Cluster 2 presents higher index values as a result of a greater distance from non-natural sources and a more lively biophonic presence. This result is confirmed by the aural survey revealing a more intense and richer singing activity in cluster 2 and with a traffic noise perceived as continuous and less intense. The analysis performed on the other recording time-slots (26–29 May 2015) confirms the results, as illustrated throughout the paper (data of 25 May 2015), suggesting both the robustness of the analysis and the stationarity of the sound environment during the short period under analysis.Additionally, the NDVI index does not seem to provide evidence that the vegetation coverage is the main cause of the observed results, as it does not change significantly within the areas associated with each cluster. Owing to the limited extension of the recorded tracks (3.5 h), this work represents a feasibility study, showing the potentiality of the adopted method to describe the acoustic complexity of an urban park and highlighting areas with different sound components. The inherent sound changes involved in environmental dynamics could take advantage of this approach, which can be used to evaluate ecosystem health trends over long periods.In general, mapping environmental sound over large areas by means of eco-acoustic indices could be applied as an innovative diagnostic tool able to account for the effect of climate change in different biomes. The sensitivity of the sonic performances of animals even under the modest modification of the physical parameters of the environment  allows to investigate with great efficiency the effects of human intrusion and climate change. The fine scale of resolution of the eco-acoustics approach can be easily integrated with the new generation of satellite and terrestrial remote sensing techniques . The initial effects of global change on physiology and the behaviour of organisms can be evaluated, saving important time otherwise requested to detect the effects on the environment at a scale of decades.The information gained by eco-acoustics surveys can be used as anticipatory tools to suggest immediate actions and producing precious indications to stakeholders and policymakers before irreversible environmental changes occur, saving time and economic resources. The analysis of the collected recordings is oriented to discover and describe eco-acoustic events of relevance for better understanding the dynamics activated by climate change. The latter is an important point to encourage the world-wide diffusion of this approach that requires a relatively modest investment in ground-based technology. As future development of this work, we are planning to extend this approach to two different habitats, namely Parco del Ticino, a natural park of north Italy, and along the marine coastline of Liguria sea with the goal of validating the methodologies to use eco-acoustic information on the large scale to optimise the investigation and monitor the evolution of the two sound environments.


Aiming at the problem of low control accuracy caused by nonlinear disturbances in the operation of the PLS-160 wheel–rail adhesion test rig, a linear active disturbance rejection controller (LADRC) suitable for the wheel–rail adhesion test rig was designed. The influence of nonlinear disturbances during the operation of the test rig on the control accuracy was analyzed based on SIMPACK. The SIMAT co-simulation platform was established to verify the control performance of the LADRC designed in this paper. The simulation results show that the speed and creepage errors of the test rig under the control of the LADRC met the adhesion test technical indicators under four different conditions. Compared with the traditional PID controller, the creepage overshoot and response time with the LADRC were reduced by 1.27% and 60%, respectively, under the constant creepage condition, and the stability recovery time was shorter under the condition of a sudden decrease in the adhesion coefficient. The LADRC designed in this paper shows better dynamic and anti-interference performance; therefore, it is more suitable for a follow-up study of the PLS-160 wheel–rail adhesion test rig. When a train runs on a rail surface with pollutants such as water and engine oil, low adhesion and large creep occur, which seriously affect traction/braking performance and operation safety. The existing wheel–rail adhesion theories mainly study the small creep stage without pollutants on the rail surface, which cannot truly reflect the wheel–rail state in the large creep stage with pollutants. The existing wheel–rail adhesion test rigs are mainly double-disc rolling test rigs ,2,3,4, wAs a problem with great research value in the control field, disturbance rejection has attracted the attention of many researchers in recent years. Shen et al. proposed data-driven control strategies for networked nonlinear systems with event-triggered output . The proThe PLS-160 wheel–rail adhesion test rig uses a permanent magnet synchronous motor (PMSM) as the power source, and its control methods are various. At present, many scholars have carried out relevant research. The control methods of PMSM mainly include proportional–integral–differential (PID) control, adaptive control, model predictive control (MPC), and active disturbance rejection control (ADRC). The classical PID control method does not depend on the model. The method is relatively mature and easy to implement, so it has a wide range of applications. However, the traditional PID controller has a long adjustment time and large overshoot, and its dynamic performance is not ideal. To address these problems, Cui et al. put forward an adaptive variable universal fuzzy PID compound control strategy and applied it to the vector control of the PMSM servo system based on the speed loop . The strThere are strong nonlinear disturbances in the operation of the PLS-160 wheel–rail adhesion test rig. In order to ensure the accuracy of the test results, it is necessary to improve the control performance and ensure the control accuracy. The parameters tuned by the PID controller cannot effectively adapt to interference factors in the system or the environment. The adaptive control and MPC methods largely depend on the model accuracy, but in practical application, it is difficult to obtain accurate system parameters of the test rig due to a variety of environmental interference factors. The ADRC controller has too many parameters to be tuned, so it is difficult to apply in practice. Therefore, there is presently no controller suitable for precise creepage control of the PLS-160 wheel–rail adhesion test rig.To achieve accurate creepage control of the PLS-160 wheel–rail adhesion test rig, in this paper we analyzed the nonlinear disturbances existing in its actual operation. The SIMPACK dynamic simulation model of the test rig was established with the nonlinear disturbances as the input parameters. The dynamic response of the test rig under the motor open-loop control was analyzed. A linear active disturbance rejection controller (LADRC) suitable for the PLS-160 wheel–rail adhesion test rig was designed based on the double closed-loop speed and torque control strategy. The SIMAT co-simulation platform was established to verify the control performance and effect of the creepage controller designed in this paper.To study the wheel–rail adhesion characteristic of a train under large creep conditions, the Braking Technology Institute of Tongji University designed a new type of circulator wheel–rail adhesion test rig, called PLS-160, with a design speed of up to 160 km/h. vc. The other wheel is in the state of rolling with slip, and its speed simulates the axle speed The test rig is co-driven by the vehicle speed motor and wheel speed motor. One wheel is in a pure rolling state when running, and its speed simulates the vehicle speed The technical indicators of the adhesion test on the PLS-160 according to the need to find the second peak point in the large creep stage  are showThere are various nonlinear disturbances during the operation of the PLS-160 wheel–rail adhesion test rig. To suppress the influence of nonlinear disturbances on creepage control and make the control more accurate, the main nonlinear disturbances during the test, including air resistance, adhesion coefficient–creepage characteristic, and mechanical structure transmission vibration, were analyzed.The adhesion test rig uses the rotation motion of the rotary arm to simulate the vehicle running speed. There is a nonlinear air resistance effect in the rotation process of the rotary arm, and its value is proportional to the speed quadratic. When the test rig is running at the maximum speed of 160 km/h, the rotation angular velocity of the rotary arm is up to 44.44 rad/s. The generated air resistance torque should be calculated through simulation to judge its impact on the operation of the test rig.Based on CFD flow field simulation analysis, three-dimensional models of the adhesion test rig rotary arm and the flow field domain are established by using UG software, the model is meshed based on ANSYS ICEM, the flow field in the high-speed rotation of the adhesion test rig is simulated and numerically solved using Fluent, and the results are post-processed based on Tecplot. The calculated air resistance torque of the rotary arm under different vehicle speed conditions through simulation is shown in According to Rail vehicle traction and braking are restricted by adhesion force, and the adhesion characteristic is a unique property of rail vehicles. The adhesion coefficient and the creepage between wheel and rail is a nonlinear relationship.According to traditional adhesion theory, the adhesion coefficient increases linearly with creepage in the small creep area and presents zero slope or negative slope characteristics in the large creep area ,19,20,21To sum up, the adhesion coefficient and creepage between the wheel and the rail show a nonlinear relationship of unknown size and variation trend in the large creep area, which leads to higher requirements for accurate adhesion test rig creepage control under the variable creepage condition. Therefore, the adhesion coefficient–creepage characteristic is also a nonlinear disturbance that cannot be ignored.The transmission system of the adhesion test rig is mainly composed of multiple bevel gear pairs, which will inevitably generate vibration during operation. As an elastic mechanical system, the gear transmission system will have the corresponding dynamic response with the influence of external dynamic excitation, and will generate nonlinear vibration, which makes it difficult to control the system accurately.The external dynamic excitation of the gear transmission system can be categorized into two types: external and internal excitation. External excitation includes the excitation generated by the operation of the power sources (two drive motors of the adhesion test rig), the mechanical load, and other components such as rolling bearings in the mechanical transmission system. In particular, there is also the impact effect of the wheel and the rail in this system. The internal excitation of gears can be divided into four forms: stiffness, error, meshing impact, and gear tooth damage excitation. Stiffness excitation refers to the situation where the gears are engaged, and meshing stiffness and load show a periodic time-varying law, so a periodic time-varying gear force is applied to the system. Error excitation refers to machining and installation errors of the gears, causing a change in the instantaneous transmission ratio when engaging, resulting in periodic displacement excitation. Meshing impact excitation is caused by a gear approach point or recess point position error and elastic deformation caused by the gear on its own load when the gear enters the mesh. Gear tooth damage excitation refers to the impact excitation generated by gear tooth surface damage, such as peeling or root crack. Because internal excitation is related to the structural characteristics of the transmission system itself, whether the external excitation exists or not, the gear system will still be affected and will generate nonlinear vibrations.To sum up, the excitation sources and types of vibration during the operation of the adhesion test rig are complex and diverse, and the generated vibration response is nonlinear and time-varying. Therefore, the influence of mechanical structure transmission vibration should be considered in the accurate control of the adhesion test rig.As described in this section, the influence of nonlinear disturbances such as air resistance, adhesion coefficient–creepage characteristic, and mechanical structure transmission vibration cannot be ignored during the operation of the PLS-160 wheel–rail adhesion test rig, and should be considered in the creepage control of the test rig. As described in the following section, the creepage control of the adhesion test rig was studied by establishing simulation models.To verify the influence of nonlinear disturbances on the adhesion test rig and carry out creepage control on this basis, based on SIMPACK multi-body dynamic software, a dynamic model of the adhesion test rig was established, and the nonlinear disturbances were taken as the model input so that the model could fully reflect the dynamic characteristic of the rig during operation.According to the actual bevel gear pair parameters of the test rig see , the PLSThe three nonlinear disturbances described in The vehicle speed and wheel speed motor output shaft rotation speeds were set to simulate two creepage conditions (constant and variable creepage), and the dynamic response of the adhesion test rig under open-loop motor control was studied.Under the constant creepage condition, the simulation vehicle speed was 50 km/h and the creepage was 0.1. The dynamic response of the adhesion test rig in this condition is shown in It can be seen from Under the variable creepage condition, the simulation vehicle speed was 50 km/h, the creepage changed in a sinusoidal function within the range of 0.01–0.3, and the change period was 6 s. The dynamic response of the adhesion test rig in this condition is shown in It can be seen from As described in this section, the dynamic simulation model can reflect the influence on the dynamic characteristic of nonlinear disturbances of the test rig during operation. Under open-loop motor control, the maximum creepage error of the test rig reaches 4.9%, and does not meet the adhesion test technical indicators. Since the adhesion coefficient in the large creep area varies greatly with creepage, the small creepage control error will also lead to the amplification of the adhesion coefficient error in the tests, resulting in poor accuracy of the test results. Therefore, it is necessary to study the control strategy and the control algorithm to achieve accurate speed and creepage control of the test rig.The control strategy and control algorithm comprise the creepage control core of the adhesion test rig. To achieve accurate creepage control, the basic framework of the creepage control strategy should be constructed first, and then the control algorithm should be studied and the controller designed on this basis.Since the power source of the PLS-160 wheel–rail adhesion test rig is the alternating current permanent magnet synchronous motor (ACPMSM), to achieve accurate creepage control, the control strategy framework can be divided into two parts: the ACPMSM control strategy and the creepage control strategy. Finally, based on the idea of cascade control, the creepage control strategy framework of the adhesion test rig is constructed.The ACPMSM has a complex structure and is difficult to control. According to the characteristics of the PLS-160 wheel–rail adhesion test rig motor, a mathematical model of the ACPMSM is decoupled and its dimension is reduced based on the vector control method to make it equivalent to a DC motor for control. This paper uses the current feedback control method; under the control mode of The control of the adhesion test rig creepage is essentially the control of the simulated vehicle and axle speed. The specific formula is as follows:According to Formula (2), the creepage of the adhesion test rig is generated by wheel axle rotation angular velocity and rotary arm revolution angular velocity, and the essence of angular velocity control is motor output torque control. Therefore, the double closed-loop speed and torque control system is adopted as the framework, and the designed control strategy is shown in Based on the double closed-loop creepage control strategy framework in At present, there are various control methods for the PMSM. In addition to the traditional PID control, the methods also include adaptive control, sliding film variable structure control, model predictive control, and active disturbance rejection control.As mentioned in The basic structure of the current inner loop PI controller is as follows:Taking the wheel speed motor as an example, a speed outer loop LADRC suitable for the wheel–rail adhesion test rig was designed.Based on the working principle of the wheel–rail adhesion test rig, the test rig stress analysis was carried out, as shown in According to The torque equation of the rotation output small bevel gear is:If the target simulation wheel speed is set as The motor vector control of Formula (1) is substituted into Formula (6), and the differential equation between the output current tuned by the current inner loop control and the simulated wheel speed is obtained:If the control quantity of the current inner loop given by the speed outer loop is set as Based on the principle of active disturbance rejection control ,28,29, tThe LADRC is mainly composed of linear extended state observer (LESO), linear state error feedback (LSEF), and other structures. LESO and LSEF are the results linearized by extended state observer (ESO) and nonlinear state error feedback (NLSEF), respectively, in ADRC .According to the principle of LESO and Formula (9), the outer loop augmented form of the wheel speed motor after expansion is:The differential equation of LESO is as follows:According to Formula (12), if the estimated value of According to the principle of LSEF, the control quantity By compensating the estimated disturbance value obtained by the observer to the control quantity, the final control quantity input form of the controlled object is:After the above operations, the LADRC converts the nonlinear control system of the adhesion test rig into an integrated linear series system. To suppress the overshoot problem, a linear tracking differentiator (LTD) is added to the controller. Its structure is as follows:To sum up, the structural diagram of the LADRC of the wheel speed motor is shown in The stability of the LESO is analyzed as follows.The observer error can be obtained by subtracting the system state space form (11) from the LESO Equation (13). Let The stability proof of the observer can be converted to the stability proof of Equation (18). The characteristic polynomial of the error Equation (18) isAccording to the sufficient and necessary condition for the stability of the control system, if the system is stable, the roots of the characteristic equation must be located on the left half of the andwidth , we set Therefore, the correction gains of the observer areSetting ion (18) . TherefoTo verify the creepage control performance of the LADRC, described in The SIMAT co-simulation platform is mainly composed of five parts: creepage calculation module, starting module, speed outer loop controller, PMSM torque controller, and dynamic simulation module, respectively, corresponding to Parts 1–5 in To verify the control effect and adaptability to different conditions of the creepage controller designed in this paper, four simulation conditions were set up: constant creepage, variable creepage, sudden decrease in adhesion coefficient, and variable adhesion characteristic. Based on the SIMAT co-simulation platform, the control effects of the traditional PID controller and LADRC designed in this paper were compared and analyzed.Under the constant creepage condition, the target simulation vehicle speed was set at 50 km/h, with 0–1 s as the test rig starting process, and the target creepage was 0.1 after 1 s. The dynamic response of the adhesion test rig simulation model under the control of the PID controller and the LADRC is shown in It can be seen from According to Under the variable creepage condition, the target simulation vehicle speed was set at 50 km/h, with 0–1 s as the test rig starting process, creepage changed in a sinusoidal function within the range of 0.01–0.3 after 1 s, and there was a change period of 6 s. The dynamic response of the adhesion test rig simulation model under the control of the PID controller and the LADRC is shown in It can be seen from Under the condition of a sudden decrease in the adhesion coefficient, the target simulation vehicle speed was set at 50 km/h, with 0–1 s as the test rig starting process, target creepage of 0.1 after 1 s, and a sudden decrease in the adhesion coefficient to 1/5 of the original after 2 s to simulate wheels running on a clean and smooth rail surface to a low-adhesion rail surface with pollutants. The dynamic response of the adhesion test rig simulation model under the control of the PID controller and the LADRC is shown in It can be seen from According to The target simulation vehicle speed was set at 50 km/h, with 0–1 s as the test rig starting process, the creepage changed in a sinusoidal function within the range of 0.01–0.3 after 1 s, and the change period was 6 s. The dynamic response of the adhesion test rig simulation model under the control of the PID controller and the LADRC is shown in It can be seen from In summary, under conditions of constant creepage, variable creepage, sudden decrease in adhesion coefficient, and variable adhesion characteristic, the speed error under LADRC control designed in this paper is less than 1 km/h and the creepage error is less than 1%, meeting the adhesion test technical indicators. Compared with the traditional PID controller, the LADRC designed in this paper has faster response speed, less overshoot, stronger anti-interference performance, and shows good adaptability to different nonlinear adhesion characteristic curves. Therefore, the LADRC designed in this paper can ensure the accuracy of adhesion test results and is more suitable for the follow-up study of the PLS-160 wheel–rail adhesion test rig.At present, the PLS-160 wheel–rail adhesion test rig has been put into use, and the creepage errors under both constant and variable creepage conditions meet the technical indicators, showing good control stability and following performance, as shown in In the future, a series of adhesion tests will be carried out based on the PLS-160 wheel–rail adhesion test rig under the large creep condition with different third-body media between the wheel and the rail.In this paper, an LADRC suitable for the PLS-160 wheel–rail adhesion test rig was designed and its control effect was verified by co-simulation.(1) The SIMPACK dynamic simulation model of the PLS-160 wheel–rail adhesion test rig was established, various nonlinear disturbances existing in its operation process were inputted, and the test rig model was simulated. The results show that the creepage error of the test rig under open-loop motor control was up to 4.9%, which does not meet the adhesion test technical indicators. It is necessary to accurately control the creepage of the test rig.(2) Based on the double closed-loop speed and torque creepage control strategy, an LADRC suitable for the PLS-160 wheel–rail adhesion test rig was designed. The SIMAT co-simulation platform was established to study the control performance of the LADRC designed in this paper. The results show that under various conditions, the speed error of the adhesion test rig under LADRC control was less than 1 km/h and the creepage error was less than 1%, meeting the adhesion test technical indicators. The LADRC designed in this paper can adapt to a variety of complex conditions, showing good control stability and following performance.(3) Compared with the traditional PID controller, the creepage overshoot of the adhesion test rig under the LADRC control designed in this paper was reduced by 1.27%, the response time was shortened by 60% under the constant creepage condition, and the stability recovery time was shorter under the condition of a sudden decrease in adhesion coefficient, showing better dynamic and anti-interference performance. Therefore, this LADRC is more suitable for follow-up study of the PLS-160 wheel–rail adhesion test rig.(4) In addition to accurately controlling creepage for the PLS-160 wheel–rail adhesion test rig, the principle of LADRC designed in this paper is also applicable to other mechanical equipment that is subjected to large nonlinear disturbances and needs to be accurately controlled. In the future, the parameters of the controller will be further adjusted and optimized to give the control system better robustness and anti-interference ability, and to improve adhesion test accuracy.


Unified jet-DBD design,  Plasma components including 2. Plasma sustains the biofilm disinfection protocols including safety, efficiency, and cost-effectiveness3.Plasma jet produces non-thermal plasma propagating away from the confined electrode assembly into the atmospheric air and provides reactive species like 4. The electric potential enhances the fraction of electron–ion pairs subjected to the electric field to the point where the current is saturated. Beyond saturation potential, the electric current rises up exponentially by increasing the voltage. At this stage, the intense electric field sets the primary electrons, which are small and have higher mean free path compared with ions, to gain required energy to ionize the neutral atoms in the gas on their way toward anode and the secondary electrons are produced. Higher electric field makes secondary electrons to further ionize the neutrals and supply the electron avalanche. The region where current was increasing exponentially is called the Townsend discharge. Prior to the electrical gas breakdown, corona discharges occur in the regions where the electric field is strong, such as sharp points, in the so-called Townsend dark discharge regime. Glow discharge occurs at higher electric currents where visible light is emitted. At a low electric field where the corona discharge is active, the filamentary configuration is formed which is referred to as streamers5.Electric discharge is initiated in a neutral gas by setting the electrons to be free using some procedures such as external photons. Such free electrons are accelerated subsequently by an electric field, which is required to be present in the mediumExtra secondary electrons emitted from the cathode due to the ion/photon impact lead to the electric breakdown in the gas. At the breakdown phase the electric current rises up by a few orders of magnitude, and the gas state moves into the natural glow discharge regime.6 for Atmospheric plasma sources, such as DBD, are equipped with a barrier-like configuration to produce the plasma, which is confined geometrically to the inter-electrodes area. Alternatively, in the plasma jet configuration the plasma is blown away to an unbound area. Electric field is increased by the applied potential, and higher frequency results in larger input power to the discharge. However, the optimum frequency related to the suitable applied power needs to be characterized, since frequency beyond a certain limit does not necessarily improve the plasma attributes, as reported in Refscale sharp configuration15. Unified jet-DBD design, DBD generates extensive plasma except that is bound in the inter-electrode spacing or attached to the single electrode. In the plasma jet, the gas flowing through the device extends the plasma as an efflux into the ambient air with mm-16. Radial component of the electric field guides the electron drift velocity and drives the discharge propagation and expansion into the surrounding air. Thus, higher electron density in this area yields homogenous radial discharge.Due to the electric field and electrode configuration, the plasma plume is forced out of the tube into the open air, yet a common drawback in the plasma jet is the relatively small dimension of the discharge demanding noble gas equipped with a flow controller. Inherent in every AC voltage cycle is a controlling plasma-off that reduces the charge in the central electrode tip neighborhood and subsequently the metastable atoms are blown away leading to path preferences. The recombination process generates high density metastable atoms accompanied with an efficient ionization if combined well with the seed electronsmentclass2pt{minimMass fraction, Constitutive momentum equation of a continuous fluid, Navier–Stokes, models the plasma flow and the chemistry governs the space charge density.Secondary electron emission within the walls imposes definitive boundary conditions, Fig. 18.Multiple chemical reactions of mentclass2pt{minimIn order to converge the solution to the equations, maximum and minimum element size were set to be A set of electrostatics equation and Laminar flow of the plasma are solved simultaneously with initial values of velocity on the Detailed Analysis of 19. Peak electron density occurs at Figure Typical voltage and current characteristic signal of the non-thermal plasma suggest that the average power consumed in the plasma is expressed by Recorded images of two 20.The discharge characteristic is different for each cycle of the 21. Phase shift is a measuring procedure to probe the plasma state, observe the impedance of the circuit, and look into the circuit behavior as a whole. Figure Power in the plasma dissipates through ohmic losses governed by the electron-neutral collisions. The plasma inductance is determined by the electron quantities opposing the electric field variationsPlasma acts as an additional nonlinear load into the circuit. When plasma is not formed, phase difference between voltage and current waveforms is about Capacitive reactance builds up as a result of extended electrodes gap, corresponding to the maximum sheath/space charge width. At higher electric fields, the ion density increases due to the high electron concentration, representing a collisional heating source thus the power is escalated.22. At lower current, the phase shift is uniform and cluster about Figure 23, and compared to a few designed Figure


Recent evolution in the field of data science has revealed the potential utility of machine learning (ML) applied to criminal justice. Hence, the literature focused on finding better techniques to predict criminal recidivism risk is rapidly flourishing. However, it is difficult to make a state of the art for the application of ML in recidivism prediction. In this systematic review, out of 79 studies from Scopus and PubMed online databases we selected, 12 studies that guarantee the replicability of the models across different datasets and their applicability to recidivism prediction. The different datasets and ML techniques used in each of the 12 studies have been compared using the two selected metrics. This study shows how each method applied achieves good performance, with an average score of 0.81 for ACC and 0.74 for AUC. This systematic review highlights key points that could allow criminal justice professionals to routinely exploit predictions of recidivism risk based on ML techniques. These include the presence of performance metrics, the use of transparent algorithms or explainable artificial intelligence (XAI) techniques, as well as the high quality of input data. Recidivism rates have a major impact on public safety and increase the cost of incarceration. An estimate of economic and social costs of recidivism has been provided by one study conducted in England and Wales on a 12-month follow-up, indicating GBP 18.1 billion for the 2016 criminal cohort [A discipline that in recent years has provided an important contribution by attempting to provide for criminal recidivism is data science. Indeed, data science is the application of quantitative and qualitative methods to solve relevant problems and predict outcomes ,4,5. In This review aims to deepen these debated topics. Indeed, despite the extensive development of these approaches and a promising assessment of the reliability of ML models to support criminal justice , they arThe methods for systematic review have been structured according to the PRISMA Statement. No language, publication date, or publication status restrictions were imposed. The features of included studies are the following: (1) the aim of the study is to predict recidivism; (2) the study has explicit accounting of data collection methods; and (3) the study has proper description of the methodologies, including the applied machine learning methods.In contrast, the authors did not include studies in which one or more of the following criteria were satisfied: (1) the main purpose of the study is to reduce the bias of the ML model ; (2) the study has the aim to predict the psychiatric characteristics in the reoffender ; and (3) the study lacks the accuracy (ACC) or the Area Under the Curve (AUC) metrics necessary to evaluate machine learning models.Studies have been selected from two online databases: Scopus and Pubmed. We used the following equation searching by title, abstract and keywords for: ((“crim*”) OR (“offen*”) OR (“violat*”)) AND ((“recidiv*”) OR (“relapse”)) AND ((“machine learning”) OR  OR (“deep learning”)) resulting in a total of 79 bibliographic records. References listed in the included papers have also been examined to identify studies meeting our inclusion and exclusion criteria. The search was last performed in January 2022. We first screened titles and excluded those clearly not meeting the eligibility criteria. Then abstracts were examined, and lastly, full texts were read, eventually leading to the inclusion or exclusion of the papers according to the above described criteria. The screening of the literature was performed in blind by two investigators (S.B. and F.P.) In the case of disagreement, a third reviewer (M.B.) assessed the paper to achieve a consensus.The ROBIS tool was used to assess the risk of bias of the included systematic reviews . The ROBThe purpose of fourteen papers was to reduce model bias;One paper assessed only the psychiatric characteristic of repeat offenders;Three papers did not clearly describe the methodology.A total of 16 duplicates were identified and removed from the 79 preliminary results. In addition, 33 articles were removed by looking at the title and abstract only since they did not match the criteria. The remaining papers were selected or excluded after a comprehensive analysis of the full text. Among those papers, 18 were excluded since they did not satisfy eligibility criteria for the following reasons: A total of 12 studies were finally selected. To present the results of the studies, we divided them into three sections. The first one analyses dataset and ML techniques applied within the study. We first focused on the characteristics of datasets. Then we checked whether in the studies the authors have used ML techniques such as data pre-processing or cross validation (CV). The first one is a technique to transforming raw data into an understandable format for the ML models. The CV, instead, is a technique to estimate if the ML models are able to correctly predict data not yet observed. This first section is important because different datasets and different ML techniques can greatly influence the final performance of ML models. In the second section, we analysed the type of recidivism that each study aimed to predict. Then we selected the ML model that in the study obtained the best performance. Finally, in the third section, by dividing the studies into four categories based on their aim, we compared the performance of each ML model based on specific metrics.The main features of the considered studies are listed in The datasets are different in each study. Two of them used only data from the correctional institution or the justice system. The first one was based on 3061 youth charged with a sexual offense in Florida who have been monitored over two years after the initial charge to determine sexual recidivism . The aimFive papers refer to risk assessment tools created specifically to predict recidivism across the country. Among them Karimi-Haghighi and Castillo used RisCanvi, a risk assessment protocol for violence prevention introduced in the Catalan prison during 2009 in which professionals conducted interviews resulting in the creation of a risk score through some risk elements . The eleAnother study that combined statistical features with other specific risk assessment tools is by Tolan and collaborators . The autOnly one study used the Historical, Clinical and Risk Management–20 (HCR-20) with 16 other clinical and non-clinical risk assessment factors in order to determine the likelihood of recidivism among first-time offenders (FTOs) . Data weFinally, it is important to mention the paper of Haarsma and his working group  in whichAfter compiling the dataset, each study used different ML techniques to analyse and improve the reading of the data and results. Four studies used pre-processing to improve the datasets. Two of them preferred a feature selection technique ,26. One Another relevant aspect to mention is the author’s choice to use a ML technique called cross validation (CV) in order to estimate the ability of ML models to generalize to data not yet observed. Among the studies included in the review, nine used CV.For a better comparison of the studies, it is possible to perform a sorting by the type of recurrence they aim to predict. The sorting leads to four categories: general ,28,31,32The previously observed datasets  were useIn this review, for each study, we considered only the ML models that performed better, according to the author’s observation . The mosIn In contrast, for violent recidivism , the mulIn some of the studies considered in this review, the authors described the variables that contributed most to the final evaluation. Some considerations about these results are discussed in Four top factors are identified: royal pardons or suspension, first offending age, encouragement of family members and frequency of substance abuse . Among tIn this systematic review, the datasets and ML models included have been compared simultaneously. However, for a critical evaluation of the results of ML models, it is also necessary to focus on the type of dataset used to train the model. In each study, the method of data collection is different. In some papers, the data come from the countries’ institutions, while in others they come from the checklists of risk assessment tools or neurocognitive tests. Consequently, datasets have different characteristics such as sample size, mean age, type of crime and years of recidivism follow-up. These variables can significantly modify the assessment of the ML model .Another relevant aspect to mention is that not all the papers declare the use of data pre-processing or are clearly explicit about the process used. As mentioned above, we applied the ROBIS assessment to highlight any possible systematic distortion. The current state of data science reveals that ML algorithms may be very efficient. Accordingly, the results of the papers considered in this review show that each ML model has a good performance. Taking into consideration the ACC, the mid-score is 0.81. In contrast, considering the AUC the mid-score is 0.74. Considering that the range of ACC and the AUC are from 0 (no predictability) to 1 (perfect predictability), both mid-scores show a good predictability of the models. Some studies use a risk assessment for a specific type of recidivism, crime or population, while others measure the risk of general recidivism. However, comparing the two types of studies, no significant differences emerge. The only difference observed in this review is an increase in ACC of 0.03 for the specific type of recidivism. Thus, there is no evidence that the use of a more specific risk assessment could significantly improve the ability to predict criminal recidivism. This review compares different ML methods, models and datasets used to predict recidivism. Analysing the available models, the most common technique used in these papers to predict recidivism is logistic regression, while more complex algorithms are less common. In terms of performance, a simpler prediction model such as logistic regression and more complex ones such as the random forest show similar predictive validity and performance. What emerges from the results is that it does not seem essential to focus on model complexity to improve the predictability of criminal recidivism.However, literature analysed in this systematic review pinpointed some limitations. First of all, the performance of each model does not depend only on the ML model or the dataset. The method of data collection and data pre-processing are also important. Both are aspects that can significantly affect model performance ,35. We oIn Using the ML method for risk assessment in criminal justice to predict recidivism has increased in recent years ,23. HoweFirst, we would like to point out that it would be important to pay more attention to the dataset and data processing. Taking a few steps back and focusing on these aspects could improve model performance and reduce possible bias . Moreover, in order to facilitate comparison, it would be useful to learn to compare models by having the same evaluation metrics available. Considering metrics available in the analysed papers, we observed a good overall performance of the models. This allows us to emphasize the concrete support that these tools can bring to human judgment, which is also not free of bias . The binThe latest machine learning models are like ‘black boxes’ because they have such a complex design that users cannot understand how an AI system converts data into decisions . The lacThe implementation of quantitative and qualitative methods to predict criminal recidivism could be a useful tool in the field of criminal justice ,4,5 HoweThe use of artificial intelligence in judicial proceedings and the resulting decision-making processes will be a field of wide reflection among scientists, jurists and bioethicists. This systematic review is a thorough synthesis of the best available evidence, but it is also a contribution in a field that presents many ethical, deontological and legal critical issues in the state of the art.


In the context of carbon peak and carbon neutral policies, low-carbon construction has been the focus of most countries worldwide. As one of the most effective ways to achieve green construction, many countries have launched low-carbon policies to promote the development of prefabrication. However, the effectiveness and influencing factors of low-carbon policies on prefabrication need to be further verified under the dynamic game between the government and the construction enterprise. Therefore, this study considered subsidy and carbon tax policies and developed an evolutionary game model to promote the development of the prefabricated construction market. The evolutionary stable strategy of the government and construction enterprise under different scenarios was obtained. Subsequently, a numerical analysis was conducted to further investigate the impact of the key factors on the stable strategy. The results showed that an appropriate hybrid policy of subsidies and taxes could positively promote the prefabrication implementation of the construction enterprise. The government should adopt an appropriate policy intensity according to the maturity of the market. This study can provide effective guidance and practical enlightenment for the government to achieve low-carbon, green, and sustainable construction. Conventional construction projects account for a very high proportion of the environmental load in global economic and social activities owing to their high consumption of natural resources, solid waste production, and carbon dioxide emissions. The 2021 Global Status Report for Buildings and Construction shows that the construction industry accounted for 36% and 37% of the global terminal energy consumption and energy-related carbon dioxide emissions in 2020, respectively. As a result, increasing the level of energy efficiency and low-carbon transformation in the building sector has attracted worldwide attention. For example, the European Union has revised its Emissions Reduction Sharing Regulation, the UK has proposed a “zero building” plan, and the Japanese government has published “Measures and Implementation Methods for Carbon Neutral Housing and Buildings by 2050”. Currently, the government’s low-carbon policy focuses on carbon neutrality , and proIn prefabrication, building components are manufactured in factories and transported to the construction site for installation. This approach improves construction efficiency and quality, and reduces labour requirements and resource consumption ,14,15,16Scholars have conducted in-depth studies on how governments can promote green construction and prefabrication. Currently, incentive policies for prefabricated production include financial subsidies, tax incentives, floor space incentives, loan support, land supply, mandatory policies, and non-economic incentives . For preIn order to fill this gap and maximise the overall comprehensive benefits of the exploration, reveal and guide the policy implementation, and promote active adoption of prefabricated production by construction enterprises, an evolutionary game model is constructed in this study to answer the following questions. How do the mixed policies of a carbon tax and subsidy dynamically affect the decision-making process of construction enterprises? How do the key factors affect the evolutionary behaviours of the government and construction enterprises? The research presented herein can reveal the dynamic game process between the government and construction enterprises, provide practical decision-making guidance for the government and construction enterprises, and promote high-quality development of green construction.The remainder of this paper is as follows. As the construction industry is the main source of global carbon emissions, the government should pay sufficient attention to policy making. A low-carbon policy aims to reduce the carbon emissions and energy consumption. Prefabrication is an important low-carbon production method in the construction industry. However, in the construction process of a construction project, it is challenging for the government to directly identify whether the construction enterprise (hereinafter indicated by ‘project contractor’) has adopted prefabrication. The project contractors, in turn, are risk averse and seek to maximise their own benefit. As a result, low-carbon behaviour faces uncertainties. Therefore, effective policies should be made to regulate the project contractors’ behaviour.This study aims to analyse the strategic evolution of the project contractors’ behaviour in adopting prefabrication driven by the government’s low-carbon policy. The government and project contractors are considered the two main players in the model. In the construction industry, the government usually encourages project contractors to adopt prefabrication through initiatives such as subsidies, tax policies, and regulations. However, project contractors tend to adopt conventional construction owing to high initial investment and complex technological innovation of prefabrication. As the government and project contractors are usually bounded by rationality, it is challenging for them, who are constrained by their cognitive level and reasoning ability, to make optimal decisions for the first time. The government and project contractors will adjust the strategies dynamically based on the limited information and others’ behaviour. Therefore, an evolutionary model is constructed to explore the dynamic behaviour of the government and a contractor and the effectiveness of their strategies.In the model, the following assumptions are made. The government has two strategy options. The first option is to implement low-carbon regulatory policies (hereinafter indicated by ‘Regulate’), including subsidies for prefabrication and carbon tax for all production methods. The second option is to practice a ‘laissez faire’ policy to expect the project contractor to choose the production method based on the market conditions (hereinafter indicated by ‘No-regulate’). Similarly, the project contractor also faces two strategy options, i.e., ‘Implement’ or ‘No-implement’, implying that the project contractor chooses prefabricated or conventional construction, respectively. Assuming that It is further assumed that the government adopts a low-carbon regulatory policy based on the carbon emissions of the constructed project. Let The following assumptions mainly include the costs and utilities considered in the model. The direct economic benefit obtained by the project contractor using the prefabricated production method is  changes , denotedThe model parameters, variables and their respective meanings are shown in Based on the descriptions above, the payoff matrix between the governments and the contractors can be obtained, as shown in Let The average payoff of the government, denoted as Similarly, let The average payoff of the contractor, denoted as According to the Malthusian dynamic equation, the replicator dynamic system is treated as a combination of the replicator dynamic equations of the government and contractor.According to the stability theorem of differential equations, let In order to analyse the stability of the equilibrium points, the Jacobian matrix of the above-defined replicator dynamic system is established as follows:Correspondingly,The determinant (det) and trace (tr) of The stability conditions of the replicator dynamic equations are divided into nine scenarios. The stability of each equilibrium point in each scenario is summarised in Scenario 1: When Scenario 2: When Scenario 3: When Scenario 4: When Scenario 5: When Scenario 6: When Scenario 7: When Scenario 8: When Scenario 9: When From Conclusion 1. When the government’s regulatory cost to implement the low-carbon policy exceeds the tax paid by contractors using conventional construction, that is as long as Conclusion 2. When the regulatory cost of implementing a low-carbon policy by the government is less than the difference between the tax paid by the contractor for prefabrication and the government subsidy, that is as long as Conclusion 3. When the difference between the direct economic benefit obtained by adopting prefabrication and the initial investment exceeds the direct economic benefit obtained by implementing conventional construction, that is as long as Conclusion 4. When the net profit of the project contractor by implementing prefabrication is less than that by implementing conventional construction under a low-carbon policy, that is as long as To reflect the impact of the key factors on the stable strategy further, a numerical analysis was conducted herein. Nanjing was selected as the first batch of prefabricated building demonstration cities in 2017. Under the promotion of national policies, the Nanjing Municipal Government issued the ‘Notice on the Implementation Opinions on Further Promoting the Development of Prefabricated Buildings’, proposing that, by 2020, the city’s prefabricated buildings will account for more than 30% of the proportion of new buildings. According to statistics, the proportion of newly started prefabricated buildings in the new construction area of the year has increased from 10.34% in 2016 to 38.72% in 2020. The carbon peak and carbon neutral policies were proposed in 2020. Nanjing has launched a number of policies to promote prefabricated buildings in response to carbon policies. Therefore, a prefabricated residential project in Nanjing city in China was selected as the reference for the initial values of the parameters and variables. Based on a survey and an interview, the actual data were simplified without affecting the results. The initial value used in the case analysis was set to The As shown in The As shown in The As shown in The As shown in In the low-carbon era, the problem of promoting prefabricated green construction has become highly relevant to both practitioners in the construction industry and the government. In order to analyse the green construction behaviour tendency under a low-carbon policy, an evolutionary game model between the government and construction enterprise was developed in this study. The payoff matrix under different strategies was proposed, and the replicator dynamic system was formulated. Subsequently, nine scenarios were summarised, and four conclusions were proposed. The influence of the key factors on the behaviour strategies of both the government and the construction enterprise was further investigated through numerical analysis.This study makes two contributions to the existing literature. First, this study analyses the comprehensive impact of incentives and carbon tax on prefabrication implementation, Moreover, it proposes a method for verifying the effectiveness of diversified policies in guiding the behaviour of construction enterprises. Second, this study reveals the dynamic game mechanism between the government and construction enterprises under several key factors, which can help the government adjust strategy dynamically to control the evolution direction of the system. Based on the evolutionary game analysis, the following management insights were concluded.(1) The government’s low-carbon policy has an effective guiding effect on the contractor’s prefabrication behaviour. Therefore, the government must continue to play a leading role in the contractors’ adoption of low-carbon prefabricated construction. Moreover, the government should establish an institutional framework that integrates subsidy and tax mechanisms , such as(2) The subsidy and tax intensity are important factors affecting the implementation of prefabrication by the construction enterprise. The higher the subsidy and the carbon tax, the stronger the local government’s motivation to guide the development of the prefabricated construction market. Appropriate subsidy and tax intensity should be adopted by the government to achieve a regulated and stable market. From (3) Additional initial investment directly affects the willingness of the construction enterprise to implement prefabrication . Therefo(4) The regulatory cost directly affects the willingness of the government to implement low-carbon policies . The pro(5) In different periods of market development, the government should adopt different policies. The subsidy policy should be biased towards the prefabricated market that needs to improve its maturity. Therefore, in the early stage of market development, the government should focus on providing sufficient subsidies to cover the high initial cost of prefabricated enterprises and to guide the behaviour of enterprises through the carbon tax. In the mid-term of market development, attention should be paid to dynamic adjustment of policies to ensure their effectiveness. After the market has matured, similar to the snowballing phenomenon, the construction enterprise will continue to implement prefabrication regardless of the government’s policies. At this stage, the market mechanism can play a leading role.This study has the following limitations. It only analyses the evolutionary behaviour under mixed policies of tax and subsidy. However, diversity policy should be considered in the future. The impact of the dynamics and higher incentive and penalty measures on the system, such as reputational incentives, should also be further investigated.


Digital audio watermarking is a promising technology for copyright protection, yet its low embedding capacity remains a challenge for widespread applications. In this paper, the spread-spectrum watermarking algorithm is viewed as a communication channel, and the embedding capacity is analyzed and modeled with information theory. Following this embedding capacity model, we propose the extended-codebook spread-spectrum (ECSS) watermarking algorithm to heighten the embedding capacity. In addition, the diversity reception (DR) mechanism is adopted to optimize the proposed algorithm to obtain both high embedding capacity and strong robustness while the imperceptibility is guaranteed. We experimentally verify the effectiveness of the ECSS algorithm and the DR mechanism, evaluate the performance of the proposed algorithm against common signal processing attacks, and compare the performance with existing high-capacity algorithms. The experiments demonstrate that the proposed algorithm achieves a high embedding capacity with applicable imperceptibility and robustness. With the booming development of the mobile Internet, information dissemination has changed. Internet firms such as Netflix, YouTube, and Apple have replaced those outdated CD stores—fewer and fewer music is traded via CDs and tapes. This much easier dissemination has led to a prosperous music market. However, beneath the appearance of prosperity, copyright concerns have been getting worse—a piece of music can be copied and distributed too quickly on the Internet. According to the IFPI  report , almost Engineers and researchers have also come up with several technologies, among which digital audio watermarking is quite representative , as a teimperceptibility refers to the data fidelity of the watermarked audio, indicating that the embedded watermarks can only introduce perceptually indistinguishable distortion to the host audio; the robustness refers to the reliability of the watermark that can be effectively extracted when watermarked audio has undergone some attacks, evaluated by the accuracy of the watermark extraction; the embedding capacity refers to the amount of watermark information that can be extracted from the watermarked audio [The performance of a watermarking algorithm is measured by three main criteria: imperceptibility, robustness and embedding capacity. The ed audio ,4. The eembedding strength, a crucial parameter in watermarking algorithms, controlling different performance criteria. Intuitively, the relaxed imperceptibility and strong robustness can lead to a high embedding capacity. However, existing studies lack the theoretical analysis of the embedding capacity and its dependency on other performance criteria. Therefore, improving the embedding capacity of watermarking algorithms still remains an open problem.As copyright content becomes diverse, copyright owners want to embed the licensed object, the class of license and the start and end date into the host data, leading to the embedding capacity or payload gradually becoming a bottleneck for the watermarking system. Several studies have been conducted on the embedding capacity of audio watermarking algorithms, and they use the number of watermark bits embedded per second (bps) as a metric for the embedding capacity. Nevertheless, it relates to the sample rate or the channels of the host audio and does not fully reflect the performance of watermarking algorithms. Moreover, the imperceptibility and robustness have substantial effects on the embedding capacity due to the In communication systems and watermarking systems, there are numerous paired concepts, such as the transmitter versus the embedding stage and the receiver versus the extraction stage. Actually, communication systems are a significant influence on many watermarking systems ,6,7,8. TThe spread-spectrum (SS)-based watermarking system ,9,10, thWe construct the capacity model of the SS-based watermarking algorithm, which reveals how the embedding capacity is dependent on codebook size and robustness.We propose the ECSS algorithm and analyze its embedding capacity and the accuracy of the watermark extraction. By extending the codebook, each sequence can carry more than one watermark bit, which improves the embedding capacity with applicable watermark robustness.We adopt a diversity reception mechanism for optimizing the ECSS. This mechanism repeatedly embeds the watermark into different regions of the host audio and aggregates the HSI from all repeated regions when extracting the watermark, reducing the randomness of the HSI and achieving a higher embedding capacity and stronger robustness.The remainder of this paper is organized as follows. Researchers have proposed numerous algorithms to heighten the embedding capacity of audio watermarking, which focus on proposing novel multibit embedding approaches. These algorithms can be roughly categorized into QIM-based (quantization index modulation), and SS-based embedding approaches. QIM-based embedding approaches achieve the effectiveness of multibit embedding by delicately constructing the quantized features or using more quantization levels. SVD-A-QIM  convertese codes  or orthose codes  to implese codes  used a cInformation theory, which provides several theoretical foundations, is widely used in the design of watermarking algorithms ,17,18,19gorithms ,23,24. Mgorithms  presentegorithms ,27, quangorithms , generalgorithms , Gaussiagorithms  or Gibbsgorithms  to modelIn this paper, the embedding capacity of the SS-based watermarking algorithm is analyzed using information theory. Based on the analysis, we propose an extended-codebook spread-spectrum watermarking (ECSS) algorithm which enhances the embedding capacity, and finally, we adopt a diversity reception mechanism to further optimize the embedding capacity and robustness of ECSS.signal vector of the host audio in a particular domain, pseudorandom sequence independent of As the first work to apply spread spectrum to digital watermarking, vanilla spread spectrum (VSS) has had a significant influence thanks to the anti-interference capability of the spread spectrum . It is aR has the same sign as R byIn the watermark extraction stage, according to the watermarked signal alculateR=ypTppT=m, an output codebook n and a transition matrix As defined by information theory , a commuThe channel capacity is the highest rate in bits that can be transmitted per channel use and the maximum mutual information between input and output for different input distributions. It can be expressed formulaically as ,(5)C=maT,Specifically, if the channel in According to the above introduction, the VSS watermarking algorithm can be considered a binary symmetric channel, as shown in bits/sample. It can be calculated from the channel capacity C,c is a constant factor representing the loss of capacity in the watermarking system.However, there is a slight difference between channel capacity and embedded capacity. It can be seen from Equation  that embThe output codebook size The entropy of transition probability The length of the signal vector employed to embed a symbol c in Equation Since the probability density function (PDF) of the HSI in Equation  is even,Equation ) is(23)When It is noted that Equation  does notm and the embedding strength In a nutshell, the probability that Equations  and 15)15) can eTwo error cases were analyzed in c is ignored here. Equation Ec=Ec=(28)Ecm is obtained whenSince m and the embedding strength Thus, the embedding capacity is simplified to a function of the number of sequences  It can be seen in Equation  that theThere are three strategies to improve the accuracy of the watermark extraction shown in Equation .(1)m;Reducing the number of sequences (2)Increasing the embedding strength (3)Modifying the distribution of the HSI.Both strategies (1) and (2) involve a parameter selection, and in the next section, we experiment with different parameters.M-bit watermark In this section, we adopt the diversity reception (DR) mechanism to modify the HSI distribution, a method commonly used in signal detection. The DR mechanism can effectively improve the accuracy of the watermark extraction. In brief, the Equation  can be rBy substituting the pre-extractions of Equation  into EquEquation  that theThis method of repeatedly embedding the watermark and averaging the HSI in different watermarked signal vectors to reduce the randomness of the HSI is referred to as DR in this paper. Although DR improves the accuracy of the watermark extraction, on the other hand, DR may also reduce the embedding capacity because more signal vectors are used for embedding the watermark.It seems that DR is a trade-off to balance the embedding capacity with the robustness. However, it is not the case. Even if the number of repetitions is small  and theWe selected 1000 stereo audio tracks with a sample rate of 44.1 kHz and a duration of 30 s from the FMA dataset  for the ith sample of the host audio and the watermarked audio. SWR reflects the amount of change to the host audio by the watermark embedding. Although SWR does not reflect the perceptual quality of audio locally, it is still an important metric of imperceptibility.The embedding distortion SWR  was employed to evaluate the watermark imperceptibility. The SWR is calculated as,M-bit watermark in the ECSS algorithm, while a watermark group is a single bit in the VSS algorithm. The GEP is calculated as follows,In this paper, the robustness of the watermarking algorithm was evaluated using the watermark group extraction precision (GEP). A watermark group consists of the watermark bits corresponding to a sequence, e.g., an When evaluating the robustness, we also used another metric similar to the GEP, the watermark bit detection rate (BDR). The BDR compares the embedded watermark bits with the extracted bits, and it is defined as,We used two different metrics to evaluate robustness, because(1)The BDR does not reflect the actual robustness of the algorithms if there is a use of multibit embedding, and in the case of the ECSS algorithm, e.g., when the four-bit watermark  is incorrectly extracted as , the BDR is 75%, while the GEP is 0%. The GEP reflects the fact more accurately.(2)However, not all algorithms embed the same quantity of bits once. For those algorithms that have small watermark groups, the GEP typically yields better results. The actual performance of the algorithms with various embedding bits is somewhat reflected in the BDR.We used the GEP to evaluate the robustness of the ECSS algorithm and DR, and then used the BDR, which is more common in the literature, to evaluate various attacks and compare them with existing algorithms.In this subsection, we statistically measure the GEPs of the ECSS algorithm and calculate the corresponding embedding capacity The GEP can only estimate the probability of correctly extracting the watermark group, but the complete probability transition matrix is required to calculate the embedding capacity. For this reason, we assigned the error probabilities uniformly to the other symbols to calculate the infimum of the embedding capacity. As shown in In quations  and 12)m was divOn the other hand, it is shown in M-bit watermark. The DR mechanism with repetition In the above subsection, the GEP and embedding capacity of VSS and ECSS were analyzed. However, the role of the DR mechanism is not yet clear. In this subsection, the performance of ECSS is analyzed with different repetitions of the DR mechanism combined. The relevant experimental results are shown in As the embedding strength There is no clear relationship between the GEP and the length of the signal vector, as shown in In summary, the DR mechanism effectively improves the embedding capacity and the GEP at low embedding strength, balancing the proposed watermarking algorithm’s imperceptibility, robustness and embedding capacity.In this subsection, we evaluate the BDR and embedding capacity of the proposed ECSS and ECSS+DR algorithms for some common data processing attacks. The attacks are described in In order to demonstrate the influence of the attacks on the performance of the watermarking algorithm, the parameters The effect of the signal processing attacks can be equivalent to adding a certain amount of noise to the audio, and the power of that noise is much lower than the power of the audio itself. The ECSS algorithm proposed in this paper resisted most of these attacks, where there was almost no influence in RQZ, ASC, RSP, LPF, and MP3 attacks, which reduced the average BDR of the ECSS algorithm by 0.1% to 0.5% and had negligible influence on the ECSS+DR algorithm. However, in the WGN attack, the BDR of the ECSS algorithm showed a substantial decline, where a 15 dB Gaussian noise would decrease the BDR of the ECSS algorithm by 4.1%, corresponding to a 1.0% decrease for the ECSS+DR algorithm, and a 10 dB noise would decrease the BDR of the ECSS algorithm by 11.5%, corresponding to a 5.5% decrease for the ECSS+DR algorithm.The decrease of the BDR also reduced the embedding capacity of algorithms. Among these attacks, the influence of RQZ, ASC, RSP, LPF, and MP3 attacks on the embedding capacity of the watermarking algorithms was less than We also evaluated the performance of the ECSS/+DR algorithm against a short delay attack (DLY). The BDR was reduced by 8.11% for the ECSS algorithm and by 2.51% for the ECSS+DR algorithm. Due to the change in robustness, the embedding capacity was reduced by The influence of various attacks on the performance and the equivalent noise intensity are summarized in In addition to signal processing attacks, advanced attacks such as crop, framing errors and playback scaling are also possible with watermarked audio. It is difficult to resist these attacks by considering only the embedding and extraction algorithms. Various strategies for selecting embedding regions have been proposed in the literature, among which RASE  and RFPSThe proposed ECSS+DR algorithm was also compared with existing high-embedding-capacity algorithms ,13,15,16M-bit watermark group actually used signal vectors with a total length of 32). These parameters provide a balanced performance for the ECSS+DR algorithm according to It is still evident from the experimental results in The ECSS+DR algorithm had similar embedding distortion SWR as the algorithm in  and alsoIn a nutshell, our algorithm achieved a significant advantage in embedding capacity, without any disadvantage in robustness and imperceptibility compared to other existing algorithms.In this paper, we analyzed the spread-spectrum watermarking algorithm from the perspective of the communication channel and formularized its watermark embedding capacity. According to this analysis, we proposed a watermarking algorithm using extended-codebook ECSS and optimized it by adopting the diversity reception (DR) mechanism, so that the ECSS+DR watermarking algorithm achieved a higher embedding capacity and stronger robustness while given a limited embedding strength.However, the embedding capacity formulation in this paper was only limited to the spread-spectrum watermarking algorithm, and the derived formula did not take into account the various attacks that could be encountered with the watermarked audio. Due to the excellent anti-interference performance of the spread-spectrum approach, our algorithm still resisted common signal processing attacks. Our team will subsequently try to build a more generalized embedding capacity model that takes into account watermarking algorithms from other paradigms such as QIM and deep learning, as well as considering attacks.In this paper, a Gaussian distribution was used to model the HSI, which is a heuristic method lacking a rigorous theoretical support. Although the Gaussian distribution passed the K-S test, we note that the sample points in the Q-Q plots formed an S-like curve. Therefore, there may exist a more suitable distribution for modeling the HSI.Our algorithms are not resistant to white-box attacks in which the attackers knows this algorithm. Although the embedder and the extractor of the watermarking system are the same, the security of this algorithm still needs to be improved in future work.